Open Access
Add to BibSonomy
Abstract
In this paper, a new method combining carrier transport in semiconductors with an RF equivalent circuit was put forward to simulate the frequency response of an avalanche photodiode (APD). The main trade-off between the gain-bandwidth product (GBP) and the dark current was analyzed to optimize the structure of an APD; and a separated absorption, grading, charge, multiplication, charge, transit (SAGCMCT) structure with 120 nm balanced InAlAs multiplication layer was proposed to reduce the dark current and improve the frequency response. The fabricated triple-mesa type back-illuminated InGaAs/InAlAs APD achieved the properties of low dark current of 6.7 nA at 0.9Vb and high GBP over 210 GHz.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical communication application has always been the main driving force for the sustainable development of photodetector. Compared with a pin photodiode, the internal gain of an avalanche photodiode (APD) can improve the response of the device to achieve high sensitivity. The optical receiver made with it needs no extra optical amplifiers such as semiconductor optical amplifiers. For 1550-nm high-speed detection, InAlAs is gradually developed as the avalanche material: its low ionization coefficients ratio ($k = 0.15\sim 0.3$ [1])$\; $allows higher gain-bandwidth product and lower excess noise, compared with InP ($k = 0.45$ [2]). Therefore, recently InAlAs-APDs have been intensively investigated for high speed and low noise optical receivers such as 25-Gbps and 5G front-haul transmission with middle- or long-reach systems.
In order to meet the requirements of high-speed transmission, many efforts have been made to improve the bandwidth and GBP of the device. But at the same time, the dark current became relatively high. Rouvie et al., used 200 nm InAlAs as the avalanche layer to fabricate an APD with a diameter of 30μm. Its gain-bandwidth product (GBP) reaches 140 GHz, and the dark current is 19 nA at 0.9 breakdown voltage (Vb) [3]. Nada et al., proposed an APD of 100 nm avalanche layer, that the GBP reaches 235 GHz when the diameter is 20μm. However, It’s Id (0.9Vb) is higher than 0.2μA [4]. Afterward, they decreased the avalanche layer to 90 nm. Although the GBP of 20μm diameter APD reaches 270 GHz, the dark current (0.9Vb) increases to 2μA [5]. These studies show that the thinner the multiplication layer, the larger the GBP, but the dark current increases with the decrease of the avalanche thickness. This is because when an avalanche occurs in a thin multiplication layer, the internal electric field is higher at operating bias, resulting in a lager tunneling dark current. The research of Ferraro et al., showed that when the avalanche layer increases to 400 nm with a diameter of 100μm, Id (0.9Vb) can reduce to 10 nA, but the bandwidth under this condition is only 1 GHz [6]. In order to achieve large GBP and low dark current at the same time, we should adopt the appropriate thickness of the multiplication layer.
In previous studies, people usually adopted two simulation methods to calculate the response speed of APDs. One is the Monte Carlo simulation [7], which can simulate the complex motion of carriers to obtain the frequency response of the device, but the effect of RC time in the external circuit is not considered. The other is the small-signal equivalent circuit simulation [8], which can effectively simulate the bandwidth limitation of the external circuit but can not well simulate the carrier transport process in the device. Therefore, both the above methods have their own limitations.
In this paper, we proposed a novel simulation method, in which the carrier transport process (including the electron energy level transition, carrier mobility affected by various scattering [9], and the impact ionization, etc.) was coupled with an external RF circuit to make the simulation more close to the actual device, so as to obtain the frequency response of APDs. Through this method, we analyzed the main factors that affect the bandwidth of APDs under different gain. Considering the trade-off between GBP and tunneling current, an optimized 120 nm InAlAs multiplication layer was adopted in the separated absorption, grading, charge, multiplication, charge, transit (SAGCMCT) structure. In addition, since the thin multiplication layer needs a larger electric field to avalanche, a triple-mesa structure was adopted to reduce the edge electric field of the multiplication layer, so as to suppress edge breakdown and reduce the surface leakage current induced by impurities and defects. Furthermore, we proposed a tunneling multiplication coefficient M* in components analyzing of the dark current. The fabricated InGaAs/InAlAs APD with a diameter of 14μm exhibits low dark current of 6.7 nA at 0.9Vb and high 3-dB bandwidth, about 20 GHz when the multiplication factor M is 5.
2. Device structure
In order to improve the high-frequency performance of an APD, the primary methods are reducing the thickness of the depleted region and using a partially depleted absorption layer to reduce the transit time of carriers. While reducing the thickness of the depleted region, the capacitance increases, and the RC time degrades the high-frequency characteristics. Therefore, the SAGCMCT structure is adopted. With the introduction of the new n-charge and transit layer, the capacitance of the device decreases while the total transit time of carriers keeps invariant. The specific structure presented in Fig. 1.
In this device the avalanche multiplication is initiated by electrons injection, the carrier transit time of an APD is composed of three parts: firstly, the photo-induced carriers separate in the absorption region and the electrons drift to the multiplication layer under the external electric field. Secondly, the electron-hole pairs are generated by impact ionization constantly and drift in the multiplication layer, this part of time increases with increasing of avalanche multiplication. Finally, the multiplicated electrons pass through the n-charged and transit layers, and the holes traverse the p-charged and absorption region in the reverse direction. Keeping the thickness of AGCM layers unchanged, if the transit time of multiplicated electrons is less than holes by adjusting the thickness of each layer, the newly introduced n-charge and transit layers make the thickness of the depleted region increase that decrease the capacitance but do not affect the total transit time, so as to improve the bandwidth.
In addition, a triple-mesa structure was adopted to confine the electric field to the central region of the APD, which can reduce the electric field intensity in the peripheral region of the mesa, as shown in Fig. 1. The structure of SAGCMCT was assumed as a basis for further optimization. In order to improve the GBP, reduce the dark current, and increase the unity-gain bandwidth of an APD, the multiplication, absorption, and transit layers need to be optimized by simulation. We first proposed our detailed simulation method and then made the optimizations.
3. Simulation method
The optical-microwave conversion frequency response of the APD is limited by both the time of carrier transport in the device and the external parasitic RC time constant. Figure 2(a) shows the cross-sectional view of the back-illuminated APD, and indicates how the equivalent circuit components are connected, where Rc, Rl are the electrode contact resistance and load resistance, respectively; Cj is the reverse bias junction capacitance, and Cx is the parasitic capacitance between p-electrode lead and n-electrode pad, n-electrode lead [8]. Rearrange the equivalent circuit components shown in Fig. 2(a) to give the RF equivalent circuit as shown in Fig. 2(b) (ii), which can be used to calculate the effect of the external parasitic RC time constant. As for the carrier transit time, COMSOL simulation software was used to simulate. Then, take the I-t limited by carrier transit time as a current-controlled current source (CCCS), coupled to the RF equivalent circuit [8], as shown in Fig. 2(b). Here, we defined the current source port only affected by carrier transit time as ① and the current output port coupled with RF equivalent circuit as ②.
Fig. 2. (a) Cross section of a back-illuminated APD and the corresponding equivalent circuit elements. (b) Small-signal radio frequency model of the APD: (i) current-controlled current source affected by the carrier transit time and (ii) equivalent circuit that involves the parasitic elements
Firstly, we analyzed the port 1 affected by the carrier transit time. COMSOL simulation software can simulate the whole carrier transit and impact ionization process of APDs. It includes fundamental semiconductor continuity, Poisson and current density equations. Besides, we added the modified carrier mobility model including ionized impurity scattering, lattice vibration scattering and the limitation of carrier saturation drift velocity under high field [9] of our previous research results, and the impact ionization equations of InAlAs to the semiconductor module. The generation rate of electron-hole pairs produced by impact ionization can be expressed as
Where q is the electric charge of the electron, Jn, Jp, α and β are the current density and ionization coefficients of electrons and holes, respectively. The value of α and β varies with the electric field E, which can be expressed as
The InAlAs impact ionization coefficient used in the simulation is presented in Table 1, which can be used to predict the breakdown voltage using a local model for 0.1-0.14μm InAlAs, and to calculate the GBP and the unity-gain bandwidth in our simulation. Because the ionization shows overshoot and partial oscillation [10], when calculating the GBP, the ionization overshoot in the high field may compensate for the dead space effect [11]. When calculating the unity-gain bandwidth, the time of the impact ionization accounts for a small portion compared with the carrier transit time and the external parasitic RC time.
Table 1. Impact ionization coefficient parameters
The model of the APD shown in Fig. 3 is used for simulation, assuming that the thickness of the multiplication layer is 0.12μm; the p-type absorption, intrinsic absorption and transit layer are 0.3μm. We applied a 1ps Gaussian light pulse to the APD at 10ps. Five monitor points are taken from different areas for the following transit time analysis. We will calculate the detailed carrier distribution and the transit time of electrons and holes, so as to get the frequency response of the whole device.
Fig. 3. The 5 monitors from three active layers (intrinsic absorption, multiplication and transit layers) for analyzing the carrier transit time.
When the bias voltage of the device is 11 V, the intrinsic absorption layer punches through, but no impact ionization occurs in the multiplication layer. The concentration of electrons and holes varies with time as shown in Fig. 4(a) and 4(b), respectively. Before the optical pulse, the concentrations of electrons and holes are relatively low in the depleted region; when t=10ps, the number of photo-induced carriers increases rapidly due to the incident light in the absorption region 1. Then, the peak value of electron concentration appeared in the multiplication 2, 3, 4 and transit layer 5 in turn, which indicated that the electrons drift towards the n-electrode under the external electric field. Besides, the photo-generated holes drift reversely out of the intrinsic absorption layer 1 to the p-electrode, and the hole concentrations in the multiplication and transit layers are relatively low. To facilitate comparison, we define the transit time of electrons and holes as: from the arrival of the optical pulse, the electron and the hole concentrations decrease to 1/e of the peak value in the transit and the intrinsic absorption layers, respectively. Thus, the transit time of electrons is 4.4ps, and of holes is 3.0ps, indicating that the total carrier transit time is mainly affected by electrons when the multiplication factor is 1.
Fig. 4. When the bias voltage is 11 V, the concentration of (a) electrons and (b) holes varies with time at 5 different positions. The multiplication factor M is 1.
Then, as the bias voltage increases, the electric field intensity in the multiplication layer is high enough to cause the avalanche multiplication, resulting in a large number of electron-hole pairs and the carrier transit time increases. For example, when the bias is 25.9 V, the concentration of electrons and holes varies with time as shown in Fig. 5. In the multiplication layer, the electron concentration near the n-charge layer 4 is higher than that near the p-charged 2, and the hole concentration is just on the contrary. This is because after the photo-generated electrons drifting into the multiplication layer, a large number of electron-hole pairs are generated by the impact ionization. Those electrons drift toward the n-electrode, and the holes drift to the p-electrode reversely. If the electric field is strong enough, they will impact and ionize again to produce new electron-hole pairs. Finally, the hole concentration near the p-charge layer and the electron concentration near the n-charged are higher. In the absorption layer 1, the photo-generated holes drift to the p-electrode that the hole concentration decreases at first, and then increases with the injection of the holes produced by avalanche multiplication. According to the previous definition, the transit time of electrons and holes is 30.4ps and 35.1ps, respectively. By comparing Fig. 4 and Fig. 5, we can see that when there is impact ionization the transit time increases abruptly from 4.4ps to 35.1ps, and it is clear that the increase of transit time is mainly due to the impact ionization.
Fig. 5. When the bias voltage is 25.9 V, the concentration of (a) electrons and (b) holes varies with time at 5 different positions. The multiplication factor M is 30.
For the total response time of APDs, we can derive from the frequency response of port 2, as shown in Fig. 2(b), which limited by both the carrier transit time and the external parasitic RC time constant. The transit time is coupled from port 1 to the equivalent circuit (part b) through a current-controlled current source. According to the same electrode layout and test conditions of our fabricated photodiodes previously, the capacitance and resistances obtained are brought into the equivalent circuit. Cx, Rc and Rl are 20fF, 30Ω and 50Ω, respectively. When the diameter of the device is 14μm, Cj is 40fF.
Figure 6 shows the pulse response varies with time under different gain, where the solid and dotted lines are port 1 and port 2, respectively. It can be seen that the pulse response is greatly affected by the external RF equivalent circuit when M is small. As the increase of bias voltage, the gain of photocurrent increases, and the duration of the impact ionization extended. At the same time, the proportion of the effect of the external circuit on the pulse response gradually decreases with the increase of multiplication, which indicates that the pulse response is gradually limited by the time of the avalanche multiplication.
Fig. 6. The simulated pulse response of port 1 and 2 with different M, where the solid and dotted lines are port 1 and port 2, respectively. The bias voltages corresponding to the gain of 2, 5, 10, 20, 30 and 40 are 17.8 V, 23.3 V, 24.9 V, 25.7 V, 25.9 V, and 26.0 V.
Then, we perform a fast Fourier transform (FFT) for the pulse response of port 2, as shown in Fig. 7. It can be seen that when M = 2, the 3-dB bandwidth of the device is mainly limited by the carrier transit time and RC time constant, about 25 GHz. As the bias increases, the 3-dB bandwidth decreases due to the avalanche multiplication.
According to the above method, the 3-dB bandwidth under different gain and the maximum gain-bandwidth product of the device can be obtained, which provides a theoretical basis for us to optimize the structure of the device. Our optimization mainly focuses on improving the frequency response and reducing the dark current.
4. Layer thickness and mesa profile optimization
4.1 Multiplication layer
In order to improve the GBP of the device, a thin multiplication layer is usually adopted to produce avalanche multiplication. However, it is necessary to investigate whether or to what extend the thickness of other layers affects the GBP of the device.
Taking the InAlAs multiplication layer of 0.12μm as constant, we vary the absorption and transit layers to find their relationship with response bandwidth. The diameter of the device is 14μm. Cj in the RF equivalent circuit is adjusted by the thickness of the depletion region, and Cx, Rc, Rl also take 20fF, 30Ω and 50Ω, respectively. Since the GBP is calculated under a large avalanche multiplication, to facilitate comparison, we adjusted the bias voltages of different devices to make the multiplication factor keep consistent, M=30. Figure 8 shows the frequency response of the APD with different intrinsic absorption and transit layers. It can be seen that when the multiplication layer is 0.12μm, although the signal attenuation of devices is different under high frequency, the 3-dB bandwidth is 6.6 GHz, and the gain-bandwidth product is about 200 GHz. Thus, the thickness of other layers has little effect on GBP in the case of high gain, which is because the avalanche multiplication time dominates relative to carrier drift time and RC constant.
Fig. 8. The frequency response of the APD with different thickness of intrinsic absorption dA and transit dT layers. The multiplication factor M is 30. We can see that the thickness of the absorption and transit layer has no effect on the 3-dB bandwidth.
Therefore, in order to compare the GBP with different multiplication thicknesses, we assume that the thicknesses of the absorption and transit layers are 0.3μm. Figure 9 shows the relationship between the GBP and the M only by changing the thickness of the multiplication layer. According to the simulation, the GBP of 100 nm InAlAs is 230 GHz, which is consistent with the experimental data [4,12]. We can figure that the GBP of the device increases as the thickness of the multiplication layer decreases. In order to make the gain-bandwidth product of the device greater than 200 GHz, the multiplication layer can not thicker than 0.12μm.
Fig. 9. The GBP of the device depending on the multiplication factor M with different thickness of the multiplication layer.
However, as a thinner multiplication layer increases the GBP, it also increases the tunneling current, which degrades the optical receiver sensitivity. Thus, we have to optimize the thickness of the avalanche layer to coordinate GBP and dark current.
Tunneling processes include direct band-to-band tunneling (BBT) and trap-assisted tunneling (TAT) [13]. TAT dark current can be neglected in the intrinsic multiplication region. The dark carrier generation rate per unit volume due to BBT can be expressed as:
Where Eg is the bandgap, q is the electron charge, and $\hbar $ is the reduced Planck’s constant. E is the position-dependent electric field. ${m_r}$ is the reduced mass of the light hole effective mass ${m_{lh}}$ and the conduction band effective mass mc, $1/{\textrm{m}_\textrm{r}} = 1/{\textrm{m}_{\textrm{lh}}} + 1/{\textrm{m}_\textrm{c}}$.
Assuming the APD diameter is 14μm, the relationship between the tunneling current and the electric field is shown in Fig. 10. The breakdown electric field of the 0.1μm avalanche layer is 850 kV/cm [12] that makes the tunneling current about 5μA. When the thickness of the multiplication layer increases to 0.12μm, the breakdown electric field is 760 kV/cm, and the tunneling current is low down to 0.5μA, although the two lines seem to be much alike. If the thickness of the multiplication layer continuously rises, although the tunneling current reduced, the GBP cannot exceed 200 GHz according to the above analysis, so the multiplication layer takes 0.12μm.
Fig. 10. Calculated tunneling dark current vs. electric field corresponding to the multiplication layer of 0.1μm and 0.12μm
4.2 Absorption and transit layer
Besides the multiplication layer, the absorption and transit layers are the other two very important regions in SAGCMCT avalanche photodiode. Optimizing the structure and thickness of the absorption and the transit layer is the key to improving the unity-gain bandwidth of the APD. In order to obtain sufficient responsivity, the thickness of the absorption region is designed to 0.6μm with a partially doped structure (p- and depleted InGaAs), which is called the maximized-induced current (MIC) [4] design. The MIC design can relax the trade-off between responsivity and bandwidth. That is, given the total absorption layer thickness, the carrier transit time can be minimized by adjusting the ratio between the two type absorption layers [14], and the 3-dB bandwidth determined by such a means is much larger than that for a totally depleted absorption layer. Also, the MIC design can suppress the space charge effect [15]. After the growth of an antireflection coating, an absorption layer of 0.6μm can make the general responsivity reach 0.87A/W at a unit gain.
According to the previous analysis, in order to coordinate the tunneling dark current and GBP of the APD, a 0.12μm InAlAs is used as the multiplication layer. At this time, we need to optimize the ratio of the intrinsic absorption layer and the thickness of the transit layer to maximize the 3-dB bandwidth. For this, we should comprehensively analyze the carrier transit time, including the transport of photo-generated and multiplied carriers in the whole depleted region, and reduce the impact ionization time. We take M = 2 as an example, that is, only one gain is generated. When the diameter of the device is 14μm and the total thickness of the absorption layer is 0.6μm, the 3-dB bandwidth with different intrinsic absorption and transit layers is shown in Fig. 11.
Fig. 11. The 3-dB bandwidth varies with the thickness of the transit and intrinsic absorption layers; the total absorption layer is 0.6μm and M=2. The inflection point appears due to the transit time of the multiplied electrons exceeds that of the multiplied holes.
When the multiplication factor M = 2, the main factors affecting 3-dB bandwidth are the carrier transit time and the external parasitic RC time constant. The carrier transit time is mainly divided into three parts, t1: the time photo-generated electrons diffusing in the p-doped absorption and drifting in the depleted region to the multiplication layer, t2: the time impact ionization to produce new carriers and t3: the time multiplicated carriers moving to the contact layer, in which electrons drift through n-charge and the transit layer, while holes pass through p-charge and depleted absorption layer. These two processes co-occur, and t3 is determined by carriers with longer transit time. Because different devices have the same gain, the main factors that lead to different bandwidth are t1, t3, and junction capacitance Cj.
As shown in Fig. 11, when the thickness of the transit layer dT is relatively thin, the drift time of multiplicated electrons is shorter than that of holes, thus t3 is mainly determined by the thickness of the intrinsic absorption dIA. In this case, with the increase of dIA, Cj and t3 decreases and increases, respectively. Besides, due to the MIC design, there is an appropriate proportion of the intrinsic absorption layer to make t1 reach the minimum. Therefore, under the combined influence of t1, t3 and Cj, the bandwidth increases first and then decreases with the increase of dIA. When the width of the transit layer rises, the depleted region extends, resulting in a decrease of Cj, thus increasing the 3-dB bandwidth. However, when the thickness of the transit layer is more than a specific value that the drift time of multiplicated electrons is equal to holes’, t3 is decided by dT, with a positive correlation. The influence of carrier transit time on bandwidth is more significant than that of capacitance, so the 3-dB bandwidth of the APD decreases with the increase of dT. Thus, in order to maximize the frequency response, the combination within the gray box should be considered for the thickness of the intrinsic absorption and transit layers.
4.3 Mesa etching profile
In addition, due to a 0.12μm multiplication layer, the electric field causing the avalanche is high than 700 kV/cm. In order to reduce the edge electric field of the multiplication layer to reduce the edge breakdown and the surface leakage current, which contributes to the dark current, we adopted a triple-mesa structure, as shown in Fig. 1. The etching depth and curvature of the top mesa are very important to the performance of the device.
The top mesa must be controlled in the intrinsic absorption region to define the APD active layer [16]. As shown in Fig. 12(a), when the top mesa of the APD is etched to the middle of intrinsic absorption layer, the central electric field of the multiplication layer EMC is larger than the edge electric field EME, so that the avalanche multiplication is limited to the central active region, which can reduce the surface leakage current and improve the reliability of the device. However, if the top mesa is etched to the charge layer, a large electric field will be generated at the edge of the charge or multiplication layer due to the excessive geometric curvature as shown in Fig. 12(b), which will increase the tunneling current and even cause local breakdown before punch through, so that the device no longer functions properly.
Fig. 12. The two-dimensional electric field intensity distribution in the APD with different etching depth of the top mesa, which ends at (a) the intrinsic absorption layer and (b) the charge layer, both devices are at the same bias voltage, 25 V.
Besides, the curvature of the top mesa has a great influence on the tunneling dark current in the absorption region. We can assume that the etching corner is a standard arc, and Fig. 13(b) shows the distribution of the electric field in the intrinsic absorption layer under different etching curvature of the top mesa. It can be seen that the electric field intensity at the edge of the top mesa is greater than that at the center due to the etching curvature. When the top mesa is rectangular (Rc1=0 nm), the maximum electric field reaches 300 kV/cm, resulting in a large tunneling current in the absorption layer. However, as the radius of the etching curvature increases, the electric field intensity at the edge of top mesa decreases. For example, when the radius of curvature is 150 nm, the edge electric field is about 130 kV/cm, which can greatly reduce the tunneling.
Fig. 13. (a) Cross-sectional profile of the triple-mesa structure and (b) calculated electric field (EA) against the position of the intrinsic absorption layer under different etching curvature of the top mesa.
Therefore, the intrinsic absorption layer is required to be thick enough to stop the top mesa and increase the curvature of etching. Combining with the analysis of bandwidth in Fig. 11 and the manufacturing process, we adopt a 300 nm InGaAs as the intrinsic absorption layer. At this time, when the transit layer is 300 nm, the bandwidth reaches the maximum, about 27 GHz. In addition, the dark current of high-speed APD mainly comes from the multiplication layer due to the high electric field. By using a 0.12μm multiplication layer, the tunneling current is effectively reduced while increasing the gain-bandwidth product, about 200 GHz. Besides, a triple-mesa structure also reduced the surface leakage current, thus enabling our APD to reach an optimal state.
5. Device fabrication
The optimized epitaxial layers consist of p-contact, diffusion-block, graded doped p-type absorption (300 nm), intrinsic absorption (300 nm), grading (30 nm), p-type field control (70 nm), InAlAs avalanche (120 nm), n-type field control (70 nm), transit (300 nm), and n-contact layers. All layers were grown on semi-insulating InP substrate by molecular beam epitaxy (MBE). In order to minimize dark current from tunneling, the field in the InGaAs absorption layer was kept to less 100 kV/cm by the use of a 70 nm thick p-doped InAlAs charge layer. The avalanche layer thickness of 120 nm is chosen to maximize the gain-bandwidth product and limit the breakdown dark current. In this case, the p- and n-field control layers make a ‘‘low–high–low’’ electric field profile around the avalanche layer. The 30 nm thick InGaAlAs grading layer eased carrier accumulation between the InGaAs absorption layer and the InAlAs field control layer.
The APDs were fabricated using chemical wet-etching and metal lift-off processes. Compared with dry-etching, wet-etching has less damage to the device surface and increases the radius of curvature of etching. For electrode interconnection, the mesa was passivated with a plasma enhanced chemical vapor deposited (PECVD) Si3N4 film. Metal contacts were then deposited on the anode and cathode of the diodes. The metal on the anode also acted as a mirror for light not absorbed on the first pass through the absorber. A PECVD Si3N4 antireflective (AR) coating was deposited on the polished rear side of the wafer. After wafer fabrication, devices were diced and flip-chip mounted on metal-patterned ceramic carriers for testing.
6. Test results and discussion
To investigate that our APD structure optimized by simulation contributes to reducing the dark current, preventing the edge-breakdown and improving the frequency response, we carried out I-V measurement under illumination and dark conditions and 3-dB bandwidth of the 14μm diameter APD at the wavelength of 1.55μm.
As shown in Fig. 14, (I)-V characteristics under dark and different illumination conditions, the voltages at which the photocurrent starts to flow normally (Von) and the breakdown voltage (Vb) were 9.5 and 27.5, respectively. Blow 24 V, the dark current has square root voltage dependence, indicating that G-R is the dominant mechanism. It is because the length of the space charge region rises with the increase of the bias voltage; the number of recombination centers in the space charge region multiplies, which leads to the increase of dark current. However, as the bias voltage increases to 24-27.5 V, the tunneling effect in the multiplication layer accounts for the majority of the dark current. At 0.9Vb (24.75 V), the dark current is only 6.7 nA, which is the lowest among the reported high-speed APDs [3–5]. As expected, the M rises smoothly, indicating that the fabricated triple-mesa APD eliminates edge-breakdown. On the other hand, the photocurrent gains of 1-50 under different incident light coincides, which illustrates that the M corresponding to the small optical power is mainly related to the bias voltage. Limited by the test conditions and the growth quality of the antireflection film, the unity-gain responsivity of the fabricated APD is 0.55A/W at 1.55μm, which can be further improved by optimizing the preparation process.
Fig. 14. I-V characteristics and voltage dependence of multiplication factor (M) of the fabricated APD. The optical power corresponding to photocurrent 1, 2, and 3 are 0.024μW, 0.3μW, and 2.4μW.
The dark current of APD can be expressed as
Among them, ${I_d}$ is the total dark current, ${I_{gr}}$ is the generation-recombination current, ${I_t}$ is the tunneling current, and ${I_{du}}$ is the non-multiplied dark current, mainly from the surface of the device. M is the avalanche multiplication factor of the APD.
We propose M* as the avalanche gain of tunneling dark current. As shown in Fig. 15, when the APD is reverse-biased, the energy band in the multiplication layer became bent on the application of the electric field E, which leads to an additional potential energy $\textrm{q}|\textrm{E} |\textrm{x}$ of the valence band in the P-region. As the bias voltage increases, when $\textrm{q}|\textrm{E} |{\textrm{d}_t}$ is greater than the bandgap Eg, quantum mechanics proves that the electrons at the top of valance band (point A) can pass through the band gap and reach the bottom of the condition band (point B) due to the tunneling effect [17]. Then, the electrons generated by tunneling, which occurred randomly in the multiplication layer can also avalanche multiplied in a large electric field, and the average length of that multiplication is $({{d_m} - {d_t}} )/2{d_m}$, where dm is the thickness of the multiplication layer and dt is expressed as Eg/qE. Thus, the avalanche gain of tunneling dark current is ${\textrm{M}^\ast } = ({{\textrm{d}_\textrm{m}} - {\textrm{d}_\textrm{t}}} )/2{d_m} \bullet \textrm {M}$.
Figure 16 shows the dark current versus the M. It can be seen that when M is less than 5, the external electric field of the device is so low that the tunneling dark current can be ignored. The dark current Id of the APD is a linear function of multiplication factor M; the slope Ls1 is Igr (=0.81 nA). When the device is at a gain of 5-12, the electric field in the avalanche region increases, and the tunneling dark current rises rapidly with bias. As a result, the growth rate of dark current with M is faster than before and deviates from the original linearity. When M is greater than 12, it changes faster than the change of tunneling current with bias. Id is linearly related to M again, and its slope Ls2 is ${\textrm{I}_{\textrm{gr}}} + {\textrm{I}_\textrm{t}} \times ({{\textrm{d}_\textrm{m}} - {\textrm{d}_\textrm{t}}} )/2{\textrm{d}_\textrm{m}}$ (=13.62 nA). It can be seen from the calculation that when M>12, the tunneling current is the main component of the total dark current, accounting for more than 94%.
Fig. 16. The dark current varies the multiplication factor M. The black line is the dark current-gain curve, and the linear fitting curve of that is represented by the dashed line.
In addition, the SAGCMCT structure of the APD has two electric field control layers. With the increase of bias voltage, p-charge and n-charge layers are depleted at two specific voltages respectively to make the intrinsic absorption and transit layers punch through, so that the capacitance of the device decreases rapidly. Figure 17 shows the capacitance of the APD with different top mesa diameters varies with the bias. It can be seen that the two specific bias voltages are 9.5 V and 13 V. According to I-V in Fig. 14, Von is 9.5 V, so it can be judged that 9.5 V and 13 V are the punch-through voltages of p- and n-charge layers, respectively. Besides, the measured capacitance consists of Cj and Cx. Since the electrode lead layout, fabrication process and test conditions of the three diameters are the same, their parasitic capacitance Cx is the same. The junction capacitance Cj is proportional to the area of the top mesa when the device capacitance reaches the minimum, so we can get Cx is about 60fF according to $({150\textrm{fF} - {C_x}} ):({100\textrm{fF} - {C_x}} ):({80\textrm{fF} - {C_x}} )$ approximately equal to ${30^2}:{20^2}:{14^2}$.
The Cx caused by the electrode leads also limits the bandwidth. These conclusions provide the basis for analyzing the frequency response of the device.
The frequency photo-response was on-wafer-characterized using a nonlinear vector network analyzer. To evaluate the gain-bandwidth product of the fabricated APDs, we measured its frequency response from 10 MHz to 40 GHz at 1550 nm at different bias, as shown in Fig. 18. The illustration shows that when the bias voltage is 9 V before the absorption layer punch-through, there is no obvious frequency response of the device due to the incompletely depleted p-charge layer. At 10 V bias, although the intrinsic absorption layer punched through and photo-generated carriers can be collected by electrodes, the electric field intensity in absorber is relatively low that limits the electron drift velocity, and at the same time, electrons diffuse in the transit layer that not punched through, which restricts the 3-dB bandwidth of the device. Then the bandwidth increases with the bias. When the bias is 13 V, the n-charge layer depleted, and the transit layer punch through results in the junction capacitance Cj reaching the minimum value. In addition, as the bias continues to increase, the electrons move with a saturated velocity in the whole depletion region, which improves the frequency response of the device. A maximum 3-dB bandwidth is obtained at 15 V about 24 GHz, which is slightly lower than the theoretical calculation of 27 GHz. The reason for this difference probably is that the measured Cx (∼60fF) is larger than that in simulation (∼20fF), and the bandwidth of our APDs can be further improved by adjusting the electrode lead layout. Above 15 V, the 3-dB bandwidth is gradually reduced with the increase of bias due to the limitation of avalanche multiplication.
Fig. 18. Frequency characteristics of the fabricated APD with a diameter of 14μm under different bias. The illustration shows the frequency response before and after the punch-through voltage 9.5 V, indicating that there is no light response at 9 V, and response at 10 V but low bandwidth.
According to Fig. 14 and Fig. 18, the multiplication factor M and 3-dB bandwidth at different bias voltage are obtained. Figure 19 shows the characteristics of 3-dB bandwidth versus multiplication factor. It can be seen that the 3-dB bandwidth increases at first, then decreases with increasing of M. A broad range of functional multiplication factors (1-10) is achieved with 3-dB bandwidth above 15 GHz. Due to the thickness of the multiplication layer (120 nm InAlAs), the GBP reaches 210 GHz, which is relatively consistent with the theoretical calculation.
Furthermore, we also tested the frequency response of the other two APDs with a diameter of 10μm and 20μm, in which the 3-dB bandwidth is 26 GHz and 20 GHz at 15 V bias respectively, which indicates that the ${\textrm{f}_{3\textrm{dB}}}$ is mainly limited by capacitance. Our APDs should achieve further high-speed operation by increasing the thickness of the depletion region and adjusting the electrode lead layout of the device to reduce Cj and Cx, respectively. In addition, the doping concentration of the n-charge layer should be reduced to make the transit layer punch through at the same time or earlier than the intrinsic absorption, so that the electrons can always move with a saturated velocity in the transit layer and the 3-dB bandwidth of the device reaches the maximum value when the bias voltage is above Von.
7. Conclusion
In the previous state of art, the Id (0.9Vb) of the APD with GBP over 200 GHz is usually on the order of 1μA. We have analyzed the effect of the thickness of the multiplication layer on dark current and GBP, and adopted a 120 nm InAlAs multiplication layer. A triple-mesa structure of SAGCMCT APD is designed and fabricated, which simultaneously presents the properties of low dark current (${\textrm{I}_\textrm{d}}({0.9{\textrm{V}_\textrm{b}}} )= 6.7\textrm{nA}$) and high GBP (210 GHz). At the same time, its bandwidth reaches 20 GHz at M=5, which is suitable for 25Gbit/s high sensitivity optical fiber communication and middle- or long-reach transmission systems. In addition, we proposed a new method, the small-signal pulse response to simulate the APD bandwidth, which can also be applied to PIN-PD, UTC-PD and other semiconductor photodiodes.
Funding
National Natural Science Foundation of China (61774152); National Key Research and Development Program of China (2016YFB0402404, 2019YFB2205202).
Disclosures
The authors declare no conflicts of interest.
References
1. J. C. Campbell, “Recent Advances in Avalanche Photodiodes,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, Los Angeles, California, 2015), paper M3C.1.
2. L. J. J. Tan, J. S. Ng, C. H. Tan, and J. P. R. David, “Avalanche Noise Characteristics in Submicron InP Diodes,” IEEE J. Quantum Electron. 44(4), 378–382 (2008). [CrossRef]
3. A. Rouvie, D. Carpentier, N. Lagay, J. Decobert, F. Pommereau, and M. Achouche, “High Gain x Bandwidth Product Over 140-GHz Planar Junction AlInAs Avalanche Photodiodes,” IEEE Photonics Technol. Lett. 20(6), 455–457 (2008). [CrossRef]
4. M. Nada, Y. Muramoto, H. Yokoyama, T. Ishibashi, and S. Kodama, “InAlAs APD with high multiplied responsivity-bandwidth product (MR-bandwidth product) of 168 A/W.GHz for 25 Gbit/s high-speed operations,” Electron. Lett. 48(7), 397–399 (2012). [CrossRef]
5. M. Nada, Y. Yamada, and H. Matsuzaki, “Responsivity-Bandwidth Limit of Avalanche Photodiodes: Toward Future Ethernet Systems,” IEEE J. Sel. Top. Quantum Electron. 24(2), 1–11 (2018). [CrossRef]
6. M. S. Ferraro, W. R. Clark, W. S. Rabinovich, R. Mahon, J. L. Murphy, P. G. Goetz, L. M. Thomas, H. R. Burris, C. I. Moore, W. D. Waters, K. Vaccaro, and B. D. Krejca, “InAlAs/InGaAs avalanche photodiode arrays for free space optical communication,” Appl. Opt. 54(31), F182–188 (2015). [CrossRef]
7. W. Sun, X. Zheng, Z. Lu, and J. C. Campbell, “Monte Carlo Simulation of InAlAs/InAlGaAs Tandem Avalanche Photodiodes,” IEEE J. Quantum Electron. 48(4), 528–532 (2012). [CrossRef]
8. G. Wang, T. Tokumitsu, I. Hanawa, K. Sato, and M. Kobayashi, “Analysis of high speed p-i-n photodiode S-parameters by a novel small-signal equivalent circuit model,” IEEE Microw. Wireless Compon. Lett. 12(10), 378–380 (2002). [CrossRef]
9. H. Wang, T. He, K. Liu, R. Wang, H. Ye, and X. Yang, “Photocurrent Saturation and Thermal Breakdown Mechanism in Modified Uni-Traveling-Carrier Photodetectors,” J. Nanosci. Nanotechnol. 18(11), 7369–7373 (2018). [CrossRef]
10. D. C. Herbert, “Breakdown voltage in ultra-thin pin diodes,” Semicond. Sci. Technol. 8(11), 1993–1998 (1993). [CrossRef]
11. Y. L. Goh, D. J. Massey, A. R. J. Marshall, J. S. Ng, C. H. Tan, W. K. Ng, G. J. Rees, M. Hopkinson, J. P. R. David, and S. K. Jones, “Avalanche Multiplication in InAlAs,” IEEE Trans. Electron Devices 54(1), 11–16 (2007). [CrossRef]
12. F. Nakajima, M. Nada, and T. Yoshimatsu, “High-Speed Avalanche Photodiode and High-Sensitivity Receiver Optical Subassembly for 100-Gb/s Ethernet,” J. Lightwave Technol. 34(2), 243–248 (2016). [CrossRef]
13. X. Jiang, M. A. Itzler, R. Ben-Michael, and K. Slomkowski, “InGaAsP–InP Avalanche Photodiodes for Single Photon Detection,” IEEE Journal on Selected Topics in Quantum Electronics 13(4), 895–905 (2007). [CrossRef]
14. Y. Muramoto and T. Ishibashi, “InP/InGaAs pin photodiode structure maximising bandwidth and efficiency,” IEEE J. Sel. Top. Quantum Electron. 39(24), 1749–1750 (2003). [CrossRef]
15. M. Nada, S. Kanazawa, H. Yamazaki, Y. Nakanishi, W. Kobayashi, Y. Doi, T. Ohyama, T. Ohno, K. Takahata, T. Hashimoto, and H. Matsuzaki, “High-linearity Avalanche Photodiode for 40-km Transmission with 28-Gbaud PAM4,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, Los Angeles, California, 2015), paper M3C.2.
16. M. Nada, Y. Muramoto, H. Yokoyama, N. Shigekawa, and S. Kodama, “Inverted InAlAs/InGaAs Avalanche Photodiode with Low–High–Low Electric Field Profile,” Jpn. J. Appl. Phys. 51(2), 2BG03 (2012). [CrossRef]
17. S. Chunyu, D. Yanqiu, and W. Yan, “Research on tunnel breakdown model of p-n junction,” Semiconductor Optoelectronics 31(2), 263–265 (2010).
