1. Introduction

The past 20 years have seen a revolution in far-infrared and terahertz (THz) systems, as advanced materials research provided new and higher-power sources, and the potential of THz for advanced physics research and commercial applications was demonstrated. Numerous recent breakthroughs in the field have pushed research into the center stage. As examples of milestone achievements, we can mention in particular the development of THz imaging and high-power THz generation. Devices exploiting this wavelength band are set to become increasingly important in a diverse range of human activity applications (e.g., security, biology, drugs and explosion detection, gas fingerprints, and imaging). Nowadays, infrared and THz systems are also of much use in fundamentals science, such as nanomaterials science and biochemistry. This is based on the fact that THz frequencies correspond to single and collective excitations in nanoelectronic devices and collective dynamics in biomolecules. Although many compact, electrically controlled, solid-state technologies already exist for the direct generation, manipulation, and detection of THz waves [1], they all suffer from drawbacks that are currently still limiting the widespread exploitation of THz photonics.

The unique optoelectronic properties of graphene make it a new platform for a variety of photonic applications [2,3], including fast photodetectors [4,5], transparent electrodes in displays and photovoltaic modules [6], optical modulators [7], plasmonic devices [8], and ultrafast lasers [9]. Graphene detectors play important roles in the development of innovative technologies in many fields, including imaging, military, medicine, and optical communications.

The unique properties of graphene fuel the great enthusiasm for the materials, also including its application for the realization of next generation infrared and THz photodetectors. To date, however, the performance of graphene detectors is lower in comparison with that of the detectors existing on the global market.

The main goal of this paper is to take a critical glance at the present stage of graphene detector technologies and the future development in strong global competition with existing mature material systems (especially HgCdTe, InGaAs, and type-II superlattice III-V compounds) and microbolometers. In the current mainstream of infrared technology, there are considerable efforts to decrease the imaging system size, weight, and power consumption (SWaP)—consequently reducing the system’s cost—to increase the operating temperature in so-called HOT (high-operating-temperature) detectors. In order to attain a meaningful position in the infrared detector family, graphene-based materials also have to fulfill SWaP requirements. Regarding these trends, we mostly focus our considerations on detectors operating in HOT conditions.

2. Classification of Detectors

Optical radiation is considered as radiation over the range from vacuum ultraviolet to the submillimeter wavelength (25 nm to 3000 μm). The THz region of the electromagnetic spectrum (see Fig. 1) is often described as the final unexplored area of spectrum and still presents a challenge for both electronic and photonic technologies. It is frequently treated as the spectral region within frequency range $\nu \approx 0.1–10\mathrm{THz}$ ($\lambda \approx 3\mathrm{mm}–30\mathrm{\mu m}$) and is partly overlapping with the loosely treated submillimeter (sub-mm) wavelength band $\nu \approx 0.1–3\mathrm{THz}$ ($\lambda \approx 3\mathrm{mm}–100\mathrm{\mu m}$).

 

Figure 1. Electromagnetic spectrum. Reprinted from Opto-Electron. Rev. 19, Rogalski and Sizov, “Terahertz detectors and focal plane arrays,” pp. 346–404, Copyright 2011, with permission from Elsevier [10].

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The majority of optical detectors can be classified in two broad categories: photon detectors (also called quantum detectors) and thermal detectors.

2.1. Photon Detectors

In photon detectors the radiation is absorbed within the material by interaction with electrons bound to either lattice atoms or impurity atoms or with free electrons. The observed electrical output signal results from the changed electronic energy distribution. The fundamental optical excitation processes in semiconductors are illustrated in Fig. 2. In quantum wells [Fig. 2(b)], intersubband absorption takes place between the energy levels of a quantum well associated with the conduction band ($n$-doped) or the valence band ($p$-doped). In the case of a type-II InAs/GaSb superlattice [Fig. 2(c)], the superlattice bandgap is determined by the energy difference between the electron miniband $E_1$ and the first heavy-hole state $H{H}_1$ at the Brillouin zone center. A consequence of the type-II band alignment is spatial separation of electrons and holes.

 

Figure 2. Optical excitation processes in (a) bulk semiconductors, (b) quantum wells, and (c) type-II InAs/GaSb superlattices. Reprinted with permission from [11]. Copyright 2018 SPIE.

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The relative response of infrared detectors is plotted as a function of wavelength with either a vertical scale of ${\mathrm{W}}^{-1}$ or ${\text{photon}}^{-1}$ (see Fig. 3). The photon detectors show a selective wavelength dependence of the response per unit incident radiation power. Their response is proportional to the rate of arrival photons as the energy per photon is inversely proportional to the wavelength. As a consequence, the spectral response increases linearly with increasing wavelength [see Fig. 3(a)], until the cutoff wavelength is reached, which is determined by the detector material. The cutoff wavelength is usually specified as the long-wavelength point at which the detector responsivity falls to 50% of the peak responsivity.

 

Figure 3. Relative spectral response for a photon and thermal detector for (a) constant incident radiant power and (b) photon flux. Reprinted with permission from [11]. Copyright 2018 SPIE.

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Thermal detectors tend to be spectrally flat in the first case (their response is proportional to the energy absorbed); thus they exhibit a flat spectral response [see Fig. 3(a)], while photon detectors are generally flat in the second case [see Fig. 3(b)].

Photon detectors exhibit both good signal-to-noise performance and a very fast response. But to achieve this, the photon IR detectors may require cryogenic cooling. This is necessary to prevent the thermal generation of charge carriers. The thermal transitions compete with the optical ones, making non-cooled devices very noisy.

Depending on the nature of the interaction, the class of photon detectors is further sub-divided into different types. The most important are intrinsic detectors, extrinsic detectors, and photoemissive detectors (Schottky barriers) [12]. Different types of detectors are briefly characterized in Table 1.

Table 1. Photon Detectors^a

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There is a fundamental relationship between the temperature of the background viewed by the detector and the lower temperature at which the detector must operate to achieve background-limited performance (BLIP). HgCdTe photodetectors with cutoff wavelength of 12.4 μm operate at 77 K. One can scale the results of this example to other temperatures and cutoff wavelengths by noting that for a given level of detector performance, $T{\lambda }_c\approx \text{constant}$ [13]; i.e., the longer ${\lambda }_c$ is, the lower $T$ is, while their product remains roughly constant. This relation holds because quantities that determine detector performance vary mainly as an exponential of $E_{\mathrm{exc}}/kT=hc/kT{\lambda }_c$, where $E_{\mathrm{exc}}$ is the excitation energy, $k$ is Boltzmann’s constant, $h$ is Planck’s constant, and $c$ is the velocity of light.

The detector temperature of operation can be approximated as

 

Figure 4. Operating temperatures for low-background material systems with their spectral band of greatest sensitivity. The dashed line indicates the trend toward lower operating temperature for longer-wavelength detection. Reprinted with permission from [11]. Copyright 2018 SPIE.

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The most widely used photovoltaic detector is the p–n junction, where a strong internal electric field exists across the junction even in the absence of radiation. Photons incident on the junction produce free hole–electron pairs that are separated by the internal electric field across the junction, causing a change in voltage across the open-circuit cell or a current to flow in the short-circuited case. Due to the absence of recombination noise, the limiting p–n junction’s noise level can ideally be $\surd 2$ times lower than that of the photoconductor.

Photoconductors that utilize excitation of an electron from the valence band to the conduction band are called intrinsic detectors. Those that operate by exciting electrons into the conduction band or holes into the valence band from impurity states within the band (impurity-bound states in energy gap, quantum wells or quantum dots) are called extrinsic detectors. A key difference between intrinsic and extrinsic detectors is that extrinsic detectors require much cooling to achieve high sensitivity at a given spectral response cutoff in comparison with intrinsic detectors. Low-temperature operation is associated with longer-wavelength sensitivity to suppress noise due to thermally induced transitions between close-lying energy levels. Intrinsic detectors are most common at the short wavelengths, below 20 μm. In the longer-wavelength region the photoconductors are operated in extrinsic mode. One advantage of photoconductors is their current gain, which is equal to the recombination time divided by the majority-carrier transit time. This current gain leads to higher responsivity than is possible with nonavalanching photovoltaic detectors. However, a serious problem of photoconductors operated at low temperature is nonuniformity of the detector element due to recombination mechanisms at the electrical contacts and its dependence on electrical bias.

Recently, interfacial work-function internal photoemission detectors, and quantum-well and quantum-dot detectors, which can be included with extrinsic photoconductors, have been proposed, especially for the IR and THz spectral bands [12]. The very fast time response of quantum-well and quantum-dot semiconductor detectors makes them attractive for heterodyne detection.

2.2. Thermal Detectors

The second class of detectors is composed of thermal detectors. In a thermal detector shown schematically in Fig. 5, the incident radiation is absorbed to change the material temperature, and the resultant change in some physical property is used to generate an electrical output. The detector is suspended on lags, which are connected to the heat sink. The signal does not depend upon the photonic nature of the incident radiation. Thus, thermal effects are generally wavelength independent [see Fig. 3(a)]; the signal depends upon the radiant power (or its rate of change) but not upon its spectral content. Since the radiation can be absorbed in a black surface coating, the spectral response can be very broad. Attention is directed toward three approaches that have found the greatest utility in infrared technology, namely, bolometers, and pyroelectric and thermoelectric effects. The thermopile is one of the oldest IR detectors, and is a collection of thermocouples connected in series to achieve better temperature sensitivity. In pyroelectric detectors a change in the internal electrical polarization is measured, whereas in the case of thermistor bolometers a change in the electrical resistance is measured. For a long time, thermopiles were slow, insensitive, bulky, and costly devices. But with developments in semiconductor technology, thermopiles can be optimized for specific applications. Recently, thanks to conventional complementary metal-oxide semiconductor (CMOS) processes, the thermopile’s on-chip circuitry technology has opened the door to mass production.

 

Figure 5. Schematic diagram of thermal detector. Reprinted with permission from Rogalski, J. Appl. Phys. 93, 4355–4391 (2003) [14]. Copyright 2003 AIP Publishing LLC.

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Usually the bolometer is a thin, blackened flake or slab, whose impedance is highly temperature dependent. Bolometers may be divided into several types. The most commonly used are metal, thermistor, and semiconductor bolometers. A fourth type is the superconducting bolometer. This bolometer operates on a conductivity transition in which the resistance changes dramatically over the transition temperature range. Figure 6 shows schematically the temperature dependence of the resistance of different types of bolometers.

 

Figure 6. Temperature dependence of the resistance of three bolometer material types. Reprinted with permission from [11]. Copyright 2018 SPIE.

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Many types of thermal detectors are operated in wide spectral range of electromagnetic radiation. The operation principles of thermal detectors are briefly described in Table 2.

Table 2. Thermal Detectors^a

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Microbolometer detectors are now produced in larger volumes than all other IR array technologies together. At present, ${\mathrm{VO}}_x$ microbolometer arrays are clearly the most used technology for uncooled detectors. ${\mathrm{VO}}_x$ is the winner in the battle between amorphous silicon bolometers and barium strontium titanate (BST) ferroelectric detectors.

3. Detector Figures of Merit

It is difficult to measure the performance characteristics of infrared detectors because of the large number of experimental variables involved. A variety of environmental, electrical, and radiometric parameters must be considered and carefully controlled. With the advent of large, two-dimensional (2D) detector arrays, detector testing has become even more complex and demanding.

This section is intended to serve as an introductory reference for the testing of infrared detectors. Numerous texts and journals cover this issue, including Infrared System Engineering [15] by Hudson; The Infrared Handbook [16], edited by Wolfe and Zissis; The Infrared and Electro-Optical Systems Handbook [17], edited by Rogatto; and Fundamentals of Infrared Detector Operation and Testing [18] by Vincent, and the second edition of the last book [19]. In this section we have restricted our consideration to detectors whose output consists of an electrical signal that is proportional to the radiant signal power.

3.1. Responsivity

The responsivity of an infrared detector is defined as the ratio of the root mean square (rms) value of the fundamental component of the electrical output signal of the detector to the rms value of the fundamental component of the input radiation power. The units of responsivity are volts per watt (V/W) or amperes per watt (amp/W).

The voltage (or analogous current) spectral responsivity is given by

An alternative to the above monochromatic quality, the blackbody responsivity, is defined by the equation

3.2. Noise Equivalent Power

The noise equivalent power (NEP) is the incident power on the detector generating a signal output equal to the rms noise output. Stated another way, the NEP is the signal level that produces a signal-to-noise ratio (SNR) of 1. It can be written in terms of responsivity:

The NEP is also quoted for a fixed reference bandwidth, which is often assumed to be 1 Hz. This “NEP per unit bandwidth” has a unit of watts per square root hertz ($\mathrm{W}/{\mathrm{Hz}}^{1/2}$).

3.3. Detectivity

The detectivity $D$ is the reciprocal of the NEP:

Useful equivalent expressions to Eq. (6) include

Spectral detectivity curves for commercially available IR and THz detectors are shown in Fig. 7. Interest has focused mainly on the two atmospheric windows of 3–5 μm [medium-wavelength infrared (MWIR)] and 8–14 μm [long-wavelength infrared (LWIR)]. (Atmospheric transmission is the highest in these bands, and the emissivity maximum of the objects at $T\approx 300\mathrm{K}$ is at the wavelength $\lambda \approx 10\mathrm{\mu m}$). However, in recent years there has been increasing interest in longer wavelengths stimulated by space and THz applications. The spectral character of the background is influenced by the transmission of the atmosphere that controls the spectral ranges of the infrared for which the detector may be used when operating in the atmosphere.

 

Figure 7. Comparison of the $D^{*}$ of various available detectors when operated at the indicated temperature. The chopping frequency is 1000 Hz for all detectors except the thermopile (10 Hz), thermocouple (10 Hz), thermistor bolometer (10 Hz), Golay cell (10 Hz), and pyroelectric detector (10 Hz). Each detector is assumed to view a surrounding hemisphere (2π field of view) at a temperature of 300 K. Theoretical curves for the background-limited $D^{*}$ (dashed lines) for ideal photovoltaic and photoconductive detectors and thermal detectors are also shown. PC, photoconductive detector; PV, photovoltaic detector; PEM, photoelectromagnetic detector; HEB, hot-electron bolometer. Reprinted from Prog. Quantum Electron. 36, Rogalski, “Progress in focal plane array technology,” pp. 342–473, Copyright 2012, with permission from Elsevier [21].

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3.4. Quantum Efficiency

A signal whose photon energy is sufficient to generate photocarriers will continuously lose energy as the optical field propagates through the semiconductor. Inside the semiconductor, the field decays exponentially as energy is transferred to the photocarriers. The material can be characterized by an absorption length α and a penetration depth $1/\alpha$. The penetration depth is the point at which $1/e$ of the optical signal power remains.

The power absorbed in the semiconductor as a function of position within the material is then

Figure 8 shows the quantum efficiency of some of the detector materials used to fabricate arrays of ultraviolet (UV), visible, and infrared detectors. Photocathodes and AlGaN detectors are being developed in the UV region. Silicon p-i-n diodes are shown with and without antireflection coating. Lead salts (PbS and PbSe) have intermediate quantum efficiencies, while PtSi Schottky barrier types and quantum-well infrared photodetectors (QWIPs) have low values. InSb can respond from the near UV out to 5.5 μm at 80 K. A suitable detector material for the near-IR (1.0–1.7 μm) spectral range is InGaAs lattice matched to the InP. Various HgCdTe alloys, in both photovoltaic and photoconductive configurations, cover from 0.7 μm to over 20 μm. InAs/GaSb strained layer superlattices have emerged as an alternative to HgCdTe. Impurity-doped (Sb, As, and Ga) silicon BIB detectors operating at 10 K have a spectral response cutoff in the range of 16–30 μm. Impurity-doped Ge detectors can extend the response out to 100–200 μm.

 

Figure 8. Quantum efficiency of different detectors. Reprinted with permission from [11]. Copyright 2018 SPIE.

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There are different methods of light coupling in a photodetector to enhance quantum efficiency [22]. A notable example of a method described for thin film solar cells [23,24] can be applied to infrared photodetectors. In general, these absorption enhancement methods can be divided into four categories that use optical concentration, antireflection structures, optical path increase, or light localization, as shown in Fig. 9. They are briefly described in Chapter 8 of the monograph Antimonide-Based Infrared Detectors: A New Perspective [11].

 

Figure 9. Different methods of absorption enhancement in a photodetector use an optical concentrator, an antireflection structure, structures for optical path increase (cavity enhancement), and light localization structures. Reprinted with permission from [11]. Copyright 2018 SPIE.

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4. Fundamental Detector Performance Limits

4.1. Photon Detectors

In general, the photon detector can be considered as a slab of homogeneous material with actual “electrical” area $A_e$, thickness $t$, and volume $A_{e}t$. Usually, the optical and electrical areas of the device are the same or similar. However, the use of some kind of optical concentrator can increase the $A_o/A_e$ ratio by a large factor.

The detectivity $D^{*}$ of an infrared photodetector is limited by the generation and recombination rates $G$ and $R$ (in ${\mathrm{m}}^{-6}{\mathrm{s}}^{-1}$) in the active region of the device [25,26]. It can be expressed as

For a given wavelength and operating temperature, the highest performance can be obtained by maximizing the ratio of the quantum efficiency to the square root of the sum of the sheet thermal generation and recombination rates $\eta /{[(G+R)t]}^{1/2}$. This means that high quantum efficiency must be obtained with a thin device.

A possible way to improve the performance of IR detectors is to reduce the physical volume of the semiconductor, thus reducing the amount of thermal generation. However, this must be achieved without a decrease in the quantum efficiency, optical area, and field of view (FOV) of the detector.

At equilibrium, the generation and recombination rates are equal. If we further assume $A_e=A_o$, the detectivity of an optimized infrared photodetector is limited by thermal processes in the active region of the device. It can be expressed as

The ratio of the absorption coefficient to the thermal generation rate, $\alpha /G$, is the fundamental figure of merit of any material intended for infrared photodetection. The $\alpha /G$ ratio versus temperature for various material systems capable of bandgap tuning is shown in Fig. 10 for a hypothetical energy gap equal to 0.25 eV ($\lambda =5\mathrm{\mu m}$) [Fig. 10(a)] and 0.124 eV ($\lambda =10\mathrm{\mu m}$) [Fig. 10(b)]. Procedures used in calculations of $\alpha /G$ for different material systems are given in Ref. [14]. Analysis shows that narrow-gap semiconductors are more suitable for high-temperature photodetectors in comparison to competing technologies such as extrinsic devices and QWIP and QDIP (quantum-dot IR photodetector) devices. The main reason for the high performance of intrinsic photodetectors is the high density of states in the valence and conduction bands, which results in strong absorption of infrared radiation. Figure 10(b) predicts that a recently emerging competing IR material, the type-II superlattice, is the most efficient material technology for IR detection in the long-wavelength region, theoretically perhaps even better than HgCdTe if the influence of the Shockley–Read–Hall lifetime is not considered. It is characterized by a high absorption coefficient and a relatively low fundamental (band-to-band) thermal generation rate. However, this theoretical prediction has not been confirmed by experimental data. It is also worth noting that theoretically AlGaAs/GaAs QWIP is also a better material than extrinsic silicon.

 

Figure 10. $\alpha /G$ ratio versus temperature for (a) MWIR ($\lambda =5\mathrm{\mu m}$) and (b) LWIR ($\lambda =10\mathrm{\mu m}$) photodetectors based on HgCdTe, QWIP, Si extrinsic, and type-II superlattice (for LWIR only) material technology. Reprinted with permission from [11]. Copyright 2018 SPIE.

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The ultimate performance of infrared detectors is reached when the detector and amplifier noise is low compared to the photon noise. The photon noise is fundamental in the sense that it arises not from any imperfection in the detector or its associated electronics but rather from the detection process itself, as a result of the discrete nature of the radiation field. The radiation falling on the detector is a composite of that from the target and that from the background. The practical operating limit for most infrared detectors is not the signal fluctuation limit but the background fluctuation limit, also known as the background-limited infrared photodetector (BLIP) limit.

The expression for shot noise can be used to derive the BLIP detectivity,

Planck’s photon emittance (in units of photons ${\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{\mu m}}^{-1}$) at temperature $T_B$ is given by

4.2. Thermal Detectors

Thermal detectors operate on a simple principle that when heated by incoming radiation their temperature increases and the temperature changes are measured by any temperature-dependent mechanism, such as thermoelectric voltage, resistance, or pyroelectric voltage.

The simplest representation of the thermal detector is shown in Fig. 5. The detector is represented by a thermal capacitance $C_{\text{th}}$ coupled via a thermal conductance $G_{\text{th}}$ to a heat sink at a constant temperature $T$. In the absence of a radiation input, the average temperature of the detector will also be $T$, although it will exhibit a fluctuation near this value. When a radiation flux, ${\mathrm{\varphi }}_o$, is received by the detector, the rise in temperature, $\mathrm{\Delta }T$, is found by solving the heat balance equation as [27,28]

Equation (16) shows that as $\omega$ is increased, the term ${\omega }^2{C}_{\text{th}}^2$ will eventually exceed $G_{\text{th}}^2$ and then $\mathrm{\Delta }T$ will fall inversely as $\omega$. A characteristic thermal response time for the detector can therefore be defined as

For further discussion, we introduce the coefficient $K$, which reflects how well the temperature changes translate into the electrical output voltage of the detector,

As stated previously, the thermal conductance (thermal resistance) from the detector to the outside world should be small (high). The smallest possible thermal conductance would occur when the detector is completely isolated from the environment under vacuum with only radiative heat exchange between it and its heat-sink enclosure. Such an ideal model can give us the ultimate performance limit of a thermal detector. This limiting value can be estimated from the Stefan–Boltzmann total radiation law.

If the thermal detector has a receiving area $A$ of emissivity $\epsilon$, when it is in thermal equilibrium with its surroundings, it will radiate a total flux $A\epsilon \sigma T^4$, where $\sigma$ is the Stefan–Boltzmann constant. Now if the temperature of the detector is increased by a small amount $dT$, the flux radiated is increased by $4A\epsilon \sigma T^{3}dT$. Hence, the radiative component of the thermal conductance is

The minimum detectable signal power—or noise equivalent power (NEP)—is defined as the rms signal power incident upon the detector required to equal the rms thermal noise power. Hence if the temperature fluctuation associated with $G_R$ is the only source of noise,

To determine the detectivity ($D^{*}$) of a detector, it is necessary to define a noise mechanism. For any detector there are several noise sources that impose fundamental limits on the detection sensitivity.

One major noise is the Johnson noise. Two other fundamental noise sources are important for assessing the ultimate performance of a detector: thermal fluctuation noise and background fluctuation noise.

Thermal fluctuation noise arises from temperature fluctuations in the detector. These fluctuations are caused by heat conductance variations between the detector and the surrounding substrate with which the detector element is in thermal contact.

The variance in temperature (“temperature” noise) can be shown to be [27,28]

In addition to the fundamental noise sources mentioned above, $1/f$ is an additional noise source that is often found in the thermal detector and can affect the detector performance.

The detectivity of a thermal detector is given by

The fundamental limit on the sensitivity of any thermal detector is set by the temperature fluctuation noise. Under this condition at low frequencies ($\omega \ll 1/{\tau }_{\text{th}}$), from Eq. (31) results

Figure 11 shows the dependence of detectivity on the temperature and thermal conductance plotted for different detector active areas. It is clearly shown that improved performance of the thermal detectors can be achieved by increasing the thermal isolation between the detector and its surroundings.

 

Figure 11. Temperature fluctuation noise limited detectivity for thermal infrared detectors of different areas plotted (a) as a function of the detector temperature and (b) as a function of the total thermal conductance between the detector and its surroundings. Reprinted with permission from [29]. Copyright 2003 Marcel Dekker.

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If radiant power exchange is the dominant heat exchange mechanism, then $G$ is the first derivative with respect to the temperature of the Stefan–Boltzmann function. In that case, known as the background fluctuation noise limit, from Eqs. (7) and (30) we have

Equations (32) and (33) assume that background radiation falls upon the detector from all directions when the detector and background temperature are equal, and from the forward hemisphere only when the detector is at cryogenic temperatures. Even if the detector or background (not both) are cooled to absolute zero, the detectivity would improve only by the square root of 2. This is the basic limitation of all thermal detectors. The background-noise-limited photon detectors have higher detectivities because of their limited spectral responses (which is shown in Fig. 7).

In many practical instances, the temperature of the background, $T_b$, is room temperature, 290 K [28]. Figure 12 shows the background-limited detectivity, as a function of the sensor temperature, for an ideal thermal detector having an emissivity of unity.

 

Figure 12. BLIP detectivity of a thermal sensor as a function of the sensor temperature for $2\pi$ FOV and $\epsilon =1$.

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We see that the highest possible $D^{*}$ to be expected for a thermal detector operated at room temperature and viewing a background at room temperature is $1.98\times {10}^{10}\mathrm{cm}{\mathrm{Hz}}^{1/2}{\mathrm{W}}^{-1}$.

Most thermal detectors can be tailored to have somewhat different properties, and the user should contact the manufacturer for detailed information. Table 3 gives the general flavor of the performance of different thermal detectors.

Table 3. General Properties of Thermal Detectors

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5. Relevant Graphene Properties

Graphene has been extensively studied since 2004 due to its unique electronic and optical properties [30–32]. The most intriguing electronic property of graphene is its linear dispersion relation between the energy and the wave vector. This relativistic-like energy dispersion is accompanied by electrons traveling at a Fermi velocity only 100 times smaller than the speed of light.

Graphene is made of $s{p}^2$ hybridized carbon atoms arranged on a honeycomb lattice with lattice constant $a=1.42\AA$. The formed valence and conduction bands touch at the Brillouin zone corners (so-called Dirac points) making graphene a zero-bandgap semiconductor, as shown in Fig. 13. Due to the zero density of states at the Dirac points, the electronic conductivity is quite low. However, the Fermi level can be changed by doping (with electrons or holes) to create a material that is potentially better at conducting electricity than, for example, copper at room temperature. Carbon atoms have a total of six electrons: two in the inner shell and four in the outer shell. The four outer-shell electrons in an individual carbon atom are available for chemical bonding, but in graphene, each atom is connected to three other carbon atoms on the 2D plane, leaving one electron freely available in the third dimension for electronic conduction. These highly mobile electrons are called π-electrons and are located above and below the graphene sheet. $\pi$-orbitals overlap and help to enhance the carbon-to-carbon bonds in graphene. Fundamentally, the electronic properties of graphene are dictated by the bonding and antibonding (the valance and conduction bands) of these $\pi$-orbitals.

 

Figure 13. (a) Band structure of graphene in the honeycomb lattice. The enlarged picture shows the energy bands close to one of the Dirac points. (b) Schematic of electron $\sigma$- and $\pi$-orbitals of one carbon atom in graphene.

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Graphene boasts the potential for ballistic carrier transport with an inferred mean-free path $>2\mathrm{\mu m}$ at room temperature [33]. Its carriers propagate via diffraction (like optical light in a waveguide), rather than by carrier diffusion as is common with carriers in conventional semiconductors.

The electrical engineers are interested in the high carrier mobility and saturation velocity in graphene, which offer the promise of graphene-based high-speed photonic devices [34]. Graphene layer structures with long momentum relaxation time of electrons and holes promise a significant enhancement of the performance of future optoelectronic devices. Theoretically, graphene possesses a room-temperature electron mobility of $250,000{\mathrm{cm}}^2/\mathrm{Vs}$; however, the transport behavior is extremely dependent on the local environment and processing done to the material. Vacuum suspended graphene achieved via exfoliation is characterized by extremely high carrier mobilities $>200,000{\mathrm{cm}}^2/\mathrm{Vs}$ at room temperature. Unfortunately, these films have a very small area ($100{\mathrm{\mu m}}^2$), and this makes them expensive for industrial applications. When placed on a substrate, charged impurity scattering and remote interfacial phonon scattering reduce mobility (see Fig. 14). On ${\mathrm{SiO}}_2$, interfacial phonon scattering limits the graphene mobility to $40,000{\mathrm{cm}}^2/\mathrm{Vs}$ [33]. Atmospheric exposure and processing contaminants such as resist residue, water, and metallic impurities also act as scattering sources and degrade the mobility.

 

Figure 14. Electron mobility in graphene at room temperature in comparison with other material systems.

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Another feature that makes grapheme of interest is its high thermal conductivity (about $10\times$ cooper and $2\times$ diamond) and high conductivity (about $100\times$ copper). It is also characterized by high tensile strength (130 GPa, compared to 400 MPa for A36 structural steel).

Unlike metals with an abundance of free charges, graphene is a semimetal, where carriers can be induced through chemical doping or electrical gating with great ease due to its 2D nature. In this way, a doping concentration from ${10}^{12}$ to ${10}^{13}{\mathrm{cm}}^{-2}$ can be obtained, which is significantly smaller than that of 1 per noble metal. Therefore, the semimetalic nature of graphene allows for electrical tenability not possible with conventional metals.

The optical properties of grapheme are also fascinating [35]. Its optical conductivity is universal conductance, $\pi \beta$, where $\beta$ is equal $(1/4\pi {ϵ}_o)(e^2/\hslash c)$, $e$ is the electron charge, $\hslash$ is Planck’s constant, and $c$ is the speed of light. This provides graphene with broadband (visible and infrared) linear absorption of 2.3% per monolayer. For its 0.33 nm continuous monolayer thickness, it absorbs roughly 2.3% of the incident light, which makes it $10-1000\times$ more absorbing than semiconductors such as Si and GaAs, while covering a much broader spectral bandwidth.

The bandgap structure of graphene can be modified in a different way: by the addition of multiple layers as shown in Fig. 15(a), by substitutional doping [Fig. 15(b)], and by the addition of two layers [Fig. 15(c)] and a doping bilayer [Fig. 15(d)]. The doping of the graphene layer can move the Fermi level either up or down, which results in a decrease in the carrier mobility (both electrons and holes). The thickness restriction for graphene creates a large resistance and chemical inertness, making its use for pure conductive applications less attractive.

 

Figure 15. Modification of graphene’s bandgap structure: (a) Dirac Fermi cone, (b) substitutional doping, (c) bilayer graphene, and (d) doped bilayers.

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Graphene has the highest specific interaction strength (absorption per atom of material) known. Silicon has typically a 10 μm absorption depth, which causes 2.3% of the light to be absorbed in a 200 nm thickness as opposed to the same optical absorption in a much smaller 0.3 nm thickness (interplane spacing) of graphene.

Figure 16 illustrates a typical absorption spectrum of doped grapheme [36]. In the THz region, in the energy range below $2E_F$, the absorption is mainly imparted to a Drude peak response. In doped graphene in the mid-infrared region, the optical absorption is minimal and the residual absorption is generally attributed to disorder in imparting the momentum for the optical transition. A transition occurs around $2E_F$, where direct interband processes lead to a universal 2.3% absorption.

 

Figure 16. Typical absorption spectrum of doped graphene. Reprinted with permission from Low and Avouris, ACS Nano 8, 1086–1101 (2014) [36]. Copyright 2014 American Chemical Society.

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6. Graphene-Based Detectors

Graphene detectors can be separated into two separate categories: either thermal (the bolometer effect) or photon detectors (the photovoltaic effect); see Section 2. Another more recent study utilized the photothermoelectric effect (Seebeck effect) to create a net electric field due to electron diffusion into dissimilar metal contacts. In the following, we describe these mechanisms.

Photovoltaic (PV) photocurrent generation is based on the separation of photogenerated electron–hole pairs by built-in electric fields at junctions between positively ($p$-type) and negatively ($n$-type) doped regions of graphene (see Fig. 17). The same effect can be achieved by applying a source–drain bias voltage, producing an external electric field. In the last case, however, this effect is generally avoided, since graphene is a semimetal and therefore it generates a large dark current. The built-in field can be introduced in different ways: by local chemical doping, electrostatically using (split) gates, or by taking advantage of the work-function difference between graphene and a contacting metal. Typically, $p$-type doping is achieved for metals with a work function higher than that of intrinsic graphene (4.45 eV), whereas the graphene channel can be adjusted to $p$- or $n$- state by the gate.

 

Figure 17. Separation of electron and hole by an internal electric field.

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Electron–electron scattering in graphene can lead to the conversion of one high-energy e–h pair into multiple e–h pairs of lower energy, which can potentially enhance the photodetection efficiency [37].

Figure 18 shows the graphene phototransistor design together with the short-circuit current induced by light. In the absence of an applied bias between the source and the drain, minimal photocurrent is recorded when the light spot is focused on the middle of the graphene channel. Significant photocurrent is observed when the light is incident on the metal–graphene interface area, which is attributed to the conventional PV effect. The built-in electric field in graphene (due to different work functions of the graphene and metal) separates electron–hole pairs, and hence photocurrent is created in the external circuit. In the middle of the channel, there is no built-in electric field, and as a result, no photocurrent is observed. The built-in electric field can be further adjusted by a gate bias, which influences the value the photocurrent.

 

Figure 18. Graphene phototransistor: (a) structure of transistor and (b) schematic view of photocurrent generation.

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The photothermal electric effect (PTE; Seebeck effect) also plays an important role in photocurrent generation [36,37]. Because the optical phonon energy in graphene is large ($\sim 200\mathrm{meV}$), hot carriers created by the radiation field remain at a temperature higher than that of the lattice for many picoseconds. Equilibration of the hot electrons and the lattice occurs via the slower scattering between charge carriers and acoustic phonons (nanosecond timescale), although there is a substantial speed-up attributed to disorder-assisted collisions. Incident radiation of the light spot induces carrier temperature variations, and hot carriers generated by photons diffuse due to the temperature gradient, leading to photocurrent generation, as shown in Fig. 19—the carrier and lattice can have different temperatures. The polarities of the photocurrent due to both photovoltaic (PV) and PTE effects are the same, making the experimental determination of their relative contributions difficult.

 

Figure 19. Photocurrent generation in a graphene p–n junction: (a) profile of carrier concentrations due to light intensity distribution; (b) built-in electric field of p–n junction as well as photothermal electric effect leading to photovoltaic current flowing from the $n$-type region to the $p$-type region. © 2013 IEEE. Reprinted, with permission, from Xia et al., Proc. IEEE 101, 1717–1731 (2013) [34].

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Ryzhii et al. have proposed to utilize multiple graphene layer structures with lateral p-i-n junctions for THz detection [38,39]. The $p$- and $n$-regions of the structure are formed due to the voltages, $V_p$ and $V_n$, and the $i$-region consists of several graphene layers [see Fig. 20(a)]. As in customary p-i-n photodiodes, the electrons and holes photogenerated in the $i$-region induce the terminal current constitutes for output electric signal. It was predicted that these structures can exhibit high responsivity and detectivity in the THz region at room temperatures. Due to the relatively high quantum efficiency and low thermal generation rate, the photodetectors can substantially surpass other THz detectors.

 

Figure 20. Structure of graphene-based photodetectors with (a) electrically induced p-i-n junction and (b) resonance-based detector.

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Another design of graphene detector is a resonant structure of two graphene sheets separated by a dielectric to tune the photon wavelength of absorption as shown in Fig. 20(b). The responsivity of the detector exhibits resonant peaks when the frequency of incoming THz radiation approaches the resonant plasma frequencies. These frequencies are tuned by the bias voltage [40]. The pronounced resonant response of the detector requires the frequency of electron and hole collisions with impurities and acoustic phonons to be sufficiently low.

Graphene can be also used for the detection of THz radiation as a field effect transistor (FET). The use of FETs as detectors of THz radiation was first proposed by Dyakonov and Shur in 1993 [41] based on a formal analogy between the equations of the electron transport in a gated 2D transistor channel and those of shallow water, or acoustic waves in music instruments. As a consequence, hydrodynamic-like phenomena should also exist in the carrier dynamics in the channel. Instability of this flow in the form of plasma waves was predicted under certain boundary conditions.

The detection by FETs is due to the nonlinear properties of the transistor, which lead to the rectification of the ac current induced by the coming radiation. As a result, a photoresponse appears in the form of a dc voltage between source and drain. This voltage is proportional to the radiation intensity (photovoltaic effect). In the so-called resonant regime, the plasma waves are weakly damped (when a plasma wave launched at the source can reach the drain in a time shorter than the momentum relaxation time); the detection mechanism exploits interference of the plasma waves in the cavity, which results in a resonantly enhanced response [41,42]. Figure 21 schematically shows the resonant oscillation of plasma waves in a gated region of the FET. Even in the absence of an antenna, the THz radiation is coupled to the FET by contact pads and bonding wires. Significant progress in sensitivity can be obtained by adding a proper antenna or a cavity coupling. Broadband detection occurs when plasma waves are overdamped, when plasma waves launched at the source decay before reaching the drain.

 

Figure 21. Schematic of (a) THz CMOS detector and (b) plasma oscillations in a transistor.

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Room-temperature THz detectors based upon the PTE effect [43] and antenna-coupled graphene FETs [44–47] have been demonstrated. The dependence of the photovoltage on the carrier density in the FET channel also displays PTE contributions. Figure 22 explains schematic representation of two competitive independent detection mechanisms: the plasmonic detection due to the electron transport nonlinearity and the thermoelectric effect due to the presence of carrier density junctions and an induced temperature gradient across the FET channel. The red-shaped area shows the locally heated area due to the carrier density junction at the interface of ungated and gated regions with thermopower $S_{ug}$ and $S_g$, respectively. Plasma-wave detection is the dominant mechanism, even though it is strongly counterbalanced by the thermoelectric response.

 

Figure 22. Schematic representation of the detection mechanism in graphene FET THz photodetector.

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In Ref. [44] the plasma waves excited by THz radiation were overdamped, and thus the detectors did not operate in the resonant regime. Figure 23(a) shows plasma-wave FET employing a top-gate antenna-coupled configuration. These detectors demonstrated a $\mathrm{NEP}\sim {10}^{-9}\mathrm{W}/{\mathrm{Hz}}^{1/2}$ in the range of 0.29–0.38 THz. During measurements of a target at room temperature, the bilayer-graphene-based FET at $V_g=3\mathrm{V}$ was mounted on a $x–y$ translation stage having a spatial resolution of 0.5 μm. The THz image consists of $200\times 550$ scanned points, collected by raster scanning the object in the beam focus, with integration time of 20 ms/point [see Fig. 23(b)].

 

Figure 23. Plasma-wave FET terahertz detector: (a) schematics of the THz detection configuration in a FET embedding the optical image of the central area of a bilayer graphene-based FET and (b) 0.3 GHz transmission mode image of a leaf. Reprinted by permission from Macmillan Publishers Ltd.: Vicarelli et al., Nat. Mater. 11, 865–871 (2012) [44]. Copyright 2012.

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Further improvement in THz detection has recently been described by Liu et al. [47] The detector was built from split-finger gated graphene-based FETs coupled with a logarithmic antenna. Its NEP value determined by the Johnson–Nyquist noise was less than $0.1\mathrm{nW}/{\mathrm{Hz}}^{1/2}$ at both 0.04 and 0.14 THz. The achieved performances are competitive with those of commercially available detectors, in terms of both sensitivity and NEP.

In comparison with plasmonic THz detectors fabricated by exfoliated graphene [45] or CVD graphene transferred on $\mathrm{Si}/{\mathrm{SiO}}_2$ substrates [48], the epitaxial graphene grown on SiC is more promising [46]. The photoresponsivity of the bilayer-graphene FET channel grown on SiC substrate was estimated in $\approx 0.25\mathrm{V}/\mathrm{W}$ and $\mathrm{NEP}\approx 80\mathrm{nW}/\surd \mathrm{Hz}$.

The key parameters of a bolometer are the thermal resistance and the heat capacity (see Subsection 4.2). Graphene has a small volume for a given area and low density of states, which results in low heat capacity, and thus a fast device response. The cooling of electrons by acoustic phonons is inefficient (owing to the small Fermi surface), and cooling by optical phonons requires high temperature ($kT>200\mathrm{meV}$). Thus thermal resistance is relatively high, giving rise to high bolometric sensitivity [37,49].

Two types of graphene-based bolometers are shown in Fig. 24. Yan et al. have considered graphene as a hot-electron bolometer [50]. The device structure is shown in Fig. 24(a). Due to weak electron–phonon interaction, they used bilayer graphene, which has a tunable bandgap. Application of a perpendicular electric field gives rise to electron-temperature-dependent resistance at low temperature, making the device suitable for thermometry. The extrapolated NEP value for a $1{\mathrm{\mu m}}^2$ sample at 100 mK is about $5\times {10}^{-21}\mathrm{W}/{\mathrm{Hz}}^{1/2}$, like the state-of-the-art TES (transition edge sensor) bolometer. A schematic view of the graphene-based detector with temperature coefficient of resistance (TCR) above 4%/K is shown in Fig. 24(b), where the pyroelectric response of a ${\mathrm{LiNbO}}_3$ crystal is transduced with high gain (up to 200) into modulation for graphene [51]. This is achieved by fabrication a floating metallic structure that concentrates the pyroelectric charge on the top-gate capacitor of the graphene channel.

 

Figure 24. Schematic view of graphene bolometers: (a) side view of the bilayer graphene hot-electron bolometer (semitransparent NiCr top gate covers the graphene device and silicon oxide surrounds the graphene); (b) pyroelectric bolometer (conductance of graphene channel is modulated by the pyroelectric substrate and by a floating gate).

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The main obstacle in the development of high sensitivity of graphene bolometers is the weak variation of electrical resistance with temperature. Recently published papers by El Fatimy et al. [52] have shown that quantum dots of epitaxial graphene on SiC exhibit an extraordinarily high variation of resistance with temperature due to quantum confinement, higher than $430\mathrm{M\Omega }/\mathrm{K}$ at 2.5 K, leading to responsivities for absorbed THz power above $1\times {10}^{10}\mathrm{V}/\mathrm{W}$. In these hot-electron bolometers with nano-patterned dots in epitaxial graphene, a bandgap is induced via quantum confinement (without the need for gates) using a simple single-layer structure. Figure 25(a) shows the NEP at 0.15 THz as a function of temperature from 2.5 to 80 K, calculated for 30 nm and 150 nm dots. The NEP value is about one order of magnitude lower than the best commercial cooled bolometer and has a much faster time (a few nanoseconds, compared to milliseconds for commercial bolometers). These quantum-dot bolometers work in a very broad spectral range from THz to ultraviolet radiation with responsivity independent of wavelength; see Fig. 25(b).

 

Figure 25. Quantum-dot bolometers: (a) NEP versus temperature at 0.15 THz for 30 nm and 150 nm quantum dots. Reprinted by permission from Macmillan Publishers Ltd.: El Fatimy et al., Nat. Nanotechnol. 11, 335–338 (2016) [52]. Copyright 2016. (b) Responsivity as a function of absorbed power at different wavelength. Inset: NEP as a function of absorbed power at various wavelengths. Reprinted with permission from El Fatimy et al., Nanophotonics 7, 735–740 (2018) [53]. Copyright 2018 De Gruyter.

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7. Responsivity-Enhanced Graphene-Based Detectors

Most graphene photodetectors utilize graphene–metal junctions or graphene p–n junctions to spatially separate and extract photogenerated carriers. However, for the development of high-responsivity photodetectors, graphene represents the two major challenges: the low optical absorption inside the active detector’s region junctions ($\sim 100–200\mathrm{nm}$) and the short photocarrier lifetime. Thus, the existing graphene photodetectors remain limited by tradeoff between high responsivity, ultrafast temporal response, and broadband operation.

Responsivity-enhanced photodetection in graphene can be achieved by increasing the photocarrier lifetime through band-structure engineering and defect engineering. For example, carrier trapping mechanisms and patterned graphene nanostructures have been utilized to introduce bandgap and midgap defect states in graphene [3,37,54]. In this case, however, the response time is limited by long carrier trapping times due to introduced defect and edge states. Figure 26 shows an example of the broadband absorption of a graphene quantum-dot (GQD) detector reported by Chinese researchers [55]. The response was shown from the visible (532 nm), near-infrared (1.47 μm), and mid-infrared ($\sim 10\mathrm{\mu m}$) ranges with photoresponses of 1.25, 0.2, and 0.4 A/W, respectively. The high responsivity of the monolayer graphene detector [see Fig. 26(b)] is partially attributed to internal gain of four times, called multi-excitation generation of carriers caused by impact ionization. The increased performance is enhanced by the introduction of electron trapping centers and by optimizing a bandgap through band-structure engineering. However, electron trapping has serious limitations on the response time [see Fig. 26(b)].

 

Figure 26. Broadband graphene quantum-dot photodetector: (a) device design and (b) slow response to light at 1.47 μm. Reprinted by permission from Macmillan Publishers Ltd.: Zhang et al., Nat. Commun. 4, 1811 (2013) [55]. Copyright 2013.

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Table 4 presents several kinds of novel responsivity-enhanced photodetector structures consisting of graphene and additional light-absorption mediums (e.g., quantum dots, fluorographene, nanowires, and bulk semiconductors) [37,60,80–82].

Table 4. Responsivity-Enhanced Graphene-Based Detectors

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The built-in field formed by graphene and light-absorption mediums can separate the photoinduced carriers generated at the absorption mediums and then inject holes/electrons into graphene. The photoresponse beyond the light-absorption region of semiconductors can also be detected contributing to the photoinduced carriers provided by graphene. Unlike the pure graphene photoconductor, the built-in field at the interface can efficiently separate the photoinduced carriers and prolong their lifetime (it is photogating effect), resulting in the relatively high responsivity.

Figure 27 schematically explains the differences between a pure graphene photoconductor and a hybrid photoconductor. This comparison also concerns differences between ultrafast and ultrasensitive graphene photodetectors. In the early reports, photocurrent was generated by local illumination of one of the metal/graphene interfaces of a back-gated graphene FET. An asymmetric metallization scheme was used to break the mirror symmetry of the built-in potential profile within the channel, allowing us to give the overall photocurrent. Interdigitated metal fingers were used, leading to the creation of a greatly enlarged, high electric field, light-detection region [see Fig. 27(a)]. The high carrier mobility and short carrier lifetime in graphene [see Fig. 27(c)] allow metal–graphene–metal photodetectors to operate at high data rates.

 

Figure 27. Ultrafast and ultrasensitive graphene photodetectors: (a) schematic structure of metal–graphene–metal photodetector, (b) band profile, (c) recombination mechanism, and (d) hybrid graphene/quantum-dot photodetector. Reprinted by permission from Macmillan Publishers Ltd.: Konstantatos et al., Nat. Nanotechnol. 7, 363–368 (2012) [56]. Copyright 2012. (e) Trapping process and (f) dynamic process at the interface of graphene/quantum dots.

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The main feature of the hybrid photodetector [see Fig. 27(d)] is its ultrahigh gain, which originates from the high carrier mobility of the graphene sheet and the recirculation of charge carriers during the lifetime of the carriers that remain trapped in the quantum dots [Fig. 27(e)]; also other light-absorbing media (e.g., carbon nanotubes and nanoplates) can be used. Photoexcited holes in the quantum dots are transferred to the graphene layer and drift by means of a voltage bias $V_{\mathrm{DS}}$ to the drain, with a typical timescale of transit, ${\tau }_{\text{transit}}$, which is inversely proportional to the carrier mobility. Electrons remain trapped (with a typical lifetime, ${\tau }_{\text{lifetme}}$) in the quantum dots. Multiple circulation of holes in the graphene channel following a single electron–hole photogeneration leads to strong photoconductive gain. The photoconductive gain defined as the number of charge carriers passing contacts per one generated pair, $g={\tau }_{\text{lifetme}}/{\tau }_{\text{transit}}$, indicates the importance of a long lifetime and high carrier mobility. Konstantatos et al. have demonstrated the gain of ${10}^8$ electrons per photon and a responsivity of $\sim {10}^7\mathrm{A}/\mathrm{W}$ in short-wavelength hybrid phototransistors [56].

Hybrid photodetectors offer improvements in responsivity; however, the majority of these devices have a limited linear dynamic range due to the charge relaxation time, which quickly saturates the available states for photoexcitation, leading to a drop in responsivity with incident optical power. For example, Fig. 28 shows the gain as a function of excitation intensity, as compared to the theory (solid line), for a hybrid single-layer graphene/ZnO quantum-dot (QD) detector. This ZnO QD/graphene hybrid structure shows a photoconductive gain as high as ${10}^7$. A drop in reponsivity versus absorber power is also observed for graphene bolometers [see Fig. 25(b)].

 

Figure 28. Gain as a function of excitation intensity for hybrid graphene/ZnO quantum-dot detector. The circles are experimental data, and the solid curve is the theoretical plot with best fitting. Guo et al., Small 9, 3031–3036 (2013) [58]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

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The light–matter interaction in 2D materials to improve the performance of the 2D material-based photodetectors can also be realized through introducing optical structures (e.g., plasmonic nanostructures, photonic crystals, optical cavities, and waveguides) onto the device [8,36,65–77]. When the energy of the plasma-wave frequencies is quantized, the quanta are called plasmons. Two key factors are important: (i) matching the size and shape of the metal pattern so the desired wavelength will generate plasmons and (ii) the coupling of the plasmons to the detector. The generation of plasmons depends significantly on the metallic pattern. The dimensions of the metal grating should be like the metal strip width to permit the plasmon fields to enter the detector below the grating. Usually, a thin dielectric layer is placed over the detector and a metal grid is placed on top of the dielectric layer. As the plasmons are traveling parallel to the surface, a large optical path can be obtained for absorption without requiring a thick absorbing layer.

In some architectures, however, the above-mentioned limited linear dynamic range is compensated by the high sensitivity (low NEP). The speed of these devices is limited by operating bandwidths between $\sim 1\mathrm{Hz}$ and $\sim 10\mathrm{kHz}$. Other limitations of biased graphene detectors are the high noise levels and power consumption given the large dark current present.

The optimal strategy to achieve high responsivity with fast photoresponse is to improve the generation rate of photoinduced carriers in graphene while maintaining the appropriate carrier lifetime. This method has recently been demonstrated for short-wavelength graphene photodetectors [77]; see Fig. 29. Under light illumination, the light with wavelength matching with plasmonic resonance is trapped by Au nanoparticles and is absorbed by graphene. A vertical built-in field is employed in the graphene channel for trapping the photoinduced electrons and leaving holes in graphene, which results in a prolonged photoinduced carrier lifetime.

 

Figure 29. Schematic diagram of the concept of SWIR graphene photodetector. Reprinted with permission from Chen et al., ACS Nano 11, 430–437 (2017) [77]. Copyright 2017 American Chemical Society.

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The responsivity of the detector is enhanced by plasmonic Au nanoparticles and is the highest reported among the SWIR based on grapheme—83 A/W at 1.55 μm. However, a limitation of the response time to about 600 ns still exists because of the surface traps in the surface of the hybrid structure as well as the traps in nanoparticles. Despite this, the SWIR graphene detector is characterized by the fastest response speed in the hybrid graphene photodetector/transistor.

The unique electrical and optical characteristics of gold-patched graphene nanostripe photodetectors have been demonstrated by Cakmakyapan et al. [83]. Commercially available chemical vapor deposition (CVD)-grown graphene was first transferred to a high-resistivity silicon wafer covered with a 130-nm-thick thermally grown ${\mathrm{SiO}}_2$ layer. Next, gold patches, graphene nanostripes, Ti/Au contacts, and gate pads were patterned by different combinations of optical lithography and plasma etching. The gate voltage applied to the Si substrate, $V_g$, controls the Fermi energy level of the graphene nanostripes. The gold patches have a width of 100 nm, periodicity of 200 nm, height of 50 nm, length of 1 μm, and a tip-to-tip gap size of 50 nm (see Fig. 30).

 

Figure 30. Photoconductive nanostructures based on gold-patched graphene nanostripes: (a) operation principle of the photodetector and (b) optical microscope and scanning electron microscopy (SEM) images for a fabricated photodetector. Reprinted by permission from Macmillan Publishers Ltd.: Cakmakyapan et al., Light: Sci. Appl. 7, 20 (2018) [83]. Copyright 2018.

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The photodetector has an ultrabroad spectral response from the visible to the infrared regime with high-responsivity levels ranging from 0.6 A/W at wavelength of 800 nm to 11.65 A/W at a wavelength of 20 μm, as illustrated in Fig. 31. This wide photodetection bandwidth and high responsivity are enabled using the gold-patched graphene nanostripes. As expected, higher photoconductive gains are obtained at lower wavelengths, where excitation to higher energy levels gives rise to the excitation of secondary electron–hole pairs by transferring more energy during relaxation (see the inset of Fig. 31).

 

Figure 31. Responsivity, photoconductive gain, and noise equivalent power (optical chopping above 1 kHz) of the fabricated photodetector at an optical power of 2.5 μW, gate voltage of 22 V, and bias voltage of 20 mV. Reprinted by permission from Macmillan Publishers Ltd.: Cakmakyapan et al., Light: Sci. Appl. 7, 20 (2018) [83]. Copyright 2018.

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The photodetector also shows operation speeds exceeding 50 GHz, which is more than seven orders of magnitude faster compared to higher-responsivity hybrid graphene/quantum dots [56,59] and tunneling barriers [61]. Figure 32 compares the speed of room-temperature operation high-performance graphene photodetectors reported in the literature including Ref. [83].

 

Figure 32. Comparison of the responsivity and speed operation for the room-temperature graphene photodetectors reported in the literature. (a) Reprinted with permission from Chen et al., ACS Nano 11, 430–437 (2017) [77]. Copyright 2017 American Chemical Society. (b) Reprinted by permission from Macmillan Publishers Ltd.: Cakmakyapan et al., Light: Sci. Appl. 7, 20 (2018) [83]. Copyright 2018.

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8. Related Two-Dimensional Material Detectors

The performance of photodetectors is mainly dependent on the inherent characteristics of the photodetector’s active materials, such as the absorption coefficient, the lifetime of the electron–hole pair, and the charge mobility. The high dark current of conventional graphene materials arising from the gapless nature of graphene significantly reduces the sensitivity of photodetection and restricts further developments of graphene-based photodetectors. The discovery of new 2D materials with direct energy gaps in the infrared to the visible spectral regions has opened up a new window for photodetector fabrication.

Graphene is one of a large number of possible 2D crystals. There are hundreds of layered materials that retain their stability down to monolayers, and whose properties are complementary to those of graphene [3,5,84–86]. Even though the technology readiness levels are still low and device manufacturability and reproducibility remain a challenge, 2D materials technology can be found in research labs around the globe including materials such as silicene, germanene, stanene and phosphorene, transition metal dichalcogenides (TMDs), black phosphorus, and recently discovered all-inorganic perovskites. Compared to graphene, TMDs, like molybdenum disulfide (${\mathrm{MoS}}_2$), tungsten disulfide (${\mathrm{WS}}_2$), and molybdenum diselenide (${\mathrm{MoSe}}_2$), exhibit even higher absorption in the visible and the near-infrared range, i.e., above their respective energy bandgaps, which makes this 2D material class a candidate to act as the thinnest photoactive material 2D semiconductors covering a very broad portion of the spectrum from infrared to the ultraviolet. Figure 33 shows the responsivity against the response time for 2D materials (graphene-based devices and TMDs). It can be seen that photodetectors based on semiconducting layered materials display a large (about 10 orders of magnitude) variation in their responsivity. Their response time is considerably longer than commercial silicon and InGaAs photodiodes and is longer than $\sim 1\times {10}^{-2}\mathrm{ms}$. The slow response is attributed to traps and enhanced capacitance. However, there are multiple ways to reduce trap times and densities.

 

Figure 33. Responsivity against response time for two-dimensional materials in comparison with commercial silicon and InGaAs photodiodes. At the bottom, the bandgaps of the different layered semiconductors and electromagnetic spectrum are shown. The exact bandgap value depends on the number of layers, strain level, and chemical doping. The asterisk indicates that the material’s fundamental bandgap is indirect. FIR, far infrared; MIR, mid infrared; NIR, near infrared; UV, ultraviolet. Reprinted with permission from Buscema et al., Chem. Soc. Rev. 44, 3691–3718 (2015) [84].

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TMDs show a direct, finite bandgap (0.4–2.3 eV), which endows them with a very high carrier density tunability (on/off current ratios in a transistor up to ${10}^{10}$), but limits the carrier mobility to relatively low values, typically less than $250{\mathrm{cm}}^2/\mathrm{Vs}$. TMDs-based phototransistors have relatively poor responsivity owing to their weak optical absorption. This limitation has been addressed by 2D material synthesized with other material (semiconductor, different 2D materials). In this context, black phosphorus (bP) appears as a natural tradeoff between graphene and TMDs [87,88]. With its thickness-dependent energy gap, spanning from 0.3 eV in the bulk case to 1.7 eV of the monolayer case (phosphorene), bP can reach an on/off ratio up to ${10}^5$ in a FET, retaining a room-temperature mobility above $1000{\mathrm{cm}}^2/\mathrm{Vs}$. Viti et al. [88] have reviewed recent achievements in the development of bP-based FET photodetectors operating in the 0.3–3.4 THz with NEP value lower than $10\mathrm{nW}/{\mathrm{Hz}}^{1/2}$. Relatively high carrier mobility and unique anisotropic transport properties are useful in specific applications of bP, while one fatal problem is structure instability.

By varying the composition of arsenic, $x$, in the black arsenic phosphorus ${\mathrm{As}}_x{\mathrm{P}}_{1-x}$(b-AsP), the bandgap correspondingly changes from 0.3 to 0.15 eV. This change in energy gap suggests that b-AsP may interact with light, whose wavelength is as long as 8.25 μm. Long et al. [89] have reported about b-AsP long-wavelength IR photodetectors, with room-temperature operation to 8.2 μm. However, degradation in air and other environments is an unresolved issue that may limit future applications. bP degrades rapidly under room conditions, affecting its structure and properties.

Another way to enhance the optoelectronic properties of graphene is modification by noncovalent and covalent functionalization. Due to robust chemistry, graphene itself is a chemistry inert material. The so far established chemistries lead to graphene derivatives with a low degree of functionalization (typically 1%–3%) [90]. Fluorographene (FGr) is prepared by fluorination of graphene, and mechanical or chemical exfoliation of graphite fluoride. The bandgap of FGr can be tuned from the ultraviolet to near-infrared by controlling the degree of fluorination. A recently published paper has demonstrated the Gr/FGr photodetector with spectral range spanning from 255 nm to 4.3 μm; see Fig. 34 [60]. This broadband response arises from the quantum confinement of graphene regions by fluorine adatoms. The rehybridization of carbon with fluorine results in a mixture of ${\mathrm{sp}}^2$ and ${\mathrm{sp}}^3$ nanodomains, inducing a series of discrete states for trapping of photoexcited charge carriers. Despite the high photoresponsivity of our Gr/FGr photodetector over a broadband range, it operation speed is slow—about 200 ms. It is suggested that the reason for this is the long trapped carrier lifetime in both the ${\mathrm{sp}}^2$ and the ${\mathrm{sp}}^3$ domains.

 

Figure 34. Spectral responsivity of graphene-based photodetectors compared with commercial photodetectors. Dotted line shows 100% quantum efficiency. Red and green colors denote $\le 1$-ns response times, while blue color denotes $\ge 1$-s response times. The graphene photodetectors are labeled with their reference as well as a brief description of the photodetector style. The commercial photodiodes are shown in green. The Gr/FGr photodetector in the MWIR range was tested only at temperature of 77 K. Many data are reprinted with permission from Currie, “Applications of graphene to photonics,” NRL/MR/5650-14-9550 (Naval Research Laboratory, 2014) [91].

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9. Graphene-Based Detector Performance: The Present Status

Since its discovery, graphene has been extensively studied for potential wide-ranging use in photodetectors in a wide range of the electromagnetic spectrum. Most activity has been devoted to visible and near-infrared photon detectors [5,37]. In this section we concentrate mainly on infrared and THz graphene photodetectors.

In Fig. 34 the spectral responsivity of graphene photodetectors, operated in visible and near-infrared spectral ranges, is compared with that of commercially available silicon and InGaAs photodiodes. As is shown, graphene’s high mobility together with the trapped-charge lifetimes in the quantum dots produced a photodetector responsivity of ${10}^7\mathrm{A}/\mathrm{W}$ [56]. The high responsivity makes this a useful device for measuring low-level signals. However, due to the long lifetime of the traps, the demonstrated operation speed is very slow ($<10\mathrm{Hz}$).

Literature data for longer-wavelength infrared graphene-based photodetectors, with cutoff wavelength above 3 μm, are limited. Here we present results for a Gr/FGr photodetector tested in the MWIR range at 77 K [60]; see Figs. 34 and 35.

 

Figure 35. Typical spectral detectivity curves of HgCdTe photodiodes and PbSe photoconductor operated at 300 K. BLIP detectivity is calculated for $\mathrm{FOV}=2\pi$. Spectral detectivity curves for the Gr/FGr photodetector and two b-AsP photodetectors are also shown for comparison.

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Interesting results are published for room-temperature-operated photodetectors (entering the second atmospheric transmission window) based on b-AsP. Detectivity higher than $4.9\times {10}^9$ Jones was obtained in the 3 to 5 μm range [89]. The photodetector works in a zero-bias photovoltaic mode, enabling low dark noise and response time in the milisecond range. Figure 35 compares the detectivity of b-AsP photodetectors with commercially available HgCdTe photodiodes and PbSe photoconductors operated at room temperature. Their detectivity is similar to HgCdTe detectors; however, the response time of HgCdTe detectors is considerably shorter—typically on the order of nanoseconds.

Particular attention in the development of THz imaging systems is devoted to the realization of sensors with a large potential for real-time imaging while maintaining a high dynamic range and room-temperature operation. CMOS process technology is especially attractive due to the low price tag for industrial, surveillance, scientific, and medical applications. However, the CMOS THz imagers developed thus far have mainly operated single detectors based on the lock-in technique to acquire raster-scanned imagers with frame rates on the order of minutes. With this mind, many of the recent developments are directed towards three types of focal-plane arrays (FPAs):

SBDs respond to the THz electric field and usually generate an output current or voltage through a quadratic term in their current-voltage characteristics. In general, the NEP of SBD and FET detectors is better than that of Golay cells and pyroelectric detectors around 300 GHz. Both the pyroelectric and the bolometer FPAs with detector response times in the millisecond time range are not suited for heterodyne operation. FET detectors are clearly capable in heterodyne detection with improving sensitivity. Diffraction aspects predict FPAs for higher frequencies (0.5 THz and above) and in conjunction with large $f/\#$ optics.

Owing to its high carrier mobility, graphene is a very promising material for the development of room-temperature detectors operating across the far infrared, with high room-temperature performance for high spectral bandwidth covering the full THz range (0.1–10 THz).

At the present stage of technology, the most effective graphene THz detectors utilize plasma rectification phenomena in FETs, where plasma waves in the channel are excited by incoming THz waves modulating the potential difference between gate and source/drain being rectified via nonlinear coupling and transfer characteristics in FET. The next two figures compare the NEP values of graphene-based FET room-temperature detectors with those of existing market-dominating THz photon detectors (Fig. 36) and thermal detectors (Fig. 37).

 

Figure 36. Spectral dependence of NEP for graphene FET detectors and different photon THz (CMOS-based, Schottky diodes).

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Figure 37. Spectral dependence of NEP for graphene FET detectors and microbolometer THz FPAs.

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Most experimental data gathered in the literature is given for single graphene detectors operated above a wavelength of 100 μm (frequency below 3 THz). Generally, the performance of graphene FET detectors is poorer in comparison with CMOS-based and plasma detectors fabricated using Si-, SiGe-, and InGaAs-based materials. However, in comparison with vanadium oxide and amorphous silicon microbolometers, the performance of graphene detectors is close to the trend line estimated for microbolometers in the THz spectral region (see Fig. 37). The best quality vanadium oxide bolometer arrays are characterized by an NEP value of about $1\mathrm{pW}/{\mathrm{Hz}}^{1/2}$ in the LWIR range ($\approx 10\mathrm{\mu m}$). It should be marked here, however, that microbolometer data are addressed to monolithic arrays. In this case an important issue for FPAs is pixel uniformity. It appears, however, that the production of monolithically integrated THz detector arrays encounters so many technological problems that the device-to-device performance variations and even the percentage of non-functional detectors per chip tend to be unacceptably high.

Adaptation of infrared microbolometers to the THz frequency range after the successful demonstration of active THz imaging [92] entails that in the period of 2010–2011 three different companies/organizations announced cameras optimized for the $>1$-THz frequency range: NEC (Japan) [93], INO (Canada) [94], and Leti (France) [95]. Figure 37 summarizes the NEP values for bolometer FPAs fabricated by three vendors. The FPAs optimized for 2–5 THz exhibit impressive NEP values below $100\mathrm{pW}/{\mathrm{Hz}}^{1/2}$. It can be seen that the wavelength dependence of the NEP is quite flat below 200 μm. Further improvement of performance is possible by increasing the number of pixels, or by modification of the antenna design while preserving the pixel pitch, readout integrated circuit (ROIC), and technological stack.

Summarizing the above discussion about the present status of graphene-based detectors, we can conclude the following:

10. Focal-Plane Arrays

The term “focal-plane array” (FPA) refers to an assemblage of individual detector picture elements (“pixels”) located at the focal plane of an imaging system. Although the definition could include 1D (“linear”) arrays as well as 2D arrays, it is frequently applied to the latter. Usually, the optics part of an optoelectronic images device is limited only to focusing of the image onto the detector array. These so-called “staring arrays” are scanned electronically usually using circuits integrated with the arrays. The architecture of detector-readout assemblies has assumed a number of forms, which are described in detail, e.g., in Refs. [10,17,96]. Information about the assemblies and applications can be found at different vendor websites. FPA technology has revolutionized many kinds of imaging from $\gamma$ rays to the THz and even radio waves; the rate at which images can be acquired has increased by more than a factor of a billion in many cases.

Figure 38 illustrates the trend in array size over the past 50 years. Imaging IR FPAs have been developing in-line with the ability of silicon integrated circuit (ICs) technology to read and process the array signals, and also to display the resulting image. The progress in IR arrays has also been steady, mirroring the development of dense electronic structures such as dynamic random access memories (DRAMs). FPAs have had nominally the same development rate as DRAM ICs, which have followed Moore’s law with a doubling-rate period of approximately 18 months, however, with FPAs lagging behind DRAMs by about 5–10 years. The 18-month doubling time is evident from the slope of the graph presented in the inset of Fig. 38, which shows for MWIR FPAs the log of the number of pixels per array as a function of the first year of commercial availability. Charge coupled devices (CCDs) above 3 gigapixels offer the largest formats.

 

Figure 38. Imaging array formats compared with the complexity of silicon microprocessor technology and dynamic access memory (DRAM) as indicated by transistor count and memory bit capacity. The timeline design rule of MOS/CMOS features is shown at the bottom. Reprinted with permission from [97]. Copyright 2003 Marcel Dekker.

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IR array sizes will continue to increase but perhaps at a rate that falls below the Moore’s law trend [98]. An increase in array size is already technically feasible. However, the market demand for larger arrays is not as strong as before the megapixel milestone was achieved. In particular, astronomers were the driving force towards the day when optoelectronic arrays could match the size of the photographic film. Since large arrays dramatically multiply the data output of a telescope system, the development of large format mosaic sensors of high sensitivity for ground-based astronomy is the goal of many astronomic observatories around the world. Raytheon manufactured a $4\times 4$ mosaic of $2\mathrm{k}\times 2\mathrm{k}$ HgCdTe sensor chip assemblies (SCAs) with 67 million pixels and assisted in assembling it to the final focal-plane configuration to survey the entire sky in the Southern Hemisphere at four IR wavelengths [99].

The trend of increasing the pixel’s number is likely to continue in the area of large format arrays. This increase will be continued using a close-butted mosaic of several SCAs. Butting refers to tiling closely together separate pieces of semiconductor to come to one large sensitive array operated as a single image sensor that is larger than the FOV of the lithographic equipment used during the fabrication of the imagers.

The FPA is the heart of most modern day infrared imaging systems, and they may be classified as hybrid and monolithic, but these distinctions are often not as important as proponents and critics state them to be. In the monolithic approach, both detection of light and signal readout (multiplexing) is done in the detector material rather than in an external readout circuit. The integration of the detector and readout onto a single monolithic piece reduces the number of processing steps, increases yields, and reduces costs. Common examples of these FPAs in the visible and near infrared are found in camcorders and digital cameras. In the case of the hybrid approach, dominated in infrared detector technology, we can optimize the detector material and multiplexer independently. Other advantages of hybrid-packaged FPAs are near-100% fill factors and increased signal-processing area on the multiplexer chip.

10.1. CCD Versus CMOS

Two generic types of silicon technology provide the bulk of devices in these markets: CCDs and CMOS imagers. CCD technology has achieved the highest pixel counts or largest formats with numbers above ${10}^9$ (see Fig. 38). At present, CMOS with minimum features of $\le 0.1\mathrm{\mu m}$ makes possible monolithic visible CMOS imagers because the denser photolithography allows for low-noise signal extraction and high-performance detection with high optical fill factor within each pixel. The pixel’s architecture is changed to improve the resolution by shrinking the pixel size. Figure 39 is a roadmap of where the CMOS pixel pitch became smaller than the CCD due to the described technological development in 2010 [100]. Designers of image sensors are actively working on super-small 0.9 μm pixels. Reducing pixel size below 1 μm will allow more interleaving functions to be implemented without scaled loss of resolution and open up new opportunities for extended functionality. CMOS imagers are also rapidly moving to large formats and at present are competing with CCDs for large format applications. The silicon wafer production infrastructure that has put high-performance personal computers into many homes makes CMOS-based imaging in consumer products such as video and digital still cameras widely available.

 

Figure 39. Roadmap of CMOS pixel pitch development. © 2013 IEEE. Reprinted, with permission, from Hirayama, IEEE Asian Solid-State Circuits Conference (2013), pp. 5–8 [100].

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Figure 40 compares the principle of CCDs and CMOS sensors. Both detector technologies use a photosensor to generate and separate the charges in the pixel. Beyond that, however, the two sensor schemes differ significantly. During CCD readout, the collected charge is shifted from pixel to pixel all the way to the perimeter. Finally, all charges are sequentially pushed to one common location (floating diffusion), and a single amplifier generates the corresponding output voltages. On the other hand, CMOS detectors have an independent amplifier in each active pixel sensor (APS). The amplifier converts the integrated charge into a voltage and thus eliminates the need to transfer charge from pixel to pixel. The voltages are multiplexed onto a common bus line using integrated CMOS switches. Analog and digital sensor outputs are possible by implementing either a video output amplifier or an analog-to-digital (A/D) converter on the chip.

 

Figure 40. Comparison between the CCD-based and CMOS-based image sensor approaches.

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The processing technology for CMOS is typically two to three times less complex than standard CCD technology. In comparison with CCDs, CMOS multiplexers exhibit important advantages due to high circuit density, fewer drive voltages, fewer clocks, much lower voltages (low power consumption), packing density compatible with many more special functions, and lower cost for both digital video and still camera applications. The minimum theoretical read noise of a CCD is limited in large imagers by the output amplifier’s thermal noise after correlated double sampling (CDS) is applied in off-chip support circuits. The alternative CMOS paradigm offers lower temporal noise because the relevant noise bandwidth is fundamentally several orders of magnitude smaller and better matches the signal bandwidth. While CCD sensitivity is constrained by the limited design space involving the sense node and the output buffer, CMOS sensitivity is limited only by the desired dynamic range and operating voltage. CMOS-based imagers also offer practical advantages with respect to on-chip integration of camera functions including command and control electronics, digitization, and image processing. CMOS is now also suitable for time delay and integration (TDI) type multiplexers because of the availability from foundries of design rules lower than 1.0 μm, more uniform electrical characteristics, and lower noise figures.

10.2. Trends in Infrared Focal-Plane Arrays

Infrared system performance is highly scenario dependent and requires the designer to account for numerous different factors when specifying detector performance. It means that a good solution for one application may not be as suitable for a different application. In general, detector material is primary selected based on the wavelength of interest, performance criteria, and operating temperature. At present the largest interest for infrared detector technology includes HgCdTe, InSb/III-Vs, Si:As BIB, and microbolometers (see Fig. 41).

 

Figure 41. Detector materials that have the largest interest for infrared detector technology. Reprinted with permission from [101]. Copyright 2016 SPIE.

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A suitable detector material for the near-IR (1.0–1.7-μm) spectral range is InGaAs lattice matched to the InP. Various HgCdTe alloys, in both photovoltaic and photoconductive configurations, cover 0.7 μm to more than 20 μm. InAs/GaSb strained layer superlattices have emerged as an alternative to HgCdTe. Impurity-doped (Sb, As, and Ga) silicon BIB detectors operating at 10 K have a spectral response cutoff in the range of 16–30 μm.

Ge:Ga photoconductors are the best low-background photon detectors for the wavelength range from 40 to 120 μm operated at about 2 K.

Although focal-plane array imagers are very common in our lives, they are quite complex to fabricate. Depending on the array architecture, the process can include more than 150 individual fabrication steps. The hybridization process involves flip-chip indium bonding between the “top” surfaces of the ROIC and detector array. The indium bond must be uniform between each sensing pixel and its corresponding readout element in order to ensure high-quality imaging. After hybridization, a backside thinning process is usually performed to reduce the amount of substrate absorption. The edges off the gap between the ROIC and FPA can be sealed with low-viscosity epoxy before the substrate is mechanically thinned down to several micrometers. Some advanced FPA fabrication processes involve complete removal of the substrate material.

Innovations and progress in FPA fabrication are dependent on adjustments to the material growth parameters. Usually in-house growth has enabled manufacturers the ability to maintain the highest material quality, and to customize the layer structures for multiple applications. For example, since HgCdTe material is critical to many principal product lines, and comparable material is not available externally, most global manufacturers continue to supply their own wafers. Figure 42 shows the process flow for integrated infrared FPA manufacturing. As is shown, boule growth starts with the raw materials, polycrystalline components. In the case of the HgCdTe FPA process, polycrystalline ultrapure CdTe and ZnTe binary compounds are loaded into a carbon-coated quartz crucible. The crucible is mounted into an evacuated quartz ampoule, which is placed in a cylindrical furnace. Large-crystal CdZnTe boules are produced by mixing and melting the ingredients, followed by recrystallizing with the vertical gradient freeze method. Their standard diameters reach 125 mm. The boule substrate material is then sawn into slices, diced into squares, and polished to prepare the surface for epitaxial growth. Typical substrate sizes up to $8\mathrm{cm}\times 8\mathrm{cm}$ have been produced. The HgCdTe layers are usually grown on top of the substrate by molecular beam epitaxy (MBE) or metalorganic chemical vapor deposition (MOCVD). In the case of MOCVD epitaxial technology, large-size GaAs substrates are also used. The selection of substrate depends on the specific application. The entire growth procedure is automated, with each step being programmed in advance.

 

Figure 42. Figure 42. Process flow for integrated infrared FPA manufacturing. Reprinted with permission from [11]. Copyright 2018 SPIE.

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MBE and MOCVD growth methods are well established in the II-VI and III-V semiconductor materials. At present, MBE offers low-temperature growth under an ultrahigh vacuum environment, in situ n-type and $p$-type doping, and control of composition, doping, and interfacial profiles, and is now the preferred method for growing complex layer structures for multicolor detectors and for avalanche photodiodes.

After growing the detector epitaxial structures, the wafers are nondestructively evaluated against multiple quality specifications. They are then conveyed to the array processing line, where the sensing elements (pixels) are formed by photolithographic steps, including mesa etching, surface passivation, metal contact deposition, and indium bump formation. After wafer dicing, the FPAs are ready for mating to the ROICs. The ROIC branch of the process is shown in the lower right of Fig. 42. For each pixel on the detector array, there is a corresponding unit cell on the ROIC to collect the photocurrent and process the signal. Each design is delivered to a silicon foundry for fabrication. Next, the ROIC wafers are diced and are ready for mating with the FPA. The most advanced flip-chip bonders, utilizing laser alignment and submicrometer-scale motion control, bring the two chips together (see the center of Fig. 42). At present FPAs with a pixel pitch size below 10 μm are aligned and hybridized with high yield. Each FPA with attached ROIC is tested according to a defined protocol and is installed in a sensor module. Finally, associated packaging and electronics are designed and assembled to complete the integrated manufacturing process.

10.3. Infrared FPA Considerations

The configuration of the thermal imaging system is shown in Fig. 43. On the graph shown in this figure, $A_s$ and $A_d$ are, respectively, the surfaces of the object and the detector, $r$ is the distance of the object to the lens (system optics), and $A_{ap}=\pi D^2/4$ and $D$ are the surface and the diameter of the lens (aperture, entrance pupil). The detector is placed in the focal plane of the system in the distance $\approx f$ to the entrance pupil. The optic’s system is characterized by the so-called $F$-number—i.e., $f/\#=f/D$.

 

Figure 43. Thermal imaging system configuration.

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For arrays the relevant figure of merit for determining the ultimate performance is not the detectivity, $D^{*}$, but the noise equivalent difference temperature (NEDT) and the modulation transfer function (MTF). These are considered the primary performance metrics to thermal imaging systems: thermal sensitivity and spatial resolution. Thermal sensitivity is concerned with the minimum temperature difference that can be discerned above the noise level. The MTF concerns the spatial resolution and answers the question, how small an object can be imaged by the system?

It is well known that the detector size, $d$, and the $F$-number ($f/\#$) are the primary parameters of infrared systems [102]. These two parameters have a major impact on both the detection/identification range and the NEDT, since they depend on $F\lambda /d$ [103]:

Most military systems today have the classical view presented in Fig. 44 [104], where the detector size ranges from 10 to 50 μm. For long-range identification systems, high $f/\#$ optics are used (for a given aperture) to reduce the detector angular subtense. On the other hand, wide-field-of-view (WFOV) systems are typically low $f/\#$ systems with short focal lengths since the focal plane has to be spread over wide angles. In recently published papers, it has been shown that long-range identification does not need to be limited to high $f/\#$ systems and that very small detectors enable high performance with a smaller package [105,106].

 

Figure 44. $F\lambda /d$ space for infrared system design. Straight lines represent constant NEDT. There are an infinite number of combinations that provide the same range. Reprinted with permission from [104]. Copyright 2014 SPIE.

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It is generally interesting to investigate pixel scaling beyond the diffraction limit using wavelength- and even subwavelength-scale optics that are enabled by modern nanofabrication. (The diffraction-limited pixel size is still relatively large compared with the feature size that can be achieved with state-of-the-art nanofabrication approaches.)

FPAs of $1{\mathrm{cm}}^2$ still dominate the IR market, while the pixel pitch has decreased to 15 μm during the last few years, now reaching 12 μm [107], 10 μm [108,109], 8 μm [110], and even 5 μm in test devices [111,112]. This trend is expected to continue. Systems operating at shorter wavelengths are more likely to benefit from small pixel sizes because of the smaller diffraction-limited spot size. Diffraction-limited optics with low $f$-numbers (e.g., $f/1$) could benefit from pixels on the order of one wavelength across. Oversampling the diffractive spot may provide some additional resolution for smaller pixels, but this saturates quickly as the pixel size is decreased. Pixel reduction is also mandatory to cost reduction of a system (reduction of the optics diameter, dewar size, and weight, together with the power, and increasing the reliability). In addition, smaller detectors provide better resolution [113]. Reduction of the focal plane proportionally to the detector size has not changed the detector FOV, so in the optics-limited region, smaller detectors have no effect on the system spatial resolution.

The detector-limited region occurs when $F\lambda /d\le 0.41$, and the optics-limited one occurs when $F\lambda /d\ge 2$ (see Fig. 44). When $F\lambda /d=0.41$, the Airy disk is equal to the detector size. A transition in the region $0.41\le F\lambda /d\le 2.0$ is large and represents a change from detector-limited to optics-limited performance. The condition $F\lambda /d=2$ is equivalent to placing 4.88 pixels within the Rayleigh blur circle. The lines presenting a constant $F\lambda /d$ indicate a constant range and NEDT. For a given aperture $D$ and operating wavelength $\lambda$, the detection range is given by the optimum resolution condition $F\lambda /d=2$ and a minimum NEDT for a given ${\tau }_{\mathrm{int}}$ [see Eq. (35)]. From these considerations result that the system $f/\#$ should be locked to the pixel size to predict the potential limiting performance of IR systems.

Figure 44 also includes experimental data points for various classes of thermal imaging systems that have been produced at DRS Technologies including both uncooled thermal imagers and cooled photon imagers. The earliest uncooled imagers fabricated at the beginning of the 1990s (BST dielectric bolometers and ${\mathrm{VO}}_x$ microbolometers) had large pixels of approximately 50 μm pitch and fast optics to achieve useful system sensitivities. With the decrease of the detector size, the relative apertures remained around $f/1$. As is shown in Fig. 44, as the pixel dimensions shrink over time, uncooled systems steadily progress from the “detector-limited” regime to “optics-limited” ones. However, they are still far from the ultimate range capacity for $f/1$ optics.

The cooled thermal imagers include early LWIR scanning systems and modern staring systems operating in both MW and LWIR bands. It is shown that LWIR imaging systems typically approach the $F\lambda /d=2$ condition, whereas for MWIR systems values of $F\lambda /d$ less than 2 are typically employed—lower available photon flux makes it difficult to maintain system sensitivity.

The system MTF is dominated by the optics, detector, and display MTFs and can be cascaded by simply multiplying the MTF components to obtain the MTF of the combination. In spatial frequency terms, the MTF of an imaging system at a particular operating wavelength is dominated by limits set by the size of the detector and the aperture of the optics.

Figure 45 summarizes the different behavior of the system MTF. The transition region can be further split by setting the optics cutoff frequency to equal the detector cutoff frequency, resulting in $F\lambda /d=1.0$ [114]. When $F\lambda /d=1.0$, the spot size equals 2.44 times the size of the pixel. The “optics-dominated” region lies between the diffraction-limited one and this curve, while the “detector-dominated” region is located between this curve and the detector-limited curve. In the optics-dominated region, changes to the optics have a greater impact on the system MTF than the detector. The same is true for the detector-dominated region. Historically, most systems have been designed to have a resulting optics blur (to include aberrations) of less than 2.5 pixels ($\sim F\lambda /d<1.0$). This is of course very dependent on the application and range requirements.

 

Figure 45. System MTF curves illustrating the different regions with the design space for various $F\lambda /d$ conditions. Spatial frequencies are normalized to the detector cutoff. Reprinted with permission from [114]. Copyright 2013 SPIE.

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As is shown in Ref. [106], with $f/1$ optics, the smallest useful detector size is 2 μm in the MWIR and 5 μm in the LWIR. With more realistic $f/1.2$ optics, the smallest useful detector size is 3 μm in the MWIR and 6 μm in the LWIR. Challenges that must be addressed in the fabrication of small-pixel FPAs concerned are considered in Refs. [103,115].

NEDT can be determined knowing the dark current density, $J_{\mathrm{dark}}$, the background flux (system optics), ${\mathrm{\varphi }}_B$, and the integration time, ${\tau }_{\mathrm{int}}$, according to relations [103]

From Eq. (36) results that if the value of the $J_{\mathrm{dark}}/J_{\mathrm{\varphi }}$ ratio increases and/or the value of $\eta$ decreases, more integration time and faster speed of the optics are required. Thus, inefficient detectors can be utilized in faster optics and slower frame rate systems. On the other hand, efficient pixel detectors are characterized by low dark current density and high quantum efficiency and can be used in thermal imagers with slow optics and faster frame rates.

Current readout technology is based on CMOS circuitry that has benefited from dramatic and continuing progress in miniaturizing circuit dimensions. Second-generation infrared imagers, containing staring arrays, provide NEDT of about 20 mK with $f/2$ optics and are limited by readout circuits (by storage capacity of the ROIC). In this case [116]

The above considerations are valid assuming that the temporal noise of the detector is the main source of noise. However, this assertion is not true for staring arrays, where the nonuniformity of the detectors’ response is a significant source of noise. This nonuniformity appears as a fixed pattern noise (spatial noise). It is defined in various ways in the literature; however, the most common definition is that it is the dark signal nonuniformity arising from the electronic source (i.e., other than thermal generation of the dark current)—e.g., clock breakthrough or from offset variations in row, column, or pixel amplifiers/switches. So, estimation of the IR sensor performance must include a treatment of spatial noise that occurs when FPA nonuniformities cannot be compensated correctly.

Mooney et al. [117] have given a comprehensive discussion of the origin of spatial noise. The total noise of a staring arrays is the composite of the temporal noise and the spatial noise. The spatial noise is the residual nonuniformity $u$ after application of nonuniformity compensation, multiplied by the signal electrons $N$. Photon noise, equal to $N^{1/2}$, is the dominant temporal noise for the high IR background signals for which spatial noise is significant. Then, the total NEDT is

The dependence of the total NEDT on detectivity for different residual nonuniformity is plotted in Fig. 46 for 300 K scene temperature and the set of parameters shown in the inset of the figure. When the detectivity is approaching a value above ${10}^{10}\mathrm{cm}{\mathrm{Hz}}^{1/2}/\mathrm{W}$, the FPA performance is uniformity limited prior to correction and thus essentially independent of the detectivity. An improvement in nonuniformity from 0.1% to 0.01% after correction could lower the NEDT from 63 to 6.3 mK.

 

Figure 46. NEDT as a function of detectivity. The effects of nonuniformity are included for $u=0.01\%$, 0.1%, 0.2%, and 0.5%. Note that for $D^{*}>{10}^{10}\mathrm{cm}{\mathrm{Hz}}^{1/2}/\mathrm{W}$, detectivity is not the relevant figure of merit. Reprinted with permission from Rogalski et al., J. Appl. Phys. 105, 091101 (2009) [118]. Copyright 2009 AIP Publishing LLC.

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The nonuniformity value is usually calculated using the standard deviation over mean, counting the number of operable pixels in an array. For a system operating in the LWIR band, the scene contrast is about 2%/K of the change in scene temperature. Thus, to obtain a pixel-to-pixel variation in apparent temperature to less than, e.g., 20 mK, the nonuniformity in response must be less than 0.04%. This is almost impossible to obtain in the uncorrected response of the FPA, so a two-point correction is typically used.

Tables 5 and 6 contain a description of representative microbolometer and photon IR FPAs that are commercially available as standard products and/or catalogue items from the major manufacturers.

Table 5. Representative Commercial Uncooled Infrared Bolometer Array

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Table 6. Representative IR Hybrid FPAs Offered by Some Major Manufacturers

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There are considerable efforts to decrease the system size, weight, and power consumption (SWaP)—as a consequence reducing the system’s cost—to increase the operating temperature in HOT detectors. The ultimate goal is the fabrication of a detector with dark current less than the system background flux current and with $1/f$ noise insignificant relative to the shot noise of the background flux. Smaller pixels enhance the value of proposition of the imaging systems and their functionality. Further improvement in SWaP is achieved in HOT conditions. Recently, it has been estimated [119,120] that low doping fully depleted p-i-n HgCdTe photodiodes operated at reasonable reverse bias voltage can be considered as HOT devices with significantly lower dark current than now typically achieved. Smaller pitches are scheduled in the short term for both photon and thermal detectors (see Fig. 47) [121,122].

 

Figure 47. Pixel pitch for (a) HgCdTe photodiodes and (b) amorphous silicon microbolometers has continued to decrease due to technological advancements. Reprinted with permission from Destefanis et al., Proc. SPIE 8012, 801235 (2011) [121]; N. Oda, private communication [122].

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11. Graphene-Based Detectors for the Future

In 2013, the European Union launched the Future and Emerging Technology Graphene Flagship program to accelerate research into technologies based on graphene and related materials. Recently, within the framework of this program, hybrid graphene-colloidal QD photodetector arrays fully vertically integrated into a CMOS readout chip have been demonstrated (see Fig. 48). These $388\times 288$ pixel cameras are operated in the UV–visible–SWIR range from 300 to 2000 nm. Pixels of the image sensor (see Table 4, first line) are characterized by high gain of ${10}^7$ and responsivity above ${10}^7\mathrm{A}/\mathrm{W}$. The size of pixels is large (20 μm, which limits spatial resolution) for operation in the visible and SWIR range in comparison with present commercial CMOS images operated in the visible region (see Fig. 39). Also, the operability of the arrays estimated as 95% is poor [123]. The fixed pattern noise (spatial noise) has a strong influence on the noise equivalent irradiance of the arrays, especially if the array’s pixels are hybrid (graphene QDs). It is well known that nonuniformity of QDs limits the performance of QD photodetector arrays [125].

 

Figure 48. (a) Monolithically integrated graphene quantum-dot photodetector array (courtesy Frank Koppens ICFO/D. Bartolome) [123] and (b) side view of detector and the underlying readout circuit. Reprinted by permission from Macmillan Publishers Ltd.: Goossens et al., Nat. Photonics 11, 366–371 (2017) [124]. Copyright 2017.

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Although the photodetection platform based on graphene and related materials has demonstrated a variety of detector applications, outstanding challenges remain to implement the real potential and to exploit the distinct advantages of new 2D crystals. The prospects for commercialization will depend not only on the detector performance, but also on some of the distinct advantages and capabilities in the ability to realize the production of large-scale high-quality 2D materials at a low cost. The final goal is establishing large-scale integration of 2D crystals with existing photonic and electronic platforms, such as CMOS technologies.

Bulk crystal detectors such as HgCdTe, III-V materials (AlGaAs, InSb, and InGaAs) have been widely commercialized since the 1950s due to the ease of large-scale fabrication, high responsivity, and flexibility in the absorption wavelengths covering almost all IR bands. At present, the III-V antimonide-based detector technology is under strong development as a possible alternative to HgCdTe detector material. During the last decade, antimonide-based FPA technology has achieved a level close to HgCdTe [11]. The apparent rapid success of the type-II superlattice (T2SL) photodetectors depends not only on the previous five decades of III-V materials, but also mainly on novel ideas coming recently in the design of infrared photodetectors (barrier detectors). III-Vs material structures offer similar performance to HgCdTe at an equivalent cutoff wavelength, but with a sizeable penalty in operating temperature, due to the inherent difference in SRH lifetimes. The important advantages of T2SLs are their high quality, high uniformity, and stable nature. In general, III-V semiconductors are more robust than their II-VI counterparts due to their strong covalent chemical bonding. As a result, III-V-based FPAs excel in operability, spatial uniformity, temporal stability, scalability, producibility, and affordability—the so-called “ibility” advantages.

As shown in Section 4, the ratio of the absorption coefficient to the thermal generation rates, $\alpha /G$, is the main figure of merit of any material for infrared photon detectors. Next, the thermal generation rate is inversely proportional to the recombination lifetime. Graphene is an attractive material for optical detection due to its broad absorption spectrum and ultrashort response time. Due to ultrahigh mobility, it is suitable for high-speed communications. However, it remains a great challenge to achieve high responsivity in graphene detectors because of weak optical absorption (only 2.3% in the monolayer graphene sheet) and short carrier lifetime ($<1\mathrm{ps}$). In other words, the applications of graphene-based photodetectors are limited in comparison to traditional detectors. Various approaches have been proposed to enhance the sensitivity by the introduction of a bandgap, electron trap layers (quantum-dot structures), or nanoribbons; however, these methods degrade the electronic performance of graphene, such as the high mobility. Ultrahigh responsivity and ultrashort time response cannot be obtained at the same time in practice. The overall quantum efficiency of graphene is quite low compared to conventional materials (HgCdTe and III-V semiconductors). Despite the large amount of funding and research invested in 2D materials, there is currently a very limited set of 2D material covering the infrared and THz regions of the spectrum. The intricate technology of sensitive graphene-based detectors (hybrid and functionalized graphene detectors) creates pixel nonuniformity, which has a detrimental influence on the performance of FPAs (NEDT).

12. Conclusions

There are many critical challenges for future civilian and military infrared and THz detector applications. For many systems, such as night-vision goggles, the IR image is viewed by the human eye, which can discern resolution improvements only up to about one megapixel, roughly the same resolution as high-definition television. Most high-volume applications can be completely satisfied with a format of $1280\times 1024$ pixels. Although wide-area surveillance and astronomy applications could make use of larger formats, funding limits may prevent the exponential growth that was seen in past decades.

The future applications of imaging infrared systems require the following:

Small-pitch IR FPAs will require the development of larger effective ROIC well capacities per unit area, possibly faster optics than $f/1$, and improved hybridization technologies that currently dominate IR array fabrication. Leveraging deeply scaled CMOS process technology enables designers to miniaturize the pixel pitch and/or increase the on-chip processing capability depending on application-specific needs. Array sizes will continue to increase but at a rate that falls below the Moore’s law curve. An increase in array size is already technically feasible. However, the market forces that have demanded larger arrays are not as strong now that the megapixel barrier has been broken.

Considering fundamental material properties and seeing the present stage of graphene technology, it is rather difficult to predict a stronger position of graphene in the next decade of imaging infrared systems fulfilling the above requirements. Graphene-based materials suffer from a low absorption coefficient, a high sensitivity to the ambient, and a large area fabrication limitation. So far, most device applications of graphene remain suggestions rather than demonstrated capabilities. The assumption that graphene is always a perfect 2D crystal in isolation from its environment is, in most cases, not valid. There are significant challenges faced by materials scientists to improve graphene growth techniques.

Graphene-based detector challenges include the limited linear dynamic range of operation, the lack of efficient generation and extraction of photoexcited charges, the smearing of photoactive junctions due to hot-carrier effects, large-scale fabrication, and ultimately the environmental stability of the constituent materials [81].

The performance of graphene-based infrared and THz detectors is lower in comparison with those detectors existing on the global market, especially HgCdTe, InGaAs, type-II superlattice III-V compounds, and microbolometers. The most effective single graphene detectors operated at room temperature are THz detectors that utilize plasma rectification phenomena in FETs. Their performance is close to the trend line estimated for microbolometer monolithic arrays in the THz spectral region. In this place it should be insisted, however, that the production of monolithically integrated THz detector arrays encounters so many technological problems that the device-to-device performance variations and even the percentage of non-functional detectors per chip tend to be unacceptably high.

There are considerable efforts to decrease infrared imaging systems’ SWaP by increasing the detector arrays’ operating temperature. In Kinch’s recently published monograph [103] it is clearly shown that the ultimate cost reduction for an IR system will only be achieved by the room-temperature operation of depletion-current limited arrays with pixel densities that are fully consistent with background- and diffraction-limited performance due to the system optics. This mandates the use of an IR materials with a long S-R lifetime. Currently, the only material that meets this requirement is HgCdTe. Kinch predicted that large area ultrasmall pixel diffraction-limited and background-limited photon detecting MW and LW HgCdTe FPAs operating at room temperature will be available within the next 10 years [126]. In this context it will be rather difficult to find a place for graphene and related materials.

The development of a scalable graphene detector array concept with appropriate fabrication tools can be a noteworthy indicator that the graphene can enable new detector systems. The combination of scalability, the prospects for integration with Si platforms, and the potential for implementing flexible devices can make graphene attractive for the future generation of detection systems. However, at the present stage of detector technology, it will be rather difficult to improve the graphene position in the mature global market detector family in the near future. From the economical point of view and future technology perspective, an important aspect concerns industry fabrication of detector arrays with high operability, spatial uniformity, temporal stability, scalability, producibility, and affordability. All these aspects are in the infancy stage of graphene manufacturability.