Modeling and Simulation of a Resonant-Cavity-Enhanced InGaAs / GaAs Quantum Dot Photodetector

We simulated and analyzed a resonant-cavity-enhancedd InGaAs/GaAs quantum dot n-i-n photodiode using Crosslight Apsys package.The resonant cavity has a distributed Bragg reflector (DBR) at one side. Comparing with the conventional photodetectors, the resonant-cavity-enhanced photodiode (RCE-PD) showed higher detection efficiency, faster response speed, and better wavelength selectivity and spatial orientation selectivity. Our simulation results also showed that when an AlAs layer is inserted into the device structure as a blocking layer, ultralow dark current can be achieved, with dark current densities 0.0034A/cm at 0V and 0.026A/cm at a reverse bias of 2V. We discussed the mechanism producing the photocurrent at various reverse bias. A high quantum efficiency of 87.9% was achieved at resonant wavelength of 1030 nmwith a FWHM of about 3 nm.We also simulated InAs QD RCE-PD to compare with InGaAs QD. At last, the photocapacitance characteristic of the model has been discussed under different frequencies.


Introduction
Low dimensional III-V semiconductor nanostructures have been widely studied on their electronic and optical properties for device applications.Among the nanostructures, the resonant-cavity-enhanced photodetectors (RCE-PDs) have been extensively studied due to their novel physical mechanism and special device applications over the past two decades [1][2][3][4][5][6][7].A RCE-PD is usually constructed by placing multiple active layers at the peak positions of a standing wave in a resonant cavity, sandwiched between two distributed Bragg reflectors (DBRs).
The DBR mirrors are usually made of quarter wave stacks with a periodic modulation of refractive indices.Metals are usually not used as mirrors because they do not provide wavelength selectivity [2].RCE-PDs also have the ability of wavelength selectivity.When light is incident on the detector, the light will enter the cavity and interfere in the internal cavity which consisted of two mirrors if the wavelength and the cavity mode match.So optical field is enhanced and more light will be absorbed, generating more carriers in the cavity.Compared with the conventional detectors, the responsivity is greatly improved.This makes the RCE-PD with high detection efficiency, fast response speed, ability to work in the absence of bias voltage, and their wavelength selectivity and spatial orientation selectivity especially suitable for optical fiber communication system that requires high wavelength accuracy.
1.06 m is a specific wavelength used in Nd:YAG laser systems.These systems have been widely deployed in industrial manufacturing, medicine, remote sensing, space communication, and so forth.To achieve high sensitive detection at this wavelength, resonant-cavity-enhanced-(RCE-) PDs with quantum dots (QDs) as absorption layers were explored to reach a peak quantum efficiency of 65-75% [8][9][10].However, DBR mirrors make it difficult for the device to extract photogenerated carriers.To solve this problem, Bennett et al. and Sun et al. fabricated an InGaAs/GaAs quantum dot n-i-n RCE-PDs with only a bottom DBR mirror which still has the resonant coupling nature and achieved peak photoresponsivity of 0.75 A/W at 1.4 V [11,12].

Materials and Methods
The device structure to be imported into APSYS was constructed according to the structure in [12].As shown in  Figure 3(a) is the simulated QD PL spectrum at room temperature.The peak at 1.13 m is emission from the quantum dots and 960 nm is from the wetting layer [9,13].the main mechanism for photocurrent generation is due to thermal ionization.We also found that as the bias increased from 0.5 V to 2 V the photocurrent density increased 1 order of magnitude from 0.02 A/cm to 0.34 A/cm.This rapid increase of photocurrent density is because the interaction of thermal ionization and tunneling ionization caused exciton ionization.

Results and Discussion
We also simulated - characteristic curve at high bias, as shown in Figure 4(a) inset.Photocurrent increases as the bias voltage increases.But when bias voltage exceeds 2 volts, photocurrent stays at about the same value as the bias voltage increases.This is because the majority of excitons are ionized when bias voltage is above 2 volts and thus would not generate photocurrent.
The electric current characteristic (-) of InAs QD RCE simulated still to compare with InGaAs QD.But it is seen from Figure 4(b) that the photocurrent reaches saturation under low bias.So, the paper has discussed the effect of the resonant cavity, showing why the InGaAs/GaAs quantum dot is, rather than others quantum dot (InAs/GaAs).
The quantum efficiency of a QD-RCE photodetector is determined by the cavity resonant wavelength relative to the exciton absorption peak.When these two wavelengths overlap, the photodetector has the ideal quantum efficiency, Responsivity (A/W) showing wavelength selectivity.Full width at half maximum (FWHM) can reflect the wavelength selectivity of RCE photodetector.Consider Here,  1 and  2 are the reflection coefficients of the top DBR and the bottom DBR, respectively. is the absorption coefficient and  the thickness of the absorption layer. eff is the equivalent cavity length,   is the group refraction rate,  0 is the mode wavelength, and  is the standing wave enhancement factor.
The device photocurrent spectra at different bias voltages were simulated.Figure 5 shows the spectral responsivity simulation of the RCE photodetector under different applied reverse bias voltages.The resonant peak wavelength was at 1030 nm with 3 nm full width at half maximum (FWHM).The responsivity increases with the applied reversed bias between 0 V and 3 V and maintains the same shape.The responsivity is approximately 0.25 A/W at 1.0 V bias and increases to 0.73 W/A upon 1.4 V bias and the quantum efficiency is 30.1% and 87.9%, respectively, which agrees with the reported results in [12].
Figure 6(a) shows the - simulation performed at  = 100 KHz, 1 MHz, and 10 MHz in InGaAs QDs.More carriers will extend across the QDs and the excited state and the ground state will be filled with increasing reverse bias.So, the higher the reverse bias, the larger the capacitance value, as a result of the greater portion of the QD assembly being populated [14][15][16][17].We also simulated - characteristic of InAs QD RCE to compare with InGaAs QD as shown in Figure 6(b).The photocurrent has reached saturation at 1.0 V.It is similar to Figure 4(b), the - characteristic.The theoretical fit of the capacitance is obtained using a simple model based on the definition of the capacitance ( = /) [18] where the charge is given by the integral of the density of states and the energy distribution: The summation is assumed over all  subbands, where   (,  dot ) is the electron density of state for th subband in QDs, (,  dot ) is the Fermi-Dirac energy distribution,  dot is the voltage across the quantum dots scaled by level-arm relation when the band bending is neglected, and  is the level arm coefficient.
Comparing with 90.3%, the experimentally measured results for quantum efficiency and the discrepancy in the device responsivity in our computed result can be attributed to the number of quantum dots used in simulation.The device in the experimental result has 22 pairs of QDs, whilst in simulation the lowest quantum dot number allowed was limited by the calculation procedure.And to some extent, this result further demonstrated QD RCE-PD's potential in achieving high quantum efficiency, high response rate, and better wavelength selectivity.

Conclusions
In summary, we have simulated an n-i-n RCE photodetector grown on a GaAs substrate with operating wavelength at 1.03 m.The responsivity is 0.73 A/W at 1.4 V bias with a FWHM of 3 nm.A high quantum efficiency of 87.9% was observed in the calculation.The device has reduced dark current of 0.0034 A/cm at the bias of 0 V and 0.026 A/cm at the reverse bias of 2.0 V.

Figure 1 (
Figure1(a), it consists of a Si-doped 1 m GaAs buffer layer and a DBR (-doped) with 30 pairs of quarter-wavelength (/4) GaAs/AlAs layers.The active region is 380 nm thick undoped GaAs spacer and 23 periods of 6 nm-In0.5Ga0.5AsQDs layers.Finally, the top layers in sequence are 50 nm undoped GaAs spacer, 3 nm thick AlAs blocking layer, 157 nm GaAs spacer, and a 175 nm  + GaAs cap layer.The doping concentration for all the  + layers is 1 × 10 18 cm −3 .QD sheet density of 3 × 10 10 cm −2 and a square (80 m × 80 m) opening was left on the top for optical access.The temperature is set to be room temperature.Plotted in Figure1(b) is a simplified 3D structure view of the device constructed by Lumerical software.The energy band diagram of the device at thermal equilibrium along the epitaxial growth direction is plotted in Figure2.Figure3(a) is the simulated QD PL spectrum at room temperature.The peak at 1.13 m is emission from the quantum dots and 960 nm is from the wetting layer[9,13].Figure 3(b) is the gain of the absorption layer at different incident wavelengths.The largest gain appearing at 1.13 m indicated that electron-hole pairs generated in the active region reached a maximum.
Figure1(a), it consists of a Si-doped 1 m GaAs buffer layer and a DBR (-doped) with 30 pairs of quarter-wavelength (/4) GaAs/AlAs layers.The active region is 380 nm thick undoped GaAs spacer and 23 periods of 6 nm-In0.5Ga0.5AsQDs layers.Finally, the top layers in sequence are 50 nm undoped GaAs spacer, 3 nm thick AlAs blocking layer, 157 nm GaAs spacer, and a 175 nm  + GaAs cap layer.The doping concentration for all the  + layers is 1 × 10 18 cm −3 .QD sheet density of 3 × 10 10 cm −2 and a square (80 m × 80 m) opening was left on the top for optical access.The temperature is set to be room temperature.Plotted in Figure1(b) is a simplified 3D structure view of the device constructed by Lumerical software.The energy band diagram of the device at thermal equilibrium along the epitaxial growth direction is plotted in Figure2.Figure3(a) is the simulated QD PL spectrum at room temperature.The peak at 1.13 m is emission from the quantum dots and 960 nm is from the wetting layer[9,13].Figure 3(b) is the gain of the absorption layer at different incident wavelengths.The largest gain appearing at 1.13 m indicated that electron-hole pairs generated in the active region reached a maximum.

Figure 4 (Figure 3 :Figure 4 :
Figure4(a) is the current-voltage characteristics of the InGaAs QD RCE photodetector simulated at 1030 nm wavelength.The suppressed dark current in the n-i-n structure is attributed to the blocking effect by the AlAs layer.The current increases as the reverse bias increases.In the process of optical transition, the excited electrons from the conduction band and the excited holes from the valence band will form excitons in QDs.The quantum dots can capture the excitons very effectively.Potential barrier prevents the electron-hole from moving in the opposite direction.Thus the tunneling probability through the potential barrier is very small.Exciton ionization is mainly thermal ionization.The electron can escape from the quantum dots producing a photocurrent at a certain temperature.The escape of electrons and holes changes electric potential, resulting in a decrease of the effective potential barrier, which makes bound electrons and holes in the quantum dots tunnel through the barrier, thus increasing the photocurrent.It is observed that the dark current increases a little at 0.5 V or less.When the bias is 0.5 V, photocurrent is only 0.02 A/cm.The slow increase of photocurrent density at lower applied voltage is because

Figure 5 :
Figure 5: Responsivity spectra of the RCE photodetector under different reverse bias voltages.

Figure 6 :
Figure 6: (a) - simulation figure of the InGaAs QD RCE photodetector under different frequents.(b) - characteristics of the InAs QD RCE photodetector.