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 
https://doi.org/10.1051/epjpv/2012007
Modelling on cSi/aSi:H wire solar cells: some key parameters to optimize the photovoltaic performance
LGEP, UMR 8507 CNRS, SUPELEC, UPMC, Université ParisSud
11, 11 rue JoliotCurie, Plateau de
Moulon, 91192
GifsurYvette Cedex,
France
^{a}
email: farret@lgep.supelec.fr
Received: 21 November 2011
Accepted: 23 April 2012
Published online: 18 July 2012
Solar cells based on silicon nano or microwires have attracted much attention as a promising path for low cost photovoltaic technology. The key point of this structure is the decoupling of the light absorption from the carriers collection. In order to predict and optimize the performance potential of p (or n) doped cSi/ n(or p) doped aSi:H nanowirebased solar cells, we have used the SilvacoAtlas software to model a singlewire device. In particular, we have noticed a drastic decrease of the opencircuit voltage (V_{oc}) when increasing the doping density of the silicon core beyond an optimum value. We present here a detailed study of the parameters that can alter the V_{oc} of cSi(p)/aSi:H (n) wires according to the doping density in cSi. A comparison with simulation results obtained on planar cSi/aSi:H heterojunctions shows that the drop in V_{oc}, linked to an increase of the dark current in both structures, is more pronounced for radial junctions due to geometric criteria. These numerical modelling results have lead to a better understanding of transport phenomena within the wire.
© Owned by the authors, published by EDP Sciences, 2012
This is an Open Access article distributed under the terms of the Creative Commons AttributionNoncommercial 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 pn junction are of great interest as potentially lowcost 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 photogenerated carriers. This last property enables the use of low purity Si substrates with a short minority carrier diffusion length.
Fig. 1 Structures of solar cells based on (a) a radial pn junction, (b) a planar pn junction. Light penetration into the cell is characterized by the parameter 1/α, α being the wavelengthdependent absorption coefficient. The diffusion length of the generated minority carriers is given by L_{diff}. In the case of the radial junction, light absorption and carrier collection are decoupled. 
The vapourliquidsolid (VLS) technique [7] assisted by gold catalyst is one of the most current methods to grow micro and nanowires 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 deeplevel 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 deeplevel defects. Nevertheless, Al is a ptype dopant and the wires can be strongly pdoped. It is not obvious to know whether the performances of the solar device are strongly influenced by such a ptype doping level. In that case, numerical modelling can be of great help. In this modelling work, we have studied one singlewire Si solar cell which consists in a ptype crystalline silicon (cSi) core surrounded by a ntype hydrogenated amorphous silicon (aSi:H) thin layer. Cell efficiency, opencircuit voltage (V_{oc}), shortcircuit current (I_{sc}) and fill factor (FF) under AM 1.5 spectrum have been calculated as a function of the ptype doping density (N_{a}) in the core. A drastic decrease in V_{oc} has been observed when N_{a} reaches values higher than 1 × 10^{17 } 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 singlewire cSi/aSi:H radial heterojunction solar cell were performed using ATLAS Silvaco software [10]. The geometry of the radial pn junction studied here is given in Figure 2. The design was defined as a simulation plane in 2dimensional 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 ptype cSi core (radius of 800 nm) is surrounded by a thin layer (10 nm) of ntype doped aSi: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.
Fig. 2 Singlewire geometry of the model. 
For the aSi: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 donorlike and one acceptorlike. 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 E_{c}. The electron and hole mobilities were taken equal to μ_{n} = 20 cm^{2} V^{1} s^{1} and μ_{p} = 5 cm^{2} V^{1} s^{1}, respectively. In the cSi 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 N_{a} was varied between 1 × 10^{15 } cm^{3} and 1 × 10^{19 } cm^{3} such that the Fermi level at room temperature moves from 0.25 eV above the valence band edge E_{v} to a position very close to E_{v}, respectively.
Fig. 3 Variations of the efficiency (a) and of the opencircuit voltage V_{oc} (b) of the modeled singlewire cell as a function of the ptype doping density Nain the cSi core. These results are compared to those calculated for an equivalent cSi(p)/aSi: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 driftdiffusion model in ATLAS, and ShockleyReadHall recombination was considered. The AM1.5 solar spectrum was used for the optical generation, the wire being under vertical illumination (see Fig. 2). Currentvoltage characteristics (I(V)) were calculated in the dark and under standard onesun illumination conditions. The opencircuit voltage, the shortcircuit 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 opencircuit voltage of the singlewire device is given as a function of the doping density N_{a} 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 aSi:H(n) layer (10 nm) on a 25 μmthick cSi(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 shortcircuit current density was found constant and equal to 32.1 mA/cm^{2} for both cylindrical and planar geometries.
It can be observed on Figures 3a and 3b that the efficiency and V_{oc} increase with log(N_{a}) when N_{a} increases until an optimum value N_{aopt} which differs in both structures. In the case of the wire cell, N_{aopt} is found equal to 1 × 10^{17 } cm^{3}. Beyond N_{aopt}, there is a strong decrease of the efficiency which is mainly due to a heavy drop in the V_{oc}, and this behavior is more important in the silicon wire than in the planar device.
The V_{oc} is given by the relationship : V_{oc} = nkT/q ln(I_{sc}/I_{o}), where n is the diode ideality factor, k the Boltzmann’s constant, T the temperature, q the electronic charge and I_{o} the dark reverse saturation current. Since I_{sc} remains constant with N_{a}, the variation of the V_{oc} is related to the dark current. Thus, for the singlewire structure, the I(V) characteristics in the dark (I_{dark}) were calculated for different values of N_{a} between 1 × 10^{15 } cm^{3} and 1 × 10^{19 } cm^{3} and the results are presented in Figure 4.
Fig. 4 Forward dark current characteristics I_{dark}(V) for different doping density N_{a} in the cSi(p) core of the wire. For cm^{3}, the fits of the curves with the exponential law I_{0}exp(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 I_{dark} decreases when N_{a} increases, which is a classical behavior in a pn junction. A change in the slope of the curves can be observed, which indicates two current regimes : at high forward bias (V), the I_{dark}(V) curves can be fitted by the expression I_{dark} = I_{0}exp(qV/kT) as shown in Figure 4, which corresponds to an ideal diode behavior with a diffusion current. The values of I_{0} deduced from these fits are found inversely proportional to N_{a}, which explains the variations of the V_{oc} previously described in this range of N_{a}. At low forward bias, the dark current seems to be dominated by a recombination/generation current in the aSi:H layer. At high doping density (N_{a} > 1 × 10^{17 } cm^{3}), no part of the I_{dark}(V) characteristic at forward bias can be fitted by the previous exponential law and the recombination current in the aSi:H shell becomes predominant all over the forward bias range. This is illustrated in Figure 5 where I_{dark}(V) characteristics are calculated for various defect density N_{defect} in the aSi:H layer and a given value of N_{a} equal to 1 × 10^{19} cm^{3}. It can be observed that the dark current in the wire decreases when N_{defect} increases.
Fig. 5 Forward dark current characteristics I_{dark}(V) for various values of the defect density N_{defect} in the aSi:H layer and a given doping density N_{a} in the cSi(p) core equal to 1 × 10^{19} cm^{3}. 
Fig. 6 Mapping of the dark current density distribution near the cSi(p)/aSi:H(n) heterointerface of the wire for N_{a} = 1 × 10^{17} cm^{3} and N_{a} = 1 × 10^{19} cm^{3}. Most of the current is concentrated at the bottom interface for the lowest value of N_{a} whereas it is homogeneously spread all over the pn junction for the highest one. 
The heavy drop in V_{oc} at high doping density of the cSi(p) core is directly related to a strong increase of the dark current which, at such N_{a} values, mainly becomes a recombination current in the defectstates rich aSi: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 cSi(p)/aSi:H(n) heterointerface of the single wire is presented in Figure 6 for N_{a} = 1 × 10^{17 } cm^{3} and N_{a} = 1 × 10^{19 } cm^{3}. It can be observed that for the lowest N_{a} value, most of the current is concentrated at the bottom interface of the structure whereas it is homogenously spread all over the junction for N_{a} = 1 × 10^{19 } cm^{3}. Simulations have shown that this difference in the current distribution appears around N_{a} = 1 × 10^{17} cm^{3}.
Fig. 7 Forward dark current characteristics I_{dark}(V) for two wirelength values (L = 25 μm and L = 250 μm) at N_{a} = 1 × 10^{17} cm^{3} and N_{a} = 1 × 10^{19} cm^{3}. 
Consequently, the active junction surface that really contributes to the dark current becomes wider when N_{a} 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 pn 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 N_{a} = 1 × 10^{17 } cm^{3}, the high forward bias dark current does not depend on the wirelength whereas it increases with L for N_{a} = 1 × 10^{19 } cm^{3} due to an homogeneous current distribution all over the wirelength. Thus, at high values of N_{a}, we should obtain a comparable decrease in V_{oc} 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 V_{oc} with an increasing doping density is much more pronounced for the singlewire cell than for the planar one.
Fig. 8 Mapping of the dark current density distribution near the cSi(n)/aSi:H(p) heterointerface of the wire with ΔE_{v} = 0.42 eV and ΔE_{v} = 0.15 eV. For the highest value of ΔE_{v}, most of the current is concentrated at the bottom interface in the crystalline core. For ΔE_{v} = 0.15 eV, an homogeneous current distribution is obtained all along the heterointerface. 
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 N_{a} = 1 × 10^{17} cm^{3} and N_{a} = 1 × 10^{19} 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 cSi(p) surface. Indeed, the band offsets between aSi:H and cSi can provide a strong band bending which results in a strong inversion layer at the cSi surface [11, 12, 13]. For cSi(p)/aSi:H(n) structures, it has been shown from numerical calculations that the inversion layer occurs even at low values of the conduction band offset ΔE_{c} and that the electron concentration in the interface region of cSi strongly increases with ΔE_{c} as soon as eV [12]. In the case of cSi(n)/aSi:H(p) structures, a lower limit of the valence band offset ΔE_{v} has been found equal to 0.25 eV [13] such that ΔE_{v} can be varied in a wider range than ΔE_{c} 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 presenceor not of an inversion surface layer, we have made some calculations on a cSi(n)/ aSi:H(p) radial cell for different values of the valence band offset. A mapping of the dark current components near the cSi(n)/aSi: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 ptype core as shown in Figure 9. The I_{dark}(V) characteristics follow the exponential law given above with a dependence on the wirelength (not shown here). To come back to our cSi(p)/aSi: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 cSi(p)/aSi:H(n) wire based solar cell through 2D numerical modelling. We have noticed in particular a drastic drop of the opencircuit voltage when the ptype doping density N_{a} of the wire core increases beyond an optimum value equal to 1 × 10^{17 } cm^{3}. This loss in V_{oc} is linked to an increase of the dark current with N_{a}, the transport in the forward bias region being dominated by recombination current in the aSi:H layer at high values of N_{a}. Moreover, the decrease in V_{oc} is less pronounced for an equivalent planar cSi(p)/aSi: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 pn junction area. In conclusion, this study shows that the doping density N_{a} of the cSi core should be kept below an optimum value of 1 × 10^{17 } cm^{3} and that any VLS catalyst which introduces a higher ptype 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. ANR08HABISOL010).
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All Figures
Fig. 1 Structures of solar cells based on (a) a radial pn junction, (b) a planar pn junction. Light penetration into the cell is characterized by the parameter 1/α, α being the wavelengthdependent absorption coefficient. The diffusion length of the generated minority carriers is given by L_{diff}. In the case of the radial junction, light absorption and carrier collection are decoupled. 

In the text 
Fig. 2 Singlewire geometry of the model. 

In the text 
Fig. 3 Variations of the efficiency (a) and of the opencircuit voltage V_{oc} (b) of the modeled singlewire cell as a function of the ptype doping density Nain the cSi core. These results are compared to those calculated for an equivalent cSi(p)/aSi:H(n) planar structure. 

In the text 
Fig. 4 Forward dark current characteristics I_{dark}(V) for different doping density N_{a} in the cSi(p) core of the wire. For cm^{3}, the fits of the curves with the exponential law I_{0}exp(qV/kT) corresponding to an ideal diode behavior is also given (dash lines). 

In the text 
Fig. 5 Forward dark current characteristics I_{dark}(V) for various values of the defect density N_{defect} in the aSi:H layer and a given doping density N_{a} in the cSi(p) core equal to 1 × 10^{19} cm^{3}. 

In the text 
Fig. 6 Mapping of the dark current density distribution near the cSi(p)/aSi:H(n) heterointerface of the wire for N_{a} = 1 × 10^{17} cm^{3} and N_{a} = 1 × 10^{19} cm^{3}. Most of the current is concentrated at the bottom interface for the lowest value of N_{a} whereas it is homogeneously spread all over the pn junction for the highest one. 

In the text 
Fig. 7 Forward dark current characteristics I_{dark}(V) for two wirelength values (L = 25 μm and L = 250 μm) at N_{a} = 1 × 10^{17} cm^{3} and N_{a} = 1 × 10^{19} cm^{3}. 

In the text 
Fig. 8 Mapping of the dark current density distribution near the cSi(n)/aSi:H(p) heterointerface of the wire with ΔE_{v} = 0.42 eV and ΔE_{v} = 0.15 eV. For the highest value of ΔE_{v}, most of the current is concentrated at the bottom interface in the crystalline core. For ΔE_{v} = 0.15 eV, an homogeneous current distribution is obtained all along the heterointerface. 

In the text 
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 N_{a} = 1 × 10^{17} cm^{3} and N_{a} = 1 × 10^{19} cm^{3}. 

In the text 
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