In this section, we will demonstrate our simulation results by combining the aforementioned theories and models. We built our device model by using Matlab®
coding, commercial software Silvaco® and APSYS®. A proper inclusion of quantum-dot-related carrier absorption is adapted through modified extinction coefficient k, and effective band gap of the device. The final calculation shows good agreement to measurement. This platform has great potential to analyze novel photovoltaic devices.
3-1 Simulation software
Next, I will give a brief introduction for the software I use to calculate the structure.
3-1-1 Silvaco®
We used software is called TCAD® by corporation Silvaco® and use the modular Atlas® to do device simulation. ATLAS provides general capabilities for physically-based two (2D) and three-dimensional (3D) simulation of semiconductor devices. ATLAS is a physically-based device simulator. There are three basic semiconductor equations to solve the device calculation. There are: Poisson’s equation, carrier continuity Equations, the transport Equations [26].
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3-1-2 Matlab®
MATLAB® is a programming environment for algorithm development, data analysis, visualization, and numerical computation. Using MATLAB®, you can solve technical computing problems faster than with traditional programming languages. In my simulation, I use the 2-2-5 Quantum Dot Solar Cell I mentioned formula to calculate the structure[27].
3-1-3 APSYS®
APSYS® is a general purpose 2D/3D modeling software program for semiconductor devices. Based on finite element analysis, it includes many advanced physical models. APSYS® offers a very flexible and simulation environment for modern semiconductor devices. The variety of physical phenomena in a semiconductor require many different physical models. However, Poisson’s equation, carrier continuity equations, the transport equations are the most basic since many of the well known characteristics of a semiconductor device[28].
3-2 Simulated structure
3-2-1 Single junction solar cell
First, we use the scheduling function of VWF Silvaco® simulation software to identify most of the material added thickness and doping concentration. VWF can
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carry out experiments, where a chosen optimization algorithm is used to vary split parameters so that a defined target is minimized[26].
(a) (b)
Fig. 3-1 Optimization of the solar cell (a) GaAs single cell (b) InGaP single cell
The structure of the solar cell is composed of GaAs /InGaP materials. After optimization of the design, we find out that the structures of the GaAs cell and InGaP solar cells shows in Fig. 3-2
(a) (b) Fig.3-2 The optimize structure of single cells (a)InGaP cell (b) GaAs cell
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Calculation of the use of Silvaco® software, we designed the structure the jsc of InGaP is 9.69 mA/cm2 and voc of InGaP is 1.32 V; the jsc of GaAs is 23.21 mA/cm2 and voc of GaAs is 0.92 V. Then we use the other two software which are Matlab® and APSYS® to campare the calculation result in Fig 3-3. We can see that the calculated results are quite similar.
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Fig.3-3 Calculated EQE / IV characteristics of InGaP and GaAs solar cell by softwares (a)and(c) EQE versus wavelength (b)and (d) IV curves.
3-2-2 Solar cell with quantum dots
This chapter, we added quantum dots GaAs solar cells we design (as shown in Fig 3-4) . First of all, we used the simulation software APSYS® to calculated the quantum dot same thickness but the density is not the same, on the solar cell affect.
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Fig. 3-4 Schematic diagram of the quantum dots in solar cell
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Fig 3-5. The different density of quantum dots on GaAs solar cell calculated by APSYS®(a) EQE versus wavelengthand (b) IV curves.
GaAs cell is added to the quantum dots, EQE shows different quantum efficiency, but APSYS keeps Jsc the same.
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Fig. 3-6 The different percentage of quantum dots in the i-layer of GaAs solar cell APSYS® [(a) and (b)] ,and Silvaco® [(c) and (d)]
By Fig. 3-6 can be seen, in APSYS calculation, the higher the percentage of quantum dots in the i region and EQE in a long wavelength pick more obvious, but the efficiency, current density and voc are decreased. In Silvaco the calculation under, this software model of the quantum dots is not enough to complete the calculation,
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Cause the QD different percentages in the i layer EQE considerable confusion.
Then we will use the the simulation software silvaco to do simulate different wavelength absorption quantum dots (as shown in Fig 3-7) in GaAs solar cells i region to know the impact of the cell.
Fig. 3-7 The different position of the absorption of the quantum dots
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Fig. 3-8 Different QDs wavelength absorption in solar cell calculated by Silvaco (a) EQE versus wavelength (b) IV curves
Under in simulation software silvaco calculation, we can see that in the quantum dots in the different position of absorption, the current-voltage characteristic of the solar cell does not impact (as shown in Fig. 3-8).
Next use the software Silvaco® to simulation the different intensities of quantum dots absorption (I call test 56 in my research) in GaAs solar cell.
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Fig. 3-9 Different intensities of quantum dots absorption
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Fig. 3-10 different QDs intensities in solar cell calculated by Silvaco (a) EQE versus wavelength (b) IV curves
Under in simulation software Silvaco® calculated, by Fig. 3-10 seen, when the increase in the intensity of the absorption of the quantum dots, the current density will rise, but under in silvaco calculation, the increase in the absorption intensity of the quantum dots in the open-circuit voltage does not affect.
Next we compare the measured data to our calculation. A single junction AlGaAs/GaAs/InAs QD solar cell device (shown in Fig. 3-11)[29]
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Fig. 3-11 The schematic diagram of a single junction InAs-QD solar cell.
(a) (b)
Fig. 3-12 Single junction InAs-QD solar cell Energy band (a) V=0 (b) V=0.5.
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Fig. 3-13 Comparison of calculated and measured EQE / IV characteristics of GaAs solar cell with QD by Silvaco® [(a) and (b) with QD×3] ,[(c) and (d) with QD×5]
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Table 3-1 Simulated in Silvaco® and measured values Device
type
Jsc (mA/cm2) Voc (V)
Measurement Calculation Measurement Calculation
QD*3 8.5 8.6 0.72 0.72
QD*5 8.4 8.48 0.54 0.57
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Fig. 3-14 Comparison of calculated and measured EQE / IV characteristics of GaAs solar cell with QD byMatlab® [(a) and (b) with QD×3] ,[(c) and (d) with QD×5]
Table 3-2 Simulated in Matlab® and measured values Device
type
Jsc (mA/cm2) Voc (V)
Measurement Calculation Measurement Calculation
QD*3 8.5 8.3 0.72 0.72
QD*5 8.4 8.4 0.57 0.57
We use Silvaco and Matlab to simulate the structure with different layers of quantum dot which were QDx3, QDx5, and the one QD layer's thinkness was 0.01um.
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Fig. 3-11 shows our device layer design, and Fig. 3-12 the band diagram from the software. The quantum dot layer is based on GaAs material parameters but also adapt the quantum dot absorption spectral line shape in [20]. And then we use our simulation result to compare with the measurement data. In the Fig. 3-13 to Fig. 3-14 different layers of QD were placed in the ordinary GaAs solar cell structure, and their EQE and IV were calculated. We put lots of emphasis in the fitting of wavelength dependent EQE and try to match the IV as well. From the results, we can see that the EQE with longer wavelength absorption was successfully fitted.
3-2-3 Dual junction solar cell
Reference 3-2-1 single junction solar cell design out of a solar cell data and various data related papers, we Use the tunnel junction to connection GaAs solar cells and InGaP solar cells for tandem cell[30][31].
Fig. 3-15 Optimization of the InGaP/GaAs tandem cell calculated by Silvaco® After we use the tunnel junction to connect the two single cells，we use the VWF in software to optimize the thickness of the best tandem cell. As the Fig. 3-15 shown, we
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can see when i region of InGaP cell in 0.5 µm and i region in GaAs cell in 1 µm has the maximum efficiency.
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Fig. 3-16 IV curve of tandem cell simulated by three software (a) Matlab® (b) Silvaco® (c) APSYS®
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Fig. 3-17 EQE vurses wavelength of tandem cell simulated by three software (a) Matlab® (b) Silvaco® (c) APSYS®
Use of three different software simulation the tandem cell structure I design, we can see three software calculation results are quite close.
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3-2-4 Dual junction solar cell with quantum dots
InGaP p-i-n
Fig. 3-18 InGaP/GaAs QD tandem solar cell schematic diagram
After we achieve a good fitting on the single junction InAs QD cell and good simulation of tandem cell, we can move onto a more complicated design. As shown in Fig. 3-18, a dual junction InGaP/GaAs+InAs QD is a good candidate for high efficiency devices. In our simulation, we have two types of devices to be demonstrated, one is using structure which is close to what other people implemented, and the other is the ideal device with 100% quantum efficiency[32]. Fig.3-19 shows the generic result of EQE and IV calculation from ordinary structure.
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Fig. 3-19 Calculated EQE / IV characteristics of Tandem solar cell with QD by Matlab®[(a) and (c)], and Silvaco® [(b) and (d)]
The QD absorption is marked at the longer wavelength band (> 880nm). With full current-voltage characteristics obtained, the final PCE can be found as well. In Fig.
3-20, we calculated power conversion efficiency (PCE) versus the percentage of
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quantum dot volume in the intrinsic region with three different designs: the bottom two curves are practical structures, and the top one is the ideal cell result. From the calculation, several observations can be deducted: first, the ideal enhancement brought by quantum dot can be estimated to 11% at most, which is consistent with our detailed balance model [33].
Second, if we use the structures published in most papers, the efficiency tends to drop when QD layer is added (as the green curve in Fig. 3-20), and only when we increase the intrinsic region
thickness to ensure at least 90% quantum efficiency, the addition of QD layer is beneficial (the blue curve in Fig. 3-20). Third, we found there are knee-like features in the plot (like in ideal case), which is rising from the crisscross of the shortcircuit current between the top and bottom cells.
Fig. 3-20 Efficiency vs. percentage of QD volume in the intrinsic region calculated by Matlab®.
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From our calculation, we found that in most of the cases, the QD devices generate inferior PCE compared to pure GaAs/InGaP tandem cells. Although this is not very encouraging, they do agree with most of the experimental data so far [34]. The calculation makes the authors to believe that the utilization of the photon in the cell has to be nearly perfect for QD layer to be useful. As we see in the ideal case, a perfect quality of the material growth will be required for IBSC device to outperform the ordinary device.
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