Investigation of Low Frequency Noise-current Correlation for the InAs/GaSb T2SL Long-wavelength Infrared Detector

In this paper, a mesa-type 256×8 long-wavelength infrared detector is prepared by using InAs/GaSb type-II superlattice material with double barrieres structure. the area of each pixel is 25 × 25 μm 2 . The cut-off wavelength and dark current density of the detector at -0.05 V bias with liquid nitrogen temperature is 11.5 μm and 4.1 × 10 -4 A/cm 2 , respectively. The power spectrum of low-frequency noise ( 1/f noise) at different temperatures have also been fitted by the Hooge model, and the correlations with dark current are extracted subsequently. The results shown that the 1/f noise of the detector is mainly caused by the generation-recombination current at a low reverse bias, however, when the reverse bias is high, the 1/f noise should be expressed by the sum of I gr noise and I btb noise which is ignored in the previous research . The 1/f noise-current correlation assessed in this work can provide insights into the low frequency noise characteristics of long-wavelength T2SL InAs/GaSb detectors, and allow for a better understanding of the main source of low-frequency noise. revise bias is low, the total 1/f noise for device can be expressed by I gr noise. However, when the revise bias is large, the total 1/f noise is indeed related to I btb and can be expressed by the sum of I gr noise and I btb noise. The findings in this study may guide us to reduce the device noise and improve the signal-to-noise ratio of the detector.


Introduction
Since Smith and Mailhiot proposed the possibility of superlattice in the last century [1], because of the advantage of low auger recombination rate, low tunneling current, flexible band gap engineering, and high uniformity [2], InAs/GaSb type-II superlattice (T2SL) has been developed into an important material system for long-wavelength infrared detection. For a InAs/GaSb T2SL detector, electrical noise, as an important merit, is always used to define the signal-to-noise ratio and determine the "true" detectivity, which includes frequency-independent shot noise, thermal noise and frequency-dependent generate-recombination (g-r) noise, 1/f noise.
In general, the 1/f noise is considered as the major influence of device performance, although many studies have been done before [3][4][5][6][7][8][9], it still has no precise or general physical model to perform in infrared device noise analysis. Baile Chen et al. studied the origin of 1/f noise in Hg1-xCdxTe detectors and founded that the 1/f noise mainly comes from diffusion current (Idiff), generationrecombination current (Igr), and shunt current (Ishunt) [10]. However, different from the way of MCT changing the material composition, T2SL engineers its effective band gap by adjusting the thickness of layers. Therefore, the mini energy band of T2SL is much more complex and the role of band-toband tunneling current (Ibtb) in the process of noise generation should not been ignored. For this reason, we would like to understand whether the 1/f noise is related to band-to-band tunneling current, so that we can improve the performance of InAs/GaSb detectors at low frequency.
In this paper, system work has been done to analysis the noise characteristic of InAs/GaSb T2SL long-wavelength infrared detector. we simulated the dark current dates at liquid nitrogen temperature with different biases to get the main parameters related to dark current firstly. Then we optimized these parameters through bias-dependence dark current fitting at variable temperatures. Finally, the noise coefficient of different dark currents at different experimental conditions are performed based on Hooge's model.

Device and Measurements
In this experiment, a double barrier structure was used. The specific details have been introduced in the previous article [11]. Compared with single barrier structure, the structure can reduce Shockley-Read-Hall processes in the depletion region, and restrain the movement of majority carriers to low the diffusion dark currents more effectively. [12] The epitaxial material was grown biased on a 3-inch n-type GaSb (100) substrate by a solid source molecular beam epitaxy system. The format of the detector arrays is 256×8 and the area of each pixel is 25×25 μm 2 . For further electrical characterization, the detector was mounted into a liquid-nitrogen-cooled Dewar, the spectral response was tested by a Fourier transform infrared spectrometer, the dark current of the detector was tested by 6430 Semiconductor Analyzer, and the low frequency noise of the detector was measured by FS-PRO Dynamic Signal Analyzer. As shown in Fig.1, the 100% cut-off wavelength of the device is about 11.5 μm, which indicates the Eg of the detector is about 0.109 eV at a liquid nitrogen temperature.

Results and discussion
At present, 1/f noise is recognized to be sensitive to the material growth quality and the passivation process of device [13], which will introduce some surface states or impurity defects to a certain extent. However, there is no a universal model to forecast the exact 1/f noise value for a given detector. In the 1/f noise research, the most usual method which is also applied in this study is the Hooge model [14], by this model, the individual contribution of each dark current to the total 1/f noise can be expressed as the following formula where (f) means the total 1/f noise power special density (PSD), Ik is the k-component of the dark currents that have contribution to the total PSD. αk and βk are the noise coefficient and the current exponent of k-component, respectively.

I The simulation of dark current
Before studying the dependences of 1/f noise and dark currents, different kinds of dark current should be decomposed firstly. Usually, the dark current of infrared photodetectors is composed of the following five components: band-to-band tunneling current, trap-assisted tunneling current (Itat), generation-recombination current, diffusion current and surface leakage current [15]. It is worth mentioning that, in this report, there was no surface leakage current component was found through the fabrication of detectors with different perimeter-area-ratios (P/A), as shown in Fig.2. Based on the expression of each dark current component we can find that, Idiff has a liner relation with 1 , Igr is positively related to 1 2 while Itat and Ibtb are temperature independent. Therefore, according to the relationship between the dark current of detector and the temperature, the activation energy of the detector can be calculated. Thereby, it is possible to analyze which kind of the dark current in the detector is the main mechanism in a specific temperature range.
As shown in Fig.3, the dark currents were obtained at the temperature of 40 K to 200 K with the bias voltage of -0.05 V and -0.5 V. For fig. 3(a) V=-0.05 V, it indicates an active energy about 0.0478 eV, about half of the bandgap energy, when the temperature below to 60 K. It also demonstrates that the main mechanism of the dark current is the generation-recombination current. As the temperature rises, the diffusion current component increases gradually and the detector becomes diffusion-limited from 140 K onward. But for fig. 3(b) V=-0.5 V, when the temperature is lower than 60 K, the active energy is close to 0 eV which demonstrates that the tunneling current is playing a key role of the dark current in this temperature range. However, when the temperature increases to 120 K, the diffusion current is coming to work with an active energy about 0.1073 eV. In conclusion, the diffusion current is the dominant current at high temperature whether it stands at low or high reverse bias. In order to have an in-depth understanding of the influence of different dark currents on the overall current at different measure conditions, we simulated the dark currents at different temperatures using the expressions in the Ref. 15 with the bias voltage between -0.01 V to -0.5 V. Fig.4 shows the experimental and simulated dark current with the conventional photodetector theory model at 80 K, it can be seen from the picture, the model established by us can fit the experimental data well. The values of partial parameters used are shown in table.1. The dark current density at 80 K and -0.05 V is only 4.1×10 -4 A/cm 2 which is considerably lower and indicates an extremely high performance. When the reverse bias is -0.3~0 V, the dominant mechanism of dark current is Igr, which is consistent with the previous fitting results of dark currents under variable temperature at -0.05 V. On the other hand, when the revise bias is higher than -0.3 V, Ibtb comes to be the main dark current. The inset pictures express that the simulation of total dark currents corresponding well to the measured results at all temperatures, which lays a foundation for the following noise analysis. Fig. 4 Experimental and simulated dark current with the conventional photodetector theory model at 80 K, the inset is the temperature-dependence dark current fitting at -0.5 V and -0.05 V.  Fig. 5 shows the noise PSD of the InAs/GaSb T2SL infrared detector at the reverse bias of -0.05 V and the temperature range of 80 K to 200 K. When the frequency is lower than 10 4 Hz, the noise shows a phenomenon that is inversely proportional to the frequency, called 1/f noise. When the frequency increases to 10 4~1 0 6 Hz, the noise becomes almost frequency-independent, this is the result of white noise which generated by the random thermal motion of charge carriers [16]. It is also worth to know that as the temperature elevates, the value of the turning frequency is also rising due to the 1/f noise covers the effects of white noise. There was no G-R noise was depicted in the spectral of noise power density curve which indicated the good quality of our material growth [17]. On the other hand, at 200 K temperature, the noise value at 1Hz is about 1×10 17 A 2 /Hz, which is relatively lower at high temperature. Previous study has shown that diffusion current has negligible impact on 1/f noise [18], as the dominate dark current in low bias and high bias are Igr and Ibtb, respectively. Thus, the conventional Igr and Ibtb are utilized to characterize the temperature dependence of noise PSD, the current exponents, βgr and βbtb, are set to 2 and 1, respectively.

II The noise power spectral density
The simulation results show that, at low reverse bias of V=-0.05 V, 1/f noise is generated entirely from generation and recombination currents in all temperature ranges. But for high reverse bias of V=-0.5 V, when the temperature is lower than about 120 K, band-to-band tunneling current is the main noise contributor with the αbtb of 3.4×10 -14 . As the temperature rises, the noise related to generation and recombination current becomes more and more important and plays a leading role when temperature is higher than 150 K. It worth to know, the values of αgr for the high and low revise biases are different, they are 7×10 -8 and 2×10 -8 , respectively.
Consequently, the total 1/f noise for device at low reverse bias V=-0.05 V with temperature T and frequency f can be expressed by the sum of Igr noise: On the other hand, the total 1/f noise for device at high reverse bias V=-0.5 V should be expressed by the sum of Igr noise and Ibtb noise Equations (2) and (3) conclude the relationship between dark current and 1/f noise in InAs/GaSb T2SL detectors at different reverse biases with various operation temperature, which would provide a useful guidance to improve the performance of InAs/GaSb T2SL device especially for the 1/f noise reducing. Fig.6 The measurements and fitting of PSD at different temperatures with reverse bias of (a)-0.05V and (b)-0.5V

Conclusion
In this work, the low frequency noise and dark current with various temperature and bias of InAs/GaSb T2SL infrared detector has been studied. There was no G-R noise was funded in our research which indicated the good growth quality of our material. It was also indicated that when revise bias is low, the total 1/f noise for device can be expressed by Igr noise. However, when the revise bias is large, the total 1/f noise is indeed related to Ibtb and can be expressed by the sum of Igr noise and Ibtb noise. The findings in this study may guide us to reduce the device noise and improve the signal-tonoise ratio of the detector.