## Abstract

In this work, we demonstrated a normal incident PIN InGaAs/GaAsSb type-II multiple quantum wells (MQW) photodiode on InP substrate for 2 μm wavelength high-speed operation. The photodiode has a responsivity of 0.35 A/W at room temperature at 2 μm, and a 3 dB bandwidth of 3.7 GHz. A carrier dynamic model is developed to study the bandwidth of the multiple quantum wells photodiode. Simulation results match the experimental data well, and analysis shows that hole transport limits the 3 dB bandwidth performance. By optimizing the MQW design, higher bandwidth performance (>10 GHz) can be achieved.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Recently high speed photodetectors operating at 2 μm wavelength have been gaining increasingly popularity due to its applications on new-generation fiber communication system and gas sensing. The relatively low attenuation at 2 μm of the hollow core photonic bandgap fiber has enabled the new spectral window at this band [1], which demands high speed photodetectors for optical communication. Meanwhile, 2 μm high speed photodetectors also act as the key components of optical lidar system, especially for atmospheric CO2 profile detection [2].

In conventional high speed photodetectors, lattice matched InGaAs photodiodes on InP substrate are widely used due to the high speed and low dark current performance [3]. However, for 2 μm application, In-rich InGaAs has to be used to extend the absorption wavelength, which is lattice mismatched to InP substrate and results in high dark current [4]. Another solution is using InGaAsSb/GaSb based materials [5], but it is expensive and the process technology is not mature. The InGaAs/GaAsSb type-II quantum wells structure lattice matched to InP has been demonstrated for short wavelength infrared operation between 2 and 3 μm [6–9], which shows low dark current and high detectivity (D*) performance at room temperature. Currently, the 3dB bandwidth performance of InGaAs/GaAsSb has been reported in a waveguide-integrated photodiode [10,11], but the device physics has not been fully investigated. For bulk PIN photodiode, existing theoretical model can predict the bandwidth characteristics well [12]. However, it cannot be applied on MQW structure. In reference [13], a thermal activated tunneling model was built to modeling the bandwidth characteristics of quantum dot photodetectors, which agrees with the experiments and shows the physical mechanism of the device. Here, a theoretical model is needed to better understand the frequency response of these type-II QWs devices.

In this work, we, for the first time, developed a carrier transport model based on the rate equation to study the frequency response of these InP based type-II QWs photodiodes, which can also be used to study the other multiple QWs PIN devices. To verify the model, we also processed and characterized the normal incident PIN photodiode with InGaAs/GaAsSb quantum wells absorption layer. The diode shows dark current density around 12 mA/cm^{2}, with optical responsivity of 0.35 A/W at 2 μm and 300 K. The 3 dB bandwidth of the device at different bias is characterized, the highest 3 dB bandwidth of 3.7 GHz can be achieved with a relatively high reverse bias of −14 V. The model we developed in this work can match well the experimental 3 dB bandwidth data at different bias. The results show that the slow hole transport is the main limitation of 3 dB bandwidth performance. The model also shows the potential approaches to enhance the 3 dB bandwidth.

## 2. Device structure and fabrication

The device structure was epitaxially grown with molecular beam epitaxy (MBE), as listed in Table 1. Between p-type and n-type InGaAs contact layers, the absorption layer consists of 50 periods of InGaAs (5 nm)/GaAsSb (5 nm) type II quantum wells. All these compounds are lattice matched to InP substrate.

The diode mesa was patterned by photolithography and then wet etched to the expected height. The contacts were deposited by e-beam evaporation. In order to perform high speed measurement, GSG pads with 150 μm pitch were fabricated by electroplating, and before that, an insulating layer of 2 μm SU-8 was coated and patterned, to separate the pads from the conducting substrate.

## 3. Measurement result

#### 3.1 DC characteristics

The dark current density of the diodes was measured at various temperature (from 77 K to 300 K). Figure 1 (a) shows the dark current density-voltage (J-V) curves of a 130 μm diameter diode. At 300 K, the dark current density is 12 mA/cm^{2} at −5 V bias. The dark current scales linearly with device area, indicating that the dark current is mainly bulk component instead of surface leakage. The Arrhenius plot of dark current at −1 V in Fig. 1 (b) shows the activation energy of 0.313 eV, which is around 63% of effective bandgap (0.5 eV), indicating that both the diffusion component and generation-recombination component dominates the dark current. The dark current can be further suppressed by proper passivation or improved structure design [14–16].

The spectral responsivity at 0 V was measured by a Fourier transform infrared (FTIR) spectrometer, as shown in Fig. 1 (c). Around 2 μm wavelength, the responsivity increases with the rise of temperature. This is due to the red shift of bandgap as temperature increases. For short wavelength below 1.9 μm, the responsivity decreases at the temperature increase, which may be due to the fact that the absorption region is not fully depleted at 0 V, and the photo generated carrier collection drops. Result shows that a 0.35 A/W responsivity is achieved at 2 μm and the cut-off wavelength exceeds 2.4 μm at 300 K. The device saturation performance was also studied in this work as in Fig. 2 (a), since it could be an important parameter in some optical communication systems. No obvious saturation was observed at optical current of 1.2 mA with the reverse bias of −5 V. It is noted that limited by the coupling loss between the fiber and the diode, the slope of the curve shown in Fig. 2 (a) is lower than the real responsivity of the diode. A good crystal quality can be verified by comparing the simulation and measured peaks in the X-ray diffraction patterns as shown in Fig. 2 (b).

#### 3.2 RF characteristics

The total 3 dB bandwidth of a photodiode is mainly limited by transit limit and resistance-capacitance (RC) limit [17]:

where*f*is the transit limit bandwidth, and

_{T}*f*is the RC limit.

_{RC}In order to extract the transit limit bandwidth of the device, the RC limit bandwidth was also studied by fitting the S11 parameter of the device with the equivalent circuit as shown in Fig. 3 (a) using Advanced Design System (ADS) software. Figure 3 (b) show that the S11 of circuit model can match the experimental result very well with the series resistance *R _{s}* of 5.5 Ohm and the junction capacitance

*C*of 309.3 fF in the Fig. 3 (a). The bandwidth

_{j}*f*can be simulated based on the equivalent circuit of Fig. 3 (a), which is 9.2 GHz as shown in Fig. 3 (c). The C-V curve measured by LCR meter in Fig. 3 (d) shows that the device is fully depleted at −1 V. It is also noted the measured capacitance is slightly larger than the fitted value in Fig. 3(a), which may be due to the different circuit model used in LCR meter.

_{RC}The total 3 dB bandwidth was measured with the vector network analyzer (VNA) along with 2000 nm fiber laser light modulated by a high speed Mach-Zehnder modulator as shown in Fig. 4 (a). Figure 4 (b) shows the measured frequency response of a 40 μm diameter device at different bias voltages. The 3 dB bandwidth is hundreds of megahertz at low bias, and is significantly improved with the rise of bias voltage. This indicates that the response speed is mainly limited by carrier transit time, since the RC time constant of the diode almost remains constant after depletion and does not vary with the bias voltage. The largest 3 dB bandwidth is 3.7 GHz at −14 V bias. With the experimental 3 dB bandwidth and simulated RC limited bandwidth, the transit time limited bandwidth can be calculated to study the carrier dynamics of the photodiodes.

## 4. Carrier dynamics and modeling

In this section, a model is developed to study the 3 dB bandwidth of the multiple quantum wells PIN photodiodes, based on the carrier dynamics in these MQW devices. In the model, the transient of carriers between bound states and continuous states are considered, which also includes the carrier thermionic emission and tunneling process within MQW region. The photocurrent and frequency response were calculated afterward based on the rate equation.

#### 4.1 Carrier dynamics

With input light of 2 μm wavelength, the optical-generated carriers are expected to be at their lowest bound states in each quantum wells, assuming the carrier at excited states will quickly relax to ground state in each well by phonon scattering. Here we denote *q _{k}* the charge of electron at bound state in

*k*-th well, and denote

*q*'

*the charge of electron at continuous state within the range of*

_{k}*k*-th well, as shown in Fig. 5. The carrier in continuous states has a chance to be re-trapped by the nearest quantum well after it escaped to continuous states [18]. We denote this probability to be $1-p$, which means the larger

*p*is, the less chance that carrier would be re-trapped. So the rate equation of electrons/holes in bound states is expressed as:

*G*is the electron generation rate in

_{k}*k*-th well,

*τ*and

_{E,l}*τ*are thermal emission time the carrier needs to overcome the left or right energy barrier,

_{E,r}*τ*and

_{T,l}*τ*are tunneling time to tunnel to the left or right adjacent wells,

_{T,r}*τ*is electron life time, and ${t}_{D}=W/\left(N{v}_{e}\right)$ is the drift time over one period of quantum well,

*W*is the total thickness of multiple quantum wells,

*N*is the number of MQW periods and

*v*is the electron drift velocity. Similarly, the rate equation of electrons/holes in continuous states is expressed as:

_{e}In these two equations, each term describes a mechanism that increasing rate of the carrier at bound state or continuous state within one period. The time constants for thermal emission and tunneling can be calculated as the discussion below, and the carrier life time is relatively long and has little effects on results. The only unknown parameter is the probability *p*. We will discuss the effect of *p* later with the simulation results. Note that the above equations are applicable for both electron and hole.

Thermal emission and tunneling are included in our model, which are the two dominant mechanisms to sweep out carriers. The time constants of thermal emission and tunneling process can be calculated by [19,20]:

*m*

_{*}is the effective mass of carrier in wells,

*m*is the effective mass in barrier layers,

_{*,b}*L*,

_{w}*L*are the thickness of well and barrier,

_{b}*k*is Boltzmann constant,

_{B}*ħ*is Planck constant,

*T*is temperature, and

*H*is the left or right effective barrier height which varies in different electrical field [21]:where

_{l,r}*E*is the effective barrier height in zero electrical field and is calculated with a kp model [22–24],

_{l,r}*q*is the elementary charge, and

*F*is the electrical field intensity.

Table 2 shows the key parameters used in our simulation, which is based on the literature [25,26], and the absorption coefficient is derived by the measured responsivity. With rate equation and the carrier initial profile, we can calculate the carrier transient progress and then obtain the photocurrent and the frequency response.

#### 4.2 Photocurrent and frequency response

The photocurrent created by the motion of carrier can be calculated by [27]

*x*is the center position of

_{k}*k*-th quantum well.

We can then use an impulse response technique to get the frequency response by applying Fourier transform to the photocurrent of pulse input to calculate the power spectral density [28]. In our simulation, the pulse width of the input light is short enough (less than 10 fs) so that the power spectral density of the photocurrent can accurately represent the frequency response of the diode. Note that the bandwidth we get from the impulse response is the transit limit bandwidth.

Figure 6 (a) shows the simulated photocurrent in different bias voltage and fixed trap probability. And Fig. 6 (b) shows the corresponding frequency response. The total current consists of both electron current and hole current. The pulse width of the total current becomes narrower when the bias voltage increases, this is because the stronger electrical field shortens the time constant as expressed in Eqs. (4) and (5), which leads to a faster sweeping out process and a higher bandwidth. The power spectral density of total current along with the electron and hole current is shown in Fig. 6 (b). It is found that the hole current is very small in time domain and contributes a long tail in the total current, which significantly limits the 3 dB bandwidth of the device.

Since the carrier trap probability in the quantum well is not easy to be evaluated theoretically, we use it as a phenomenological parameter to understand the process of carrier dynamics in these multiple quantum wells. The effect of probability *p* on device bandwidth was studied as below. For convenience, we denote *p _{e}* to be the probability of electrons not being trapped by the nearest well after thermionic emission out of the quantum well, and

*p*is the probability for holes. Larger

_{h}*p*means the carrier has less chance to be trapped again by the wells, so that it takes a shorter time for the carriers to be swept out, which leads to higher bandwidth.

Figure 7 (a) depicts the effect of *p _{e}* on total bandwidth. It shows that the bandwidth is almost constant with different

*p*. In contrast, bandwidth rises significantly with the increase of

_{e}*p*as shown in Fig. 7 (b). That is due to the reason that hole transport is much slower than electrons, and the faster electron transport with larger

_{h}*p*does not help to improve the total 3 dB bandwidth of the devices. This once again indicates that hole transport limits the total bandwidth.

_{e}The transit limit of the demonstrated diode was compared with the simulation results at various *p _{h}* as shown in Fig. 8. For each bias voltage, we can find the corresponding

*p*. At low bias voltage (less than −4 V), the bandwidth is too low, and is sensitive to measurement error and fitting error, so the values are not taken into account. For voltage from −6 V to −12 V, the corresponding

_{h}*p*increase from 0.94 to more than 0.98. This is because carriers obtain larger energy in higher field, and thus it is harder for them to be trapped. However, at −14 V bias, the best fitted

_{h}*p*decreases slightly. That could originate from the avalanche gain in the photodiodes. With such high field (around 280 kV/cm) in the absorption region, some avalanche gain happens and competes with the improvement of the 3 dB bandwidth under higher electrical field. Even though, the 3 dB bandwidth at −14 V is still higher than −12 V, but the avalanche process could degrade the performance slightly [29]. Since the avalanche effect is not yet included in our model to refer this degradation of the bandwidth, the best fitted

_{h}*p*decreases slightly to compensate the avalanche effect.

_{h}## 5. Bandwidth optimization

In this section, we will study whether the bandwidth can be enhanced by optimizing the MQW structure. According to Eq. (4) and (5), the carrier sweeping out time is related to the effective barrier height, and layer thickness. Since the bandwidth is limited by long hole transport time, one possible method to achieve higher bandwidth is reducing the thickness of the GaAsSb layer in MQW. Here we simulated the bandwidth variation with respect to the thickness of GaAsSb layers, as shown in Fig. 9. The bandwidth is enhanced when the thickness of GaAsSb layer decreases from 5 nm to 2 nm. This is because the hole bound state energy level rises, which shorten thermal emission time and tunneling time for holes as indicated in Fig. 9 (b). However, the thickness cannot be too thin due to the cut-off wavelength limitation as shown in Fig. 9 (a).

Another method to improve the bandwidth is using strain balanced InGaAs/GaAsSb type-II quantum wells as absorber in the diode. Increasing the In composition in InGaAs and decreasing the Sb composition in GaAsSb can reduce the valance band offset between InGaAs and GaAsSb, and thus lower the effective barrier height as indicated in Fig. 10 (b). Figure 10 (a) shows the bandwidth simulation results in different In composition. The bandwidth enhancement appears when In composition increases from 0.53 to 0.68. In the simulation, it should be noted that the Sb-composition in GaAsSb also varies from 0.49 to 0.35 to maintain zero strain. The bandwidth exceeds 10 GHz when In_{0.68}Ga_{0.32}As/GaAs_{0.62}Sb_{0.38} is used, meanwhile, the cut-off wavelength is still larger than 2 μm.

## 6. Conclusion

A theoretical model is built to investigate the frequency response of the normal incident InGaAs/GaAsSb type-II quantum wells PIN photodiode for 2 μm high speed operation. The simulation results of the dynamic model match the experimental data very well with different reverse bias. Analysis shows that the 3 dB bandwidth of the PIN diode is limited by hole transport, and some bandwidth optimization strategies are discussed. Even though further optimization of the device is needed for future improvement of speed performance, the model developed in this work should pave a way for future exploration of high speed type-II MQW photodiodes.

## Funding

Shanghai Sailing Program (17YF1429300); ShanghaiTech University startup funding (F-0203-16-002)

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