Utmost response time of long-wave HgCdTe photodetectors operating under zero voltage condition

Abstract

The paper reports on the long-wave infrared HgCdTe detector for utmost short response time operating for unbiased and room temperature condition. The response time was calculated at the level of ~ 220–520 ps for zero bias condition. It was shown that depending on architecture extra series resistance ≤ 20 Ω related to the processing allows to reach response time within the range ~ 220 ps. The highest detectivity of the simulated structure was assessed at the level of ~ 10⁸ Jones assuming immersion.

1 Introduction

Applications requiring frequencies > 1 GHz and operating under zero voltage and room temperatures contribute to the development of the new device architectures (Piotrowski and Rogalski 2007; Rogalski 2011; Wojtas et al. 2012). That trend is also visible in the long-wave (8–12 μm, LWIR) range HgCdTe detectors. Reaching the utmost response time (τ _s ), the detectivity (D ^*) will be reduced without any prospect of the background limited photodetection (BLIP) condition. According to experimental data the LWIR N⁺pP⁺n⁺ based photodetectors with doping and composition gradient layers at particular heterojunction reach response time in several nanoseconds range while designed for non-equilibrium condition and operating under zero voltage and room temperature. Figure 1 presents measured response time for the LWIR multilayer N⁺pP⁺n⁺ detector with proper interfaces at heterojunctions versus voltage with nominal active layer composition, x _Cd  = 0.196 and doping N _A  = 5 × 10¹⁶ cm⁻³ confirming that for zero voltage, τ _s stays within the range 5–10 ns for operating temperature, T ~ 200–300 K. If presented detector is highly biased, response time was assessed at the level of 200 ps (V = − 700 mV) for all analyzed temperatures. Within the range 200–230 K response time saturates for voltages V > − 300 mV while the highest τ _s is reached for biases within the range (50–100 mV). For room temperature operation, the highest response time is reached for V = − 250 mV. The higher temperature the peak value of the response time moves to higher reverse voltages. At the same time, assuming that detector is immersed, those devices exhibit D ^* ~ 10⁹ Jones (Madejczyk et al. 2013; Pawluczyk et al. 2015; Madejczyk et al. 2017).

Fig. 1

Measured response time of the LWIR multilayer HgCdTe N⁺pP⁺n⁺ structure with proper interfaces at heterojunctions versus voltage (nominal active layer x _Cd  = 0.196 and N _A  = 5 × 10¹⁶ cm⁻³)

2 Simulation procedure and results

Our approach to maximize response time in comparison with the three-layer N⁺pP⁺ structure invented and introduced by Elliot et al. for non-equilibrium conditions is lowering of the P⁺ barrier layer by composition gradient within p⁺-n⁺ transition layer (gradient-contact layers) (Ashley and Elliott 1985; Irvine 1992; Elliot et al. 1996). P⁺ barrier composition, x _Cd was reduced to the LWIR absorber’s level, i.e. 0.19. P⁺ barrier composition directly influences detector’s dark current deteriorating detectivity. The nominal HgCdTe multilayer graded gap structure with doping and composition gradients at particular heterojunctions is presented in Fig. 2. The highly doped N _A  = 10¹⁷ cm⁻³ active layer with thickness d = 1 μm was implemented to reach ultrafast detector. Device architecture was changed by composition gradient of the p⁺-n⁺ transition layer within the range x _Cd  = 0.1–0.19. Low frequency resistance was calculated to be at the level of ~ 1.5 Ω for all analyzed structures. Detector structure was simulated with software APSYS by Crosslight Inc. (2016). The photocurrent’s time dependence was simulated based on Li and Dutton model (1991). Theoretical simulations of the ultrafast HgCdTe heterostructures have been performed by numerical solving of Poisson’s and the electron/hole current continuity equations by the Newton-Richardson method. The equations describing the drift-diffusion model are presented in detail in the APSYS manual (2016). The used model assumes electrical and optical properties to include the influence of radiative, Auger, Shockley-Read-Hall (SRH) generation-recombination (GR) mechanisms at any mesh point within the device. Auger GR mechanism was simulated using Casselman and Petersen approximation of parabolic bands and non-degenerate statistics (Casselman and Petersen 1980). Energy bandgap was calculated by Hansen’s paper et al. (1982). The zero bias electron mobility was taken from the formula based on Scott’s paper, where the hole mobility was assumed as 1% of the electron mobility (Scott 1972). Intrinsic concentration’s Cd composition (x _Cd ) and temperature dependence was calculated using Hansen and Schmidt model (1983).

Fig. 2

LWIR HgCdTe structure exhibiting response time, τ _s  < 1 ns for unbiased condition and room temperature operation

Since detector structure is intended to operate at zero bias condition the both band-to-band (BTB) and trap-assisted (TAT) tunneling mechanisms were not included in simulations. An absorption was assumed in active layer region and absorption coefficient was estimated according to Kane model including its composition, doping and temperature dependences. Proper doping and composition grading were introduced to prevent form discontinuities in energy band profiles between contact-absorber (N⁺-p), absorber-barrier (p-P⁺) and finally barrier-contact (P⁺-n⁺) heterojunctions. The detailed parameters taken in modelling of LWIR HgCdTe heterostructures are presented in Table 1.

Table 1 Parameters taken in modelling of LWIR utmost response time of HgCdTe heterostructures

Energy band diagrams for selected p⁺-n⁺ transition layer composition within the range x _Cd  = 0.1–0.19 were presented in Fig. 3a–d.

Fig. 3

Energy band diagram for LWIR HgCdTe structure for short response time for selected p⁺-n⁺ transition layer composition, x _Cd  = 0.1 (a); x _Cd  = 0.12 (b); x _Cd  = 0.15 (c); x _Cd  = 0.19 (d)

Corresponding electric field drop along the simulated LWIR HgCdTe structure for short response time and selected p⁺-n⁺ transition layer composition, x _Cd  = 0.1–0.19 was presented in Fig. 4.

Fig. 4

Electric field drop along LWIR HgCdTe structure for short response time and selected p⁺-n⁺ transition composition, x _Cd  = 0.1–0.19

Response time was derived from photocurrent dependence on time where time for ~ 1/e drop from photocurrent’s maximum value was assessed. Simulated photocurrent versus time was presented in Fig. 5.

Fig. 5

Normalized photocurrent versus time and selected p⁺-n⁺ transition layer composition, x _Cd  = 0.1–0.19

Since detector operates under zero bias, it was assumed that detectivity was limited by thermal Johnson-Nyquist noise and assessed according to the relation:

$$D^{*} = \frac{{n^{2} R_{i} }}{{\left( {4k_{B} T/R_{o} A} \right)^{0.5} }}$$

(1)

where R _i , k _B , R _o , A, n stands for current responsivity, Boltzmann constant, resistance at zero bias, detector’s electrical area and GaAs substrate refractive index respectively. D ^* for immersed detector was assessed at the level of ~ 10⁸ Jones. Figure 6 presents D ^* dependence on p⁺-n⁺ transition layer composition, x _Cd  = 0.1–0.19. D ^* increases nearly three times within analyzed p⁺-n⁺ transition layer composition.

Fig. 6

Detectivity versus p⁺-n⁺ transition layer composition, x _Cd  = 0.1–0.19

Figure 7 presents simulated response time versus p⁺-n⁺ transition layer composition for selected extra series resistance R _Series  = 0–20 Ω. The higher p⁺-n⁺ transition layer composition the shorter response time could be reached τ _s  = 220 ps. Changing x _Cd of the p⁺-n⁺ transition layer the electric field decreases versus x _Cd saturating at the level of ~ 5000 V/cm (see also Fig. 3a–d). The diffusion component of the response time was estimated at the level of ~ 152 ps (active layer N _A  = 10¹⁷ cm⁻³ and d = 1 μm, ambipolar diffusion coefficient, D _a  = 2.73 × 10⁻³ m²/s).

Fig. 7

Simulated response time of the LWIR HgCdTe structure for short response time versus p⁺-n⁺ transition layer composition for selected extra series resistance, R _Series  = 0–20 Ω

For each extra R _Series drastic drop of the τ _s  ~ 500–325 ps is observed within the range x _Cd  ~ 0.1–0.12. Response time exhibits two slope behavior where response time dependence on x _Cd of the p⁺-n⁺ transition layer is nearly linear. That behavior is related to the detector resistance dependence on p⁺-n⁺ transition layer x _Cd composition being correlated with electric field drop on that transition layer.

Only for p⁺-n⁺ transition x _Cd  = 0.1 the response time increases versus extra R _Series within the range 500–520 ps (R _Series  = 0–20 Ω). For p⁺-n⁺ transition x _Cd  > 0.1 the extra series resistance lowers response time and for R _Series  > 6 Ω response time saturates for all analyzed p⁺-n⁺ transition layer compositions what was presented in Fig. 8. Saturation region means that detector net resistance is dominated by detector internal resistance, R _D (R _Series  > R _D ). Below R _Series  < 6 Ω, and p⁺-n⁺ x _Cd  = 0.1 detector resistance R _D  > R _Series meaning that response time depends on R _Series .

Fig. 8

Simulated response time of the LWIR HgCdTe structure for short response time versus extra series resistance for selected p⁺-n⁺ transition layer compositions, x _Cd  = 0.1–0.19

3 Conclusions

Theoretical utmost short response time τ _s  ≤ 520 ps for LWIR HgCdTe structure exhibiting D ^* ~ 10⁸ Jones was presented. That level of detectivity was calculated assuming immersion. Improvement in response time could be achieved by increasing composition of p⁺-n⁺ transition layer, however by optimization of the detector in terms of the response time detectivity deteriorates.