Surface illuminated interdigitated Ge-on-Si photodetector with high responsivity

Yuxuan Li; Xiaobin Liu; Xuetong Li; Shuai Wang; Han Ye; Lanxuan Zhang; Yingzhi Li; Shengxian Sun; Baisong Chen; Yao Ma; Pengfei Guo; Fengli Gao; Xueyan Li; Guoqiang Lo; Junfeng Song; Junfeng Song

doi:10.1364/OE.427343

1. Introduction

In recent years, emerging technologies such as optical communication, unmanned driving, and quantum information technology have been developed rapidly in the direction of longer reach and larger bandwidth. These in turn demand higher performance of existing short-wave infrared detectors [1,2]. The Ge-on-Si PD is considered as silicon-based CMOS technology, which realizes compact monolithic integration with existing integrated circuits and integrated optical systems. Compared with III-V devices, it is not only low in cost, but can also be integrated with other Si photonics components effectively, in order to improve the overall stability of the detection system [3]. Because of the superior impact ionization characteristics of Si compared with traditional III-V photodiodes, APD with Si avalanche region can well realize unit-carrier avalanche with the reduced excess noise, leading to improved sensitivity [4].

To improve the responsivity of the PD, there are approaches coupling the light into the Ge absorption layer by using the end-fire coupling method [5,6] or grating coupling method [7–10]. Compared with the traditional surface illuminated detectors [11–13], the waveguide integrated PD has a much longer absorption length, which results responsivity easily higher than 0.7 A/W. However, these micro-nano optical structures cannot effectively receive scattered light signals in the domain of free space communication, so the waveguide integrated PD cannot meet the detection requirements of unmanned driving and radar detection. To address the aforementioned issue, this work proposes a large-size surface illuminated interdigitated “finger-type” PD. Since no doping or metallic contact in Ge absorption layer, the propagation loss of photons in the interdigitated PD is less than vertical p-i-n-based PD. Meanwhile, the interdigitated doped regions increase the equivalent area of the lateral p-i-n junction, which can increase the distribution of the electric field in the absorption layer, results in the improvement of the surface illuminated PD’s responsivity.

2. Device design and fabrication

The interdigitated PD and APD were fabricated using the standard process of Advanced Micro Foundry (AMF) in Singapore. The devices were built on silicon-on-insulator (SOI) wafer with 220 nm top-silicon. The top-silicon layer was etched to define Si mesa patterns. Arsenic and boron implantations were performed to form N- and P-regions, respectively. A schematic of the doped regions is shown in Fig. 1(a). The doping concentrations of both N- and P-regions are ∼10¹⁹ cm^-3. Heavily doped N++- and P++-regions with concentration of ∼10²⁰ cm^-3 were subsequently formed as the contact. In order to enable these devices to collect weak light signals from the free space effectively, the dimensions of epitaxial Ge were designed to be 44 µm (length) × 40 µm (width) × 720 nm (height). Various interdigitated detectors with different finger width of 2 µm to 2.6 µm and finger length of 36.9 µm to 38 µm were fabricated, to investigate the effects on the dark current performance. The dark current density of the PDs at 0.5 V reverse bias is shown in Fig. 1(b), considering the balance between dark current and bandwidth performance of the device, the PD with finger width of 2.2 µm, finger lengths of 37 µm, and spacing between fingers of 3 µm was screened out finally. Conventional vertical p-i-n-based PD [14] with P-region in Si and N-region in Ge was fabricated together with the interdigital PD.

Fig. 1. (a) Structure diagram of the large-size interdigitated PD’s Si substrate; (b) Dark current density of detectors at reverse bias of 0.5 V.

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3. Device performance and simulation

3.1 I-V and responsivity

The PD is characterized using KEYSIGHT N7714A laser of 1550 nm wavelength as light source. Light is illuminated directly above the Ge active layer of the detectors through the optical fiber. Meanwhile, the probes contacted to the PD’s electrode pads are connected to KEYSIGHT 4200-SCS for data reading.

PD’s photocurrent is tested under the incident optical power of -30 dBm, -20 dBm, -10 dBm, 0 dBm, and 10 dBm. As shown in Fig. 2(a), dark current of the device in the absence of light gradually increases with the increase of the reverse bias. The order of dark current is in scale of 100 nA. Photocurrent increases by the same multiple as the incident light power increases by ten times. From Figs. 2(b) and 2(c), it can be seen that when the device is irradiated by low optical power light such as -30 dBm, -20 dBm, and -10 dBm, with ∼0.5 V reverse bias, the electric field in the Ge absorption layer sweep the photo-generated carriers to the cathode and anode completely. After that, the photocurrent hardly changes with the increase of the bias. Because the dark current will gradually become larger as the bias increases, the responsivity [Eq. (1)] and external quantum efficiency [Eq. (2)] will gradually decrease after the PD is fully depleted [15,16].

Fig. 2. Response characteristic curve of Ge-on-Si interdigitated PD at 1550 nm: (a) I-V curve of the interdigitated PD at different incident optical power; (b) Responsivity versus reverse bias at different incident optical power; (c) External quantum efficiency versus reverse bias at different incident optical power; (d) Responsivity versus light power with 1 V and 3 V reverse bias voltages; (e) External quantum efficiency versus light power with 1 V and 3 V reverse bias voltages.

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When the optical power increases to 0 dBm, the optical responsivity and external quantum efficiency of the device exhibit a similar trend as increasing first and then stabilizing. This is because a large number of photo-generated carriers are generated in the Ge absorption layer, which results in a space charge effect [17–20], causing the overall resistance inside the PD to be decreased. As a result, the electric field in Ge is reduced. Therefore, by applying a reasonably high voltage, the electric field in the device can be sufficiently large to sweep the photo-generated carriers in Ge completely to the electrodes at both ends. Figures 2(d) and 2(e) show the curve of responsivity and external quantum efficiency as function of light power, tested with reverse bias of 1 V and 3 V separately. It can be seen that when the incident light power is 0 dBm, the interdigitated PD is not completely depleted yet at 1 V bias, and the photo-generated electron-hole pairs cannot be completely extracted, so the responsivity is lower than the one in the -10 dBm. However, under the condition of being applied with a higher voltage of 3 V, the PD is basically in full depletion, so that the responsivity of the device is optimized under 0 dBm light irradiation. For 10 dBm, the photoelectric conversion in Ge is still saturated, and most of the photons pass directly through the absorption layer and do not contribute to photo-generated carrier generation. Therefore, the response characteristics of the device are relatively poor.

(1)$$R\textrm{ = }{{({{I_{\textrm{light}}} - {I_{\textrm{dark}}}} )} / {{P_{\textrm{photon}}}}},$$

(2)$$QE\textrm{ = }{{h\nu \cdot ({{I_{\textrm{light}}} - {I_{\textrm{dark}}}} )} / {({e \cdot {P_{\textrm{photon}}}} )}},$$

The responsivity and external quantum efficiency of the interdigitated PD and vertical p-i-n PD are calculated when the incident optical power is -20 dBm. As shown in Fig. 3, the interdigitated PD demonstrates a great improvement in the responsivity and external quantum efficiency as compared with the p-i-n-based PD at reverse bias of 0 to 4 V. with the bias voltage increased to 0.5 V, the electric field can extend to the entire Ge layer of interdigitated PD along the vertical (Z) direction. The photo-generated electron-holes are completely concentrated in the electrode with the action of the electric field. The responsivity of the device can reach ∼0.64 A/W, and the external quantum efficiency corresponds to 51%. After that, with the bias voltage up to 2 V, the responsivity of the device is ∼0.62 A/W, and the external quantum efficiency drops to 49%.

Fig. 3. Comparison of two type PD devices’ light response characteristics: (a) The responsivity of interdigitated PD and the p-i-n-based PD with the power of -20 dBm; (b) The quantum efficiency of interdigitated PD and the p-i-n-based PD with the power of -20 dBm.

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In order to study the electric field distribution of the interdigitated PD, we use TCAD software to simulate the electrical performance of the detector. Figure 4 describes the simulated electric field distribution in Ge layer at 0 V and 0.5 V. By comparing Fig. 4(a) with 4(c), it can be seen that with 0.5 V reverse bias applied, the electric field in Si substrate fully extends to the Ge absorption layer and is strong enough to sweep the photo-generated electron-hole pairs in absorption layer to the electrodes. Figure 4(d) shows that the electric field at the top of Ge is close to 4.5×10⁵ V/m at 0.5 V, which is 4 times larger than that at 0 V. This also explains the trend of the interdigitated PD’s responsivity in Fig. 3.

Fig. 4. The sketch of the electric field simulation of the interdigitated PD: (a) The simulated electric field profile of the Ge layer at 0 V bias; (b) Curve of the electric field distribution at the middle of the Ge absorption layer at 0 V; (c) The simulated electric field profile of the Ge layer at 0.5 V bias; (d) Curve of the electric field distribution at the middle of the Ge absorption layer at 0.5 V.

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With 0 V reverse bias applied, the detector’s static response characteristics in the C- and L-band are studied. As Figs. 5(a)-(c) show, at -30 dBm, -20 dBm, and -10 dBm, even if the interdigitated PD does not be applied an external bias voltage, the detector’s responsivity in the C-band is always greater than 0.5 A/W, this is because the built-in electric field of the interdigitated PD can sweep the majority of electron-hole pairs to electrodes, and the device has the best responsivity at 1550 nm light. When the optical power is increased to 0 dBm, a large number of photo-generated carriers are accumulated in the Ge absorption layer, which causes the space charge effect to weaken the built-in electric field and deteriorate the responsivity. As for 10 dBm, a large number of incident photons directly pass through the PD, and the responsivity of the device drops to ∼0.1 A/W. As the wavelength increases from 1570 nm to 1600 nm, the photons are more difficult to excite the energy level transition of electrons in the Ge material. The responsivity and external quantum efficiency decrease rapidly as the wavelength increases [16]. However, due to the saturation of the photoelectric effect, the velocity of decline will gradually decrease with the increase of light power.

Fig. 5. Static characteristics of the interdigitated PD in the C- and L-band: (a) Current–wavelength plot at 0 V; (b) Responsivity–wavelength plot at 0 V; (c) Quantum efficiency–wavelength plot at 0 V; (d) Current–wavelength plot at 5 V; (e) Responsivity–wavelength plot at 5 V; (f) Quantum efficiency–wavelength plot at 5 V.

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With 5 V bias applied, the internal electric field of the detector is effectively enhanced, which has an offsetting effect on the photo-generated space charge effect. Comparing Figs. 5(e) and (f) with 5(b) and (c), The PD's response characteristics with 0 dBm and 10 dBm incident light in the C- and L-bands can be significantly improved at 5 V bias. In the C-band, the responsivity and external quantum efficiency of the interdigitated PD with 0 dBm exceed the ones with -30 dBm, -20 dBm, and -10 dBm light power. But for 10 dBm, the device still has the saturation of photoelectric conversion. Meanwhile, with the optical power in the range of -30 dBm to -10 dBm, the Ge material has a higher absorption rate at short-wavelength light, the responsivity of the device at 1540 nm and 1530 nm is higher than the one at 1560 nm and 1570 nm respectively.

However, as the incident light power increases to 0 dBm and above, since the number of photons at 1560 nm and 1570 nm is more than that at 1540 nm and 1530 nm. The responsivity and quantum efficiency at 1560 nm and 1570 nm eventually exceed the ones at 1540 nm and 1530 nm separately. For the L-band wavelengths, the light absorption rate of Ge material is so weak that the responsivity of the PD is optimal with 10 dBm incident light power.

By comparing the current, responsivity and external quantum efficiency at different voltages in Fig. 6, it can be found that with the -20 dBm light power and no bias applied, the photoelectric performance of the interdigitated PD at 1560 nm and 1570 nm is better than the one at 1540 nm and 1530 nm, respectively. Due to the Franz-Keldysh effect [21–24], with 2 V and above bias applied, the absorption coefficients of the Ge material at different wavelengths can be changed, results in the photoelectric performance of the device at 1540 nm and 1530 nm exceed the one at 1560 nm and 1570 nm finally.

Fig. 6. Response characteristics of the interdigitated PD in the C- and L-band light at -20 dBm optical power: (a) Current versus wavelength at 0 V, 2 V and 5 V bias; (b) Responsivity versus wavelength at 0 V, 2 V and 5 V bias; (c) Quantum efficiency versus wavelength at 0 V, 2 V and 5 V bias.

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In summary, this surface illuminated interdigitated Ge-on-Si PD has good electro-optic characteristics for near-infrared light. which can well meet the needs of autonomous driving and other domains of week light detection.

3.2 3 dB bandwidth

The 3 dB bandwidth of the interdigitated PD versus bias voltage is shown in Fig. 7. Blue squares represent the experimental data and the dashed line is the polynomial fitting curve. Since the p-i-n junction of Si substrate is horizontal, meanwhile, the Ge absorption layer and the Si substrate are vertically distributed, so the direction of the electric field in the p-i-n junction is not strictly consistent with the one of carriers’ movement. Therefore, with 0.1 V bias applied, the built-in electric field is not enough to sweep the photo-generated carriers at saturation speed, the 3 dB bandwidth is only 3.5 KHz. As the increase of the bias voltage, the electric field in Si substrate gradually extends to the Ge absorption layer and keeps increasing, which accelerates the electrons and holes. When the reverse bias voltage reaches ∼3.5 V, the photo-generated carriers in the Ge absorption layer move toward the Si substrate at the saturation drift velocity, and the interdigitated PD achieves the maximum bandwidth of 1.537 MHz.

Fig. 7. Sketch of interdigitated PD’s 3 dB bandwidth versus bias voltage.

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The huge area of p-i-n junction results a large RC time coefficient [25], which reduces the bandwidth performance of device. Nevertheless, for the existing Lidar ranging systems with integrated optical phased array chip [26–28], the 3 dB bandwidth of MHz can meet their measurement requirements.

3.3 Equivalent circuit model

The interdigitated PD can be equivalent to a three-port current source in the spice simulation [29]. According to the actual bandwidth of the device, the substrate parasitic capacitance and resistance of the PD can be calculated. To take the Franz-Keldysh effect into account, the absorption coefficients of Ge layer at different bias voltages are calculated, and the absorption layer can be equivalent to a current source which is related to the reverse bias: the carriers generated in Ge move to the intrinsic and doped regions of the Si substrate in the form of drift and diffusion respectively. The current of the interdigitated PD is the sum of the drift current and the minority carrier diffusion current in the lateral p-i-n junction which can be calculated through the carrier rate equation Eqs. (3)-(6) [29].

(3)$$\frac{{{P_{in}}}}{{{V_{Ge}}}} = {C_{no}}\frac{{d{V_p}}}{{dt}} + \frac{{{V_p}}}{{{R_p}}} + {I_p},$$

(4)$$\frac{{{P_{in}}}}{{{V_{Ge}}}} = {C_{no}}\frac{{d{V_n}}}{{dt}} + \frac{{{V_n}}}{{{R_n}}} + {I_n},$$

(5)$$\frac{{{P_{in}}}}{{{V_{Ge}}}} = {C_{no}}\frac{{d{V_i}}}{{dt}} + \frac{{{V_i}}}{{{R_{nr}}}} + {I_i} - {I_n},$$

(6)$${V_{Ge}} = \frac{{h\nu }}{{q\left( {1 - r} \right)\left[ {1 - exp \left( { - {\alpha _{Ge}}{t_{Ge}}} \right)} \right]}},$$

where P_in represents the incident light power and r is the reflection coefficient. Because fiber coupling angle is less than 5°, the reflection of incident light can be ignored (r≈0). V_Ge is related to the photoelectric conversion efficiency of Ge layer on the N-, intrinsic and P-regions, meanwhile, α_Ge and t_Ge represent the absorption coefficient and thickness of the Ge absorption layer separately. P_n and N_p are the excess hole and electron concentrations in the N-doped and P-doped region, and N_i and P_i are the excess electron and hole concentrations in the intrinsic region. V_p=(q·P_n)/C_no, V_n=(q·N_p)/C_no and V_i=(q·N_i)/C_no are the voltages of the corresponding regions, and C_no is the normalization coefficient. R_n=τ_n/C_no and R_p=τ_p/C_no are the resistances respectively related to the lifetime of electrons and holes in the P- and N-regions, at the same time, I_i =V_i/R_nt is the drift current of electrons, R_nr=τ_nr/C_no and R_nt=τ_nt/C_no are the resistances respectively related to the recombination lifetime and the drift-time of electrons in the intrinsic region. τ_n and τ_p are the lifetimes of electrons and holes respectively. τ_nr and τ_nt=W_i/v_n are the recombination lifetime and drift-time of electrons in the intrinsic region, where W_i is the width of the intrinsic region and v_n is the drift velocity of electrons. I_n and I_p are the minority carrier diffusion currents in the doped regions. Through the bipolar transport equations, the expressions of I_n and I_p can be Eqs. (7) and (9).

(7)$${I_n} = \frac{{{V_n}}}{{{R_{nd}}}} + {\beta _n}{P_{in}} + {I_{n0}},$$

(8)$${R_{nd}} = {R_n}\left( {ch\left( {\frac{{{W_p}}}{{{L_n}}}} \right) - 1} \right),$$

(9)$${I_p} = \frac{{{V_p}}}{{{R_{pd}}}} + {\beta _p}{P_{in}} + {I_{p0}},$$

(10)$${R_{pd}} = {R_p}\left( {ch\left( {\frac{{{W_n}}}{{{L_p}}}} \right) - 1} \right),$$

I_n0 and V_n/R_nd constitute the dark diffusion current, β_nP_in is the photocurrent, and the same is true for the Eq. (9) [29]. W_p and W_n are the widths of the P- and N-regions, ${L_n} = \sqrt {{D_n} \cdot {\tau _n}}$and ${L_p} = \sqrt {{D_p} \cdot {\tau _p}}$ are the diffusion lengths of electrons and holes, meanwhile, D_n and D_p are electron and hole diffusion coefficients separately.

The equivalent circuit model is shown in Fig. 8, where I_on, I_oi and I_op represent the primary photocurrents that flow into the Si substrate from the Ge absorption layer. I_t is the tunneling current in the Si substrate. m*_c is the effective mass of electrons, γ depends on the tunneling barrier, E_g is the energy gap of Si, A is the area of the Ge absorption layer, V is the value of the reverse bias and E is the average electric field in the intrinsic region. R_d is the leakage resistance of the device, which is related to the surface recombination and leakage current at the interface between silicon and germanium. R_s and C_t are the parasitic resistance and total capacitance of the device separately.

Fig. 8. Three-port equivalent circuit model of the Ge-on-Si interdigitated PD.

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In addition to the above-mentioned parameters, the parameters seen in Table 1 are also used in the spice electrical simulation [30]. In order to calculate the photo-dark current of the interdigitated PD conveniently, we take the `W_p and `W_n as the equivalent widths of P- and N-regions. N_i, N_A, and N_D are the intrinsic carrier concentration, the acceptor concentration, and the donor concentration respectively.

(11)$${I_t} = \frac{{\frac{{\sqrt {2m_c^\ast } }}{{{E_g}}} \cdot {q^3}}}{{({4{\pi^2}{\hbar^2}} )}} \cdot A \cdot V \cdot E \cdot \exp \left( {\frac{{ - \gamma \sqrt {m_c^\ast{\cdot} {E_g}} }}{{q\hbar E}}} \right),$$

After constructing the spice circuit model of the interdigitated Ge-on-Si PD, the absorption coefficients of the Ge layer in the C-band are calculated by Eq. (12) [22]. The interdigitated PD is mainly used in the domains of weak light detection, so the photo-generated space charge effect under strong light is not considered here. Figure 9 shows the absorption coefficients of the device under -20 dBm optical power irradiation. In order to take the Ge absorption coefficients with the Franz-Keldysh effect into the spice model, a polynomial fitting Eq. (13) is used to obtain the relationship between the absorption coefficients at 1550 nm and the applied bias voltages.

(12)$${\alpha _{Ge}} ={-} \frac{1}{{{t_{Ge}}}}\ln \left( {1 - \frac{{1240}}{\lambda } \cdot \frac{{{I_{ph}}}}{{{P_{in}}(1 - r)}}} \right),$$

(13)$$\begin{array}{l} {\alpha _{Ge}}({1550} )= 2.414 \cdot {|{V - 0.5} |^5} - 31.551 \cdot {|{V - 0.5} |^4} + 151.233 \cdot {|{V - 0.5} |^3}\\ \textrm{ } - 279.625 \cdot {|{V - 0.5} |^2} - 162.336 \cdot |{V - 0.5} |+ 10825.747, \end{array}$$

Figure 10 shows the photo-dark current calculated by the spice model at 1550 nm under different incident light power, the diamonds represent the simulation result and the dots are the experiment result. It can be seen that when the leakage resistance R_d is 11.8 MΩ, the model can fit the dark current of the interdigitated PD well. Due to the epitaxial buffer layer contains a large number of defects at the interface of Ge and Si, the actual dark current at bias lower than 1.5 V is slightly higher than the simulation result. As for the photocurrent, the model has a good fitting under -30 dBm and -20 dBm incident optical power. As the optical power increases to -10 dBm and above, because of the space charge effect, the PD needs a reasonably higher bias to completely sweep the photo-generated carriers to the electrodes, so the photocurrent increases first and then stabilizes with the increase of voltage. However, the model does not contain the space charge effect, with the incident optical power higher than −10 dBm, the simulated photocurrent is slightly different from the experiment.

Fig. 9. Absorption coefficients of Ge-on-Si PD at different wavelengths in the C-band.

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Fig. 10. The current versus bias voltage at different optical power.

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Table 1. Spice Simulation Parameters

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Because the direction of the electric field in the p-i-n junction is not strictly consistent with the one of carriers’ movement, it is impossible to accurately calculate the transit time and RC coefficient of the interdigitated PD. For this reason, the equivalent capacitance C_t and parasitic resistance R_s are used to form a low-pass filter to represent the bandwidth performance of the interdigitated PD [31]. The simulated radio frequency (RF) response at 3.5 V is shown in Fig. 11. The red points are experiment data and the blue line is the AC simulation result. As mentioned above, with 3.5 V bias applied, the 3 dB bandwidth of the device is ∼1.537 MHz, corresponding to the parasitic resistance R_s of 1 Ω and the C_t of 1.73 nF.

Fig. 11. RF response–frequency plot for the interdigitated PD at 3.5 V.

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Then we extend the Franz-Keldysh effect to the whole C-band. The dots in Fig. 12 are the experiment result under -20 dBm optical power, and the diamonds represent the result simulated by Eq. (14) in spice model. The coefficients of Eq. (14) in the C-band are shown in Table 2. The spice model with Franz-Keldysh effect can show the distinctions between the PD’s light absorption ability in the C-band and the simulated photocurrent with different bias applied has the same tendency as the experiment data, which can be applied to detectors and electro-absorption modulators of different materials used in communication bands [32–34].

(14)$$\begin{aligned} {\alpha _{Ge}}(\lambda )&= A(\lambda )\cdot {|{V - {V_m}(\lambda )} |^5} + B(\lambda )\cdot {|{V - {V_m}(\lambda )} |^4} + C(\lambda )\cdot {|{V - {V_m}(\lambda )} |^3}\\ &\textrm{ + }D(\lambda )\cdot {|{V - {V_m}(\lambda )} |^2}\textrm{ + }E(\lambda )\cdot |{V - {V_m}(\lambda )} |+ F(\lambda ), \end{aligned}$$

As seen from Table 3, the surface illuminated interdigitated Ge-on-Si PD in this work has good electro-optic characteristics for near-infrared light. Although the bandwidth is not the highest, it is sufficient to meet the needs of week light detection domains such as Lidar ranging systems. It provides an alternative solution for the scenarios where optical fibers and gratings cannot be used effectively to collect light signals.

Fig. 12. The simulated photocurrent of the spice model at different wavelengths under -20 dBm optical power.

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Table 2. Polynomial Fitting Coefficients of Absorption Rate

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Table 3. Device Performance of Surface Illuminated PD

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3.4 Ge-on-Si finger APD

In order to further optimize the performance of dark current, we designed a kind of Ge-on-Si APD with interdigitated structure. As shown in Fig. 13(a), all the interdigitated regions in the Si substrate are replaced with P-region, a Si intrinsic region with width of 0.5 µm between the heavily doped N++-region and the P-region is designed to achieve electron avalanche multiplication. The APD has the same doping levels as the interdigitated PD. In order to ensure the lowest dark current at room temperature, according to the Fig. 13(b), we finally chose the APD with finger width of 2.2 µm, finger length of 38 µm and spacing between fingers of 2 µm for performance measurement, by comparing the dark current density in all samples.

Fig. 13. (a) The diagram of large-size interdigitated APD’s Si substrate; (b) Dark current density of APDs at reverse bias of 5 V bias.

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As shown in Fig. 14, the electric field is mainly concentrated in the avalanche region, rather than the Si interdigitated region, which avoids the generation of large dark current at the interface between Ge absorption layer and Si substrate. The dark current performance of the interdigitated APD shown in Fig. 15(a) is significantly improved compared to the interdigitated PD. The dark current in linear region is at nA order, which is two orders of magnitude lower than the PD.

Fig. 14. Electric field distribution of interdigitated Ge-on-Si APD with 13.3 V bias applied.

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Fig. 15. Photoelectric characteristics of interdigitated Ge-on-Si APD: (a) I-V characteristic curve of APD; (b) APD responsivity at -20 dBm light power; (c) Avalanche multiplier gain at -20 dBm light power; (d) RF response–frequency plot for the interdigitated APD at 0.95 V_br.

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But it is difficult for the electric field to extend into the Ge absorption layer and sweep the photo-generated carriers to the electrodes of the interdigitated APD. When the device is under the 1550 nm light illumination at different power, the photocurrent in the linear region does not show a linear increase trend with the increase of the light power like the interdigitated PD. We set the voltage corresponds to the 100 µA dark current as the breakdown voltage V_br [9,25,38] and it can be seen from Fig. 15(a) that V_br is ∼13.3 V. Due to the space charge effect, as the incident optical power increases, the APD needs a larger bias voltage to achieve avalanche multiplication, and the V_br increases with the increase of light power.

As the photo-generated carriers in Ge absorption layer move longitudinally to the Si substrate, meanwhile, the avalanche multiplication occurs in the lateral p-i-n junction of the Si substrate. The depletion of the absorption layer and electron avalanche occur simultaneously, and the unity gain of the interdigitated APD cannot be directly determined. We define the 2 V bias as the unity gain voltage of the APD (V_Gain₌₁) and use Eq. (15) to obtain the avalanche multiplication gain of the device. As shown in Fig. 15, the dark current of the APD device is ∼200 nA at 0.95 V_br and optical responsivity is ∼0.243 A/W with a gain of ∼2. At the same time, the 3 dB bandwidth of the APD is ∼84.3 KHz, which corresponds to a gain-bandwidth product (GBP) of ∼169 KHz. Because the electric field does not extend effectively over the entire Si substrate, the carriers in the device cannot drift at saturation speed. In addition, the capacitance of this large-size APD is 1000 to 10000 times larger than the reported devices, leading to a poorer 3 dB bandwidth and GBP as compared with the existing results. However, as shown in Table 4, the merit of lower dark current allows the interdigitated APD to be used for weak light detection. With the optimization of device structural parameters and circuit coordination, we believe the interdigitated APD has application value in domains which require low dark count noise, such as optical communication and cloud computing.

(15)$$M(V )= \frac{{{I_{\textrm{light}}}(V )- {I_{\textrm{dark}}}(V )}}{{{I_{\textrm{light}}}({{V_{\textrm{Gain} = 1}}} )- {I_{\textrm{dark}}}({{V_{\textrm{Gain} = 1}}} )}},$$

Table 4. Device Performance of Surface Illuminated APD

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4. Conclusion

To address the problem of surface illuminated detectors being of low responsivity, this work proposes a large-size Ge-on-Si PD with interdigitated structure. the Ge absorption layer area of the detector reaches 44 µm × 40 µm. The optimal responsivity of the interdigitated PD reaches ∼0.64 A/W at 0.5 V and ∼0.62 A/W at 2 V bias corresponding to the dark current is ∼200 nA. The optimal 3 dB bandwidth reaches ∼1.537 MHz with 3.5 V applied voltage. Then we design a current source model with Franz-Keldysh effect which can show the distinctions between the PD’s light absorption ability at different wavelengths and be applied to detectors and electro-absorption modulators of different materials used in communication bands. In order to further optimize the dark current performance, an interdigitated Ge-on-Si APD with the same size of Ge absorption layer was designed, whose breakdown voltage is designed ∼13.3 V at room temperature and the dark current density in linear region is at mA/cm² order. The PD and APD with interdigitated structure provide hardware support for weak light detection at room temperature.

Funding

National Key Research and Development Program of China (2016YFE0200700); National Natural Science Foundation of China (61627820, 61934003, 62090054); Jilin Scientific and Technological Development Program (20200501007GX).

Acknowledgments

We thank Prof. Liu-Qiang Zhang in Chongqing University for spice simulation.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter	Quantity	Parameter	Quantity
A (µm²)	1760	N_i (cm^-3)	1.5E16
λ (nm)	1550	N_A (cm^-3)	1E19
r	0	N_D (cm^-3)	1E19
`W_n (µm)	23.42	τ_n (ns)	7.9
W_i (µm)	3.72	τ_p (ns)	7.9
`W_p (µm)	23.42	m_c*	0.98 m₀
R_d (MΩ)	11.8	ɛ_Si	11.7
R_s (Ω)	1	E_g (eV)	1.12
C_t (nF)	1.73	C_no (pF)	3
v_n (m/s)	1.1E5	v_p (m/s)	9.5E4
τ_nr (ns)	630	τ_pr (ns)	630
D_n (cm²/s)	25	D_p (cm²/s)	10

Wavelength (nm)	1530	1540	1550	1560	1570
A (λ)	0.757	2.132	2.414	0.265	-2.389
B (λ)	-11.684	-26.821	-31.551	-1.438	35.956
C (λ)	67.970	128.539	151.233	-11.099	-208.752
D (λ)	-166.054	-261.816	-279.625	141.484	613.677
E (λ)	19.597	-18.616	-162.336	-691.517	-1096.121
F (λ)	8271.162	10019.885	10825.747	10322.982	8403.385
V_m (λ)	1.2	0.85	0.5	0.3	0.0

Reference	Dark Current (A)	Responsivity (A/W)	3 dB Bandwidth (Hz)
[35]	10⁻⁵	∼0.41	-
[36]	10⁻⁶	0.64	-
[37]	10⁻⁸	0.47	3.6E10
This Work	10⁻⁷	0.64	1.53E6

Reference	λ (nm)	Dark Current (A)	Responsivity (A/W)	GBP (Hz)
[12]	1310	∼10⁻⁶	5.88	3.40E11
[13]	1310	10⁻⁶	-	1.50E11
[39]	1550	10⁻⁶	-	1.80E11
[40]	1310	∼10⁻⁶	6.54	1.80E11
This Work	1550	10⁻⁷	0.243	1.69E5

Parameter	Quantity	Parameter	Quantity
A (µm²)	1760	N_i (cm^-3)	1.5E16
λ (nm)	1550	N_A (cm^-3)	1E19
r	0	N_D (cm^-3)	1E19
`W_n (µm)	23.42	τ_n (ns)	7.9
W_i (µm)	3.72	τ_p (ns)	7.9
`W_p (µm)	23.42	m_c*	0.98 m₀
R_d (MΩ)	11.8	ɛ_Si	11.7
R_s (Ω)	1	E_g (eV)	1.12
C_t (nF)	1.73	C_no (pF)	3
v_n (m/s)	1.1E5	v_p (m/s)	9.5E4
τ_nr (ns)	630	τ_pr (ns)	630
D_n (cm²/s)	25	D_p (cm²/s)	10

Surface illuminated interdigitated Ge-on-Si photodetector with high responsivity

Abstract

1. Introduction

2. Device design and fabrication

3. Device performance and simulation

3.1 I-V and responsivity

3.2 3 dB bandwidth

3.3 Equivalent circuit model

3.4 Ge-on-Si finger APD

4. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (15)

Tables (4)

Equations (15)

Optics Express