1. Introduction

Surface plasmons (SPs), as coherent oscillations of free electrons in metals, can either decay radiatively [1] into re-emitted photons or nonradiatively [2,3] into “hot” electrons. Hot electrons may experience thermal loss that limits the performance in many plasmonic devices, but may also be collected before thermalization to generate response in some devices with specific structures, which can be harnessed for photodetection [4–18]. These devices are typically formed by placing a metal and a semiconductor surface in contact, forming a Schottky barrier. Hot electrons can be transmitted across the Schottky barrier at the metal–semiconductor interface to form photocurrent for detecting photons with energy below the semiconductor band gap. A variety of structures have been demonstrated, including plasmonic nanoantennas [5,12] plasmonic crystals [7,10], connected gold islands [17], nanowires [18], gratings [8,15,16], and waveguides [18–24]. Periodic arrays of cavities covered with a thin metal layer were adopted to achieve enhanced photoresponse in periodic nanostructured devices [13,14]. It is interesting to further comprehend the plasmonics in this type of structures to achieve optimization of device performance.

In this article, we investigate plasmonic characteristics of a periodic array of cavities in a silicon substrate covered by a 10s nm-thick gold film for hot-electron photodetection. Based on simulation using the finite-difference time-domain (FDTD) method, resonances of cavity surface plasmons (CSPs) bound to air cavities and silicon cavities, and resonance of Bragg-surface plasmon polaritons (Bragg-SPPs) are illustrated on the map of metal absorption. The photoresponse is further obtained using the analytical probability-based electrical model for thin-film Schottky barrier photodetectors. Simulation results show that by properly engineering the structural parameters of the hot-electron photodetector, plasmonic resonance can be readily tuned to the target single communication band or dual-bands for enhancing photoresponse.

2. Optical analysis

An array of cuboid cavities on a Si substrate coated with a thin conformal gold film is illustrated in Fig. 1(a), where w, h, t, and p denote the width and the height of cavities, the thickness of the gold film, and the period of the array, respectively. Optical and electrical models were developed to discuss the physical property of the structure under the condition of top illumination. The optical model is based on the electromagnetic description, being calculated by the FDTD method. The complete periodic boundary condition was adopted, and identical structural parameters were assigned in the x and y directions order to obtain polarization insensitive response. The optical absorbance is defined as A = I_abs/I_inc, where I_abs and I_inc are the absorbed and the incident powers, respectively. The reflectance R and the transmittance T were obtained by FDTD simulation. The absorption spectra is then determined using A = 1 − T – R by ignoring scatterings which is shown to be less than 1% [25]. The absorption spectrum was also shown to be greatly in accordance with the attenuation spectrum [14]. The optical constants of Si and Au were adopted from [26], in simulation.

 

Fig. 1 (a) Schematic diagram of the cavity array photodetector with hot electrons excited by using the surface cavity array covered by a gold film. (b) schematic diagram of Au-Si junction under zero bias in section, hot electrons excited in the Au layer diffuse towards the M/S interface generating a hot electrons photocurrent.

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The optical tunability of the plasmonic structure is illustrated in Fig. 2, where the absorption in the Au film is mapped versus wavelength and cavity width with a setting of P = 1400nm and h = 1200nm for various thicknesses of the gold film. These maps consistently show a number of absorption peak lines denoting plasmonic resonances. The horizontal peak line shown in these maps at λ = 1.42μm is independent of the cavity width, denoting resonance of the Bragg-SPPs. The Bragg−SPP mode depends on the period of the structure, satisfying,

 

Fig. 2 Absorption in the plasmonic crystal as a function of wavelength and cavity width for the different metal thickness under consideration t = (a) 15nm, (b) 30nm, (c) 50nm and (d) 100nm, P = 1400nm, h = 1200nm.

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$\frac{2\pi }{P}=k_0\sqrt{\left({\epsilon }_m\cdot {\epsilon }_e\right)/\left({\epsilon }_m\cdot {\epsilon }_e\right)},$ (1)where k₀ is the wavenumber of light in vacuum, and ε_m and ε_e are the metal and ambient permittivities, respectively.

Besides that, the diagrams in Fig. 2 show a peak line with resonance wavelength increasing with increasing width of air cavities and a set of of lines with resonance wavelength decreasing with increasing width of air cavities, for which the resonances are identified as CSP_Au-air and CSP_Au-Si modes, respectively. The CSPs are surface modes confined in cavities, originating from coupling of light to collective oscillation of electrons [27].The fields localized in the cavities. CSP_Au-air is excited in air cavities, while a portion of incident light passes through the thin Au film and forms CSP_Au-Si modes in Au-Si cavities. From Figs. 2(a)-2(d), the absorbance peak lines of CSP_Au-Si modes fade out due to decreasing transmission with increasing film thickness, which is different from that of the CSP_Au-air mode. As better show in Fig. 2(c), up to the third-order CSP mode in Au-Si cavities due to large permittivity of the cavity material, i.e. silicon.

Interestingly, Fig. 2 shows different crossing behaviors between resonance lines of plasmonic modes with different localizations. The resonance lines of CSP_Au-air and Bragg-SPP are anticrossing, as indicated in Fig. 2(d), but they both are crossing the CSP_Au-Si resonance lines as seen in Fig. 2(b). The CSP_Au-air and the Bragg-SPP are both localized to the Au-air interface. Thus, as their resonance frequencies approach to each other, the resonance lines split upon strong coupling. The electric field distributions are plotted in Figs. 3(a)-3(c) for the structures with parameters indicated by P₁-P₃ in Fig. 2, respectively. The electric field distribution shown in Fig. 3(c) for P₃ is more Bragg-SPP-like, but with some amount of the CSP_Au-air component localized at cavity openings. In contrast the electric field distribution shown in Fig. 3(b) for P₂ is more CSP_Au-air-like, but with some amount of Bragg-SPP component. In another word, there is no longer pure mode of Bragg-SPP or CSP_Au-air due to their strong coupling in the anticrossing vicinity, where the hybrid mode can enhance absorption as clearly illustrated in Fig. 2(b).

 

Fig. 3 Distributions of the electric fields: (a) with an input wavelength of 1300 nm for point P₁ in Fig. .2(a). (b) Distributions of the electric fields of electrodes with an input wavelength of 1680 nm for point P₂ in Fig. .2(d). (c) Electric fields with an input wavelength of 1680 nm for point P₃ in Fig. .2(d).

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There is no obvious anticrossing effect between CSP_Au-Si and either CSP_Au-air or Bragg-SPP due to different localizations, as shown in Fig. 2(a) and 2(b). In Fig. 3(a), the electric field distribution for P₁ is strongly localized at Au-Si interfaces of the sidewalls, which can be clearly identified as CSP_Au-Si. Thus, hybrid modes, as denoted in Fig. 2(b), are formed upon coexistence of CSP_Au-Si with either CSP_Au-air or Bragg-SPP. These hybrid modes present the most intense absorption as shown in Fig. 2(b). It should be mentioned that the absorption due to the CSP_Au-air resonance become almost invariant for h>800nm, while the cavity depth plays an important role in influencing the absorption due to by CSP_Au-Si resonance. This can be understood from their different localizations. The field of CSP_Au-air is localized near openings of air cavities, while the field of CSP_Au-Si distributes along sidewalls.

3. Structure design for hot-electron photodetection

The electrical model has been developed in Scales and Berini’s work [28]. Spicer [29] intuitively described the internal photoemission process from a metal film as proceeding via a series of three consecutive steps. Firstly, photons of energy hν excite plasmon resonance in the metallic nanostructure, generating a large amount of hot electrons. Then, hot electrons with kinetic energy arrive at the metal-semiconductor interface. Finally, hot electrons are transmitted across the Schottky barrier with a certain probability and collected as photocurrent. The responsivity R is given by the ratio of the photocurrent to the incident optical power and can be expressed as

$R=\frac{A\eta q}{hv},$ (2)where η is the internal quantum efficiency, q is the elemental charge, h is the Planck’s constant, and $í$ is the optical frequency. In the Fowler’s model [27,30], η is subject to the internal photoemission process and is given by

$\eta =\frac{{(hv-{\varphi }_b)}^2}{8E_{F}hv},$ (3)where the metal Fermi energy E_F ~5.5eV for Au [31] and${\varphi }_b$ is the barrier height. This treatment simplifies the practical situation by ignoring plasmon decay and the geometric enhancement factors [16,28]. Otherwise, a device-specific Fowler emission coefficient that depends on device-specific details has to be employed and extracted by fitting experimental data [14]. The emission probability is overestimated for hot electrons excited at the gold-air interface, while the overall emission probability is underestimated due to ignoring the emission enhancement effects [16,28]. Such compromise might boost the accuracy of this simplified treatment. Practically, a 1~2nm-thick titanium layer is often deposited as the adhesion layer. The ultrathin titanium layer is crucial for determining the Schottky barrier height, and thus ${\varphi }_b~0.54eV$ [14] is adopted in our calculation. Such a thin titanium layer damps the plasmon response weakly, especially at near infrared region, and is ignored in our optical analysis as done in published papers [4,15,16].

Hybrid modes formed by CSP_Au-Si, CSP_Au-air and Bragg-SPP can be utilized in design for enhanced hot-electron photodetection. To optimize photoresponse targeting at a single wavelength, the CSP_Au-air-3rd-order CSP_Au-Si hybrid mode is tuned to align at the target wavelength as shown in Fig. 4(a), and the spectra of absorbance and responsivity are plotted in Fig. 4(b) for a device with structural parameters p = 1.3um, w = 0.71um and t = 30nm. The simulated peak absorbance is 0.88 and the corresponding responsivity is 4.1mA/W. To obtain photoresponse in dual communication bands at 1310nm and 1550nm, the Bragg-SPP-CSP_Au-air and CSP_Au-air-3rd-order CSP_Au-Si hybrid modes can be adopted together as illustrated in Fig. 4(c), and the spectra of absorbance and responsivity are plotted in Fig. 4(d) for a device with structural parameters p = 1.22um, w = 0.75um and t = 15nm. The absorbances and responsivities are 0.68 and 4.5 mA/W at 1310nm, and 0.72 and 2.4mA/W at 1550 nm, respectively. It is worth noting that thinner metal film is advantageous for optical absorption in Au-Si cavities, so the thickness is reduced to t = 15nm for the latter case. Hiring a back electrode layer, as adopted in [13], may further enhance the absorption and thus the responsivity.

 

Fig. 4 Absorbance and responsivity as functions of the photon wavelength for two devices with different device dimensions: (a) and (b) for remarkably intense absorption, (c) and (d) for double wavelength absorption of 1310 nm and 1550 nm.

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4. Conclusion

In summary, a structure of plasmonic cavity array for enhanced hot-electron photodetection is investigated using FDTD simulation and the analytical probability-based electrical model. Apart from the Bragg-SPP mode in the periodic metal structure, there exist the Au-air and Au-Si CSP modes Apart from the Bragg-SPP mode in the periodic metal structure, The Bragg-SPP and Au-air CSP modes are anticrossing at strong coupling, whereas the Au-Si CSP modes allow crossing with the other two types of modes. Hybrid modes formed with combination of these modes can strongly enhance absorption in metal and be exploited to design hot-electron photodetectors. With ease of fabrication, the structure can be adjusted to optimize photoresponse in single or dual bands of optical communication.