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Abstract
This paper introduces an automatic intelligent design method for the modified uni-traveling carrier photodetector (MUTC-PD). The conventional photodetector design process often relies on the numerical solution of complex nonlinear partial differential equations to simulate and optimize device performance, which is not only computationally intensive but also inefficient. To overcome this challenge, we apply the charge control principle to calculate the photodetector bandwidth, which improves the computational speed by a factor of approximately 1800 compared to the numerical solution of nonlinear partial differential equations. To further optimize the structure of the photodetector, we incorporate the Velocity Varying Climbing Particle Swarm Optimization (VVCPSO) algorithm. This is an improved algorithm based on the traditional particle swarm algorithm, which is able to quickly find the optimal solution in a complex parameter space. By applying the VVCPSO algorithm, we successfully fine-tuned the photodetector structure and obtained structural parameters with optimal performance. Our thorough verification process confirms that the proposed method is consistent with the results of ATLAS simulation software. Automated design has resulted in a high-performance MUTC-PD with a responsivity of 0.52A/W and a bandwidth of 60 GHz (@-3 V) at a mesa diameter of 16µm. Compared to the pre-optimized device, the bandwidth is increased to three times the original. By reducing the mesa diameter to 4µm, the bandwidth can be further increased to 82 GHz (@-3 V). The proposed method's calculation speed is fast enough, enabling extensive parameter studies to optimize device performance.
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1. Introduction
Semiconductor photodetectors convert incident light signals into electrical signals and are widely used in optoelectronics and RF photon applications that require bandwidth, high efficiency and low dark current, such as optical communication [1], [2], [3]. However, a key bottleneck for photodetectors is the constraint between bandwidth and quantum efficiency [4], [5], [6], [7], and different design schemes have been proposed to overcome this challenge, among them, by increasing the equivalent absorption length: PINIP photodetectors [8], PININ photodetectors [9], Resonant Cavity Enhanced photodetectors (RCE) [10]. By mitigating the space charge effect, there are Partially Depleted Absorber photodetectors (PDA) [11] and Dual-depletion Region photodetectors (DDR) [12]. Another successful solution is the uni-traveling carrier photodetectors (UTC), which improves the bandwidth of the photodetector by introducing an undepleted P-doped InGaAs absorber layer [13], so that only the electrons act as carriers, thus mitigating the space charge effect. In 2006, in order to further optimize bandwidth and responsiveness, Jun et al. [14] reported a modified uni-traveling carrier photodetector (MUTC-PD) with a mixed absorber. The structure was designed by inserting an undoped InGaAs layer between the InP drift layer and the P-type InGaAs absorber. By optimizing the layer thickness, higher bandwidth and responsiveness can be obtained. The study of Wang et al. [15] shows that this structure has higher bandwidth, responsiveness and saturation characteristics.
In the design process of MUTC, the total thickness of the mixed absorber is kept constant, and the bandwidth can be maximized by appropriately selecting the thickness ratio of the two absorption layers [16]. However, the layer structure is more complex, it is difficult to find the corresponding layer structure to achieve the maximum bandwidth only by artificially scanning the thickness and doping concentration of each layer. In addition, if we find the optimal doping concentration and thickness of a certain layer through scanning, when the structure of other layers changes, the optimal situation of the layer may change. On the other hand, each numerical calculation takes about a few minutes. If the thickness and doping concentration of each layer are accurately scanned, this workload will require huge time, and the optimal structure will not be found in most cases. Therefore, the traditional scanning method cannot consider the synergistic effect of the overall structure, and it is difficult to play the potential of device performance. In order to further improve the bandwidth of the photodetector while maintaining the same responsivity, we propose an automated intelligent design scheme for the MUTC-PD, and calculate the RF output power spectrum by combining the charge control principle. This allows quick numerical results to help reduce computing costs and save time. At the same time, the inverse design platform based on velocity-varying climbing particle swarm optimization algorithm (VVCPSO) is used, which can quickly and efficiently calculate the corresponding layer structure to achieve the maximum bandwidth, and maximize the performance potential of the device. As shown in Fig. 1, we demonstrate the automated intelligent design process of the MUTC-PD.
In this work, we first introduce VVCPSO and charge control principle used in MUTC-PD automated design process, and then analyze the feasibility of this principle from four aspects: transport bandwidth, capacitance effect, total bandwidth and doping concentration. Finally, we design a MUTC-PD using this method and compare the performance of the device before and after optimization, thus proving the efficiency and accuracy of the whole method.
2. Principle
The algorithms used for inverse design are mainly divided into three categories: heuristic algorithm, gradient algorithm and neural network algorithm.
Heuristic algorithm is suitable for global search and parameter optimization problems, such as light detectors with multi-layer complex structures, lasers, etc. The velocity varying climbing particle swarm optimization algorithm is a kind of heuristic algorithm. In addition, this algorithm can help the particle swarm to jump out of the local extreme value and converge at a faster speed. Gradient algorithm is suitable for optimization problems with clear objective function and computable gradient, because the gradient of photodetector is not easy to solve, and the optimization target may have many local extreme values, so it is not suitable for gradient algorithm. The neural network algorithm is suitable for dealing with complex nonlinear problems and big data scenarios, requiring thousands to tens of thousands of training samples, while the heuristic algorithm only needs to calculate less than 1,000 times to obtain the optimal solution. Therefore, for the automatic design of photodetectors, the use of heuristic algorithm is an optimal choice after weighing.
VVCPSO-based inverse design algorithm is used for automated intelligent design of MUTC-PD, and we combine charge control principle with it to characterize the bandwidth performance of the photodetector, thus serving the figure of merit (FOM) in inverse design.
2.1 Principle of VVCPSO
The iterative formulas of traditional PSO are as follows:
In the traditional particle swarm optimization, if a particle hard to find a better FOM after multiple iterations, its personal optimal position will gradually approach the global optimal position. As a result, the algorithm often becomes trapped in a local optimal solution because the particle velocity eventually converges to zero. This limits the further optimization of the calculation results. To overcome this problem, we propose a variable velocity climbing particle swarm optimization (VVCPSO) algorithm. The algorithm's core strategy is to use the historical optimal position as the starting search point for the particle in each iteration period. This aims to provide guidance for the subsequent search process using the previous best information. To break the constraint of local optimality, an independently varying random number is incorporated into the particle's velocity formula. The design allows particles to have a non-zero velocity even when the group optimal position and the local optimal position coincide. This eliminates the constraint on the particle's velocity by the local optimal position, significantly enhancing the algorithm's ability to jump out of local extreme values. As a result, the algorithm can continuously progress and explore during the optimization process. To ensure the algorithm can quickly locate the approximate region of the global optimal solution, it requires strong global search ability. Additionally, to accurately lock the global optimal position, the algorithm also needs strong local search ability. To achieve this, we employ a variable-velocity particle swarm strategy, giving each particle a different maximum velocity. The algorithm's search capabilities are balanced between global and local exploration, allowing for extensive exploration in a wide solution space and refined, in-depth search in areas near the optimal solution.
The formula of the VVCPSO is as follows:
At the same time, we adopt the variable velocity parameter matching scheme. when the particle velocity is large, the individual search plays a dominant role, which can ensure a wide range of searches, When the velocity of particles is small, the swarm search takes over, which ensures a more refined search. The parameter matching formula is as follows:
The parameters equations of VVCPSO are as follows:
In previous work, we have reported the advantages of this algorithm [17], so we will not go into details here.
2.2 Charge control principle
As shown in Fig. 2, taking two doping concentrations in the mixed absorber as an example, there are three main sources of current in MUTC-PD: the electronic current Je1 (ω, x) generated from the P-type absorber with a thickness of Wan; and the electron and hole currents Je2 (ω, x) and Jh (ω, x) generated in the depletion absorber of thickness Wad. As long as the response of the sum of Je1 (ω, x) and Je2 (ω, x) is faster than that of Jh (ω, x), the total response can be improved by adding P-type absorber [18]. This is because the final transport time is determined by the slow carriers, so the addition of P-type absorber guarantees improved responsiveness without increasing transport time.
Integrating the above three current components Je1 (ω, x), Je2 (ω, x) and Jh (ω, x) on the depletion layer, the current response of each part is obtained as follows:
For a case with a constant doping and uniform carrier generation rate [19], the delay time τan is a function of diffusivity De and thermionic emission velocity vth, and approximated to be:
The total current response of the sum of the above four currents:
3. Feasibility analysis
3.1 Transport bandwidth
The expression of the transport bandwidth is as follows:
Where the current I is shown in (9). In the following simulation work, we all use Silvaco Atlas software. Figure 3(a), (b), (c) and (d) studied the variation of 3 dB transport bandwidth with P-type absorber thickness Wan under different total absorber thicknesses when the thickness of the collection layer is 0.6µm, 0.7µm, 0.8µm and 0.9µm respectively. In the actual simulation process, the device mesa diameter is 16µm, the operating bias is -3 V, and the incident light wavelength is 1.31µm. These conditions are adopted in the following research, and will not be introduced one by one. It can be found that the variation trend of the transport bandwidth obtained by theoretical calculation is completely consistent with the actual simulation results. For the same collection layer thickness, the thicker the absorber is, the smaller the transport bandwidth is. For the same thickness of the absorber, the thicker the collection layer is, the smaller the transport bandwidth is. However, although the trend of theoretical calculation and actual simulation is consistent, the proportion of P-type absorber corresponding to the maximum bandwidth can be predicted, but there are some errors between them. The main reason for this error is that the influence of contact layer, electron barrier layer and spacer layer is not considered in the theoretical calculation process. In the actual simulation, these layers increase the carrier transport distance, resulting in a decrease in the actual transport bandwidth.
Fig. 3. The relation of 3 dB transport bandwidth with P-type absorber thickness Wan under different absorber thicknesses. The thickness of the collection layer is: (a) 0.6µm. (b) 0.7µm. (c) 0.8µm. (d) 0.9µm. In the legend, (a) represents the actual simulation result, and (t) represents the theoretical calculation result.(All the graphs below are the same.)
In Fig. 3(a), the total thickness of the mixed absorber is 0.3µm, 0.4µm, 0.5µm and 0.6µm, respectively, and the collection layer remains unchanged at 0.6µm. When Wan = 0 in the figure, the device is traditional pin-PD or dual depletion region pin-PD. When the Wan is 0.3µm, 0.4µm, 0.5µm, and 0.6µm respectively (i.e., when Wad = 0), the device is pure UTC-PD. In pure UTC-PD mode, the theoretical 3 dB bandwidth increases from 16 GHz to 58 GHz as the Wan decreases from 0.6µm to 0.3µm. This is only the result of Tan shortening, the bandwidth improvement is even more significant of the mixed absorber model, and when the Wan is further reduced, the transport bandwidth can theoretically be increased to 140 GHz. In pin-PD mode, that is, when Wan = 0, the 3 dB bandwidth is increased from 79 GHz to 130 GHz when the absorber thickness is reduced from 0.6µm to 0.3µm.
Based on this method, when the total thickness of the mixed absorber and the thickness of the collection layer are given, we can predict the structure of the mixed absorber that can achieve the maximum transport bandwidth.
We studied the variation between 3 dB transport bandwidth and P-type absorber thickness Wan under different collection layer thicknesses when the total thickness of the mixed absorber is 0.2µm, 0.3µm, 0.4µm and 0.5µm, as shown in Fig. 4 respectively. It can be found that the variation trend of the transport bandwidth obtained by theoretical calculation is completely consistent with the actual simulation results. For the same thickness of the mixed absorber, the thicker the collection layer is, the smaller the transport bandwidth is, because the thicker the collection layer increases the transit distance of electrons, which reduces the transport bandwidth. Meanwhile, for the same thickness of the mixed absorber, the thicker the collection layer is, the more consistent the theoretical calculation is with the actual simulation results. When the thickness of the collection layer is 1µm, the theoretical calculation is basically consistent with the simulation results in the above four cases.
Fig. 4. The relation of the 3 dB transport bandwidth with the thickness Wan of P-type absorber under different thicknesses of collection layer. The thickness of the mixed absorber is: (a) 0.2µm. (b) 0.3µm. (c) 0.4µm. (d) 0.5µm.
3.2 Capacitance effect
RC time constant is one of the main limiting factors of photodector’ bandwidth, so small junction capacitance is the key condition to ensure the high speed performance of photodetector. The junction capacitance of a photodetector is similar to that of a parallel-plate capacitor, so it can be written as [16]:
However, the traditional capacitance calculation method above is only applicable to the case of high doping concentration of P-type absorber, because the total depletion region width is equal to the sum of the width of the depletion absorber and the width of the collection layer, which is consistent with the total depletion region width adopted in our theoretical calculation method. However, when the doping concentration of P-type absorber is low, the total depletion region width is greater than the sum of the width of the depletion absorber and the collection layer. Below, we analyze the electric field, potential and energy of different doping concentration respectively to prove the problem.
As shown in Fig. 5, we studied the variation of electric fields and band energy in the absorber and collection layer with the doping concentration in the P-type absorption region.
Fig. 5. The variation of (a) electric field and (b) band energy in the absorber and collection layer with the doping concentration in the P-type absorber.
As shown in Fig. 5(a), when the doping concentration in the P-type absorber is low, the P-type absorber is completely depleted. With the increase of the doping concentration in the P-type absorber, the electric field in the depletion absorber and the collection layer increases, and the width of the depletion region in the mixed absorber gradually decreases, while the width of the depletion region in the collection layer gradually increases. When the doping concentration of P-type absorber is high, such as 1e18cm-3, the total depletion region width is equal to the sum of the width of the depletion absorber and the collection layer, which is consistent with the total depletion width adopted in our theoretical calculation method. As shown in Fig. 5(b), with the increase of doping concentration in the P-type absorber, the energy band becomes more inclined, which also helps to prove the above conclusion.
In order to calculate the device junction capacitance with low P-type absorber doping concentration, we use high order polynomial fitting to obtain the junction capacitance with different doping concentration, different P-type absorber thickness and different depletion thickness.
As shown in the Fig. 6, we used Atlas software to simulate the relationship between the junction capacitance of the photodetector and the doping concentration of the P-type absorber and the thickness of the P-type absorber when the total thickness of the 90 groups of mixed absorber was 0.4µm. Figure 6(a) is a graph. Figure 6(b) is a contour map. As can be seen from Fig. 6(a), when the thickness of the P-type absorber is fixed, the junction capacitance of the photodetector will have a minimum value with the change of the doping concentration of the P-type absorber, and the higher the proportion of the P-type absorber thickness in the total mixed absorption region, the lower the doping concentration of the P-type absorber corresponding to the minimum junction capacitance. The contour map of Fig. 6(b) just helps to illustrate this problem. The dark blue region is the minimum capacitance part, and the higher the proportion of P-type absorber in the total mixed absorber, the lower the doping concentration of P-type absorber corresponding to the dark blue region.
Fig. 6. When the total thickness of the mixed absorber is 0.4µm, the junction capacitance of the photodetector varies with the doping concentration and the thickness of the P-type absorber. (a) Graph. (b) Contour map.
In the above research, both the thickness of P-type absorber and the doping concentration of P-type absorber can cause the change of junction capacitance, especially in the case of low concentration doping of P-type absorber, the theoretical thickness is inconsistent with the actual depletion region. Therefore, we can use VVCPSO algorithm to fit the relationship between actual junction capacitance and P-type absorber thickness, theoretical depletion region thickness and P-type absorber doping concentration. The high order polynomial fitting formula is as follows:
The above formula is expanded as:
Among them, a total of nine coefficients X0-X222 are unknowns that need to be fitted. We selected 90 sets of observation data from the above simulation for fitting, where d1 is the thickness of P-type absorber, d2 is the thickness of depletion absorber, N is the doping concentration of P-type absorber, and fc is the actual simulated device junction capacitance.
The fitting results are shown in the Fig. 7, where the horizontal axis represents the 90 groups of observation data we selected, and the vertical axis represents junction capacitance. It can be seen that after VVCPSO calculation, the actual data is highly consistent with the fitting data, which once again proves the advantages of our VVCPSO's wide application range and strong computing power.
Finally, after verification, we found that second-order polynomial fitting had the best fitting effect, so we got the values of X0-X222 nine coefficients as shown in Table 1:
3.3 Total bandwidth
The equation of the total bandwidth is as follows:
Fig. 8. The relation of the 3 dB total bandwidth with the thickness Wan of P-type absorber under different thicknesses of absorber. The thickness of the collection layer is: (a) 0.6µm. (b) 0.7µm. (c) 0.8µm. (d) 0.9µm.
After looking at Fig. 8(a) (b) (c) (d) above, we can find that for the same absorber thickness, the total bandwidth does not decrease with the thickening of the collection layer, because although the carrier transport time increases, the junction capacitance decreases, and there is a trade-off between the two. Therefore, the design of photodetector is a relatively complex process, in which there are many constraints, the analysis process is more complicated. This highlights the advantages of inverse design, we eliminate the complex design process, directly from the results, through the algorithm can calculate the structure that meets our design requirements.
In Fig. 8(a), the total thickness of the mixed absorber is 0.3µm, 0.4µm, 0.5µm and 0.6µm, respectively, and the collection layer remains unchanged at 0.6µm. When the thickness of the mixed absorber decreases from 0.6µm to 0.3µm, the actual total bandwidth of 3 dB increases from 51 GHz to 59 GHz, and the theoretical total bandwidth of 3 dB increases from 62 GHz to 69 GHz.
In the following Fig. 9, we studied the relationship between the total bandwidth of 3 dB and the thickness of P-type absorber at different thickness of the collection layer when the total thickness of the mixed absorber was 0.2µm, 0.3µm, 0.4µm and 0.5µm, respectively. It can be found that the variation trend of the total bandwidth obtained by theoretical calculation is basically consistent with the actual simulation results. When the total thickness of the mixed absorber is 0.2µm, both theoretical calculation and actual simulation show that the smaller the Wan, the higher the corresponding total bandwidth, which means that when the thickness of the absorber is small, the adoption of the mixed absorber mode is unfavorable to the bandwidth, and the traditional pin structure is a better choice. When the total thickness of the mixed absorber is 0.3µm, 0.4µm and 0.5µm, there is an error of about 0.025µm between the Wan at the maximum bandwidth corresponding to the theoretical calculation and the actual simulation. When we study the transport bandwidth above, we can know that for the same mixed absorber thickness, the thicker the collection layer, the smaller the transport bandwidth, which is also very easy to understand, thicker collection layer increases the electron transit distance, resulting in reduced transport bandwidth. However, for the same mixed absorber thickness, the thicker the collection layer, the larger the total bandwidth, the main reason is that the junction capacitance plays a key role in it, the thicker collection layer reduces the capacitance, and effectively improves the total bandwidth. When the thickness of the collection layer is further increased, for example, when the thickness of the collection layer is increased from 0.8µm to 1µm, the increase in the total bandwidth is very small. In this case, the bandwidth determined by the carrier transit time plays a key role, limiting the further improvement of the total bandwidth.
Fig. 9. The relation of the 3 dB total bandwidth with the thickness Wan of P-type absorber under different thicknesses of collection layer. The thickness of the absorber is: (a) 0.2µm. (b) 0.3µm. (c) 0.4µm. (d) 0.5µm.
3.4 Doping concentration
As shown in Fig. 10(a), we studied the theoretical variation of the transport bandwidth for different mixed absorber modes with different doping concentrations in the P-type absorber. Figure 10(b) shows the actual simulation results of Atlas software. It can be seen that the trend of change and relative relationship between theory and practice are consistent. Therefore, the charge control principle can not only calculate the bandwidth of the fixed doping concentration, but also calculate the bandwidth of the device efficiently when the doping concentration of the P-type absorber changes, and it is in good agreement with the practice.
Fig. 10. The bandwidths of different mixed absorber modes change with the doping concentration in P-type absorber. (a) Theoretical calculation (b) Actual ATLAS simulation.
After the demonstration of the above four aspects, we can prove that the charge control principle can well characterize the transport mechanism of the carriers in the photodector, and the combination of the charge control principle and capacitance effect can quickly calculate the total bandwidth, and then through the inverse design, we can efficiently calculate the photodetector structure with the best performance.
4. Automated intelligent design results of MUTC-PD
In Table 2, we summarized the parameters used in the automated design process of MUTC. It is worth noting that, except De, µe, N and d are variables, all other parameters are fixed, because De and µe are related to the doping concentration in the P-type absorber, and our automated design is to calculate the maximum bandwidth by changing the doping concentration and thickness of each layer. Therefore, by giving the De, µe, N, d, we can find the maximum bandwidth of MUTC within the parameter range
Table 1. The Values of X0-X222 Nine Coefficients
Table 2. Parameters Used in The Automated Design Process
In the calculation of VVCPSO, we express the FOM as:
Based on the above FOM, we use VVCPSO to carry out automated intelligent design of MUTC-PD. The computing trend of 3 dB bandwidth is shown in Fig. 11.
The MUTC-PD optimized by VVCPSO algorithm has 8 layers. The material, thickness and doping concentration of each layer before and after optimization are shown in Table 3. The PD operates at a reverse bias (Vbias = −3 V) and is illuminated by a 1310 nm continuous wave laser. It has a diameter of 16 µm, a load resistance of 65Ω and a parasitic capacitance of 5fF.
Table 3. The Material, Thickness And Doping Concentration of Each Layer Before And After Optimization
In order to verify the efficiency and accuracy of this method, the bandwidth performance of the MUTC-PD before and after optimization is studied. As shown in Fig. 12(a), we can see that the bandwidth of the device before optimization is about 20 GHz, after 1500 calculations, we increase the total bandwidth of devices with the same material distribution to about 60 GHz, resulting in a three-fold increase in bandwidth performance that exceeds the optimized photodetector performance recently reported by other researchers [20]. Figure 12(b) shows the responsivity characteristics of MUTC-PD. Since the total mixed absorber width before and after optimization is 0.4µm, the responsivity remains unchanged. It can be seen that the responsivity of the device is about 0.52A/W. Through the above research, prove the application value of this method in optimizing the device bandwidth.
Fig. 12. (a) The bandwidth of the device before and after optimization. (b)The responsivity characteristics of MUTC-PD.
In our study, only a single layer structure is used in the P-type absorber, through optimization of the algorithm, the total bandwidth of MUTC-PD with a mesa diameter of 16µm can reach more than 60 GHz. If the mesa diameter is reduced to 4µm, the total bandwidth can reach 82 GHz. Assuming that the P-type absorber uses multilayer gradient doping, the bandwidth is increased more. This also demonstrates the application potential of our method in the automated design of photodetectors.
5. Conclusion
In this paper, we propose an automatic intelligent design method for MUTC-PD based on charge control model. By comparing the numerical results with the simulation results, we show that the method can approximate and quickly estimate the wideband RF output spectrum of MUTC-PD. Through automated design, we have tripled the bandwidth of MUTC-PD. In addition, the calculation speed of this method is about 1800 times faster than that of simulation software, so extensive parameter studies can be performed to optimize device performance. This method plays an important role in improving the performance of the photodetector.
Funding
National Natural Science Foundation of China (62021005); National Key Research and Development Program of China (2018YFB2200803).
Disclosures
The authors declare no conflicts of interest.
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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