High-performance HgCdTe avalanche photodetector enabled with suppression of band-to-band tunneling effect in mid-wavelength infrared

HgCdTe avalanche photodiodes promise various fascinating applications due to the outstanding capability of detecting weak signals or even single photon. However, the underlying transport mechanisms of diverse dark current components are still unresolved at high reverse bias, thus limiting the development of high-performance devices. Here, we establish an accurate model to demonstrate the competitive mechanism between band-to-band and avalanche dark currents in positive-intrinsic-negative structures. Based on the high consistency between the simulated and measured results, we find that both components jointly dominate overall dark current but with a larger avalanche current. This breaks the conventional cognition that band-to-band dark current contributes the majority. With the guidance, we reconstruct an optimized device and achieve gain 1876 (6153) and dark current 10−10 (10−9) A at bias −10 (−10.5) V, respectively. Comparisons of dark current and gain with reported single-element devices further confirm the outstanding performance of our device.


INTRODUCTION
Mid-wavelength infrared (MWIR), one of three transparent atmospheric windows, has a unique advantage in full-time and allweather space-to-ground communication applications due to its excellent capacities of small attenuation, broad bandwidth, and strong anti-interference from the background radiation of sun 1,2 . Besides, various characteristic spectra of molecules locate around the MWIR regime. Therefore, the effective and sensitive detection of MWIR photons plays a crucial role in remote sensing, national defense, and other areas [3][4][5][6] . HgCdTe-based avalanche photodetectors (APDs) are the most promising detection candidate due to the outstanding merits in the tunable bandgap, high sensitivity, low power consumption, small size, and light weight 7,8 . Compared with complex configurations like separate absorption multiplication 9 or n-Barrier-n 10 in the detection of ultra-weak [11][12][13] or even single photon [14][15][16] , positive-intrinsic-negative (PIN) structure has proved its outstanding merits in aspects of easy fabrication, high reproducibility, and excellent flexibility in manufacturing focal plane array 3,[17][18][19][20][21] . With its great potentials, PIN HgCdTe APD has attracted much attention and found various applications, such as three-dimensional laser radar and deep space detection.
Dark current and gain are a set of key indicators that always need trade-offs in practical implementations of APDs 19,22 . Researchers have proposed various mechanisms and configurations to enhance the gain and suppress the overall dark current. For instance, Kopytko et al. successfully managed the unfavorable tunneling process by controlling the doping concentration of multiplication layer 23 . Li et al. utilized the guard ring structure to break the surface local electric field to prevent the edge prebreakdown effect and reduce the excess noise factor 24 . Besides, Singh et al. manufactured an MWIR APD with high gain based on band-to-band tunneling (BBT) mechanism at high bias 25 . However, current HgCdTe APDs always operate at linear mode, in which larger bias voltage always indicates high gain while dark current would also inevitably increase. At high bias, especially approaching breakdown point, the underlying physics that governs diverse contributing dark current components is still unclear, especially the competition between the BBT and avalanche currents, which results in the obvious deviations between the simulations and experiments and thus limiting the realization of extremeperformance single-photon avalanche detectors.
In this paper, we establish an accurate model to clarify the underlying current mechanisms of PIN HgCdTe APDs. With the excellent agreement between measured and simulated results, we explicitly demonstrate the competition between the BBT and avalanche currents and reconstruct a structure with optimized thickness and concentrations. Voltage amplification measurement is also built to characterize the blackbody responsivity and photocurrent of the designed detector at high bias. Finally, we compare the gain and dark current with the reported ones to further illustrate the superiorities of our device and confirm the flexibility and validity of our model to achieve high-performance photodetectors. Our work provides a route towards achieving perfect optoelectronic devices and may find various applications in the relatively immature but very promising MWIR regime.

RESULTS
Energy band structure and dark current analysis Three-dimensional and cross-section views of the planar PIN APD are shown in Fig. 1a, b, respectively. The device is designed to operate in MWIR based on Hg 1−x Cd x Te material. Cd component 1 fraction is 0.3. The device simulations are conducted with commercial software-Sentaurus technology computer-aided design. Different physical models of the currents are adopted to perform the simulation. Details can be found in the "Methods" section.
We start with the analysis of the energy bandstructure of conventional planar PIN HgCeTe APD. Without any bias, the interdiffusion of electron and hole emerge at the interface of pn − junction and lead to the bending of energy band and form a potential difference, i.e., the built-in electric field. For the interface at n − n + junction, the difference of doping concentration also results in the energy difference and we define the electric field here as the initial electric field. Once applying a reverse bias, the potential difference between n − layer and p layer increases. At low bias, the n − layer is not fully depleted. The built-in electric field and the initial electric field both exist as shown in Fig. 1c. However, at high voltage, the potential difference further increases, and the build-in electric field would overlap the initial electric field until the width of the depletion region is approximately the same as the thickness of n − layer, which is shown in Fig. 1d. The carriers' multiplication occurs as the width of the depletion region is greater than the mean free path between the two ionizing impacts, hence leading to the avalanche effect.
In order to achieve a high-performance avalanche structure in Fig. 1a, the simulation results from the developed accurate model are compared with the experiments to validate the model in predicting the current behaviors. As shown in Fig. 2a, solid lines and triangle points which respectively represent simulated and measured results of dark current and photocurrent agree well with each other, revealing the availability to simulate the real device. The doping concentration and thickness of n − layer are 5 × 10 14 cm −3 and 2 μm in simulation, which is consistent with the measured result. High consistency between simulated and measured results indicates the accuracy of the proposed model. Based on our model, the current components as a function of the bias voltage are illustrated in Fig. 2b. It can be seen that Shockley-Read-Hall (SRH) and TAT currents are the main mechanism before the threshold voltage, which is defined as the voltage where avalanche multiplication current is larger than SRH recombination. It's worth mentioning that BBT and avalanche effect dominates the current transport after threshold voltage. However, the avalanche effect is greater than the BBT effect, which is in contradiction with the conventional structures. The abnormally large avalanche current with low doping concentration 5 × 10 14 cm −3 originates from two aspects. The minority carriers-electrons that are drifted to n + region under reverse bias transport through the multiplication layer and form avalanche current. For n − layer with low doping concentration, electric field intensities around pn − and n − n + junction are comparable. For certain concentrations, the electric field of n − n + junction is even larger than that of pn − junction. With external bias, both electric fields at the interfaces contribute to the avalanche multiplication. Besides, electrons tunneling from the valance band to the conductive band also participate in the avalanche process and enhance the avalanche current. It is also worth mentioning that low doping concentration would lead to the widening of effective bandgap and do benefit to the suppression of the tunneling electrons. A thorough investigation of the competitive mechanism between avalanche and BBT dark current under high bias plays a key role in the realization of high-performance HgCdTe APDs. Besides, Auger and radiative recombination have less effect on total dark current due to their strong temperature dependence.
Since the n − layer is the multiplication layer of the avalanche detector, its geometry and doping play a key role in the device performance at different biases. Figure 2c shows the I-V characteristics with various doping concentrations. It can be seen that the doping concentration of 5 × 10 14 cm −3 has the lowest overall dark current among the range from 1 × 10 14 to 1 × 10 16 cm −3 under high bias. The phenomenon that the dark current level is lower than those with concentrations of 1 × 10 14 and 1 × 10 15 cm −3 can be attributed to the fact that the dark current is dominated by avalanche current under high bias and the electric field determines the avalanche multiplication. The dark current with a doping concentration of 5 × 10 14 cm −3 at high bias is the lowest. Simulation results of other doping concentrations can be found in Supplementary Note 1. In order to illustrate this, the electric field is plotted in the inset of Fig. 2c. It can be seen that the electric field of the doping concentration 1 × 10 14 cm −3 is larger than those of 5 × 10 14 and 1 × 10 15 cm −3 . Besides, the current of the doping concentration of 1 × 10 15 cm −3 is larger than that of 5 × 10 14 cm −3 due to the joint contributions of the electric field at pn − and n − n + interfaces. Doping concentration also imposes a significant effect on the BBT effect and the enhancement of BBT effect dominates the dramatic increase of dark current. Besides, the excessive doping concentrations result in the junction area moving to p layer, thereby invalidating the function of n − layer. We also investigate the current dependence on the thickness of n − layer through simulating the I-V curves as shown in Fig. 2d. The dominating transport mechanisms of dark current mainly depend on the doping carriers' concentration. The SRH and TAT dark current dominate the dark current at low bias, while BBT and avalanche components occupy the majority at high bias. However, the dominating dark current components are not changed with a thickness of n − layer. The n − layer acts as a depletion area and its thickness is directly related to the built electric field distributions. With this consideration, the threshold voltage increases with the thickness as shown in Fig. 2d. It is also worth noting that the thickness of n − layer also affects the quantum efficiency and response time. Therefore, an appropriate thickness is a key to achieving high-performance devices. Figure 3a exhibits the electric field with various doping concentrations as a function of the reverse bias. The electric field increases as the reverse bias increases and gradually saturates at a high bias. Similarly, the generations of BBT and impact ionization with various doping concentrations as a function of bias are illustrated in Fig. 3b, c, respectively. Notably, the BBT generation is more sensitive to the doping concentration compared with that of impact ionization due to the fact that higher doping concentration results in the narrower effective bandgap and the increase of BBT generation is more significant than that of impact ionization as the voltage increases. The doping concentration determines the critical voltage at which the BBT generation takes effect in the device, which is in consistent with the discussion above. The BBT current is the main reason for the increase of dark current in the detector with a high doping concentration in nlayer. However, for impact ionization, the saturation with reverse bias is more obvious as shown in Fig. 3c. Afterward, the impact ionization generation of the doping concentration of 1 × 10 14 cm −3 is higher than that of 1 × 10 15 cm −3 . The impact ionization with different doping concentrations agrees well with the above discussion for dark current. In order to have a direct evaluation and further clarify the influence of the doping concentration of n − layer on the device performance, the electric field, BBT and impact ionization generations as a function of doping concentration at −11 V are plotted in Fig. 3d. The electric field, BBT, and impact ionization generations are proportional to doping concentration as the doping concentration is above 1 × 10 15 cm −3 . It is should be noted that the impact of ionization generation is larger than BBT generation. For doping concentration below 1 × 10 15 cm −3 , both the BBT and impact ionization generations decrease as the doping concentration increases. However, the difference between BBT and impact ionization generation increases with the doping concentration. For doping concentration above 1 × 10 15 cm −3 , the BBT and impact ionization increase with the doping concentration but the difference between them is almost unchanged. As discussed above, the dominating mechanisms under high bias voltage are the joint BBT and avalanche ionization effects and the excessive doping concentration would cause an excessive dark current. Therefore, the doping concentration of nlayer needs to be strictly controlled below 1 × 10 15 cm −3 in the device fabrication.

Realization of high-performance HgCdTe APD
According to the optimized structural parameters, avalanche photodiodes are manufactured. The fabrication process is shown in Fig. 4a and a detailed description can be found in the "Methods" section. An optical image of the fabricated HgCdTe avalanche device is shown in Fig. 4b. Conventional measurement setup with current pre-amplifier (SR570, Stanford Inc.) no longer meets the demand of measurement at high reverse bias over 5 V adopted in our previous work 26 . In order to obtain the blackbody responsivity and photocurrent under higher bias, we further implement a voltage amplification characterization system as  shown in Fig. 4c. A detailed description of the measurement setup is illustrated in the "Methods" section. As shown in Fig. 4d, the blackbody responsivity illustrates an exponential evolution with increasing the bias voltage, which indicates that a large gain is achieved at a high bias. Besides, the spectral responses of our device and background are measured with a Fourier-transform infrared spectroscope (Nicolet 6700) to calculate the normalized spectral response of the APD in Fig. 4d. It can be seen that the cutoff wavelength of our device is approximately 5 μm. It is worth noting that the dip at about 3 μm is due to the absorptions of carbon dioxide in the atmosphere when capturing the spectrum. The experimental details can be found in Supplementary Note 2. With the normalized spectral response, the g factor is calculated as 5.7018. Together with the blackbody detectivity, D bb * , the peak photodetectivity D * is achieved as 2 × 10 14 cm Hz 1/2 W −1 at the bias voltage −7.1 V. The calculation details can be found in Supplementary Note 3. Figure 5a exhibits the experimental results of the dark current of our optimized structure. In order to have a direct evaluation of our device, reported results of single-element devices from other groups are included for comparison. The dark current of our device is 10 −10 -10 −9 A under high bias, which in others are larger than 10 −8 A at high bias 17,19,20,26 . Although the dark current of some devices is slightly lower than ours at lower bias, the gain is lower 27 . Notably, we mainly focus on the device performance under high bias. Since the larger dark current component in our device at high reverse bias is clarified as impact ionization, which is different from cases in reported works, lower overall dark current is achieved with the successful depression of BBT current.
Avalanche gain as another important indicator to characterize the performance of APDs, it can be calculated by G = [I ph (V) − I dark (V)]/I ph (V = 0) − I dark (V = 0) at the certain temperature. Figure  5b shows the experimental results of the avalanche gain as a function of reverse bias. Most of the reported avalanche devices operate in linear mode, whereas the distinction between linear mode and Geiger mode generally corresponds to the sudden change of gain. To avoid potential confusion, here we utilize two linear fittings to illustrate the evolution of the gain curve at different voltage ranges: below -6 V and between −6 and −10 V. The gain reaches 40, 1876, and 6153 at bias −6, −10, and −10.5 V, respectively. We think the voltage node around −10 V is the critical voltage of linear mode and Geiger mode. Remarkably, the gain of our device is much larger than those reported in the literature under high voltage 17,[27][28][29][30] . Together with the excellent agreements between simulations and experiments, the measured extreme low dark current and high avalanche gain of the optimized device confirm the effectiveness and flexibility in designing high-performance planar PIN HgCdTe APDs.

DISCUSSION
Single-photon detection is the detection limit in the dimension of photon quantity. Considering the unique advantages of MWIR in transmitting through the atmosphere without loss and labeling various materials with spectral fingerprints of molecules based on their characteristic vibrations, efficient and sensitive detection of weak MWIR photons is of great significance in these applications. In this work, we establish a model to clarify the dominating dark current mechanism of the PIN HgCdTe APD at high bias voltages. We find that the ionization avalanche effect and BBT effect both contribute to the overall dark current while the ionization avalanche effect is larger. This breaks the conventional cognition that band-to-band tunneling current prevails in the current competition at high bias. Based on this model with which excellent agreement between simulation and experiment is realized, we optimize the geometric and doping parameters of avalanche structure to achieve high-performance single-photon detectors. With the built voltage amplification characterization setup, we finally achieve gain 1876 (6153) and dark current 10 −10 (10 −9 ) A @-10 (−10.5) V, respectively. The comparisons with reported works further confirm the superiority of our work. The device we proposed represents a firm step forward towards highperformance photodetectors with extremely low dark current and high avalanche gain. We hope it can do benefit the development of high-performance optoelectronic devices and find applications in ultra-weak photons detection in the relatively immature MWIR regime.

Simulation model
The carrier transport is dominated by the drift-diffusion effect and it can be solved by continuity equations with charge conservation. Besides, SRH recombination 31 , trap assisted tunneling (TAT) 32 , BBT 33 , avalanche generation 34 , Auger 35 , and radiative recombination 36 models are included to perform the numerical calculations. Equations of each model 77 K are listed in Table 1. The corresponding parameters are as follow: J n ! and J p ! are the electron and hole current density. n and p are the electron and hole density. R net,n . and R net,p are the electron and hole net recombination rate, τ n , and τ p are the electron and hole lifetime, and E trap is the difference between the defect level and intrinsic level. α n,p . is the ionization coefficient, v n,p , is the velocity, and A 1 , A 7 , a and b are all dependent on the temperature T.

Fabrication process
The fabrication process of the optimized structure under our model's guidance is shown in Fig. 4a  CdTe passivation film was deposited in sequence. Afterward, the Au electrode was deposited after lithography and etching processes, and Ohmic contact was formed after the annealing process. Finally, we deposited the In (indium) bumps for the flip-chip bonding with the readout circuit. The measured doping concentration of n + layer and n − layer is 1 × 10 17 and 5 × 10 14 cm −3 , and the thicknesses of n + and n − layer are 1.5 and 2 μm, respectively. The measured parameters are all included in the simulations.

Measurement setup
Among the voltage amplification measurement setup, the APD is encapsulated in a continuous flow liquid nitrogen Dewar. Keithley 236 is used as a voltage source, and the signal generated in the APD is obtained by the lock-in amplifier after it is amplified by the voltage pre-amplifier (SR560, Stanford Inc.). Here, the load resistance is used to ensure that the alternating current (AC) circuit operates and matches the impedance of the device under test. According to AC equivalence analysis, the photocurrent can be calculated by I ph = S/G AMP /(R APD //R load ), in which S is the signals measured by a lock-in amplifier, G AMP is the amplification of SR560 preamplifier, and R APD is the dynamic resistance of APD under illumination. The black responsivity can be calculated with R bb = I ph /P bb , where P bb is the blackbody power. The radiation power of the blackbody is constant at a fixed operating temperature.