The cell parameter we attempted to optimize in this work is the active layer thickness considering other material properties as they have been earlier described.

A computer program has been developed according to the mathematical analysis, which implements the 3D model previously described. This program calculates the external quantum efficiency of the cells under consideration for wavelength range from 0.4pm to 1.1pm considering material properties such as effective recombination velocity, eq.11. The simulated illumination corresponds to the standard AM1.5 spectrum with power density of 1000 W/m2.

Initially the user must enter the data on the cell manually e. g., data on the front layer and the substrate thickness on Nd, Sf etc. These data are then used as the starting point for optimization.

The presence of any AR coating, the BSF, the grid structure of the cell (grid spacing and coverage), is inserted in the PC via the modelling procedure. The user has to define the lower and upper bounds of parameters to be optimized (epilayer thickness and doping). The program is then started in batch mode and the simulation is performed according to the input parameters. The optimization parameters are varied simultaneously in order to respect their interaction.

We obtained optimization of the cell during a procedure in which the considered parameters are adjusted through a systematic method, getting optimum design parameters. In this way, useful results have been extracted.

After it has finished, the output results are stored in a file and shown in the screen (e. g., calculation of the efficiency) for further examination.

A similar calculation is also performed in order to calculate the short circuit current, which is evaluated through numerical integration for the corresponding spectrum. As a next step, we can also investigate the dark current, the open circuit voltage, and the fill factor of the cells.


type solar cells

1.5 spectral conditions. The experimental values assigned to the model parameters are p=1Q. cm, Ln=66pm. The measured

photocurrent density for these cells is Jsc=24.07 mA/cm2 and their maximum efficiency is 8.86%.

The figure shows the influence of grain boundary recombination velocity on the photocurrent for different values of grain size.

The optimal photocurrent seems to be heavily affected from recombination in the grain boundaries for small grain sizes (50 and 100 pm).

Since such grain sizes, are smaller or comparable to the base diffusion length, it can be concluded that a significant amount of the photogenerated carriers recombine in the grain boundaries.

For high grain boundary recombination velocities (higher than 500 cm/sec) the smaller the grains the lower the photocurrent.

On the contrary, for grain sizes 250 and 500 pm the influence of grain boundary recombination velocity is not so significant.

In any case for grain boundary recombination velocities lower than 200 cm/sec the

photocurrent density becomes independent of grain size.

Figure 3 illustrates efficiency as a function of grain boundary recombination velocity for four different grain sizes, which is calculated from the optimization program for such base thickness that the efficiency is maximized for the given


It can be observed that for grain size 50 and 100 pm the efficiency is heavily affected from grain boundary recombination, where a rapid decrease appears in the values of n for recombination velocities of greater than 103 cm/sec.

On the contrary there is no significant effect of the

recombination velocity for grain sizes 250 and 500 pm, resulting to almost constant efficiency for recombination velocities lower than l03 cm/sec.

As far as the epilayer thickness is concerned, Fig. 4 shows that the quality and the solar cell efficiency is high enough if Sgb reaches 10[39] cm/sec but little is gained if Sgb is lower.

The optimal layer thickness increases when Sgb decreases (better quality, higher Ln). We observe a broad maximum in the efficiency for low grain boundary recombination velocity leading to an optimal base thickness near the value of Ln (66 pm). In this case grain boundary recombination is low and efficiency is limited from

……………. Sgb=10[40] cm/s

——— Sgb=103 cm/s

……………. Sgb=10[41] cm/s

——— Sgb=10[42] cm/s

——— Sgb=106 cm/s



11.4 11.3 11.2 11.1 11.0 10.9 10.8



bulk recombination, directly related to Ln. For large Sgb this maximum efficiency shifts to lower thickness, near 35 pm proving for such value of epilayer thickness the effect of a strong BSF and increased grain boundary recombination, confirming the ratio Ln/d2 ~2 as the optimal choice as it is already proved [2].

The external quantum efficiency curves of figure 5 shows a comparison between the 1D model presented in [3] and the 3D equivalent for a small grain cell.

We observe in Fig. 5 that the quantum efficiency of the 3D model is lower compared to the 1D equivalent for wavelengths greater than 0.5pm (visible and infrared solar spectrum) corresponding to the contribution of carriers generated in the p (base) region, due to the influence of grain boundaries.

For shorter wavelengths the blue response (contribution of n+ front region) is still low, indicating that the emitter can be improved and seems to be independent of the grain boundary recombination velocity. Therefore, the differences between 1D and 3D are

negligible. That can be explained due to emitter heavy doping which reduces the grain boundary barrier height [6] and recombination is unaffected from the grain boundaries.


We have developed a three-dimensional model for n+pp+ polycrystalline Si solar cells and found the grain size and grain boundary recombination velocity influence on photocurrent and solar cell efficiency under AM 1.5 irradiance conditions. The

calculated results show that the optimal photocurrent and conversion efficiency for small grains is heavily affected from the recombination velocity. Concerning the optimal values of epilayer thickness it is obvious that its value is lower, leading also to lower efficiency values, for higher values of grain boundary recombination velocities, confirming the ratio Ln/d2 =2 as the optimal choice for cells of such material quality. Further elaboration is needed in order to investigate other characterizing parameters such as the open circuit voltage, and the fill factor.

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