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The performance of thermal detectors is derived for devices incorporating materials with non-uniform spectral absorption. A detector designed to have low absorption in the primary thermal emission band at a given temperature will have a background-limited radiation noise well below that of a blackbody absorber, which is the condition typically assessed for ultimate thermal detector performance. Specific examples of mid-wave infrared (λ ∼ 3–5μm) devices are described using lead selenide as a primary absorber with optical cavity layers that maximize coupling. An analysis of all significant noise sources is presented for two example room-temperature devices designed to have detectivities up to 4.37×1010 cm Hz1/2 W−1, which is a factor 3.1 greater than the traditional blackbody limit. An alternative method of fabricating spectrally selective devices by patterning a plasmonic structure in silver is also considered.
© 2010 Optical Society of America
1. Introduction
For many decades, the performance limit of thermal infrared detectors has been referenced as the blackbody radiation limit [1, 2]. The objective in uncooled thermal detector design, particularly for imaging, has been to create devices with high absorption in the primary thermal radiation band to maximize sensitivity, without excessively degrading other properties such as the time constant. For example, early thermal detectors were fabricated with high absorption materials to achieve good signals in all spectral ranges, while many modern microbolometers are designed with optical cavity coupling to enhance their signal in the LWIR (λ ∼ 8–12μm) and/or MWIR (λ ∼ 3–5μm) [3,4]. Both approaches are focused on optical signal enhancement, which involves normal or nearly-normal incidence light, rather than radiation noise reduction, which involves light incident at all angles.
However, there are many detector applications where the signal of interest either does not lie within the primary thermal emission band or covers only a part of it. For example, any room temperature signal in the MWIR or the 5–8μm water absorption band will lie outside the LWIR primary emission band. A detector designed solely for high absorption will collect not only the desired signal but also irrelevant signals. Even if there is a hemispherical optical filter to cut out most of the unwanted light, the radiation emission from the detector itself will add greatly to the photon noise in undesired spectral regions.
In this paper, we describe performance limits for thermal detectors, similar to that shown in Fig. 1, that measure signals that do not include the primary thermal emission band or contain only a part of that band. These devices are composed of materials that do not absorb in the primary emission region, such as semiconductors with bandgap energy less than the photon energies of the thermal IR. Thermal detectors do not operate based on electron-hole generation and recombination as do photon detectors; therefore, non-crystalline or “low-quality” semiconductors could be used as well as crystalline ones. To maximize the performance of such detectors, any optical cavity coupling must not only increase absorption of the desired signal but also minimize radiation noise at all angles to the optical axis. For uncooled devices operating at room temperature, the ultimate detectivity in the design band easily exceeds 1.40×1010 cm Hz1/2 W−1, which is the traditional blackbody radiation limit for a device with a spherical field of view.
Fig. 1 Diagram of the proposed MWIR detector showing a surface micromachined top mirror/absorber and a bottom mirror deposited on the substrate.
2. Theory
Radiation noise serves as the fundamental limit for thermal detector performance [1,2,5]. While all other noise sources could potentially be negated by technological and material advancements, the photon fluctuations within the detector due to Planck’s law radiation will always be present. Broadband thermal detectors absorb and emit all wavelengths of thermal radiation, leading to a maximum photon noise. Current state-of-the-art thermal detectors operate near this maximum noise either by having high absorption in the peak thermal emission regions or by failing to design the optical properties and cavities of the detector to have very low absorption in this region, particularly off the optical axis, where most radiation interactions occur. For many applications, broadband absorption is not necessary, and a sensor which absorbs outside the primary thermal band is sufficient. These devices will often work with low signals. In order to minimize the photon noise and maximize performance under such conditions, the detector can be composed of materials that do not absorb at the maximum of thermal emission.
Using Planck’s radiation formula and assuming that the photons obey Bose-Einstein statistics and the device is acting as a Lambertian emitter, the mean square noise power per unit noise bandwidth can be written as
where h is Planck’s constant, c is the speed of light, A is the detector area, k is Boltzmann’s constant, T is the temperature of the emitting body, and ɛ is the angular and spectral emissivity of the body, with λ being the wavelength of incident photons, θ the polar angle, and φ the azimuthal angle. Equation 1 is a generalized form of equation 9.107 from [2] to allow for variations in emissivity with angle and wavelength. In the case of a radiation-limited detector, the noise power relates to the detectivity by . The factor of two in this equation arises from the equivalent photon fluctuations from emission from the detector and absorption from the background when the detector is in thermal equilibrium with its surroundings. If we integrate Eq. (1) over all wavelengths and angles we obtain a blackbody radiation limit of D*=1.98×1010 cm Hz1/2 W−1 for a hemispherical field of view or D*=1.40×1010 cm Hz1/2 W−1 over a full sphere at 290K. These values are have traditionally been considered the fundamental limit for thermal detector performance commonly referred to as the blackbody radiation limit [2].The blackbody radiation limit serves as a fundamental limit only for broadband detectors. The use of spectrally selective materials enables the reduction of photon noise below the black-body radiation limit. Of great interest for this purpose are semiconductors which primarily absorb photons at energies above their bandgap energy which serves as an absorption cutoff. Figure 2 demonstrates this concept by showing the radiation-limited detectivity as a function of cutoff wavelength for an ideal semiconductor. In this approximation the emissivity of the detector is assumed to be unity below the cutoff wavelength and zero above it. We can see in Fig. 2 that the radiation-limited detectivity for a detector with cutoff wavelength 5μm is 8.26×1010 cm Hz1/2 W−1, nearly 6 times the blackbody radiation limit. A device with this cutoff wavelength could be applicable for both MWIR imaging and chemical sensing, particularly for sensing hydrocarbons which have a 3.4μm emission line at room temperature. We can also see that as the cutoff wavelength goes to infinity, the radiation-limited detectivity approaches the blackbody radiation limit. This plot is very similar to that which is used to describe the performance of photon detectors [6], but differs quantitatively in that power fluctuations are being calculated rather than photon number fluctuations.
Fig. 2 Radiation-limited detectivity vs. cutoff wavelength for an ideal semiconductor where emissivity, ɛ=1 below the cutoff wavelength and ɛ=0 above the cutoff wavelength. This idealized emissivity is overlayed with the room temperature blackbody noise power spectrum in the inset.
3. Optical simulation
While there are a variety of narrow bandgap semiconductors which could be used, we have chosen to use PbSe for our simulations. Other options include HgCdTe and InSb based systems, but the higher extinction coefficient of PbSe makes it favorable for thin detectors. PbSe and other lead salts have been used in photoconductive MWIR detectors since World War II. The technology has also been revisited in depth recently [7,8]. The bandgap energy of .27eV is ideal for our application as it corresponds to a cutoff wavelength of approximately 5μm. The absorption and radiation-limited detectivity at normal incidence of a detector comprised of a single 500nm layer of PbSe can be seen in Fig. 3. This optical simulation and all others in this paper are done using the transmission matrix method outlined in [9] using optical constants from [10]. We can see in this figure that the absorption of the detector is around 60% in the MWIR and drops off abruptly at 5μm. The radiation-limited detectivity peaks at 4.84×1010 cm Hz1/2 W−1 which is hindered significantly by the low absorption of the film due to surface reflection from the high index PbSe detector. While this type of detector is theoretically interesting, it is most likely too thick to be used in a practical device due to large thermal mass. Excess thermal mass in a real detector would lead to either a high thermal time constant or high thermal conductance noise depending on the support structure, which would greatly limit the utility of the detector.
Fig. 3 Spectral characteristics of a 500nm thick layer of PbSe at normal incidence. Note that the y-axis displays the absorption on the left and the radiation-limited specific detectivity on the right.
Further optical engineering is necessary to both increase the absorption of the detector and decrease the thermal mass in order to optimize performance. To reduce thermal mass, a much thinner detector must be used. In order to maximize the amount of radiation coupled into a thin detector, optical cavity coupling can be used. The detector itself is highly reflective with PbSe having an index of refraction of 4.52 at 4μm and can be used as a semi-transparent mirror. With a distributed Bragg reflector(DBR) acting as the second mirror, an optical cavity can be formed. We have found that a 1/8th wave cavity offers the best broadband coupling over the full range of the MWIR. The absorption and radiation-limited detectivity of an example device can be seen in Fig. 4 with the optical layer structure of the device shown in Table 1. The mirrors and cavity spacing in Table 1 are designed for a center wavelength of 4μm to maximize MWIR coupling. Figure 4 shows a peak absorption of 87% corresponding to a radiation-limited detectivity of 1.25×1011 cm Hz1/2 W−1. The average absorption over the MWIR is 64% and the average radiation-limited detectivity is 9.30×1010 cm Hz1/2 W−1 in the MWIR. One simplification should be noted for this calculation. Since our simulations do not allow for the decoupling of absorption within the detector from absorption within the mirrors, the extinction coefficient was assumed to be zero for the mirror materials. This assumption is generally accurate for the DBR materials chosen, but begins to break down around 40μm. However, at this point the photon noise power is about two orders of magnitude below the peak power, so this has little effect on the final simulation result.
Fig. 4 Spectral characteristics of the example cavity coupled device defined in Table 1. Note that the y-axis displays the absorption on the left and the radiation-limited specific detectivity on the right.
Table 1. Optical design parameters for an example device
4. Practical device design
The above devices have not assumed any sort of read-out mechanism. Since the vast majority of thermal detectors today are uncooled microbolometers, we will base practical discussion on bolometers. Fortunately PbSe has a favorable temperature coefficient of resistance of −3.45%/K [11] and will be assumed as the temperature sensing material as well as the absorber, with characteristics described later.
A single, biased bolometer is susceptible to three significant noise sources, Johnson noise from the thermal excitation of carriers, 1/f noise resulting from a variety of effects in DC biased resistors, and thermal conductance noise resulting from the random fluctuations of energy quanta between the detector plate and its surroundings. This can include both phonon fluctuations through the support structure and photon fluctuations through emission and absorption in the plate. While historically thermal conductance noise has been dominated by conduction through the legs, recent work has shown that with proper engineering, bolometers can be fabricated for which radiation is the principal thermal conductance path [12].
A figure of merit for microbolometers is the noise equivalent power (NEP). The NEP is defined as the amount of incident signal power needed to obtain a signal equal to the total noise of the device and can be expressed as
Equation (2) is adapted from Eq. (92) in [14] and defines the three major sources of microbolometer noise. The first term represents the thermal conduction noise, where C is the thermal capacitance of the detector, T is the temperature, k is the Boltzman constant, and G is the thermal conductance. The thermal conductance, G, is actually the sum of the thermal conductance through the legs of the detector and the radiation thermal conductance. The radiation thermal conductance noise calculated in this manner is equivalent to the radiation noise calculation described in Eq. (1). The second term of the NEP equation represents the Johnson noise, where R is the resistance, Δf is defined as f2-f1, the upper and lower measurement cutoff frequencies. The responsivity of the bolometer is represented by ℜ and defined as αV/G in the low frequency region, where α is the temperature coefficient of resistivity (TCR) of the resistive material and V is the bias voltage. The third term of the NEP equation represents the 1/f noise, where km is the 1/f noise parameter which is material dependent.In order to demonstrate the utility of this technology for various applications, two device designs will be presented. One focuses on maximizing detectivity at the expense of increased thermal time constant, the other focuses on low thermal time constant, therefore increasing the thermal conductance noise and decreasing detectivity. Necessary material parameters for these calculations were found in [13]. Both devices use the same layer structure as shown in Table 1. However, the 1/f noise parameter of PbSe was not found in literature, so the km of vanadium oxide of 10−13 [14], a common microbolometer resistor material is used. If 1/f noise in PbSe proves to be an issue in processing, a small, electrically isolated vanadium oxide resistor could be placed on the peripheral regions of the detector plate without significant effects on the optical properties of the device. Equivalently, a thin vanadium oxide layer could be placed uniformly over the entire detector with only minor modifications to the bottom mirror. Other assumptions include a bias voltage of .1V, a device resistance of 100kΩ, and a device and heat sink temperature of 290K, all of which agree with our preliminary testing. Both devices are designed with legs 500μm in length made of nickel iron and alumina with thicknesses of 200Å and 100Å respectively. The devices are operated in chopping mode and measured every frame such that the bias is applied during one half of the frame, where f1=1/2πτ and f2=1/πτ. All other design parameters as well as noise calculation results can be seen in Table 2. The detectivity as a function of wavelength can be seen in Fig. 5. Note that Fig. 5 is a close up view of the detectivity in the MWIR as this is our region of interest. The devices are optically identical to those modeled in Fig. 4 so the spectrum applies to these devices as well, with the only change being the scaling of the y-axis due to the addition of other noise terms.
Fig. 5 MWIR spectral characteristics of the example device defined in Table 1 with all noise sources considered. The material and device parameters are defined in the text and Table 2. Note that the y-axis displays the detectivity of high D* device, [a] on the left side low τ device, [b] on the right side.
Table 2. Device design parameters, calculated thermal properties, and calculated noise levels for two example devices
We can see in Table 2 that the performance of the low τ device is limited by thermal conductance noise, primarily from thermal conductance through the legs, but it still demonstrates peak detectivity higher than the blackbody radiation limit, which is the basis for all current thermal detector theory. The thermal time constant of this device τ=18.5ms is sufficient for video frame rate operation which is required for many applications [14]. The high detectivity device exhibits much better performance and could be used in many non-video applications such as chemical sensing. Through proper optical design, support structure engineering, and fabrication methods, devices of this nature can be tailored to fit specific applications with performance equal to or greater than that presented above.
5. Spectral selectivity by plasmonic structures
Plasmonic structures offer an alternative means of achieving the spectral selectivity necessary to produce MWIR detectors operating beyond the blackbody radiation limit. Enhanced transmission through arrays of subwavelength metal nanoslits has been experimentally demonstrated [15]. In order to exploit this phenomenon, the radiation transmitted through the array must be coupled into an absorbing material forming a spectrally selective bolometer. Consider an array of nanoslits patterned as seen in the inset of Fig. 6. The nanoslits are patterned in a100nm thick silver layer on a 400nm thick polyethylene microbolometer which is then suspended over a gold mirror by a 1μm air gap. Using standard FDTD simulation methods, and optical constants from [10, 16] we can simulate the absorption spectrum of p polarized radiation for this structure as seen in Fig. 6. This figure shows two narrowly spaced absorption peaks, one at 3.5μm which corresponds to the peak plasmon resonance, and one at 3.4μm corresponding to the absorption peak of polyethylene which falls within the plasmon resonance. While this simulation method does not lend itself to full device performance analysis, we can clearly see that this type of plasmonic structure could also be used to produce MWIR microbolometers whose radiation noise properties have been manipulated in either wavelength and/or polarization.
Fig. 6 Simulated absorption spectrum of a spectrally selective plasmonic microbolometer with a diagram detailing the layout of metal nanoslits in the inset.
6. Conclusion
We have described a new class of thermal detectors that utilize materials such as narrow bandgap semiconductors and plasmonically coupled nanoslits which are fully or partially transparent in the primary thermal emission band. These devices are useful for measuring signals existing outside this band and can have uncooled detectivities that exceed the blackbody radiation limit, which was the ultimate thermal detector performance as understood by previous theory. MWIR detectors are described with detectivities of up to 4.37×1010 cm Hz1/2 W−1.
Acknowledgments
The authors would like to acknowledge Timothy Johnson, Nathan Lindquist, and Professor Sang-Hyun Oh for their assistance with FDTD simulations. The authors would also like to gratefully acknowledge the Penn State Electro-Optics Center under grant 0108.23.14 for funding this research.
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