Silicon nanowire solar cells were simulated using the Silvaco TCAD software kit. For optimization of speed the simulations were performed in cylinder coordinates with cylindrical ... In addition, simulations with a cathode contact on top of.
Mater. Res. Soc. Symp. Proc. Vol. 1322 © 2011 Materials Research Society DOI: 10.1557/opl.2011.1324
Simulation of Symmetrically Doped Silicon Nanowire Solar Cells Felix Voigt1,2, Thomas Stelzner1 and Silke H. Christiansen1,3 Institute of Photonic Technology, Jena, Germany. 2 Institute of Physics, University of Oldenburg, Germany. 3 Max Planck Institute for the Science of Light, Erlangen, Germany.
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ABSTRACT Silicon nanowire solar cells were simulated using the Silvaco TCAD software kit. For optimization of speed the simulations were performed in cylinder coordinates with cylindrical symmetry. Symmetric doping was assumed with a dopant density of 1018 cm-3 in the p-type core and inside the n-type shell. In the implementation a cathode contact was wrapped around the semiconductor nanorod and an anode was assumed at the bottom of the rod. Optimization of cell efficiency was performed with regard to the rod radius and the rod length. In both optimization processes clear maxima in efficiency were visible, resulting in an optimal radius of 66 nm with the pn junction at 43.5 nm and an optimal rod length of about 48 ȝm. The maximum of efficiency with respect to the rod radius is due to a decrease of short-circuit current density (Jsc) and an increase of open-circuit voltage (Uoc) with radius, while the maximum with respect to the rod length is explained by the combination of an increase of Jsc and a decrease of Uoc. Fill factors stay rather constant at values between 0.6 and 0.8. Further, the influence of a back surface field (BSF) layer was surveyed in simulations. Positioning the BSF next to the cathode contact considerably improved cell efficiency. In addition, simulations with a cathode contact on top of the nanowire structure were undertaken. No severe deterioration of cell performance with increasing radius was observed so far in this configuration. Hence, nanorods with much larger radii can be used for solar cells using this contact scheme. In comparison to simulations with wrapped cathode contacts, Jsc and Uoc and therefore efficiency is considerably improved. INTRODUCTION The aim of building solar cells from a nanostructured thin film compositions such as radially doped nanorods is to use low quality semiconductor material and achieve still reasonable cell efficiency [1]. One major benefit of the nanorod film is its high capability of light trapping [2]. In the proceedings papers [3, 4] calculations according to a device physics model and simulations for nanorod solar cells were presented and different types of contacting schemes were proposed. In this paper, we will extend these investigations on the influence of different contact configurations. Mainly, we will concentrate on the geometry of the cells and estimate the effect of rod radius and length variations on cell performance parameters. SIMULATIONS Simulations were undertaken within the TCAD software package of Silvaco, including the device simulator ATLAS. We used cylindrical symmetry of a silicon nanorod in order to reduce the simulation coordinate system to two dimensions. Each simulation was performed for one single rod, with given radius and length. In all simulations the unique AM0 spectrum was used for illumination as given in [5]. Simulation parameters were held constant besides the varied structural parameters of rod radius and rod length. The defaults are summarized in table. I.
Table I. Default values of physical device parameters used for simulations. Physical quantity Band gap Eg [eV] Electron effective density of states Nc [cm-3] Hole eff. dens. of states Nv [cm-3] Doping (p- and n-type) [cm-3] Electron mobility µn [cm2 V-1 s-1] Hole mobility µp [cm2 V-1 s-1] Lifetimes (electrons and holes) [s]
Value 1.12 2.86×1019 3.10×1019 1018 252 178 10-3
Doping was chosen symmetrical with high but non-degenerate doping density of 1018 cm-3, following the specifications in the paper [1] on the concept of Si nanorod cells. Electron and hole mobilities were taken from an internal lookup table of doping concentration dependent mobilities of the Atlas software. The absorption coefficient was chosen as that of crystalline silicon as given by the software. As long as not otherwise stated, lifetimes were chosen as 10-3 s in order to estimate limit values of solar cell geometries for sufficiently good material. (The mobility and lifetime input values result in unrealistically large minority carrier diffusion lengths Ln = 807 µm, Lp = 678 µm for electrons and holes at 300 K, respectively.) Recombination at the silicon/air interface was neglected. As contact scheme we started with a cathode (negative electrode) wrapped around the shell of the cylindrical nanorod. The anode (positive electrode) was assumed just below the ptype core of the rod (see figure 1 a). For complementation and further cell efficiency increase, we extended the simulations by application of a changed contacting scheme, specified by a top cathode contact as shown in figure 1 b.
Figure 1. Contact configuration schemes. The anode (positive electrode) is placed below the p-type core of the nanowire in both cases. (a) Wrapped cathode contact: cathode wrapped around the shell of the n-type cladding. (b) Top cathode contact: cathode located just on top of the nanorod. Solar cell efficiencies were optimized by variation of two structural parameters, the rod radius R and rod length L. The optimization procedure was as follows: 1. Optimization with regard to R with start value L = 3 ȝm. 2. Optimization of L with R-value obtained by step 1. 3. Second optimization of R with L-value obtained by step 2.
The location ȟ2 of pn junction was chosen in the middle region of the cell, such that on both sides of the space charge region (SCR) equal radial extensions of the quasi-neutral regions were established, in other words such that d1 = d4 was realized (see figure 2). Calculations in order to obtain values of ȟ2 for different rod radii were performed half-analytically by using Gauss’ law and half-numerically with help of a Matlab script, prior to simulations.
Figure 2. Radial variations of charge density ȡ inside a pn junction nanorod. RESULTS AND DISCUSSION For the wrapped cathode contact configuration we obtain the results in efficiency Ș, short circuit current density Jsc, open circuit voltage Uoc and fill factor FF shown in figures 3, 4. Figures 3 correspond to rod radius optimization, figures 4 to the rod length optimization process. In figure 3 a, not only cell efficiencies are displayed, but also the value of free radial space dneutr = d1 = d4, corresponding to the quasi-neutral regions in figure 2 as well as ȟ2. We increased dneutr in steps of 10 nm, starting from dneutr = 0, which corresponds to R = 59 nm. For smaller radii the SCR is not properly formed within the wire. As a workaround to further explore the performance of cells with smaller radii, ȟ1 and ȟ4 were further decreased in steps of 1 nm and 2 nm, respectively. In addition a cell with dneutr = 5 nm was simulated in order to find the optimal radial value in better precision. It is clearly seen in figure 3 a, that for radii too small to comprise the full SCR, cell efficiency strongly decreases. This is the case for radii R < 59 nm. The finding is in accord with the statement in [1] that for good cell performance “doping levels must be high enough that a rod [
…] is not fully depleted”. Or in other words, rod radii must be chosen large enough to enable the depletion region to radially find place within the wire. For a planar pn junction the total depletion width for silicon amounts to 50 nm, if symmetrically doped with 1018 cm-3. In the case of a radial pn junction the situation is slightly altered, leading to a minimal radius of 59 nm for a rod with well-formed SCR.
Figure 3. Results of simulations assuming a wrapped cathode contact, corresponding to rod radius optimization process. Closed circles denote a rod length L = 3 ȝm, whereas open circles depict L = 48 ȝm. (a) Efficiency (upper panel), dneutr and ȟ2 (lower panel). Large open circle marks maximum. (b) Short circuit current density. (c) Open circuit voltage. (d) Fill factor. For radii R > 59 nm we see a small increase in efficiency to R = 66 nm (dneutr = 5 nm), followed by a decrease for higher values of R. This decrease can be ascribed to the strong decrease of short circuit current density Jsc (conf. figure 3 b). The decrease in Jsc is due to the way of tying the junction in variation with R at about R/2 position in combination with the wrapped cathode contact configuration. The hole-type charge carriers of the excitons generated by incident light in the outer quasi-neutral region of the nanorod (denoted by d4 in figure 2) to a large extend will recombine at the wrapped around cathode contact and not contribute to the cell current. Therefore with increasing extension of d4, short circuit current density decreases. The effect is partly compensated by an increase of open circuit voltage Uoc with rod radius as seen in figure 3 c. The steep slope of Uoc vs. R for radii R < 59 nm is clear because for a non wellformed SCR the built-in voltage of the pn junction will be less than optimum and hence also Uoc will be diminished. Fill factors stay in between 0.7 and 0.8 and do only slightly change with R. In conclusion we find a maximum cell efficiency of 6.4% for the wrapped cathode contact cell configuration at a radius R = 66 nm, corresponding to a free radial space dneutr = 5 nm. All trends previously discussed apply for the simulations with rod length L = 3 ȝm, as well as for simulations with L = 48 ȝm (conf. figure 3).
Figure 4. Results for rod length optimization. Open circles (o) denote wrapped cathode contact configuration, stars (*) top cathode configuration. Additionally results under application of a back-surface field next to the cathode are included with analogous but larger symbols. (a) Efficiency. Largest circles mark maxima. (b) Short circuit current density. (c) Open circuit voltage. (d) Fill factor. For optimization of the rod length L an exponential approach was applied. Starting with a rod length L = 3 ȝm we increased (and decreased) L by steps of a factor 2. The variation process resulted in a clear maximum in efficiency located for the wrapped cathode at about L = 48 ȝm with an efficiency of 6.4% (figure 4 a) - the second optimization in R did not alter this value. The increase in efficiency Ș for small rod lengths L can be ascribed to the increase in Jsc, which is caused by enhanced total number of generated charge carriers in larger rods (figure 4 b). The decrease of Ș for large L in contrast is dominated by the decrease in open circuit voltage Uoc while Jsc approaches saturation. The decrease of Uoc can be attributed to inhomogeneous absorption of photons and therefore inhomogeneous carrier generation along the direction of illumination. For a wrapped cathode contact configuration as shown in figure 1 a one can subdivide the solar cell in small units along the rod axis with upper unit cells owing a high Uoc and lower units a lower Uoc. The Uoc of the total cell will be an average over the values of all small units. This picture lags reality because carrier transport between the unit cells will take place, but besides this it yields a qualitative understanding of the trend of Uoc vs. rod length. Fill factors remain rather constant in between limits of 0.68 and 0.75.
Top Contact configuration In figures 4 not only the results on solar cells with a wrapped cathode contact are displayed, but also results on cells owing top cathode contacts. With top contact configuration higher cell efficiencies can be achieved culminating in Ș = 11.6% for a rod length L = 96 ȝm. Here, a rod radius R = 171 nm was assumed, which was the optimal value as determined from radius variations at L fixed to 3 ȝm (not shown in this paper). The dependence of efficiency on rod radius is much different for this contact configuration with efficiency showing only shallow maxima or even asymptotic-like behavior as a function of R. For rod length L = 96 ȝm efficiency increases further with radius with a shallow maximum at R = 450 nm (not shown here). The higher efficiency as compared to the wrapped cathode configuration is due to increased open circuit voltage (overall by §100 meV) and less decrease of Jsc for larger radii (not shown here). This is due to the cathode top contact, where holes generated in the outer quasineutral region of the rod can less easily recombine than it would be the case for a wrapped cathode contact, because of larger distance to the contact – an issue which was already discussed in the previous subsection. Back surface field An extra layer of very high doping (1020 cm-3) and 10 nm extension was inserted adjacent to the electrodes. This resulted in a huge increase of efficiency for the wrapped cathode contact. Efficiency increased from 6.4% to 12.5%, in case an n-type layer was inserted next to the cathode. Much less increase in efficiency, from 11.6% to 12.4%, was achieved by an analogous BSF applied to the top cathode scheme. CONCLUSIONS We showed that the efficiencies of symmetrically doped nanorod cells exhibit higher efficiencies if contacted with a top cathode rather than with a wrapped cathode. If back surface field layers are applied next to the cathodes, the performance of cells with both contact configurations becomes almost identical with maximum simulated cell efficiencies of about 12.5%. ACKNOWLEDGMENTS Financial support by the EU project Rod-Sol and by DAAD is gratefully acknowledged. REFERENCES 1. B. M. Kayes, H. A. Atwater, and N. S. Lewis, J. Appl. Phys. 97, 114302 (2005). 2. L. Tsakalakos et al., Journal Of Nanophotonics 1, 1 (2007). 3. M. D. Kelzenberg et al., Single-nanowire si solar cells, in Proceedings of the 33rd IEEE PVSC (2008). 4. M. D. Kelzenberg et al., Predicted efficiency of si wire array solar cells, in Proceedings of the 34th IEEE PVSC, pp. 1948– 1953, 2009. 5. C. Wehrli, "Extraterrestrial Solar Spectrum", Publication no. 615, Physikalisch Meteorologisches Observatorium + World Radiation Center (PMO/WRC), Davos Dorf, Switzerland, (July 1985).
