Open Access
Add to BibSonomy
Abstract
In this paper, we investigate the temperature sensitivity of gain and breakdown voltage of detectors based on cycling excitation process (CEP), an internal signal amplification mechanism found in amorphous silicon (a-Si). Changes in gain and breakdown voltage with temperature can result in pixel-to-pixel signal variation in a focal plane array and variations in photon detection efficiency for single photon detectors. We have demonstrated athermalized CEP detectors with their gain and breakdown voltage being nearly temperature independent from 200 K to 350 K, covering the temperature range for practical applications. The device appears to be more thermally stable than avalanche photodetectors (APDs) with different gain media such as Si, InP, InAlAs, etc. The excellent thermal stability of CEP detectors is attributed to the field-enhanced tunneling process for excitation of localized carriers into the mobile bands, which dominates over the phonon excitation process.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
For optoelectronic systems such as sensing, imaging, LiDAR, and quantum communications that require high sensitivity, detectors with intrinsic amplification mechanisms are desirable. Avalanche photodetector (APD) has been a popular choice in these scenarios because the impact ionization mechanism amplifies the photocurrent via carrier multiplication to enhance sensitivity. The multiplication factor of APDs increases with the bias voltage and the devices can transition from analog mode to Geiger mode to achieve single photon sensitivity as single-photon avalanche diodes (SPADs) when biased above the breakdown voltage [1–6]. However, the intrinsic properties of impact ionization can cause some shortcomings for APDs and SPADs. The stochastic nature of the carrier multiplication process has generally low energy efficiency (i.e., requires high voltage bias) and produces high excess noise especially in the high gain regime [7–9]. When operated in Geiger mode, the gain fluctuations result in variations in the output response, lowering the dynamic range or photon number resolving capabilities and the photon detection efficiency (PDE). When SPADs are integrated into an array with readout integrated circuits (ROICs) for LiDAR, imaging, or sensing systems, another key consideration is temperature sensitivity. Temperature variations due to the ambient or local environment can cause gain fluctuations and fixed pattern noise (FPN) for APDs and PDE fluctuations for SPADs due to the temperature sensitivity of breakdown voltage [10,11].
To overcome the problems of high excess noise and large gain fluctuation, a new signal amplification mechanism, cycling excitation process (CEP), has been proposed and demonstrated [12]. CEP is an internal photocurrent amplification mechanism found to be most prominent in certain disordered materials such as amorphous Si (a-Si) [13–16]. Under a high electric field, these materials display a strong carrier multiplication effect via Auger excitation of e-h pairs to the localized states in the bandtails of conduction and valence bands. Such carrier excitation process can be more efficient than conventional impact ionization because the localized carriers involved in the process relaxes the k-selection rule, the main efficiency limiting factor [17,18]. However, for those localized electrons (holes) to contribute to the photocurrent and to gain kinetic energy from the applied field to sustain the cycling excitation process, these localized carriers need to be excited to the mobile bands. The excitation process of the localized carriers can then play the role of internal feedback to suppress gain fluctuations, thus giving rise to low excess noise in both analog mode and Geiger mode [13,14]. The previous studies inferred that the low excess noise of CEP detectors was attributed to electron-phonon coupling, considering CEP as a phonon mediated process [13,14]. In this framework, one key question is how CEP detectors respond to temperature changes. As stated before, temperature sensitivity of gain and breakdown voltage can become a significant concern for focal plane arrays or single photon detector arrays.
In this paper, we investigate the temperature sensitivity of a-Si CEP detectors and the feasibility of athermalized CEP detectors over a wide temperature range for practical applications. The device in our study utilizes a thin (35–40 nm) a-Si layer as the gain medium and n+ Si as the light absorption layer. For a temperature range from 200 K to 350 K, we have found that under low bias, the CEP gain (measured between 1 MHz and 50 MHz) shows some temperature dependence. With increasing bias voltage to achieve a higher gain, the temperature dependence decreases and eventually the gain of the device is nearly temperature independent. Similarly, the breakdown voltage of the device shows much less temperature dependence compared with conventional APDs. In other words, we have demonstrated athermalized CEP detectors between 200 K and 350 K. We attribute the weak temperature dependence of CEP gain and breakdown voltage to the effect of field-enhanced tunneling of localized electrons (holes) into the mobile bands, which dominates over phonon excitation under high electric field. We have also developed methods to quantify the relative importance of field-enhanced tunneling and phonon excitation.
2. Design and Experiment
The device has a 35 ∼ 40 nm a-Si CEP gain medium formed by plasma enhanced chemical vapor deposition (PECVD) on a n+ Si substrate. The device mesa was passivated by a 40 nm Al2O3 layer by atomic layer deposition (ALD) and a 200 nm PECVD SiO2 layer. A 150 nm indium tin oxide (ITO) layer was sputtered on top of the a-Si layer to form a transparent electrode. Finally, the Ti/Au contact pads were deposited by sputtering and lift-off process to form the cathode and anode contacts in a configuration compatible with the ground-signal-ground (GSG) co-planar probe. The device layout and cross-section are shown in Fig. 1(a,b). The device was reverse biased by applying negative voltage to the ITO contact during measurements.
Fig. 1. (a) Layout of CEP detectors designed for GSG probing and top view of the device; (b) Cross-section of the device; (c) Experiment setup for characterization of temperature dependent performance of CEP detectors.
The experimental setup for device characterization is shown in Fig. 1(c). The device was measured in a cryogenic probe station under vacuum between 200 K and 350 K. The active area of the device was 12 μm in diameter. A GSG probe in contact with the device cathode and anode was connected to a bias Tee. The DC port of the bias tee was connected to a 200 kΩ resistor and a source meter to apply bias between −1 V and −5 V. The AC port of the bias Tee was connected to a low-noise amplifier (LNA) with a 30dB gain and an RF spectrum analyzer. The incident light was provided by a 639 nm wavelength diode laser modulated at 1 MHz, 10 MHz, and 50 MHz sinusoidally by a function generator. At given temperatures between 200 K and 350 K, we measured the bias dependent photoresponse of the device from −1 V to −5 V at these frequencies using an RF spectrum analyzer with 1 Hz resolution bandwidth. The photocurrent, I0 at −1 V was considered as the primary photocurrent since the photoresponse plateaued when the bias reached −1V. The gain of the device was calculated from the ratio of the photoresponse at a certain bias, Vapp, and the primary photoresponse, I(Vapp)/I0. The gain of the device was measured at three different frequencies under various temperatures.
To measure the breakdown voltage, the reverse bias was increased gradually to the value where the gain of the device increased rapidly. We then recorded the breakdown voltage to study the temperature dependence of the breakdown voltage.
3. Experimental Results
Figure 2(a) shows DC dark current as a function of the applied bias at 200 K and 350 K measured by a source meter. Figure 2(b) shows the device gain as a function of the applied bias at 200 K and 350 K at three different frequencies: 1 MHz, 10 MHz and 50 MHz.
Fig. 2. (a) DC dark current vs. applied bias at 200 K and 350 K. (b) Device gain vs. applied bias at three frequencies: 1 MHz, 10 MHz and 50 MHz and two temperatures: 200 K and 350 K. Each dot in (b) is the mean value of three measurements and the error bar is the standard deviation.
Figure 3(a) shows the device gain as a function of temperature at 50 MHz. Each data point represents the photocurrent gain of a device at a certain temperature and applied bias. For each applied bias, a semilog fit was performed to fit $\textrm{ln}({gain} )$ vs. temperature, indicating the trend of temperature dependence at different biases. At lower bias (up to −4 V), there was a trend of slight increase of gain with increasing temperature. When the magnitude of the applied bias was high enough (e.g., −5 V), the photocurrent gain became temperature independent.
Fig. 3. (a) Temperature dependent gain measured at 50 MHz and different applied biases; (b) Normalized gain at −2 V, −3 V, −4 V and −5 V bias. The gain at each bias was normalized to the gain at 300 K.
Figure 3(b) shows the normalized gain as a function of temperature. The gain, measured at 50 MHz, was normalized to the gain at 300 K for each applied bias. The slope of each line represents the strength of temperature dependency at a given bias. The results show decreasing temperature dependence as the magnitude of reverse bias increases. At 5V reverse bias, the device gain is nearly independent of temperature between 200K and 350K.
Temperature dependence of breakdown voltage (Vbd) is a key parameter for single photon detectors in Geiger mode. The dark count rate and photon detection efficiency are sensitive to the overbias (i.e., bias above the breakdown). Hence, any change of breakdown voltage with temperature can cause significant device performance variations, especially in a single-photon detector array. Figure 4 shows the avalanche breakdown voltage from 200 K to 350 K under 639 nm wavelength illumination. Overall, the breakdown voltages lie between −6.5 V and −6.8 V over a temperature range of 150 K. In contrast to conventional avalanche photodiodes where the breakdown voltage increases with temperature, the breakdown voltage for CEP detectors decreases slightly as temperature rises, suggesting that phonon excitation plays a more significant role than phonon scattering in the cycling excitation process.
Fig. 4. Gain vs applied bias at 200 K, 250 K, 296 K, and 350 K. The measurements reach the point close to device breakdown to enable us to extract the breakdown voltage at different temperatures.
People often use breakdown voltage temperature coefficient ($\Delta {V_{bd}}/\Delta T)$ to measure temperature sensitivity of Vbd. Figure 5 includes the breakdown voltage temperature coefficients of our device and APDs using InAlAs, InP, GaAs, AlInP and Si for carrier multiplication [19–24]. Our experimental result shows that the coefficient, $\Delta {V_{bd}}/\Delta T$, for a-Si CEP devices is around −2 mV/K. This result strongly suggests that under high applied E-field and high gain value, field-enhanced tunneling becomes the dominant effect to excite the localized electrons (holes) into the mobile bands.
Fig. 5. Dependence of breakdown voltage temperature coefficient ($\Delta {V_{bd}}/\Delta T$) on the thickness of carrier multiplication region for CEP detectors (red star) and APDs having different carrier multiplication materials: InP, GaAs, InAlAs, AlInP, and Si reported in other works [17–22].
4. Discussion and Analysis
In this section, we propose a model to elucidate the observed temperature dependence of CEP mechanism and develop a method to quantify the relative importance of phonon excitation and field-enhanced tunneling in excitation of localized carriers into mobile bands to sustain the carrier multiplication process.
The band diagram of the device and the cycling excitation process under reverse bias are shown in Fig. 6. The photoexcited electrons in n-Si are collected by the electrode while the photoexcited holes enter the a-Si layer to initiate the CEP process. As shown in Fig. 6(a), the hole acquires sufficient kinetic energy from the applied E-field to excite an electron-hole pair to the localized states in the bandtails, a process that was calculated to have high probability due to relaxation of the k-selection rule [17,18].
Fig. 6. Schematic illustration of the carrier multiplication process involving excitation of localized (bandtail) states. (a) hole-initiated generation of e-h pair in localized states, (b) excitation of localized states via phonon excitation (temperature dependent) or field-enhanced tunneling (temperature independent), (c) electron-initiated generation of e-h pair in localized states, and (d) excitation of localized states via phonon excitation or field-enhanced tunneling.
As illustrated in Fig. 6(b), these localized electrons (holes) can contribute to the output signal and sustain the carrier multiplication process only after they are excited to the conduction (valence) band by either phonon absorption or field enhanced tunneling. Similarly, the secondary electron, as soon as being excited from the localized state to the conduction band, can also acquire kinetic energy from the applied E-field to excite another electron-hole pair to the localized bandtail states (Fig. 6(c)) and the localized carriers can subsequently be excited to the mobile bands via phonon-assisted excitation or field-enhanced tunneling (Fig. 6(d)) to keep the cycles of carrier multiplication process.
We assume that the probability of phonon assisted excitation increases with temperature while the probability of field enhanced tunneling increases with the electric field but is insensitive to temperature change. The data in Fig. 2(b) shows that the temperature dependence of gain decreases with increasing bias voltage and eventually becomes nearly temperature independent when the bias voltage reaches −5 V, corresponding to an E-field of around 1.2 MV/cm. This implies that under a strong enough electric field, field enhanced tunneling is the dominant mechanism for excitation of the localized carriers in the bandtails. Next, we apply a simple model to relate the ratio of probability between phonon excitation and field-enhanced tunneling to the experimental data to help us find the relative importance of phonon excitation and field-enhanced tunneling.
To model the CEP gain, we assume the number of electron-hole pairs created by an energetic electron and hole in the i-th cycle is ${X_i}$ and ${Y_i}$, respectively. The expression of the CEP amplification factor, ${G_{CEP}}$, can be represented as
where ${Y_0}$ is the number of the primary photogenerated holes in n-Si.For all X’s and Y’s, their mean values are represented by
Treating all X’s and Y’s to be independent random variables, we obtain the mean value of the multiplication factor $G$:
Since the CEP mechanism is a two-step process consisting of generation of localized e-h pairs by energetic carriers and excitation of localized carriers to their respective mobile bands, we can represent x and y by the following relations:
${M_e}(V )$ and ${M_h}(V )$ are the average number of the localized e-h pairs produced by an energetic electron and hole, and $[{{P_p}(T )+ \; {P_{pt}}({T,V} )+ \; {P_t}(V )} ]$ is the net probability of localized carrier excitation by three mechanisms:${P_p}(T )$: phonon excitation probability, which is temperature dependent.
${P_{pt}}({T,V} )$: phonon excitation probability with the effect of barrier lowering due to high electric field, which is both temperature and voltage dependent.
${P_t}(V )$: field-enhanced tunneling probability, which is voltage dependent.
We can sum up ${P_p}(T )$ and ${P_{pt}}({T,V} )$ to account for all phonon-assisted excitation processes including barrier lowering (Poole-Frenkel) and call it “temperature related” probability, ${P_{tem}}({T,V} )$. Then:
In separate experiments, we have found that under high electric field, the ionization coefficient for holes and electrons was comparable for a-Si (i.e., $y\sim x$ under high field)
For G>>1 (e.g., G > 5 for bias higher than −3V), we can approximate G as
From (5, 6, 7),
We use Eq. (9) and divide its value by the value at the lowest temperature (e.g., T = 200 K) we have measured, yielding the relation
At the lowest temperature of 200 K and high enough bias, we have ${P_t}(V )\gg {P_{tem}}({200K,V} )$ due to the low phonon population so that we can ignore the term ${P_{tem}}({200K,\; V} )$ in Eq. (10). Then Eq. (10) can be reduced to
Equation (11) enables us to find the relative importance between tunneling and phonon excitation under different operation conditions that satisfy $G({T,V} )\gg 1$. The ratio ${P_{tem}}({T,V} )/{P_t}(V )$ obtained from the measured data and Eq. (11) is plotted in Fig. 7.
Fig. 7. Ratio of phonon excitation probability, ${P_{tem}}({T,V} )$ to tunneling probability, ${P_t}(V )$ as a measure of the relative importance between phonon excitation and field-enhanced tunneling in CEP.
As shown in Fig. 7, at a bias of −3 V, ${P_{tem}}({T,V} )/{P_t}(V )\; $ increases as the temperature changes from 200 K to 350 K. However, even at the highest temperature of 350 K, the contribution of phonon excitation is only about 10% of field-enhanced tunneling. As the reverse bias increases from −3 V to −4 V, both the value and the slope of ${P_{tem}}({T,V} )/{P_t}(V )$ vs. temperature are reduced significantly, indicating that field-enhanced tunneling becomes even more dominant over phonon-assisted excitation. Eventually the tunneling process becomes totally dominant at −5 V bias or an applied field of 1.2 MV/cm.
From this study, we confirm a significant and fundamental difference between CEP effect and impact ionization in APDs. For APDs, gain decreases with temperature due to inelastic phonon scattering in crystalline material, which limits the efficiency for carriers to gain kinetic energy under high temperature, and the same mechanism also causes increase in the breakdown voltage [25]. In contrast, the disordered potential in thin amorphous material favors elastic scattering [26,27], and above all, the CEP gain is related to the excitation of localized states, mainly governed by the temperature independent tunneling process and with minor contributions from phonon excitation. This fundamental difference gives CEP detectors the athermalized characteristics over a wide temperature range of 150 K.
5. Conclusion
In this work, we investigated temperature sensitivity of the cycling excitation process in a-Si. By analyzing the effect of temperature on gain and breakdown voltage, we conclude that under high gain and high applied field, field-enhanced tunnelling dominates the localized state excitation to sustain the carrier multiplication cycles whereas phonon-assisted excitation plays some roles under low bias and moderate gain. For high sensitivity and single photon detectors, photodetectors are operated in the high gain regime or biased above breakdown. The unique athermalized property of CEP detectors offer important advantages over conventional APDs or SPADs because of the relaxed requirements for precision temperature control.
Funding
National Science Foundation (ECCS-2025752); Office of Naval Research (N00014-18-1-2486).
Acknowledgments
We thank the staff of the UCSD Nano3/SDNI facility for their technical support.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon request.
References
1. M. Ghioni, F. Zappa, V. P. Kesan, and J. Warnock, “A VLSI-compatible high-speed silicon photodetector for optical data link applications,” IEEE Trans. Electron Devices 43(7), 1054–1060 (1996). [CrossRef]
2. L. R. Canfield, J. Kerner, and R. Korde, “Stability and quantum efficiency performance of silicon photodiode detectors in the far ultraviolet,” Appl. Opt. 28(18), 3940–3943 (1989). [CrossRef]
3. B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13(2), 335–349 (2002).
4. J. C. Campbell, “Recent advances in telecommunications avalanche photodiodes,” J. Lightwave Technol. 25(1), 109–121 (2007). [CrossRef]
5. M. M. Hayat, D. A. Ramirez, G. J. Rees, and M. A. Itzler, “Modeling negative feedback in single-photon avalanche diodes,” Proc. SPIE 7681, 76810W (2010). [CrossRef]
6. S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, “Avalanche photodiodes and quenching circuits for single-photon detection,” Appl. Opt. 35(12), 1956–1976 (1996). [CrossRef]
7. I. Wegrzecka, M. Wegrzecki, M. Grynglas, J. Bar, A. Uszynski, R. Grodecki, P. Grabiec, S. Krzeminski, and T. and Budzynski, “Design and properties of silicon avalanche photodiodes,” Opto-Electron. Rev. 12(1), 95–104 (2004).
8. L. Pancheri, M. Scandiuzzo, D. Stoppa, and G. F. Dalla Betta, “Low-Noise Avalanche Photodiode in Standard 0.35-um CMOS Technology,” IEEE Trans. Electron Devices 55(1), 457–461 (2008). [CrossRef]
9. S. MohammadNejad and F. Aghaei, “Noise characteristics improvement of submicron InP/InGaAs avalanche photodiode for laser detection system,” Optics Commun. 455, 124561 (2020). [CrossRef]
10. D. Joseph, S. Collins, and S., “Temperature dependence of fixed pattern noise in logarithmic CMOS image sensors,” IEEE Trans. Instrum. Meas. 58(8), 2503–2511 (2009). [CrossRef]
11. M. Loose, K. Meier, and J. Schemmel, “A self-calibrating single-chip CMOS camera with logarithmic response,” IEEE J. Solid-State Circuits 36(4), 586–596 (2001). [CrossRef]
12. Y. Zhou, Y. H. Liu, S. N. Rahman, D. Hall, L. J. Sham, and Y. H. Lo, “Discovery of a photoresponse amplification mechanism in compensated PN junctions,” Appl. Phys. Lett. 106(3), 031103 (2015). [CrossRef]
13. Y. H. Liu, L. Yan, A. C. Zhang, D. Hall, I. A. Niaz, Y. Zhou, L. J. Sham, and Y. H. Lo, “Cycling excitation process: An ultra efficient and quiet signal amplification mechanism in semiconductor,” Appl. Phys. Lett. 107(5), 053505 (2015). [CrossRef]
14. L. Yan, Y. Yu, A. C. Zhang, D. Hall, I. A. Niaz, M. A. R. Miah, Y. H. Liu, and Y. H. Lo, “An amorphous silicon photodiode with 2 THz gain-bandwidth product based on cycling excitation process,” Appl. Phys. Lett. 111(10), 101104 (2017). [CrossRef]
15. Y. Yu, Z. Xu, S. Li, A. C. Zhang, L. Yan, Z. Liu, and Y. H. Lo, “Plasmonically enhanced amorphous silicon photodetector with internal gain,” IEEE Photonics Technol. Lett. 31(12), 959–962 (2019). [CrossRef]
16. J. Zhou, M. A. R. Miah, Y. Yu, A. C. Zhang, Z. Zeng, S. Damle, I. A. Niaz, and Y. H. Lo, “Room-temperature long-wave infrared detector with thin double layers of amorphous germanium and amorphous silicon,” Opt. Express 27(25), 37056–37064 (2019). [CrossRef]
17. I. A. Niaz, M. A. R. Miah, L. Yan, Y. Yu, Z. He, Y. Zhang, A. C. Zhang, J. Zhou, Y. H. Zhang, and Y. H. Lo, “Modeling gain mechanisms in amorphous silicon due to efficient carrier multiplication and trap-induced junction modulation,” J. Lightwave Technol. 37(19), 5056–5066 (2019). [CrossRef]
18. M. A. R. Miah, I. A. Niaz, and Y. H. Lo, “Defect assisted carrier multiplication in amorphous silicon,” IEEE J. Quantum Electron. 56(3), 1–11 (2020). [CrossRef]
19. L. J. J. Tan, D. S. G. Ong, J. S. Ng, C. H. Tan, S. K. Jones, Y. Qian, and J. P. R. David, “Temperature dependence of avalanche breakdown in InP and InAlAs,” IEEE J. Quantum Electron. 46(8), 1153–1157 (2010). [CrossRef]
20. J. S. L. Ong, J. S. Ng, A. B. Krysa, and J. P. David, “Temperature dependence of avalanche multiplication and breakdown voltage in Al0. 52In0. 48P,” J. Appl. Phys. 115(6), 064507 (2014). [CrossRef]
21. C. Groves, C. N. Harrison, J. P. R. David, and G. J. Rees, “Temperature dependence of breakdown voltage in Al x Ga 1− x As,” J. Appl. Phys. 96(9), 5017–5019 (2004). [CrossRef]
22. C. Yang, C. J. Barrelet, F. Capasso, and C. M. Lieber, “Single p-type/intrinsic/n-type silicon nanowires as nanoscale avalanche photodetectors,” Nano Lett. 6(12), 2929–2934 (2006). [CrossRef]
23. D. J. Massey, J. P. R. David, and G. J. Rees, “Temperature dependence of impact ionization in submicrometer silicon devices,” IEEE Trans. Electron Devices 53(9), 2328–2334 (2006). [CrossRef]
24. Y. Dong, W. Wang, X. Xu, X. Gong, D. Lei, Q. Zhou, Z. Xu, W. K. Loke, S. F. Yoon, G. Liang, and Y. C. Yeo, “Germanium-tin on Si avalanche photodiode: device design and technology demonstration,” IEEE Trans. Electron Devices 62(1), 128–135 (2015). [CrossRef]
25. J. Conradi, “Temperature Effects in Silicon Avalanche Diodes,” Solid State Electron. 17(1), 99–106 (1974). [CrossRef]
26. S. Kasap, J. A. Rowlands, S. D. Baranovskii, and K. Tanioka, “Lucky drift impact ionization in amorphous semiconductors,” J. Appl. Phys. 96(4), 2037–2048 (2004). [CrossRef]
27. O. Rubel, A. Potvin, and D. Laughton, “Generalized lucky-drift model for impact ionization in semiconductors with disorder,” J. Phys.: Condens. Matter 23(5), 055802 (2011). [CrossRef]
