Open Access
Issue
EPJ Photovolt.
Volume 3, 2012
Article Number 30102
Number of page(s) 6
Section Modelling
DOI https://doi.org/10.1051/epjpv/2012007
Published online 18 July 2012

© Owned by the authors, published by EDP Sciences, 2012

Licence Creative Commons
This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3.0, which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly cited.

1 Introduction

Solar cells based on Si micro- or nanowire arrays with radial p-n junction are of great interest as potentially low-cost solutions in solar cell production and have been extensively studied in the last years [1, 2, 3, 4, 5, 6]. Unlike planar structures, photon absorption and minority carrier collection are decoupled as shown in Figure 1, and are not anymore in competition when optimizing the cell dimensions. In fact, the wires can be grown long enough to optimize light absorption while being small enough in radius to collect photo-generated carriers. This last property enables the use of low purity Si substrates with a short minority carrier diffusion length.

thumbnail Fig. 1

Structures of solar cells based on (a) a radial p-n junction, (b) a planar p-n junction. Light penetration into the cell is characterized by the parameter 1/α, α being the wavelength-dependent absorption coefficient. The diffusion length of the generated minority carriers is given by Ldiff. In the case of the radial junction, light absorption and carrier collection are decoupled.

The vapour-liquid-solid (VLS) technique [7] assisted by gold catalyst is one of the most current methods to grow micro- and nano-wires for photovoltaic applications. Despite many advantages in using Au as VLS catalyst (non toxicity, chemical stability, availability), Au is known to diffuse in the nanowires [8] creating deep-level defects in Si and leading to an increase of the carrier recombination rate. Among the large number of catalyst materials that have been tested to replace Au [9], aluminium is a good candidate since it does not create deep-level defects. Nevertheless, Al is a p-type dopant and the wires can be strongly p-doped. It is not obvious to know whether the performances of the solar device are strongly influenced by such a p-type doping level. In that case, numerical modelling can be of great help. In this modelling work, we have studied one single-wire Si solar cell which consists in a p-type crystalline silicon (c-Si) core surrounded by a n-type hydrogenated amorphous silicon (a-Si:H) thin layer. Cell efficiency, open-circuit voltage (Voc), short-circuit current (Isc) and fill factor (FF) under AM 1.5 spectrum have been calculated as a function of the p-type doping density (Na) in the core. A drastic decrease in Voc has been observed when Na reaches values higher than 1 × 1017 cm-3. An insight into the transport properties of the wire in the dark can help to understand this behavior.

2 Silicon nanowire modelling : geometry and physical parameters

Simulations of the electrical characteristics of a single-wire c-Si/a-Si:H radial heterojunction solar cell were performed using ATLAS Silvaco software [10]. The geometry of the radial p-n junction studied here is given in Figure 2. The design was defined as a simulation plane in 2-dimensional cylindrical coordinates which models the 3D cylindrical structure. The wire dimensions were chosen according to experimental data of fabricated wire array cells, with a wire length of 25 μm and a radius of 810 nm. The p-type c-Si core (radius of 800 nm) is surrounded by a thin layer (10 nm) of n-type doped a-Si:H. Ohmic contacts were used, one at the bottom of the structure on the crystalline base and another one around the wire on the amorphous layer. At the bottom contact, the electron surface recombination velocity has been taken equal to 50 cm s-1. For the surrounded contact, flat band conditions were imposed.

thumbnail Fig. 2

Single-wire geometry of the model.

For the a-Si:H layer, the distribution of the density of states (DOS) is made of two exponential band tails (valence and conduction band tails) and two Gaussian distributions of deep defect states, one donor-like and one acceptor-like. The DOS and doping concentration were adjusted such that the Fermi level at room temperature was set at 0.2 eV below the conduction band edge Ec. The electron and hole mobilities were taken equal to μn = 20 cm2  V-1  s-1 and μp = 5 cm2 V-1  s-1, respectively. In the c-Si core, we fixed a value of 1 ms for the carrier lifetime which corresponds to a diffusion length much bigger than the wire radius. The doping density Na was varied between 1 × 1015 cm-3 and 1 × 1019 cm-3 such that the Fermi level at room temperature moves from 0.25 eV above the valence band edge Ev to a position very close to Ev, respectively.

thumbnail Fig. 3

Variations of the efficiency (a) and of the open-circuit voltage Voc (b) of the modeled single-wire cell as a function of the p-type doping density Nain the c-Si core. These results are compared to those calculated for an equivalent c-Si(p)/a-Si:H(n) planar structure.

The simulation is based on the resolution of Poisson’s equation and electron and hole continuity equations. The Boltzmann statistics is used with the drift-diffusion model in ATLAS, and Shockley-Read-Hall recombination was considered. The AM1.5 solar spectrum was used for the optical generation, the wire being under vertical illumination (see Fig. 2). Current-voltage characteristics (I(V)) were calculated in the dark and under standard one-sun illumination conditions. The open-circuit voltage, the short-circuit current, and the efficiency of the cell were deduced from the I(V) curves under illumination.

3 Simulation results and discussion

The variations of the efficiency and of the open-circuit voltage of the single-wire device is given as a function of the doping density Na in Figures 3a and 3b, respectively. These variations are compared to those of an equivalent planar solar cell. The planar structure was defined as a thin a-Si:H(n) layer (10 nm) on a 25 μm-thick c-Si(p) wafer. The material properties and the illuminated surface are strictly the same in both structures. Moreover, whatever the doping density in the studied range, the short-circuit current density was found constant and equal to 32.1 mA/cm2 for both cylindrical and planar geometries.

It can be observed on Figures 3a and 3b that the efficiency and Voc increase with log(Na) when Na increases until an optimum value Naopt which differs in both structures. In the case of the wire cell, Naopt is found equal to 1 × 1017 cm-3. Beyond Naopt, there is a strong decrease of the efficiency which is mainly due to a heavy drop in the Voc, and this behavior is more important in the silicon wire than in the planar device.

The Voc is given by the relationship : Voc = nkT/q ln(Isc/Io), where n is the diode ideality factor, k the Boltzmann’s constant, T the temperature, q the electronic charge and Io the dark reverse saturation current. Since Isc remains constant with Na, the variation of the Voc is related to the dark current. Thus, for the single-wire structure, the I(V) characteristics in the dark (Idark) were calculated for different values of Na between 1 × 1015 cm-3 and 1 × 1019 cm-3 and the results are presented in Figure 4.

thumbnail Fig. 4

Forward dark current characteristics Idark(V) for different doping density Na in the c-Si(p) core of the wire. For cm-3, the fits of the curves with the exponential law I0exp(qV/kT) corresponding to an ideal diode behavior is also given (dash lines).

At low doping concentration (cm-3), the trend of the curves remains the same and Idark decreases when Na increases, which is a classical behavior in a p-n junction. A change in the slope of the curves can be observed, which indicates two current regimes : at high forward bias (V), the Idark(V) curves can be fitted by the expression Idark = I0exp(qV/kT) as shown in Figure 4, which corresponds to an ideal diode behavior with a diffusion current. The values of I0 deduced from these fits are found inversely proportional to Na, which explains the variations of the Voc previously described in this range of Na. At low forward bias, the dark current seems to be dominated by a recombination/generation current in the a-Si:H layer. At high doping density (Na > 1 × 1017 cm-3), no part of the Idark(V) characteristic at forward bias can be fitted by the previous exponential law and the recombination current in the a-Si:H shell becomes predominant all over the forward bias range. This is illustrated in Figure 5 where Idark(V) characteristics are calculated for various defect density Ndefect in the a-Si:H layer and a given value of Na equal to 1 × 1019 cm-3. It can be observed that the dark current in the wire decreases when Ndefect increases.

thumbnail Fig. 5

Forward dark current characteristics Idark(V) for various values of the defect density Ndefect in the a-Si:H layer and a given doping density Na in the c-Si(p) core equal to 1 × 1019 cm-3.

thumbnail Fig. 6

Mapping of the dark current density distribution near the c-Si(p)/a-Si:H(n) heterointerface of the wire for Na = 1 × 1017 cm-3 and Na = 1 × 1019 cm-3. Most of the current is concentrated at the bottom interface for the lowest value of Na whereas it is homogeneously spread all over the p-n junction for the highest one.

The heavy drop in Voc at high doping density of the c-Si(p) core is directly related to a strong increase of the dark current which, at such Na values, mainly becomes a recombination current in the defect-states rich a-Si:H layer. However, according to Figure 3b, this behavior is much more pronounced for the radial junction than for the planar one (it has to be reminded that this comparison is presented for the same illuminated area in both structures). A mapping of the dark current components near the c-Si(p)/a-Si:H(n) heterointerface of the single wire is presented in Figure 6 for Na = 1 × 1017 cm-3 and Na = 1 × 1019 cm-3. It can be observed that for the lowest Na value, most of the current is concentrated at the bottom interface of the structure whereas it is homogenously spread all over the junction for Na = 1 × 1019 cm-3. Simulations have shown that this difference in the current distribution appears around Na = 1 × 1017 cm-3.

thumbnail Fig. 7

Forward dark current characteristics Idark(V) for two wirelength values (L = 25 μm and L = 250 μm) at Na = 1 × 1017 cm-3 and Na = 1 × 1019 cm-3.

Consequently, the active junction surface that really contributes to the dark current becomes wider when Na increases and it is expected that the ratio between the radius R of the wire (related to the illuminated area) and the wirelength L (related to the p-n junction) will affect the photovoltaic performance of the wire solar cell as soon as high doping density in the core is reached. This is also illustrated in Figure 7 where the dark current characteristics are plotted for two wirelength values L = 25 μm and L = 250 μm. For Na = 1 × 1017 cm-3, the high forward bias dark current does not depend on the wirelength whereas it increases with L for Na = 1 × 1019 cm-3 due to an homogeneous current distribution all over the wirelength. Thus, at high values of Na, we should obtain a comparable decrease in Voc between a planar and a radial junction for an aspect ratio (ratio between the illuminated area and the junction area) of the wire equal to 1. In the wire structures we have studied, the junction area is bigger than the illuminated area (ratio R/L much smaller than 1) such that the drop in Voc with an increasing doping density is much more pronounced for the single-wire cell than for the planar one.

thumbnail Fig. 8

Mapping of the dark current density distribution near the c-Si(n)/a-Si:H(p) heterointerface of the wire with ΔEv = 0.42 eV and ΔEv = 0.15 eV. For the highest value of ΔEv, most of the current is concentrated at the bottom interface in the crystalline core. For ΔEv = 0.15 eV, an homogeneous current distribution is obtained all along the heterointerface.

thumbnail Fig. 9

Mapping of the dark current density distribution near the interface of a silicon crystalline homojunction wire with a doping density of the core Na = 1 × 1017 cm-3 and Na = 1 × 1019 cm-3.

At low doping density, the current is dominated by the minority carriers diffusion and it mainly runs through a small active surface of the junction at the bottom of the structure as shown in Figure 6. This specific behavior seems to be related to the presence of a highly conductive electron interface layer at the c-Si(p) surface. Indeed, the band offsets between a-Si:H and c-Si can provide a strong band bending which results in a strong inversion layer at the c-Si surface [11, 12, 13]. For c-Si(p)/a-Si:H(n) structures, it has been shown from numerical calculations that the inversion layer occurs even at low values of the conduction band offset ΔEc and that the electron concentration in the interface region of c-Si strongly increases with ΔEc as soon as eV [12]. In the case of c-Si(n)/a-Si:H(p) structures, a lower limit of the valence band offset ΔEv has been found equal to 0.25 eV [13] such that ΔEv can be varied in a wider range than ΔEc to observe or not an interface inversion layer. Thus, in order to establish a link between the current distribution at the wire heterointerface and the presence-or not of an inversion surface layer, we have made some calculations on a c-Si(n)/ a-Si:H(p) radial cell for different values of the valence band offset. A mapping of the dark current components near the c-Si(n)/a-Si:H(p) interface is given in Figure 8 for ΔEv = 0.42eV. and ΔEv = 0.15eV. It can be observed that the current distribution is homogeneous along the wire for ΔEv = 0.15eV whereas it is concentrated at the bottom of the cell for ΔEv = 0.42eV which can be explained by a charge accumulation in the inversion layer at the interface. Furthermore, calculations performed on a single wire crystalline homojunction also show an homogeneous current distribution all along the wire interface whatever the doping density in the p-type core as shown in Figure 9. The Idark(V) characteristics follow the exponential law given above with a dependence on the wirelength (not shown here). To come back to our c-Si(p)/a-Si:H(n) wire structures, high values of the doping density in the crystalline core lead to a modification of the band bending such that no strong inversion layer occurs. An homogeneous current distribution is thus observed along the wire for cm-3. Further studies have to be done to explain more precisely the location of the “hot spot” at the bottom of the interface in the case of a non homogeneous current distribution. In particular, the geometry and position of the contacts can play a important role in that feature.

4 Conclusion

We have studied the potential performance of a single c-Si(p)/a-Si:H(n) wire based solar cell through 2D numerical modelling. We have noticed in particular a drastic drop of the open-circuit voltage when the p-type doping density Na of the wire core increases beyond an optimum value equal to 1 × 1017 cm-3. This loss in Voc is linked to an increase of the dark current with Na, the transport in the forward bias region being dominated by recombination current in the a-Si:H layer at high values of Na. Moreover, the decrease in Voc is less pronounced for an equivalent planar c-Si(p)/a-Si:H(n) heterojunction, the illuminated area of the planar and the radial modelled structures being the same. This difference can be explained by a dependence of the dark current in the wire with the wirelength. Thus, for cm-3 the wire based solar cell performance strongly depend on the ratio between the radius, which is linked to the illuminated area, and the wirelength, which is related to the p-n junction area. In conclusion, this study shows that the doping density Na of the c-Si core should be kept below an optimum value of 1 × 1017 cm-3 and that any VLS catalyst which introduces a higher p-type doping density in the core should be avoided.

Acknowledgments

This work has been supported by French Research National Agency (ANR) through Habitat intelligent et solaire photovoltaïque program (Projet Siflex No. ANR-08-HABISOL-010).

References

  1. M. Law, J. Goldberger, P. Yang, Annu. Rev. Mater. Res. 34, 83 (2004) [CrossRef] [Google Scholar]
  2. B.M. Kayes, H.A. Atwater, N.S. Lewis, J. Appl. Phys. 97, 114302 (2005) [CrossRef] [Google Scholar]
  3. L. Tsakalakos, J. Balch, J. Fronheiser, B.A. Korevaar, O. Sulima, J. Rand, Appl. Phys. Lett. 91, 233117 (2007) [CrossRef] [Google Scholar]
  4. B. Tian, X. Zheng, T.J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, C.M. Lieber, Nature 449, 885 (2007) [CrossRef] [PubMed] [Google Scholar]
  5. T. Stelzner, M. Pietsch, G. Andrä, F. Falk, E. Ose, S. Christiansen, Nanotechnology 19, 295203 (2008) [CrossRef] [PubMed] [Google Scholar]
  6. M. Kelzenberg, S. Boettcher, J. Petykiewicz, D.B. Turner-Evans, M.C. Putman, E.L. Warren, J.M. Spurgeon, R.M. Briggs, N.S. Lewis, H.A. Atwater, Nat. Mater. 9, 239 (2010) [CrossRef] [PubMed] [Google Scholar]
  7. R.S. Wagner, C.W. Ellis, Appl. Phys. Lett. 4, 89 (1964) [CrossRef] [Google Scholar]
  8. D.E. Perea, J.E. Allen, S.J. May, B.W. Wessels, D.N. Seidman, L.J. Lauhon, Nano Lett. 6, 181 (2006) [CrossRef] [PubMed] [Google Scholar]
  9. V. Schmidt, J.V. Wittemann, U. Gösele, Chem. Rev. 110, 361 (2010) [CrossRef] [PubMed] [Google Scholar]
  10. ATLAS Users’ Manual (Silvaco International, 2010) [Google Scholar]
  11. J.P. Kleider, A.S. Gudovskikh, P. Roca i Cabarrocas, Appl. Phys. Lett. 92, 162101 (2008) [CrossRef] [Google Scholar]
  12. J.P. Kleider, Y.M. Soro, R. Chouffot, A.S. Gudovskikh, P. Roca i Cabarrocas, J. Damon-Lacoste, D. Eon, P.J. Ribeyron, J. Non-Cryst. Solids 354, 2641 (2008) [CrossRef] [Google Scholar]
  13. O.A. Maslova, J. Alvarez, E.V. Gushina, W. Favre, M.E. Gueunier-Farret, A.S. Gudovskikh, A.V. Ankudinov, E.I. Terukov, J.P. Kleider, Appl. Phys. Lett. 97, 252110 (2010) [CrossRef] [Google Scholar]

All Figures

thumbnail Fig. 1

Structures of solar cells based on (a) a radial p-n junction, (b) a planar p-n junction. Light penetration into the cell is characterized by the parameter 1/α, α being the wavelength-dependent absorption coefficient. The diffusion length of the generated minority carriers is given by Ldiff. In the case of the radial junction, light absorption and carrier collection are decoupled.

In the text
thumbnail Fig. 2

Single-wire geometry of the model.

In the text
thumbnail Fig. 3

Variations of the efficiency (a) and of the open-circuit voltage Voc (b) of the modeled single-wire cell as a function of the p-type doping density Nain the c-Si core. These results are compared to those calculated for an equivalent c-Si(p)/a-Si:H(n) planar structure.

In the text
thumbnail Fig. 4

Forward dark current characteristics Idark(V) for different doping density Na in the c-Si(p) core of the wire. For cm-3, the fits of the curves with the exponential law I0exp(qV/kT) corresponding to an ideal diode behavior is also given (dash lines).

In the text
thumbnail Fig. 5

Forward dark current characteristics Idark(V) for various values of the defect density Ndefect in the a-Si:H layer and a given doping density Na in the c-Si(p) core equal to 1 × 1019 cm-3.

In the text
thumbnail Fig. 6

Mapping of the dark current density distribution near the c-Si(p)/a-Si:H(n) heterointerface of the wire for Na = 1 × 1017 cm-3 and Na = 1 × 1019 cm-3. Most of the current is concentrated at the bottom interface for the lowest value of Na whereas it is homogeneously spread all over the p-n junction for the highest one.

In the text
thumbnail Fig. 7

Forward dark current characteristics Idark(V) for two wirelength values (L = 25 μm and L = 250 μm) at Na = 1 × 1017 cm-3 and Na = 1 × 1019 cm-3.

In the text
thumbnail Fig. 8

Mapping of the dark current density distribution near the c-Si(n)/a-Si:H(p) heterointerface of the wire with ΔEv = 0.42 eV and ΔEv = 0.15 eV. For the highest value of ΔEv, most of the current is concentrated at the bottom interface in the crystalline core. For ΔEv = 0.15 eV, an homogeneous current distribution is obtained all along the heterointerface.

In the text
thumbnail Fig. 9

Mapping of the dark current density distribution near the interface of a silicon crystalline homojunction wire with a doping density of the core Na = 1 × 1017 cm-3 and Na = 1 × 1019 cm-3.

In the text

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