Skin effect photon-trapping enhancement in infrared photodiodes

Haonan Ge; Haonan Ge; Haonan Ge; Haonan Ge; Runzhang Xie; Runzhang Xie; Runzhang Xie; Yunfeng Chen; Yunfeng Chen; Peng Wang; Peng Wang; Qing Li; Qing Li; Yue Gu; Yue Gu; Jiaxiang Guo; Jiaxiang Guo; Jiale He; Jiale He; Fang Wang; Fang Wang; Weida Hu; Weida Hu; Weida Hu

doi:10.1364/OE.427714

1. Introduction

Infrared photodiodes have widespread applications in the commercial domain as well as the military domain, such as atmospheric monitoring [1], astronomy research [2], biological spectroscopy [3], night vision [4], and infrared guided missiles [5]. In short- and mid-wavelength infrared bands, photodiodes based on InAs (or InGaAs) and InSb are prevalent choices with the performance closed to the background limited [6]. In long-wavelength infrared bands, photodiodes based on HgCdTe and T2SLs including InAs/GaSb-T2SLs and InAs/InAsSb-T2SLs are favorable choices in high-performance applications [7–8]. With the flourishing application of infrared photodiodes, infrared devices are required to continue to develop in the direction of high response speed, low dark current, high responsivity. In the past decade, the advancement of growth and surface passivation technologies help researchers a lot to suppress the dark current [9]. Furthermore, the dark current can be suppressed during the growth of the material through energy-band design such as pn heterojunction, nBn structures, pBp structures [10–12]. The light absorption of the devices determines the quantum efficiency of the devices and achieving higher quantum efficiency is an important way to increase the responsivity of the devices. High quantum efficiency could be achieved by using a thick absorption layer at the cost of increasing the transport distance of the photogenerated carrier, which results in a slower response speed. On the other hand, a high frame rate imaging system requires photodiodes to have a high response speed. Thus, for a long time, there is a trade-off between light absorption and response speed of the photodiodes. Our work presents an alternative way to eliminate this trade-off and acquire high absorption and potentially high response speed at the same time. Artificial structures, such as micro-nano scale hole arrays [13], pillar arrays [14–15], and plasmonic structures [16–17], can improve the quantum efficiency of the high-speed photodiodes with a thin absorber layer. The size of plasmonic structures [18–19] are larger compared to the contemporary focal plane array (FPA) with the dispersion relation of surface plasmon polaritons (SPPs) tends to propagation mode when the wavelength goes from the optical band and near-infrared to longer wavelength, which results in low coupling efficiency and high crosstalk. As a secondary choice with higher technical difficulty, photon-trapping structures exhibit high light-matter interaction and coupling incident light into lateral propagation mode [13], which increases the transport time of the photogenerated carrier in the absorber layer. However, the device processing technology has made much advancement, and the pixel size of detectors are down to 10 µm and below [20], which needs to design a smaller size artificial structure integrated with small pixel mid-wavelength and long-wavelength infrared focal plane array.

In this paper, we propose a photon-trapping structure at a deep subwavelength scale based on the skin effect of the metal thin film. The photon-trapping structure consists of an array of artificial structures covered by a metallic film, which generates horizontal local mode by utilizing the skin effect of the very thin metallic film. We develop a simplified model consisting of a stack of the absorber layer (InAs, InSb, InAs/GaSb-T2SLs, InAs/InAsSb-T2SLs, or HgCdTe), Au film layer, and dielectric layer (air or CdTe) by the transfer matrix method [21], which guides us to design the realistic photon-trapping structure to enhance the absorption of short-wavelength InAs photodiodes at 300 K, mid-wavelength InSb photodiodes at 300 K, mid-wavelength InAs/GaSb-T2SLs photodiodes at 80 K, long-wavelength InAs/InAsSb-T2SLs photodiodes at 60 K, and long-wavelength HgCdTe photodiodes at 77 K. The optoelectrical simulation results indicate that the responsivity of the structure we proposed is significantly enhanced compared to HgCdTe photodiodes without the realistic photon-trapping structure.

2. One-dimensional simplified model of the skin effect photon-trapping enhancement

In this section, we develop a theoretical model to discuss a realistic photon-trapping infrared photodiodes structure for HgCdTe schematically shown in Fig. 1(a). The optical properties of the theoretical model are abstracted from the photon-trapping structure that has similar behavior to the realistic photon-trapping structure. Schematics for InAs, InSb, InAs/GaSb-T2SLs, and InAs/InAsSb-T2SLs are presented in Supplement 1 Fig. S1-S4. Figure 1(d) is a schematic for the plain structure and is taken as a comparison structure of Fig. 1(a). Optoelectrical simulation, including the optical simulation and semiconductor transport simulation, is performed in this work. In the optical simulation, the non-periodic realistic photon-trapping structure and plain structure could be approximated as an ideal periodic structure in the x-direction with the singe unit shown in Fig. 1(b) and 1(e). We set the left and right boundaries as periodic boundaries and set the upper and lower boundaries as perfectly matched layers (PMLs), as shown in Fig. 1(b) and 1(e). In the semiconductor transportation simulation, we set the left and right boundaries as the periodic boundary, and the electrodes are denoted as orange lines, as shown in Fig. 1(c) and 1(d). In this work, a similar structure, the photon-trapping structure, is illustrated with the potential fabrication process fabricated by high aspect ratio etching, such as plasma etching, and then evaporating metal upon it [9,22–23]. In the infrared band, the value of the skin depth of Au is in the range from 26 nm to 29 nm for λ = 2 ∼ 11 µm. When the value of tan (θ) is larger than 10, dl (in the x-direction) is few nanometers less than the skin depth of Au films, and dh (in the z-direction) is comparable to the skin depth of the Au films for encapsulating the absorber layer, which could be potentially fabricated by atomic layer deposition or thermal evaporation method and makes that the incident light propagates easier in the x-direction [23–24]. There could be a resonant mode, defined as the horizontal local mode, for light propagation in the periodic layered media [25–26] at a specific frequency, which could be controlled by the thickness of the metal film. The realistic photon-trapping structure is periodic in the x-direction, which results in a similar phenomenon that a resonant mode is supported by the horizontal propagation of the light field.

Fig. 1. HgCdTe heterojunction photodiodes. (a) Schematic of the HgCdTe photodiodes with photon-trapping structure. P, D, h₁, h₂, h₃, and θ are the period of the artificial structure, length of the longer base of the isosceles trapezoid artificial structure, thickness of the p-type layer, the thickness of the bottom part of the absorber layer, the thickness of the upper part of the absorber layer, and adjacent angle on its longer base edge, respectively. tan (θ) = dh/dl. The red dashed line in the inset shows the evanescent behavior of the wave propagating through the metal. The Au film on the photon-trapping structure surface acts as the parallel electrode connected to the common contact. (b) Single unit of the ideal periodic structure used in the optical simulation. The left and right boundaries are periodic boundary conditions. The upper and lower boundaries are perfectly matched layers (PMLs). (c) Single unit of the ideal periodic structure used in the semiconductor transportation simulation. The left and right boundaries are periodic boundary conditions. The electrodes are denoted as orange lines. (d) Conventional HgCdTe structure as a reference structure served as a comparison with HgCdTe photon-trapping structure. h₁ and h₂ are the thickness of the p-type and n-type layers. We denote the conventional HgCdTe as the plain structure. (e) Single unit of the ideal periodic structure used in the optical simulation. The left and right boundaries are periodic boundary conditions. The upper and lower boundaries are perfectly matched layers (PMLs). (f) Single unit of the ideal periodic structure is used in the semiconductor transportation simulation. The left and right boundaries are periodic boundary conditions. The electrodes are denoted as orange lines.

Download Full Size | PDF

A schematic of the simplified model is shown in Fig. 2. The dielectric function of the Au film [27] is denoted as ɛ₂, dielectric function of the absorber layer (InAs [28], InSb [28], InAs/GaSb-TS2Ls [29], InAs/InAsSb-TS2Ls [30], or HgCdTe [31–32]) is denoted as ɛ₃, and dielectric constant of the dielectric layer (Air or CdTe [33]) is denoted as ɛ₁. The thickness of the dielectric layer, Au film layer, and absorber layer are denoted as d₁, d₂, d₃, respectively. The period is P = d₁ + 2d₂ + d₃. The light field is incident from the backside of the photon-trapping structure and the photon-trapping structure changes the incident direction from the z-direction to the x-direction. In the simplified model, the incident field propagating in the x-direction is then abstracted into a plane wave source being perpendicular to the x-direction at the center of the absorber layer exciting plane waves in both the positive and the negative x-direction represented by red arrows in Fig. 2(a). S_L and S_R are the incident amplitudes of the plane wave propagation along the negative and positive x-direction, respectively. We assume the S_R = S_L = S. Under successive reflection and transmission, a standing wave is formed and represented by purple arrows in Fig. 2(a). For the contribution of the source plane wave to the amplitude of the standing wave at the interface, we use different symbols, a, b, f, and g, to denote the amplitudes of the standing wave on both sides of the interfaces and as shown in Fig. 2(a). The source plane wave first experience successive reflections within the absorber layer, which contributes to the standing wave and is denoted as the zeroth-order source below. Part of the zeroth-order source plane wave is transmitted from the absorber layer to some dielectric layers and experience successive reflections again within the dielectric layer, which is denoted as the first-order source. Then, part of the source plane wave of the first-order is transmitted back to some absorber layers and experience successive reflections again, which is denoted as the second-order source. Continue this discussion iteratively, the standing wave generated by a single source plane wave is the superposition of all orders of sources and the amplitude of this standing wave could then be expressed as a power series summing the complex amplitudes of all orders up. The ${f^{\prime}_0}$ and ${g^{\prime}_0}$ are the amplitude of the right- and left-moving standing waves at x₁ and could be written as

(1)$$\textrm{ }{f^{\prime}_0} = r{e^{i{\phi _1}}}\sum\limits_{n = 2k + 1} {{K_n}} ,\textrm{ }{g^{\prime}_0} = {e^{i{\phi _1}}}\sum\limits_{n = 2k + 1} {{K_n}} .$$

The ${f_0}$ and ${g_0}$ are the amplitude right- and left-moving standing waves at x₂ and could be written as

(2)$${f_0} = r{e^{2i{\phi _1}}}\sum\limits_{n = 2k + 1} {{K_n}} ,\textrm{ }{g_0} = \sum\limits_{n = 2k + 1} {{K_n}} .$$

Fig. 2. Schematic of the distribution of standing wave in the simplified model at different interfaces.

Download Full Size | PDF

The ${a^{\prime}_0}$ and ${b^{\prime}_0}$ are the amplitude right- and left-moving standing waves at x₃ and could be written as

(3)$${a^{\prime}_0} = {r_{31}}{e^{0.5i{\phi _3}}}{K_0} + \sum\limits_{n = 2k + 2} {{K_n}} ,\textrm{ }{b^{\prime}_0} = {e^{0.5i{\phi _3}}}{K_0} + {e^{i{\phi _3}}}\sum\limits_{n = 2k + 2} {{K_n}} .$$

The ${a_0}$ and ${b_0}$ are the amplitude right- and left-moving standing waves at x₄ and could be written as

(4)$${a_0} = {e^{0.5i{\phi _3}}}{K_0} + {e^{i{\phi _3}}}\sum\limits_{n = 2k + 2} {{K_n}} ,\textrm{ }{b_0} = {e^{0.5i{\phi _3}}}{K_0} + \sum\limits_{n = 2k + 2} {{K_n}} .$$

The ${f^{\prime}_1}$ and ${g^{\prime}_1}$ are the amplitude right- and left-moving standing waves at x₅ and could be written as

(5)$${f^{\prime}_1} = \sum\limits_{n = 2k + 1} {{K_n}} ,\textrm{ }{g^{\prime}_1} = r{e^{2i{\phi _1}}}\sum\limits_{n = 2k} {{K_n}} .$$

The ${f_1}$ and ${g_1}$ are the amplitude right- and left-moving standing waves at x₆ and could be written as

(6)$${f_1} = {e^{i{\phi _1}}}\sum\limits_{n = 2k} {{K_n}} ,\textrm{ }{g_1} = r{e^{i{\phi _1}}}\sum\limits_{n = 2k} {{K_n}} .$$

r_ij is the reflection coefficient of light through medium i to medium j (i =1, 2, 3, j = 1, 2, 3, i ≠ j). r is the reflection coefficient of light through medium 1 to remain area. ϕ_i = k_id_i (i = 1, 2, 3). n is a natural number. K₀ is the accumulated value of the plane wave in the absorber layer at the interface of the absorber layer under the successive reflection and could be written as

(7)$$S{e^{0.5i{\phi _3}}} + {r_{31}}S{e^{1.5i{\phi _3}}} + r_{31}^2S{e^{2.5i{\phi _3}}} + \cdots = \frac{{S{e^{0.5i{\phi _3}}}}}{{1 - {r_{31}}{e^{i{\phi _3}}}}} = {e^{0.5i{\phi _3}}}{K_0}.$$

K₁ is the accumulated value at the interface of the dielectric layer under the successive reflection of the plane wave transmitted from the absorber layer in the dielectric layer and could be written as

(8)$${K_1} = \frac{{{t_{31}}{K_0}}}{{1 - r{r_{13}}{e^{i2{\phi _1}}}}}\textrm{.}$$

The remaining K_n (n > 2) could be written as

(9)$${K_{2n - 2}} = \frac{{{t_{13}}r{e^{i2{\phi _1}}}{K_{2n - 3}}}}{{1 - {r_{31}}{e^{i{\phi _1}}}}},\textrm{ }{K_{2n - 1}} = \frac{{{t_{31}}{e^{i{\phi _3}}}{K_{2n - 2}}}}{{1 - r{r_{13}}{e^{2i{\phi _1}}}}}.$$

t_ij is the transmission coefficient of light through medium i to medium j (i = 1, 2, 3, j = 1, 2, 3, i ≠ j). The presence of a source in the absorber layer makes that the field could not be described directly by the propagation matrix, which only takes the wave equation into account, whereas in other areas, such as the dielectric layer, the field could be fully described by the propagation matrix.

In the periodic structure of the simplified model as shown in Fig. 3(a), the excited plane wave is also assumed to be periodic. The standing waves are inversion and translational symmetric T: x_m→x_m₊₁. The discussion of the optical properties of the simplified model could be dealt with within one period of the structure, as shown in Fig. 3(b). We assume that the amplitude S of the excited plane waves is equal to 0.5. Since the simplified model structure is homogeneous in the y and z-direction, the standing wave that satisfies Maxwell’s equations has the form ${E_\textrm{0}}{e^{i({{k_x}x + {k_y}y + {k_z}z - \omega t} )}}$, where ω is the angular frequency and k_x, k_y= 0, k_z = 0 is x, y, z components of the wave-vector. The electric field could be rewritten as

(10)$$E = {S_R}{\textrm{e}^{i{k_{mx}}x}}\textrm{ + }{S_L}{\textrm{e}^{ - i{k_{mx}}x}} = E(x )+ E({ - x} )$$

where

(11)$$E(x )= {S_R}{e^{i{k_m}x}},\textrm{ }E({ - x} )= {S_L}{e^{ - i{k_m}x}}.$$

and

(12)$${k_{mx}} = {\left[ {{\varepsilon_m}{{\left( {\frac{\omega }{c}} \right)}^2}} \right]^{1/2}},\textrm{ }m\textrm{ } = \textrm{ 1, 2, 3}\textrm{.}$$

We define

(13)$$\begin{aligned}&{F_0} = E({x_2^ - } ),\textrm{ }{G_0} = E({ - x_2^ - } ),\textrm{ }\\ &{{H^{\prime}}_0} = E({x_2^ + } ),\textrm{ }{{I^{\prime}}_0} = E({ - x_2^ + } ),\\ &{H_0} = E({x_3^ - } ),\textrm{ }{I_0} = E({ - x_3^ - } ),\textrm{ }\\ &{{A^{\prime}}_0} = E({x_3^ + } ),\textrm{ }{{B^{\prime}}_0} = E({ - x_3^ + } ),\\ &{A_0} = E({x_4^ - } ),\textrm{ }{B_0} = E({ - x_4^ - } ),\textrm{ }\\ &{{M^{\prime}}_0} = E({x_4^ + } ),\textrm{ }{{N^{\prime}}_0} = E({ - x_4^ + } ),\\ &{M_0} = E({x_5^ - } ),\textrm{ }{N_0} = E({ - x_5^ - } ),\textrm{ }\\ &{{F^{\prime}}_1} = E({x_5^ + } ),\textrm{ }{{G^{\prime}}_1} = E({ - x_5^ + } ),\\ &{F_1} = E({x_6^ - } ),\textrm{ }{G_1} = E({ - x_6^ - } ), \end{aligned}$$

where $x_l^ - $ is left side of the interface x = x_l (l = 2, 3, 4, 5, 6), $x_l^ + $ is right side of the interface x = x_l (l = 2, 3, 4, 5, 6). The thickness of the m-th layer is d_m related to the x_l by

(14)$${d_2} = {x_3} - {x_2},\textrm{ }{d_3} = {x_4} - {x_3},\textrm{ }{d_2} = {x_5} - {x_4},\textrm{ }{d_1} = {x_6} - {x_5}.$$

Using the transfer matrix and propagation matrix [21], we obtain the relation between amplitudes F₀, G₀ and ${A^{\prime}_0}$, ${B^{\prime}_0}$

(15)$$\left( {\begin{array}{c} {{F_0}}\\ {{G_0}} \end{array}} \right) = {M_{1 \to 2}}\left( {\begin{array}{c} {{{H^{\prime}}_0}}\\ {{{I^{\prime}}_0}} \end{array}} \right),$$

(16)$$\left( {\begin{array}{c} {{{H^{\prime}}_\textrm{0}}}\\ {{{I^{\prime}}_\textrm{0}}} \end{array}} \right) = {T_2}\left( {\begin{array}{c} {{H_0}}\\ {{I_\textrm{0}}} \end{array}} \right),$$

(17)$$\left( {\begin{array}{c} {{H_0}}\\ {{I_0}} \end{array}} \right) = {M_{2 \to 3}}\left( {\begin{array}{c} {{{A^{\prime}}_0}}\\ {{{B^{\prime}}_0}} \end{array}} \right),$$

(18)$$\left( {\begin{array}{c} {{F_0}}\\ {{G_0}} \end{array}} \right) = {M_{1 \to 2}}{T_2}{M_{2 - 3}}\left( {\begin{array}{c} {{{A^{\prime}}_0}}\\ {{{B^{\prime}}_0}} \end{array}} \right) = {M_{1 \to 3}}\left( {\begin{array}{c} {{{A^{\prime}}_0}}\\ {{{B^{\prime}}_0}} \end{array}} \right),$$

where M_1→2 and M_2→3 are the transfer matrix that links the amplitudes of the electric field on the two sides of the interfaces and given by

(19)$${M_{1 \to 2}} = \left[ {\begin{array}{cc} {\frac{1}{{{t_{12}}}}}&{ - \frac{{{r_{21}}}}{{{t_{12}}}}}\\ {\frac{{{r_{12}}}}{{{t_{12}}}}}&{{t_{21}} - \frac{{{r_{21}}{r_{12}}}}{{{t_{12}}}}} \end{array}} \right],\textrm{ }$$

and

(20)$$\textrm{ }{M_{2 \to 3}} = \left[ {\begin{array}{cc} {\frac{1}{{{t_{23}}}}}&{ - \frac{{{r_{32}}}}{{{t_{23}}}}}\\ {\frac{{{r_{23}}}}{{{t_{23}}}}}&{{t_{32}} - \frac{{{r_{32}}{r_{23}}}}{{{t_{23}}}}} \end{array}} \right],$$

and

(21)$${r_{12}} = \frac{{{\varepsilon _2}{k_{1x}} - {\varepsilon _1}{k_{2x}}}}{{{\varepsilon _2}{k_{1x}} + {\varepsilon _1}{k_{2x}}}},\textrm{ }{t_{12}} = \frac{{2{\varepsilon _2}{k_{1x}}}}{{{\varepsilon _2}{k_{1x}} + {\varepsilon _1}{k_{2x}}}},\textrm{ }{r_{21}} = \frac{{{\varepsilon _1}{k_{2x}} - {\varepsilon _2}{k_{1x}}}}{{{\varepsilon _1}{k_{2x}} + {\varepsilon _2}{k_{1x}}}},\textrm{ }{t_{12}} = \frac{{2{\varepsilon _1}{k_{2x}}}}{{{\varepsilon _1}{k_{2x}} + {\varepsilon _2}{k_{1x}}}}.$$

T₂ is so-called the propagation matrix, which accounts for propagation through the Au film layer. The propagation matrix T₂ is given by

(22)$${T_2} = \left[ {\begin{array}{cc} {{e^{ - i{k_{2x}}{d_2}}}}&0\\ 0&{{e^{i{k_{2x}}{d_2}}}} \end{array}} \right].$$

The matrix M_1→3 could be written as

(23)$${M_{1 \to 3}} = \left[ {\begin{array}{cc} {\frac{\textrm{1}}{{{t_{13}}}}}&{\textrm{ - }\frac{{{r_{31}}}}{{{t_{13}}}}}\\ {\frac{{{r_{\textrm{13}}}}}{{{t_{13}}}}}&{{t_{31}} - \frac{{{r_{31}}{r_{13}}}}{{{t_{13}}}}} \end{array}} \right],$$

and

(24)$${r_{13}} = \frac{{{r_{12}} + {r_{23}}{e^{2i{k_{2x}}{d_2}}}}}{{1 + {r_{12}}{r_{23}}{e^{2i{k_{2x}}{d_2}}}}}\textrm{, }{t_{13}} = \frac{{{t_{12}}{t_{23}}{e^{i{k_{2x}}{d_2}}}}}{{1 + {r_{12}}{r_{23}}{e^{2i{k_{2x}}{d_2}}}}},\textrm{ }{r_{31}} = \frac{{{r_{32}} + {r_{21}}{e^{2i{k_{2x}}{d_2}}}}}{{1 + {r_{32}}{r_{21}}{e^{2i{k_{2x}}{d_2}}}}},\textrm{ }{t_{31}} = \frac{{{t_{32}}{t_{21}}{e^{i{k_{2x}}{d_2}}}}}{{1 + {r_{32}}{r_{21}}{e^{2i{k_{2x}}{d_2}}}}}.$$

Fig. 3. Optical properties of the simplified model of the photon-trapping structure. (a) Schematic of the simplified model of the photon-trapping structure. The green regions represent the dielectric layer (Air) with dielectric function ɛ₁ and thickness d₁. The yellow regions represent the Au film layer with dielectric function ɛ₂ and thickness d₂. Blue regions represent the absorber layer (InAs, InSb, InAs/GaSb-T2SLs, InAs/InAsSb-T2SLs, or Hg_0.78Cd_0.22Te) with dielectric function ɛ₃ and thickness d₃. (b) Schematic of a period of the structure. Red arrows represent the source plane wave at the center of the HgCdTe region. Purple arrows represent the standing wave. (c) Magnitude of the amplitude A₀ for the InAs, InSb, InAs/GaSb-T2SLs, InAs/InAsSb-T2SLs, and HgCdTe simplified models. The geometric parameters are listed in Table 1. (d) Distribution of the magnitude of the electric field E (x) at the resonant peak (8.73 µm) with the HgCdTe absorber layer in Fig. 3(b). (e) Enlarged view of the dashed box in Fig. 3(d). The red dashed line shows the fitting curve of the amplitude E (x) in the Au film layer, indicating that the evanescent behavior of the wave propagating through the metal in the positive x-direction. (f) Peak of the magnitude of amplitude A₀, B₀, F₀, and G₀ for different geometrical parameters with the HgCdTe absorber layer. (g) Left side shows the photon energy band curve for the simplified model. Right side shows the magnitude of the magnitude A₀.

Download Full Size | PDF

Table 1. Key parameters of the simplified model

View Table | View all tables in this article

Noticing that there is an excited source plane wave in the absorber layer, the relationship between ${A^{\prime}_\textrm{0}}$, ${B^{\prime}_0}$ and ${A_\textrm{0}}$, ${B_\textrm{0}}$ cannot be directly expressed by the propagation matrix. We need to subtract the discontinuous part in the ${A^{\prime}_\textrm{0}}$, ${B^{\prime}_0}$, A₀, and B₀ to ensure the propagation matrix establish and is described by

(25)$$\left[ {\begin{array}{c} {{{A^{\prime}}_\textrm{0}} - s^{\prime+}_0 }\\ {{{B^{\prime}}_0} - s^{\prime-}_0 } \end{array}} \right] = {T_\textrm{3}}\left[ {\begin{array}{c} {{A_0} - s_0^ + }\\ {{B_0} - s_0^ - } \end{array}} \right],\textrm{ }$$

where

(26)$$s_0^{+} = \textrm{ }s^{\prime-}_0 {=} \frac{1}{2}\frac{{{e^{i{k_{3x}}{d_3}/2}}}}{{1 - {r_{31}}{e^{i{k_{3x}}{h_3}}}}},$$

and

(27)$$s^{\prime+}_0 {=} \textrm{ }s_0^{-} = \frac{1}{2}\frac{{{r_{31}}{e^{i{k_{3x}}{d_3}/2}}}}{{1 - {r_{31}}{e^{i{k_{3x}}{d_3}}}}},$$

respectively. The discontinuous parts $s^{\prime+}_0 $, $s^{\prime-}_0 $, $s_0^ + $, and $s_0^ - $ (More details are contained in Supplement 1, section 2) are the accumulation of plane waves at the interfaces between the absorber layer (InAs, InSb, InAs/GaSb-T2SLs, InAs/InAsSb-T2SLs or HgCdTe) and Au film. We could get the relationship between A₀, B₀, and F₁, G₁ by similar steps to Eqs. (15) to (18)

(28)$$\left[ {\begin{array}{c} {{A_0}}\\ {{B_0}} \end{array}} \right] = {M_{3 \to 1}}{T_1}\left[ {\begin{array}{c} {{F_1}}\\ {{G_1}} \end{array}} \right],$$

where

(29)$${M_{3 \to 1}} = \left[ {\begin{array}{cc} {\frac{1}{{{t_{31}}}}}&{ - \frac{{{r_{13}}}}{{{t_{31}}}}}\\ {\frac{{{r_{31}}}}{{{t_{31}}}}}&{{t_{13}} - \frac{{{r_{31}}{r_{13}}}}{{{t_{31}}}}} \end{array}} \right],$$

and

(30)$${T_1} = \left[ {\begin{array}{cc} {{e^{ - i{k_{1x}}{d_1}}}}&0\\ 0&{{e^{ - {k_{1x}}{d_1}}}} \end{array}} \right],$$

respectively. From Eqs. (18), (25), (28), the amplitudes F₀, G₀, and F₁, G₁ are related by

(31)$$\left( {\begin{array}{c} {{F_0}}\\ {{G_0}} \end{array}} \right) = {M_{1 \to 3}}{T_3}{M_{3 \to 1}}{T_1}\left( {\begin{array}{c} {{F_1}}\\ {{G_1}} \end{array}} \right) - {M_{1 \to 3}}{T_3}\left( {\begin{array}{c} {s_0^ + }\\ {s_0^ - } \end{array}} \right) + {M_{1 \to 3}}\left( {\begin{array}{c} {s^{\prime+}_0 }\\ {s^{\prime-}_0 } \end{array}} \right).$$

As mentioned above, the electric field amplitudes are periodic. The electric field amplitudes of the m^th period F_i, G_i and the (m+1)^th period, F_i₊₁, G_i₊₁ only differ by a phase φ:

(32)$$\left( {\begin{array}{c} {{F_m}}\\ {{G_m}} \end{array}} \right) = \left( {\begin{array}{cc} {{e^{ - i\varphi }}}&0\\ 0&{{e^{i\varphi }}} \end{array}} \right)\left( {\begin{array}{c} {{F_{m + 1}}}\\ {{G_{m + 1}}} \end{array}} \right),$$

where

(33)$$\varphi = {\varphi _1} + {\varphi _2} + {k_{3x}}{h_3} + {k_{1x}}{h_1},$$

(34)$${\varphi _\textrm{1}} = {\tan ^{ - 1}}\frac{{{\mathop{\rm Im}\nolimits} ({t_{13}})}}{{{\textrm{Re}} ({t_{13}})}},$$

(35)$${\varphi _2} = {\tan ^{ - 1}}\frac{{{\mathop{\rm Im}\nolimits} ({t_{31}})}}{{{\textrm{Re}} ({t_{31}})}}.$$

Using Eqs. (31) and (32), we could obtain

(36)$$\left( {\begin{array}{cc} {{e^{ - i\varphi }}}&0\\ 0&{{e^{i\varphi }}} \end{array}} \right)\left( {\begin{array}{c} {{F_\textrm{1}}}\\ {{G_\textrm{1}}} \end{array}} \right) = {M_{\textrm{1} \to \textrm{3}}}{T_3}{M_{\textrm{3} \to \textrm{1}}}{T_\textrm{1}}\left( {\begin{array}{c} {{F_\textrm{1}}}\\ {{G_\textrm{1}}} \end{array}} \right) - {M_{\textrm{1} \to \textrm{3}}}{T_\textrm{3}}\left( {\begin{array}{c} {s_0^ + }\\ {s_0^ - } \end{array}} \right) + {M_{\textrm{1} \to \textrm{3}}}\left( {\begin{array}{c} {s^{\prime+}_0 }\\ {s^{\prime-}_0 } \end{array}} \right).$$

Finally, we could get the following expressions for F₁, G₁

(37)$${F_\textrm{1}} = \frac{{{C_{\textrm{22}}}{W_{\textrm{11}}}\textrm{ - }{C_{12}}{W_{\textrm{21}}}}}{{{C_{\textrm{22}}}{C_{\textrm{11}}}\textrm{ - }{C_{\textrm{12}}}{C_{\textrm{21}}}}}\textrm{, }{G_\textrm{1}} = \frac{{{C_{\textrm{11}}}{W_{\textrm{21}}}\textrm{ - }{C_{21}}{W_{\textrm{11}}}}}{{{C_{\textrm{22}}}{C_{\textrm{11}}}\textrm{ - }{C_{\textrm{12}}}{C_{\textrm{21}}}}}\textrm{, }$$

where

(38)$$\left( {\begin{array}{cc} {{C_{\textrm{11}}}}&{{C_{\textrm{12}}}}\\ {{C_{\textrm{21}}}}&{{C_{\textrm{22}}}} \end{array}} \right)\textrm{ = }\left( {\begin{array}{cc} {{e^{\textrm{ - }i\varphi }}}&0\\ \textrm{0}&{{e^{i\varphi }}} \end{array}} \right) - {M_{\textrm{1} \to \textrm{3}}}{T_3}{M_{3 \to 1}}{T_1}\textrm{,}$$

and

(39)$$\left( {\begin{array}{c} {{W_{\textrm{11}}}}\\ {{W_{\textrm{21}}}} \end{array}} \right)\textrm{ = }{M_{\textrm{1} \to \textrm{3}}}\left( {\begin{array}{c} {s^{\prime+}_0 }\\ {s^{\prime-}_0 } \end{array}} \right) - {M_{\textrm{1} \to \textrm{3}}}{T_3}\left( {\begin{array}{c} {s_0^ + }\\ {s_0^ - } \end{array}} \right)\textrm{.}$$

The amplitude A₀ and B₀ can be obtained by Eq. (28). By optimizing d_l, d₂, and d₃, different structures are designed for InAs, InSb, InAs/GaSb-T2SLs, InAs/InAsSb-T2SLs, and HgCdTe to provide the maximum magnitude of the amplitude A₀ in respective ranges of operating wavelength, as is shown in Table 1. The magnitude of amplitudes A₀ of InAs, InSb, InAs/GaSb-T2SLs, InAs/InAsSb-T2SLs, and HgCdTe are shown in Fig. 3(c). Figure 3(d) shows the distribution of the magnitude of the electric field E(x) at the resonance peak (8.73 µm) for the HgCdTe absorber layer in the period structure. Splitting the standing wave into the right- and left-moving traveling wave. The magnitude of the electric field E(x) of the right-moving traveling wave attenuates in the absorber layer as x increases and is invariant in the dielectric layer. Figure 3(e) shows the enlarged view within the dashed box in Fig. 3(d) and the red dashed line is the fitting curve of the electric field in the Au films. This indicates that the evanescent behavior of the electric field E(x) passes through the metal. The magnitude of the peak value of the amplitudes A₀, B₀, C₀, D₀ could be manipulated by the geomatical parameters, d_l, d₂, and d₃, as is shown in Fig. 3(f). These peak values of the electric coefficients decrease with the increase of dl (keeping d₁ and d₂ constant) and d₂ (keeping d₃ and P constant). Figure 3(g) depicts the photon energy band curve of the simplified model with a frequency range of 16.67 ∼ 59 THz (5.08-18 µm). The right side of Fig. 3(g) shows the magnitude of amplitude A₀ at different frequencies.

3. Results and discussion

Discussion of the simplified model presented above guides us to design the realistic photon-trapping structure. The period of the realistic photon-trapping structure is designed to be the same value as is in the simplified model. The bottom width of the realistic photon-trapping structure D is taken to be equal to d₃ in the simplified model. The horizontal thickness of Au film dl is taken to be equal to d₂ in the simplified model. The specific parameter values of the photon-trapping structure are listed in Table 2. We simulate the optical properties of the photon-trapping structure by the finite element method and is plotted it in Fig. 4. The absorption of the InAs, InSb, InAs/GaSb-T2SLs, and InAs/InAsSb-T2SLs structures exceeds 0.8 at 2.0 ∼ 2.49 µm, 4 ∼ 5 µm, 3.8 ∼ 4.7 µm, and 8.5 ∼ 11 µm, respectively. The absorption of the HgCdTe structure exceeds 0.8 at λ = 8.0 ∼ 11 µm with a peak value at 9.73 µm marked by the star. The distribution of the electric field E_x of the HgCdTe structure at this peak value is plotted in Fig. 4(b), which shows that the energy distribution inferred from the electric field E_x is in the neighborhood of the realistic photon-trapping structure sidewall and shows the existence of a horizontal local mode. Because of the same reason as is in the simplified model, a horizontal local mode in the realistic photon-trapping structure could be observed with the same trend that the horizontal local mode strength is decreased when dl is increased.

Fig. 4. Simulated optical properties of the realistic photon-trapping structure. (a) Calculation result of the absorption spectrum of realistic InAs, InSb, InAs/GaAs-T2SLs, InAs/InAsSb-T2SLs, and HgCdTe photon-trapping structure. The geometry parameters are list in Table 2. (b) Distribution of the electric field E_x for HgCdTe structure at 9.73 µm. (c) Peak position of the magnitude of the amplitude A₀ versus d₂ for the HgCdTe simplified model. (d) Peak position of the absorption spectrum versus dl for the HgCdTe realistic photon-trapping structure. (e) Relationship between absorption peak and the sidewall angle (θ) for photon-trapping structure.

Download Full Size | PDF

Table 2. Key parameters of the photon-trapping structures

View Table | View all tables in this article

Figure S6 in the Supplement 1 indicates that the magnitude of the amplitude A₀ is decreased and the resonant peak is blue-shifted with the increase of d_2. Figure S7 in the Supplement 1 is the absorption spectrum of the HgCdTe photon-trapping structure and similar behavior like Fig. S6 could be found in Fig. S7. These results of Fig. S6 and S7 show that the electromagnetic field is difficult to penetrate the Au film as dl is increased, which leads to the decrease of the intensity of the horizontal local mode. Figure 4(c) shows the relation between the peak position and d₂ (d₃ and P keep constant) for the HgCdTe simplified model. Figure 4(d) shows the relation between the absorption peak and dl (dh, P, D, h₁, h₂, and h₃ are keeping constant). The absorption peak position in the realistic HgCdTe photon-trapping structure is red-shifted by 1 µm compared to the resonant peak position in the simplified model. The difference between the simplified model and the realistic photon-trapping structure, the aforementioned redshift comes from the following factors: (i) the sidewall angle causes the ratio of the d₂ and d₃ to be different at different heights, which results in the resonant peak moving and similar resonant peak shift of the simplified model as plotted in Fig. S8 in the Supplement 1. (ii) In the photon-trapping structure, there are both surface plasmon polaritons and localized surface plasmons excitation based on the metal film artificial structure, which also contribute to the shift of the resonance peak position. (iii) In photon-trapping structure, the refractive index of the dielectric layer is much smaller than the refractive index of the absorption layer, such that the electromagnetic field in the dielectric layer is an evanescent wave. Figure 4(e) shows the relationship between the absorption peak position and the angle of the sidewall (θ). The absorption peak shifts to a shorter wavelength with the increase of θ, and the limit of peak shifts to 9.63 µm by the fitting curve.

To evaluate the enhancement effect of the horizontal local mode in the infrared photodiode, we simulate the optoelectrical properties of the HgCdTe realistic photon-trapping structure and plain HgCdTe structure. The bandgap of Hg_1-xCd_xTe increases with the Cd component x and the working temperature [34]. Wide-gap HgCdTe layer and narrow-gap absorber layer form heterojunction to suppress dark current. It should be noticed that the dry etch technology introduces surface defects. Some works [35–36] have clarified that the surface defects affect the electrical properties of metal-semiconductor contacts, which converts the Schottky contact into the ohmic contact [37]. Therefore, in the electrical simulation, we assume the Au-HgCdTe contact is purely ohmic. In our work, SRH recombination, radiation recombination, and Auger recombination are considered [32,38]. The light intensity is chosen to be 1 W/cm². Figure 5(a) shows the dark current and photocurrent for the realistic photon-trapping structure and the plain structure. The reverse bias voltage is 100 mV. The heterojunction design with a small bias voltage guaranteed that the dark current of the HgCdTe photon-trapping structure is small enough. The current density distribution at the wavelength of 9.2 µm is shown in Fig. 5(b). There are three types of electrodes on the surface of the photon-trapping structure, including those on the shorter base edge of the trapezoid structure, those on the lateral sides of the trapezoid structure, and those between trapezoid structures. These electrodes form a parallel-connected electrode on the surface photon-trapping structure, which leads to a small built-in electric field in the upper part of the absorber layer. As is shown in Fig. 5(b) and Fig. S10 in the Supplement 1, both the drift velocity of photogenerated carriers and the photocurrent density in the upper part of the absorber layer are very small. In other words, it is difficult to collect all the photo-generated carriers generated in the upper part of the absorber layer. Despite this, the photocurrent of the HgCdTe photon-trapping structure is still much larger than the plain structure in the range of wavelength 7 ∼ 11 µm. Figure 5(d) provides a demonstration of the focal plane array application of the realistic photon-trapping structure. Our proposed structure not only has relatively high enchantment characteristics but also has the advantage of low crosstalk. To quantitively discuss the crosstalk of our proposed structure supporting the horizontal local mode, a two-dimensional HgCdTe photodiode array is taken as an example as shown in Fig. 5(e). Illuminate pixel 2 with Gaussian beam at its center, and take the crosstalk as the absorption in pixel 1. Figure 5(f) shows that the distribution of energy dissipation in different pixels. The optical crosstalk is smaller than 5% when the fill factor is 0.8 in Fig. 5(g). The black curve of the insets is the attenuation of SPPs [39] at HgCdTe/Au at λ = 9.73 µm with propagation distance and the red curve is the fitting curve of energy dissipation from the second unit structure to the seventh unit structure from right to left in pixel 1. The attenuation speed of the photon-trapping structure is much faster than the attenuation speed of SPPs, which have small optical crosstalk.

Fig. 5. Optoelectrical properties of HgCdTe photodiode. (a) Photocurrent and dark current of both HgCdTe photon-trapping structure and plain HgCdTe structure at 8-11µm. The injected power density is 1 W/cm². (b) Magnitude of the current density distribution of the structure at 9.3 µm. (c) Current responsivity spectrum of plain structure and photon-trapping structure. Blue curve is the ratio of the responsivity of the photon-trapping structure and plain structure. (d) Schematic of 2×2 array of the photon-trapping structure HgCdTe photodiodes. C_f is capacitance, V_ref is the reference voltage. Any of these four pixels consists of seven periods in the x-direction, the length of which is 13µm in the y-direction. (e) Schematic of a single-pixel (pixel 2) of HgCdTe photodiodes along with its adjacent pixels (pixel 1 and pixel 3) in the x-direction. The w is the spacing between pixels. The d is the width of the pixels. (f) Energy dissipation in different pixels. Gaussian beam is injected at the center of pixel 2 with a waist radius of 10 µm. The wavelength of the Gaussian beam is 9.73 µm. (g) Crosstalk in pixel 1. Gaussian beam is injected at the center of pixel 2 with a waist radius of 10 µm. The wavelength of the Gaussian beam is 9.73 µm. The fill factor is defined as w/(w + d). The width of the active area of the pixel is fixed as 12.6 µm. The red curve of the inset is the fitting curve of energy dissipation from the second unit to the seventh unit from right to left in pixel 1. The black curve is the attenuation of SPPs at Air/HgCdTe at λ = 9.73 µm with propagation distance.

Download Full Size | PDF

The parallel electrodes result in the disadvantages that the photogenerated carriers are not fully collected by this parallel electrode in our previously designed photon-trapping structures. Figure 6(a) shows the modified structure with a carefully designed electrode contact of the photon-trapping structure to redistribute the built-in electric field to ensure that the drift velocity of the carrier is large enough to be collected, denoted as dielectric-filled structure below. The preparation process of the dielectric-filled structure is shown in Fig. S12 in the Supplement 1. Figure 6(b)-(c) shows the absorption spectrum and distribution of the electric field E_x at the absorption peak. We found that the optical properties of the dielectric-filled structure are largely maintained compared with the photon-trapping structure. We simulate the photocurrent, current density distribution, quantum efficiency at different wavelengths to verify that the collection of photogenerated carriers has been improved, as shown in Fig. 6(d)-(f). The current density concentrates on the photon-trapping structure area. The quantum efficiency of the dielectric-filled structure is improved compared to that of the photon-trapping structure.

Fig. 6. Optoelectrical properties of the dielectric-filled structure. (a) Schematic of the dielectric-filled structure. (b) Absorption spectrum of the dielectric-filled structure. The black curve is the total absorption of the advanced structure. The red curve is the absorption of HgCdTe. (c) Distribution of the electric field E_x at 9.7 µm. (d) Photocurrent and dark current in the wavelength range of 8-11 µm for dielectric-filled structure. The injected power density is 1 W/cm². (e) Current density distribution of dielectric-filled structure at 9.2 µm. (f) Quantum efficiency of the plain structure, photon-trapping structure, dielectric-filled structure at 7-11 µm.

Download Full Size | PDF

4. Conclusion

This work provides a design method to significantly increase the absorption and reduce the dark current of long-wavelength HgCdTe photodiodes with the photon-trapping structure induced horizontal local mode utilizing the skin effect of metals. The proposed photon-trapping structure strongly control the propagation direction of incident light and generates a horizontal local mode, which is different from the conventional trapping structures such as nano-holes arrays or pillar arrays. A sophisticated one-dimensionally theoretical model is developed to accounts for the origin of the horizontal local mode and guides the photon-trapping structure design. The simulation results indicate the photon-trapping structure can significantly improve the optoelectrical conversion efficiency for photodiodes. Notably, the photon-trapping structure has small optical crosstalk due to the horizontal local mode decays with propagation distance. The photon-trapping structure enhanced infrared photodiode arrays with the different materials (InAs, InSb, InAs/InAsSb Type-II superlattices, and HgCdTe) covering from short-wavelength infrared to long-wavelength infrared photodiodes are also systematically discussed. It is shown that the proposed model and photon-trapping structure are very universal to the photodiode arrays with typical infrared materials. Our findings may provide a route to control light-matter interactions and realize low dark current, small pixel, high response speed FPA infrared photodiodes.

Funding

National Key Research and Development Program of China (2020YFB2009300); National Natural Science Foundation of China (61725505); Fund of Shanghai Natural Science Foundation (19XD1404100).

Disclosures

The authors declare that they have no competing interests.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

References

1. G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 µm,” Nat. Photonics 12(4), 202–208 (2018). [CrossRef]

2. O. Gravrand, J. Rothman, C. Cervera, N. Baier, C. Lobre, J. P. Zanatta, O. Boulade, V. Moreau, and B. Fieque, “HgCdTe Detectors for Space and Science Imaging: General Issues and Latest Achievements,” J. Electron. Mater. 45(9), 4532–4541 (2016). [CrossRef]

3. X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S. Weiss, “Quantum Dots for Live Cells, in Vivo Imaging, and Diagnostics,” Science 307(5709), 538–544 (2005). [CrossRef]

4. P. Norton, “Third-generation sensors for night vision,” Opto-Electron. Rev. 14(1), 1–10 (2006). [CrossRef]

5. G. A. Rao and S. P. Mahulikar, “New criterion for aircraft susceptibility to infrared guided missiles,” Aerosp. Sci. Technol. 9(8), 701–712 (2005). [CrossRef]

6. A. Rogalski, “History of infrared detectors,” Opto-Electron. Rev. 20(3), 279–308 (2012). [CrossRef]

7. A. Rogalski, “HgCdTe infrared detector material: history, status, and outlook,” Rep. Prog. Phys. 68(10), 2267–2336 (2005). [CrossRef]

8. D. R. Rhiger, “Performance Comparison of Long-Wavelength Infrared Type II Superlattice Devices with HgCdTe,” J. Electron. Mater. 40(8), 1815–1822 (2011). [CrossRef]

9. W. Lei, J. Antoszewski, and L. Faraone, “Progress, challenges, and opportunities for HgCdTe infrared materials and detectors,” Appl. Phys. Rev. 2(4), 041303 (2015). [CrossRef]

10. A. Varghese, D. Saha, K. Thakar, V. Jindal, S. Ghosh, N. V. Medhekar, S. Ghosh, and S. Lodha, “Near-Direct Bandgap WSe2/ReS2 Type-II pn Heterojunction for Enhanced Ultrafast Photodetection and High-Performance Photovoltaics,” Nano Lett. 20(3), 1707–1717 (2020). [CrossRef]

11. H. Kim, O. Cellek, Z. Lin, Z. He, X. Zhao, S. Liu, H. Li, and Y. Zhang, “Long-wave infrared nBn photodetectors based on InAs/InAsSb type-II superlattices,” Appl. Phys. Lett. 101(16), 161114 (2012). [CrossRef]

12. J. He, Q. Li, P. Wang, F. Wang, Y. Gu, C. Shen, M. Luo, C. Yu, L. Chen, X. Chen, W. Lu, and W. Hu, “Design of a bandgap-engineered barrier-blocking HOT HgCdTe long-wavelength infrared avalanche photodiode,” Opt. Express 28(22), 33556–33563 (2020). [CrossRef]

13. Y. Gao, H. Cansizoglu, K. G. Polat, S. Ghandiparsi, A. Kaya, H. H. Mamtaz, A. S. Mayet, Y. Wang, X. Zhang, T. Yamada, E. P. Devine, A. F. Elrefaie, S. Wang, and M. S. Islam, “Photon-trapping microstructures enable high-speed high-efficiency silicon photodiodes,” Nat. Photonics 11(5), 301–308 (2017). [CrossRef]

14. J. Schuster and E. Bellotti, “Numerical simulation of crosstalk in reduced pitch HgCdTe photon-trapping structure pixel arrays,” Opt. Express 21(12), 14712–14727 (2013). [CrossRef]

15. J. Liang, W. Hu, Z. Ye, L. Liao, Z. Li, X. Chen, and W. Lu, “Improved performance of HgCdTe infrared detector focal plane arrays by modulating light field based on photonic crystal structure,” J. Appl. Phys. 115(18), 184504 (2014). [CrossRef]

16. J. Le Perchec, Y. Desieres, and R. Espiau de Lamaestre, “Plasmon-based photosensors comprising a very thin semiconducting region,” Appl. Phys. Lett. 94(18), 181104 (2009). [CrossRef]

17. M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with Active Optical Antennas,” Science 332(6030), 702–704 (2011). [CrossRef]

18. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011). [CrossRef]

19. G. Gu, J. Vaillancourt, P. Vasinajindakaw, and X. Lu, “Backside-configured surface plasmonic structure with over 40 times photocurrent enhancement,” Semicond. Sci. Technol. 28(10), 105005 (2013). [CrossRef]

20. J. M. Armstrong, M. R. Skokan, M. A. Kinch, and J. D. Luttmer, “HDVIP five-micron pitch HgCdTe focal plane arrays,” Proc. SPIE 9070, 907033 (2014). [CrossRef]

21. P. Markos and C. M. Soukoulis, “Wave propagation: from electrons to photonic crystals and left-handed materials,” (Princeton University, 2008).

22. J. Wu, Y. Liu, Y. Guo, S. Feng, B. Zou, H. Mao, C. H. Yu, D. Tian, W. Huang, and F. Huo, “Centimeter-scale subwavelength photolithography using metal-coated elastomeric photomasks with modulated light intensity at the oblique sidewalls,” Langmuir 31(17), 5005–5013 (2015). [CrossRef]

23. W. Li and J. Valentine, “Metamaterial Perfect Absorber Based Hot Electron Photodetection,” Nano Lett. 14(6), 3510–3514 (2014). [CrossRef]

24. Z. Li, A. Rahtu, and R. G. Gordon, “Atomic Layer Deposition of Ultrathin Copper Metal Films from a Liquid Copper(I) Amidinate Precursor,” J. Electrochem. Soc. 153(11), C787–C794 (2006). [CrossRef]

25. C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt. 41(19), 3978–3987 (2002). [CrossRef]

26. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013). [CrossRef]

27. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]

28. S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, Al_xGa_1−xAs, and In_1−xGa_xAs_yP_1−y,” J. Appl. Phys. 66(12), 6030–6040 (1989). [CrossRef]

29. E. Steveler, M. Verdun, B. Portier, P. Chevalier, C. Dupuis, N. Bardou, J.-B. Rodriguez, R. Haïdar, F. Pardo, and J.-L. Pelouard, “Optical index measurement of InAs/GaSb type-II superlattice for mid-infrared photodetection at cryogenic temperatures,” Appl. Phys. Lett. 105(14), 141103 (2014). [CrossRef]

30. M. D. Goldflam, E. A. Kadlec, B. V. Olson, J. F. Klem, S. D. Hawkins, S. Parameswaran, W. T. Coon, G. A. Keeler, T. R. Fortune, A. Tauke-Pedretti, J. R. Wendt, E. A. Shaner, P. S. Davids, J. K. Kim, and D. W. Peters, “Enhanced infrared detectors using resonant structures combined with thin type-II superlattice absorbers,” Appl. Phys. Lett. 109(25), 251103 (2016). [CrossRef]

31. J. Wenus, J. Rutkowski, and A. Rogalski, “Two-dimensional analysis of double-layer heterojunction HgCdTe photodiodes,” IEEE Trans. Electron Devices 48(7), 1326–1332 (2001). [CrossRef]

32. E. Bellotti and D. D’Orsogna, “Numerical analysis of HgCdTe simultaneous two-color photovoltaic infrared detectors,” IEEE J. Quantum Electron. 42(4), 418–426 (2006). [CrossRef]

33. A. G. DeBell, E. L. Dereniak, J. Harvey, J. Nissley, J. Palmer, A. Selvarajan, and W. L. Wolfe, “Cryogenic refractive indices and temperature coefficients of cadmium telluride from 6 µm to 22 µm,” Appl. Opt. 18(18), 3114–3115 (1979). [CrossRef]

34. G. L. Hansen, J. Schmit, and T. Casselman, “Energy gap versus alloy composition and temperature in Hg1− x Cd x Te,” J. Appl. Phys. 53(10), 7099–7101 (1982). [CrossRef]

35. R. H. Williams, “Surface defect effects on Schottky barriers,” J. Vac. Sci. Technol. 18(3), 929–936 (1981). [CrossRef]

36. J. Bardeen, “Surface States and Rectification at a Metal Semi-Conductor Contact,” Phys. Rev. 71(10), 717–727 (1947). [CrossRef]

37. H. L. Mosbacker, Y. M. Strzhemechny, B. D. White, P. E. Smith, D. C. Look, D. C. Reynolds, C. W. Litton, and L. J. Brillson, “Role of near-surface states in ohmic-Schottky conversion of Au contacts to ZnO,” Appl. Phys. Lett. 87(1), 012102 (2005). [CrossRef]

38. W. Hu, X. Chen, F. Yin, Z. Quan, Z. Ye, X. Hu, Z. Li, and W. Lu, “Analysis of temperature dependence of dark current mechanisms for long-wavelength HgCdTe photovoltaic infrared detectors,” J. Appl. Phys. 105(10), 104502 (2009). [CrossRef]

39. S. A. Maier, “Plasmonics: fundamentals and applications,” (Springer, 2007), Chap. 2.

Material	Region	Thickness (nm)	P (µm)	Operating wavelength (µm)	Resonance peak (µm)
InAs	Dielectric layer (d₁)	392	0.5	1.0 ∼ 3.0	2.14
	Au film layer (d₂)	4
	Absorber layer (d₃)	100
InSb	Dielectric layer (d₁)	890	1.2	3.5 ∼ 5.5	4.70
	Au film layer (d₂)	5
	Absorber layer (d₃)	300
InAs/GaSb	Dielectric layer (d₁)	890	1.2	3.5 ∼ 5.5	4.46
	Au film layer (d₂)	5
	Absorber layer (d₃)	300
InAs/InAsSb	Dielectric layer (d₁)	1296	1.8	8.0 ∼ 11.0	8.22
	Au film layer (d₂)	2
	Absorber layer (d₃)	500
HgCdTe	Dielectric layer (d₁)	1296	1.8	8.0 ∼ 11.0	8.73
	Au film layer (d₂)	2
	Absorber layer (d₃)	500

Material	P (µm)	D (µm)	h₁ (µm)	h₂ (µm)	h₃ (µm)	dl (nm)	tan (θ)
InAs	0.5	0.1	0.05	0.09	0.16	4	10
InSb	0.9	0.3	0.10	0.17	0.43	5	10
InAs/GaSb	0.9	0.3	0.10	0.17	0.43	5	10
InAs/InAsSb	1.8	0.5	0.20	0.55	1.20	2	10
HgCdTe	1.8	0.5	0.20	0.60	1.30	2	15

Material	Region	Thickness (nm)	P (µm)	Operating wavelength (µm)	Resonance peak (µm)
InAs	Dielectric layer (d₁)	392	0.5	1.0 ∼ 3.0	2.14
	Au film layer (d₂)	4
	Absorber layer (d₃)	100
InSb	Dielectric layer (d₁)	890	1.2	3.5 ∼ 5.5	4.70
	Au film layer (d₂)	5
	Absorber layer (d₃)	300
InAs/GaSb	Dielectric layer (d₁)	890	1.2	3.5 ∼ 5.5	4.46
	Au film layer (d₂)	5
	Absorber layer (d₃)	300
InAs/InAsSb	Dielectric layer (d₁)	1296	1.8	8.0 ∼ 11.0	8.22
	Au film layer (d₂)	2
	Absorber layer (d₃)	500
HgCdTe	Dielectric layer (d₁)	1296	1.8	8.0 ∼ 11.0	8.73
	Au film layer (d₂)	2
	Absorber layer (d₃)	500

Material	P (µm)	D (µm)	h₁ (µm)	h₂ (µm)	h₃ (µm)	dl (nm)	tan (θ)
InAs	0.5	0.1	0.05	0.09	0.16	4	10
InSb	0.9	0.3	0.10	0.17	0.43	5	10
InAs/GaSb	0.9	0.3	0.10	0.17	0.43	5	10
InAs/InAsSb	1.8	0.5	0.20	0.55	1.20	2	10
HgCdTe	1.8	0.5	0.20	0.60	1.30	2	15

Skin effect photon-trapping enhancement in infrared photodiodes

Abstract

1. Introduction

2. One-dimensional simplified model of the skin effect photon-trapping enhancement

3. Results and discussion

4. Conclusion

Funding

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (6)

Tables (2)

Equations (39)

Optics Express