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Plot of the dark current (Id) and photocurrent (Ip) at 1550 nm as a function of bias voltage for a typical SPAD are obtained by current-voltage (I-V) measurement at temperature of 223-293 K and shown in Figure 2(a). It can be seen from Ip that the punch-through voltage (Vpt) is 35 V. This is desirable because such a high Vpt provides low electric field in the absorption region results in a small tunneling current. The responsivity of the SPAD is 0.9 A/W at Vpt, providing an external quantum efficiency of 72%. The operating voltage when Id is 10 μA is defined as the breakdown voltage (Vbr). The Id at 95% Vbr is 1 pA and 392 pA at 223 and 293 K, respectively. Such low Id indicates that the epi-wafer of the SPAD has excellent crystalline quality. The temperature dependency of the Vbr is shown in the Figure 2(b). The Vbr increases with increasing temperature. This is because the ionization coefficient decreases at elevated temperatures, and the threshold of electric field strength in multiplication region required for breakdown increases, which in turn causes the increase of the Vbr.
Figure 2. (a) Dark current and photocurrent at 1 550 nm as a function of bias voltage for SPAD at temperature of 223-293 K;(b) Breakdown voltage versus temperature data (symbols) and linear fitting (line)
The temperature dependency coefficient, ΔVbr/ΔT, is listed to be 100 mV/K from 53.3 V at 223 K to 60 V at 293 K. The SPDE ΔVbr/ΔT can be calculated using the following expression[16]:
$$ \frac{{\Delta {V_{{\rm{br}}}}}}{{\Delta T}} = \left[ {\left( {42.5 \times {X_{\rm{d}}}} \right) + 0.5} \right] \times \frac{\omega }{{{X_{\rm{d}}}}} $$ (1) where Xd and ω are the thickness of the multiplication layer and the total width of the depletion region respectively. It can be seen that the ΔVbr/ΔT is negatively correlated with the thickness of the multiplication layer and positively correlated with the width of the depletion region. The improvement of temperature characteristics requires the cooperation between the two factors.
As we know that SPADs are pn junctions that are biased above Vbr and operate in the so-called " Geiger mode "[17]. The SPAD is operated in gated mode in order to avoid damage to the SPAD due to long-term macroscopic current pulse[18]. The gate duration of the biased electrical pulses is 2.2 ns with a repetition frequency (f) of 1 MHz. The PDE of SPAD can be expressed as:
$$ PDE = {P_{{\rm{trigger}}}} \times QE $$ (2) where Ptrigger and QE are the probability of avalanche triggering and the absorption efficiency, respectively. The former is mainly determined by the thickness of the multiplication InP layer and the electric field in it. The latter depends on the thickness of depletion region in the absorption InGaAs layer that is determined by the epitaxial growth of the SPAD [7, 19]. Figure 3 shows PDE and DCR with temperature when the SPAD operating at Geiger-mode under an excess bias of 2 V higher than Vbr. For the typical sample device, the PDE increase from 13.69% to 20.7% and the DCR decreases from 500 kHz to 4.09 kHz over the temperature range from 293 to 223 K. PDE increases toward lower temperatures. This is because: (1) At a constant excess bias, due to the decrease in breakdown voltage, the electric field from OFF to ON in the multiplication area at lower temperatures increases more strongly, so the PDE is higher; (2) The probability of avalanche triggering (Ptrigger) enhances due to the higher impact ionization coefficient at lower temperatures.
Activation energies are calculated from the trend of DCR with temperature to investigate the source of the dark current and DCR[8]. DCR and dark current are closely related. The major source of dark current is related to generation-recombination current, surface leakage current, and tunneling current. The generation-recombination current passes through the multiplication region and has a great impact on DCR. The surface dark current does not participate in the multiplication process and does not contribute to the DCR. The tunneling current is also very weak at this operating temperature range (223-293 K) and will not contribute to the extra DCR. From this we can infer that the dark count is basically generated by the thermal generation. The DCR origin from thermal generation can be expressed as:
$$ {\rm{DCR}} \propto {n_{\rm{i}}}/{\tau _{\rm{e}}} \propto {T^2}\mathit{{\rm{exp}}}\left( { - {E_{\rm{a}}}/kT} \right) $$ (3) where ni and τe are the intrinsic carrier density and the effective lifetime, respectively, Ea is the activation energy, k is Boltzmann constant, and T is the temperature. The value of Ea can be obtained by linear fitting ln (DCR/T2) versus 1/kT. As shown in Figure 4, the fitted Ea is 0.35 eV for the DCR from 223 to 293 K. This activation energy is close to half of the band gap (0.375 eV) of the Ga0.467In0.533As (Eg=0.75 eV) absorption layer, indicating that the thermal generation in the absorption layer is dominant for the DCR in this temperature range. The method of using DCR with temperature to calculate the activation energy to obtain the source of the dark current and DCR is also involved in the references of related articles [8-9, 20]. However, the conclusions obtained are different according to the operating temperature of the SPAD.
Figure 5 shows the PDE and DCR dependence on excess bias of 25 μm diameter SPAD at 223 K. The PDE can be increased by operating at a higher excess bias voltage Vex, where Vex = V – Vbr is the bias in excess of Vbr. However, the DCR also increases with higher Vex. For a SPAD with excellent characteristics, it is generally hoped that its PDE is high enough while maintaining a low DCR, which requires tradeoff between PDE and DCR. The SPAD made in this article shows excellent detection characteristics, the PDE is 25.72% at 1 550 nm wavelength and the DCR is 9.09 kHz at 3 V excess bias.
There are inevitable defects in the material of SPAD. These defects will trap carriers in the avalanche process[21]. These carriers will be slowly released. Trapped carriers may also cause an avalanche event, resulting in APP counting before the release completed[22]. In the case of high repetition frequency and low temperature, the APP is the main factor related to the DCR. As shown in Figure 6, we test the relationship between the APP and the temperature. It can be seen from the figure that the APP gradually decreases from 3.29% to 0.77% at the operating temperature range 223-293 K. This is because the operating temperature increases and the carriers trapped by the defects can be released more quickly. So considering the APP, there is an optimum operating temperature.
Temperature dependency of InGaAs/InP single photon avalanche diode for 1 550 nm photons
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摘要: 在越来越多的光子计数应用中,用于近红外光波长领域的单光子探测器受到广泛关注。例如在量子信息处理、量子通信、3D激光测距(LiDAR)、时间分辨光谱等光子计数应用领域。文中设计并展示了用于探测1 550 nm波长光子的InGaAs/InP单光子雪崩二极管(SPAD)。这种SPAD 采用分离吸收、过渡、电荷和倍增区域结构 (SAGCM),在盖革模下工作时具有单光子灵敏度。SPAD的特性包括随温度范围223~293 K变化的击穿电压、暗计数率、单光子检测效率和后脉冲概率。25 μm 直径的 SPAD 显示出一定的温度相关性,击穿电压随温度的变化率约为100 mV/K。当SPAD在盖革模式下温度为223 K工作时,在暗计数率为4.1 kHz,后脉冲概率为3.29%的基础上,对1 550 nm光子实现了21%的单光子探测效率。文中还分析和讨论了SPAD温度相关性的单光子探测效率、暗计数率和后脉冲概率的来源和物理机制。这些机制分析、讨论和计算可以为SPAD的设计和制备提供更多的理论支持和依据。Abstract: Single-photon detectors for the near-infrared wavelength region are receiving widespread attention in an increasing number of photon counting applications. In fields such as quantum information processing, quantum communication, 3-D laser ranging (LiDAR), time-resolved spectroscopy, etc. An InGaAs/InP single photon avalanche diode (SPAD) was designed and demonstrated to detect 1 550 nm wavelength photons in this paper. The SPAD has a separate absorption, grading, charge and multiplication region structure (SAGCM) with single photon sensitivity when working in Geiger-mode. The characterization of the SPAD include breakdown voltage, dark count rate, single photon detection efficiency and after pulse probability as functions of temperature from 223 to 293 K. The 25 μm diameter SPAD shows certain temperature dependency, with breakdown voltage dependence of approximately 100 mV/K. Operating at 223 K and in Geiger-mode, the SPAD achieves a photon detection efficiency of 21% at 1 550 nm with a dark count rate of 4.1 kHz and a after pulse probability of 3.29%. The source and physical mechanism of the photon detection efficiency, dark count rate and after pulse probability of the SPAD with temperature dependency were also analyzed and discussed. The mechanism analysis, discussion and calculation can provide more theoretical basis and support for the design and fabrication of SPAD.
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