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Abstract
In this paper, low frequency noise and dark current correlation is investigated as a function of reverse bias and temperature for short-wave infrared (SWIR), mid-wave infrared (MWIR), and long-wave infrared (LWIR) HgCdTe homo-junction photodetectors. Modelling of dark current-voltage characteristics shows that the detectors have ohmic-behavior under small reverse bias, thus enabling further analysis of 1/f noise-current dependences with the empirical square-law relation (SI ∼ I2) at different temperature regions. It is found that for the SWIR and MWIR devices, the total 1/f noise spectral density at arbitrary temperatures can be modelled by the sum of shunt and generation-recombination noise as ${S_I}({T,\; f} )= [{{\alpha_{SH}}I_{SH}^2(T )+ {\alpha_{G - R}}I_{G - R}^2(T )} ]/f$, with no contribution from the diffusion component observed. On the other hand, for the LWIR device the diffusion component induced 1/f noise that cannot be overlooked in high temperature regions, and a 1/f noise-current correlation of ${S_I}({T,\; f} )= \{{{\alpha_s}[{I_{DIFF}^2(T )+ I_{G - R}^2(T )} ]+ {\alpha_{SH}}I_{SH}^2(T )} \}/f$ is proposed, with a shared noise coefficient of αs ≅ 1 × 10−9 which is close to that calculated for shunt noise. The 1/f noise-current correlation established in this work can provide a powerful tool to study the low frequency noise characteristics in HgCdTe-based photodetectors and to help optimizing the “true” detectivity of devices operating at low frequency regime.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Hg1-xCdxTe-based (MCT) infrared detectors and technologies have garnered long-standing interests in application-oriented fields such as night vision, IR sensing and imaging [1–6]. However, MCT infrared detectors and imagers operating at low frequency regime often suffer from the 1/f noise, in which the “true” detectivity is no longer determined by the frequency-independent thermal noise and shot noise, but instead by 1/f noise. It is thus crucial to understand the nature of 1/f noise in order to optimize the performance of detectors at low frequency [7]. Currently, there is no general physical model to accurately describe the 1/f noise in electronic and photonic devices. Charge fluctuation theory proposed by McWhorter states that the 1/f noise originates from the change in the concentration of carriers caused by the exchange of trap and bulk electrons [8]. The first empirical relation to quantitatively account for 1/f noise was suggested by Hooge [9–11]:
where SI is the noise power spectral density, ${\alpha _H}$ is the Hooge parameter, I is the current with the exponent $\beta $ depending on current component, and f is the frequency. Later works on MCT focal-plane arrays (FPAs) indicated that both the systemic and isolated defects associated with 1/f noise could impact the performance of device [12,13]. On the other hand, modeling of dark current in MCT detectors have been well established and understood [12,13]. In detectors with typical p-i-n structure, the dark current can be decomposed into diffusion, generation-recombination, shunt, trap-assisted tunneling and band-to-band tunneling current [14]. These mechanisms could all make observable contribution to 1/f noise according to Hooge’s theory. Ł. Ciura et al. already utilized these models to estimate 1/f noise in InAs/GaSb superlattice (SL) mid-wave infrared detector in a wide range of bias voltages and temperatures [15–17]. R.T. Westerhout et al. recognized that the 1/f noise is strongly correlated to the trap-assisted tunneling current within the mid-wave infrared MCT gated photodiodes [18]. G.M. Williams et al. [11] and X. L. Wu et al. [19] analyzed low frequency noise in MCT diodes by Hooge’s relation and discovered the 1/f noise could be induced by individual component of the device dark current. In addition, deep levels have been thought to be responsible for 1/f noise at higher temperature in mid-wave infrared photodiodes [7,20].In this paper, 1/f noise and dark current correlation in MCT homo-junction detectors operating in SWIR, MWIR and LWIR spectral range are explored systematically. Based on the bias- and temperature-dependent modelling of dark current, the major current contributors to the 1/f noise at different temperature region are investigated, and general expressions for 1/f noise magnitude at arbitrary temperature are proposed.
2. Samples and experimental details
The three MCT detectors studied in this work are based on n+/junction/p homo-junction (Fig. 1). The n+ layer was formed by B+ ion implantation, which would generate abundant Hg interstitials to occupy Hg vacancies forming n-type dopant [21]. By controlling the time of post-annealing, the p-n junction region with various thicknesses can be achieved between p and n+. Details of the material growth and device fabrication have been reported elsewhere [22]. The three detector structures have different Cd composition varied from x = 0.178 to 0.279 and 0.367. The corresponding bandgap energy is 0.38 eV (SWIR), 0.26 eV (MWIR), and 0.12 eV (LWIR), respectively.
For the dark current and low frequency noise measurements, the samples with 20 µm diameter were loaded into a probe station with temperature varied from 77 K to 300 K. The output signals were recorded and analyzed by a semiconductor parametric analyzer for the display of current-bias characteristics and noise-frequency spectra [23–25]. Noise density at 1 Hz were extracted for the analysis of 1/f noise in the rest of this paper.
3. Results and discussions
3.1 Dark current modeling
Before studying the 1/f noise and dark current dependences in these MCT detectors, different components of dark current are decomposed firstly. Table 1 summarizes the main contribution of dark current in typical p-i-n photodetector, i.e., diffusion (IDIFF), generation-recombination (IG-R), shunt (ISH), trap-assisted tunneling (ITAT) and band-to-band tunneling (IBTB) [14,15]. These equations are used for modelling the temperature and bias dependences of dark current in the SWIR, MWIR and LWIR MCT samples.
In the equations for diffusion and generation-recombination, ${n_i}$ is the intrinsic carrier concentration, ${\mu _n}$, ${\mu _p}$, ${\tau _n}$, ${\tau _p}$ are electron and hole mobility or lifetime, respectively, w is the thickness of depletion region which is calculated with an abrupt junction formula $w = \; {({2{\varepsilon_r}{\varepsilon_0}({{V_{bi}} - V} )/({q\cdot {N_{red}}} )} )^{1/2}}$, where ${V_{bi}} = ({K\cdot T/q} )\cdot ln({{N_A}\cdot {N_D}/n_i^2} )$, and ${N_{red}}$ is the reduced carrier concentration equal to ${N_A}\cdot {N_D}/({{N_A} + {N_D}} )$. ${\tau _{G - R}}$ is the generation-recombination lifetime which is a fitting parameter. The ohmic-like shunt current, i.e., surface leakage, is weakly temperature dependent and obeys the Arrhenius relation [15], where ${E_{SH}}$ is the activation energy of the shunt current. For the tunneling currents, the trap energy ${E_T}$ was considered to be half of bandgap energy$\; {E_g}$, while the effective tunneling masses$\; {m_t}$, ${m_b}$ and trap density ${N_T}$ were obtained from the best fitting. The maximum electric field is calculated by ${E_{max}} = {[{2q{N_{red}}({{V_{bi}} - V} )/{\varepsilon_\infty }{\varepsilon_0}} ]^{1/2}}$, and the transition matrix element associated with the trap potential is ${M^2} = {10^{ - 23}}e{V^2}c{m^3}$, which is commonly adopted in infrared detectors [15,26]. The material parameters used for the dark current modelling are summarized in Table 2.
Table 1. Equations used to model the dark current of PIN photodiodes.
Table 2. Material parameters used for the dark current modeling.a
Figure 2 shows the dark current-bias (I-V) characteristics of the MWIR MCT detector sample measured at 77 K, 150 K and 250 K. At 77 K, the shunt component is dominated and the tunneling current have a relatively small contribution to the device total current. It should be noted that due to the imperfection of the cold shield used in the probe station, a small photovoltaic shift (∼0.1 V) is observed in the I-V curve which causes the measured current larger than the calculated one under small reverse bias. On the other hand, when temperature increases to 150 K generation-recombination component dominates, while the trap-assisted tunneling current and band to band tunneling current could be neglected, as shown in Fig. 2(b). As temperature goes up to 250 K, diffusion current comes to be the main ingredient in contrast to the generation-recombination and shunt current, which is drawn in Fig. 2(c). The detailed dark current information with variable temperatures for the three devices were reported in the previous work [22]. It is noted that the dark current of these devices is still higher than Rule 07, which may indicate further optimization of material growth and device process is needed. Furthermore, the temperature-dependent Arrhenius plots of dark current measured from the three MCT samples under -0.2 V are depicted in Fig. 3, with different components calculated by the equations in Table 1. Again, very good agreements between experimental data and calculations are obtained, which consolidates the reliability of different dark current models used in the analysis. As can be seen in Fig. 3, no current component associated with tunneling (TAT or BTB) is apparent in any temperature range, since the bias of interest (-0.2 V) is smaller than the breakdown voltage as shown before in Fig. 2. The transition point from diffusion to G-R current (marked by dashed line) and that from G-R to shunt current (marked by dotted line) both shift to lower temperature with the increase of device detection wavelength, due to the shrinkage of bandgap from 0.38 to 0.12 eV. For the MWIR sample, the shunt current is replaced by G-R component at around 143 K and the diffusion current dominates the junction dark current when temperature is higher than 180 K, which is consistent with the I-V characteristic demonstrated for the MWIR device in Fig. 2(c). Similar transition temperature from G-R to diffusion has been reported for Hg0.7Cd0.3Te MWIR device [27]. For the LWIR device, the shunt component only affects at temperature lower than 100 K, and the junction becomes diffusion-limited from 154 K onward. The lifetime associated with G-R process (${\tau _{G - R}}$) and the activation energy of shunt current (${E_{SH}}$) are extracted from the calculations and shown in Table 3. The reduction of ${\tau _{G - R}}$ from SWIR to LWIR devices may be attributed to the faster generation and recombination of carriers as the device bandgap reduces. Moreover, the relatively small values of ${E_{SH}}$ (25-50 meV) confirm the weak temperature-dependent Arrhenius nature of shunt current in all samples, and the increase of ESH/Eg ratio is due to the decreased device bandgap.
Fig. 2. Dark current-bias characteristics of the MWIR MCT detector at (a) 77 K, (b) 150 K and (c) 250 K. The scattered dots represent experimental data, and the solid curves are fitting with corresponding models listed in Table 1.
Fig. 3. Arrhenius plots of dark current for (a) SWIR (b) MWIR and (c) LWIR MCT infrared detectors measured at -0.2 V. The dashed and dotted lines indicate the transition temperature from diffusion to G-R and from G-R to shunt current, respectively.
Table 3. Parameters extracted from dark current and noise fitting.
3.2 1/f noise and dark current correlation
As mentioned in Eq. (1), the 1/f noise magnitude can be empirically expressed by Hooge’s formula:$\; {S_I} = {\alpha _H}{I^\beta }/f$, where I is the dark current extrapolated to 1 Hz, ${\alpha _H}$ is the noise coefficient and $\beta $ is the exponent pertaining to different current component, which can be obtained by fitting the $\; {S_I}\sim {I^\beta }$ experimental data [33]. For infrared detectors operating in ohmic regime (small bias), $\beta $ is usually equal to 2 for diffusion, G-R and shunt current, while the exponent gets smaller when the detector is tunneling current-limited under high reverse bias [17]. Figure 4 shows the Arrhenius plots of 1/f noise and dark current measured at 1 Hz under -0.2 V for the three MCT samples. In the entire range of temperature, the noise magnitude as a function of temperature can be modelled very well with the relation ${S_I}(T )= {\alpha _H}{I^2}(T )/1\; Hz$ for the SWIR, MWIR and LWIR devices, thus confirming the$\; {S_I}\sim {I^2}$ dependence for all three samples operating in ohmic regime. From Figs. 4(a) and 4(b), it is clear that for both SWIR and MWIR devices the 1/f noise magnitudes follow the same temperature behavior of the corresponding dark current component at low and moderate temperature region. The noise coefficient associated with shunt and G-R component can be estimated by using Eq. (1) and the experimentally measured data: ${\alpha _{SH,G - R}} = {S_I}/I_{SH,G - R}^2(T )$. As summarized in Table 3, for the MWIR device, both ${\alpha _{SH}}$ and ${\alpha _{G - R}}$ are in the order of ∼${10^{ - 6}}$, while for the SWIR sample, ${\alpha _{G - R}}$ is still in the order of ${\sim} {10^{ - 6}}$ and the shunt coefficient increases by two orders of magnitude to ${\alpha _{SH}} = 6 \times {10^{ - 4}}$ due to the smaller shunt current compared with the MWIR sample. However, in the high temperature region where diffusion component dominates the junction current, the noise density does not follow the rapidly increasing trend of the dark current. This lack of noise-current correlation suggests that the 1/f noise in both devices at high temperature is linked to component different from diffusion current, although the dark current is dominated by diffusion component. Indeed, the coefficient related to diffusion noise is estimated as ${\alpha _{DIFF}} = {S_I}/I_{DIFF}^2(T )\cong 1 \times {10^{ - 9}}$, which is much smaller than these coefficients of the G-R current and shunt current induced 1/f noise, making the 1/f noise induced by diffusion current component far below the observable limit. As can be seen in Figs. 4(a) and 4(b), the measured noise data at high temperature region can be fitted very well with the G-R noise: ${S_I}(T )= {\alpha _{G - R}}I_{G - R}^2(T )/1\; Hz$, thus we believe in both SWIR and MWIR device the overall 1/f noise in moderate to high temperature regime are mainly produced by the G-R current component. It is noted that the lack of diffusion-induced 1/f noise was also reported in MWIR photodetectors based on InAs/GaAs type-II superlattice, particularly when the absorber doping level was high [16,34]. Regarding the fundamental reason that 1/f noise of SWIR and MWIR photodetector is not limited by diffusion component, it may be due to the relative larger bandgap of the SWIR and MWIR materials, which significantly reduces the amplitude of stochastic direct band to band generation and recombination process.
Fig. 4. Temperature-dependent Arrhenius plots of dark current and 1/f noise for (a) SWIR (b) MWIR and (c) LWIR MCT infrared detectors under -0.2 V. The scatted square/circles are measured data, while the solid and dashed curves are fitting values using equations in Table 1.
On the other hand, the LWIR device demonstrates different noise-current dependency compared with the SWIR and MWIR counterpart. As shown in Fig. 4(c), while the measured 1/f noise at low and moderate temperature region can be modelled well with the shunt and G-R current component, respectively, the noise magnitudes differ from the values predicted from the G-R current and shunt current in the high temperature region. This observation indicates that the diffusion current cannot be neglected in the total 1/f noise in this LWIR sample. From T∼ 111 K onward, it is found that the measured noise can be modelled with the relation ${S_I}(T )= {\alpha _s}[{I_{DIFF}^2(T )+ I_{G - R}^2(T )} ]/1\; Hz$ to a high accuracy, as indicated by the purple curve in Fig. 4(c). The two current components share a common coefficient of ${\alpha _s} = 1 \times {10^{ - 9}}$, which is very close to that obtained from the shunt current noise modelling (see Table 3). Consequently, the total 1/f noise for SWIR and MWIR detector at arbitrary temperature T and frequency f can be expressed as the sum of G-R and shunt current noise:
whereas for the LWIR device the diffusion noise should be taken into consideration:4. Conclusion
In conclusion, dark current and low frequency noise have been investigated as a function of bias and temperature on MCT n+/junction/p homo-junction photodetectors with three different bandgap energy. Under small reverse bias of -0.2 V, the devices have ohmic-like behavior, and temperature-dependent Arrhenius analysis shows that the junction dark current is dominated by shunt, G-R and diffusion component at low, moderate and high temperature region respectively. In order to establish a quantitative noise-current correlation, the 1/f noise measured at different temperature was modelled by the relation ${S_I}(T )= {\alpha _H}{I^2}(T )/1\; Hz$. For SWIR and MWIR devices, no 1/f noise contribution from diffusion current can be observed, and the total 1/f noise at arbitrary temperature can be predicted by the sum of G-R and shunt current induced noise. For LWIR device, the overall 1/f noise in moderate to high temperature region is governed by diffusion and G-R current induced noise, with a shared noise coefficient of 1 × 10−9 (close to that of shunt current induced noise) which suggests that diffusion component induced noise cannot be ignored in LWIR MCT detector due to very small bandgap. Similar investigation on 1/f noise-tunneling current correlation in higher bias range, which might be useful for MCT-based avalanche photodetector applications, will be remained as a topic for future study.
Funding
ShanghaiTech University (F-0203-16-002); National Key Research and Development Program of China (2019YFB2203400); National Natural Science Foundation of China (61975121); Strategic Priority Research Program of Chinese Academy of Sciences (XDA18010000).
Acknowledgments
Liqi Zhu and Zhuo Deng contributed equally to this work.
Disclosures
The authors declare no conflicts of interest.
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