We have developed quantitative device-physics models for a radial pn junction nanorod solar cell, that is, a cell which consists of densely packed nanorods attached to a conducting substrate, each nanorod with a pn junction in the radial direction. It is found that this novel design shows large improvements over the planar geometry so long as two conditions are satisfied: a) a planar solar cell made from the same material is collection limited, i.e. the diffusion length of minority carriers is too low to allow for collection of most or all of the light-generated carriers in the conventional planar geometry, and b) recombination in the depletion region is not too high, or, equivalently, the lifetime of carriers in the depletion region is not too short. In order to experimentally validate this concept, the vapor-liquid-solid (VLS) growth of silicon (Si) nanorods has been explored using metal catalyst particles that are not as deleterious to the minority carrier lifetime of Si as gold (Au), the most commonly used wire growth catalyst

Atwater, Harry A.

Kayes, Brendan M.

Lewis, Nathan S.

Richardson, Christine E.

Caltech Authors - Main

RADIAL PN JUNCTION NANOROD SOLAR CELLS: 
DEVICE PHYSICS PRlNCfPLES AND ROUTES TO FABRICATION IN SILICON 
Brendan M. Kayes, Christine E. Richardson, Nathan S. Lewis, Harry A. Atwater 
California Institute of Technology, Pasadena, CA 91 125 
ABSTRACT 
We have developed quantitative device-physics 
models for a radial pn junction nanorod solar cell, that is, a 
cell which consists of densely packed nanorods attached 
to a conducting substrate, each nanorod with a pn junction 
in the radial direction. It is found that this novel design 
shows farge improvements over the planar geometry so 
long as two conditions are satisfied: a) a planar solar cell 
made from the same material is collection limited, i.e. the 
diffusion length of minority camers is too low to allow for 
collection of most or all of the light-generated carriers in 
the conventional planar geometry, and b) recombination in 
the depletion region is not too high, or, equivalently, the 
lifetime of carriers in the depletion region is not too short. 
In order to experimentally validate this concept, the vapor- 
liquid-solid (VLS) growth of silicon (Si) nanorods has been 
explored using metal catalyst particles that are not as 
deleterious to the minority carrier lifetime of Si as gold 
(Au), the most commonty used wire growth catalyst. 
. . 
- 
INTRODUCTION 
Inexpensive semiconductor absorber materials for 
use in photovoltaic applications generally have either a 
high level of impurities or a high density of defects, 
resulting in low minority carrier diffusion lengths [l]. Use 
of low diffusion length materials as the absorbing base in a 
conventional planar pn junction solar cell geometry results 
in devices having carrier collection limited by minority 
carrier diffusion in the base region. Increasing the 
thickness of the base in such a cell will therefore produce 
more light absorption but will not result in an increase in 
device efficiency. In the absence of sophisticated light 
trapping schemes, materials with low diffusion lengths and 
low absorption coefficients therefore cannot readily be 
incorporated into high energy conversion efficiency planar 
solar cell structures [ Z ] .  - 
Radial pn junction nanorod cells provide a potential 
solution to this problem. A nanorod with a pn junction in 
the radial direction allows for separation of the 
requirements of light absorption and carrier extraction in 
two orthogonal directions. The cell can be thick in one 
dimension for optimal light absorption, while thin in 
another, for optimal carrier collection (see Fig. 1). 
Fig. I. Schematic and cross-section of the radial pn 
junction nanorod cell. Light is incident on the top surface. 
The light grey area is n-type. the dark grey area p-type. . 
DEVICE PHYSICS ANALYSIS 
The nanorod cell was analyzed by solving the 
semiconductor driftldiffusion carrier transport equations in 
cylindrical polar coordinates and comparing the result with 
the l -d transport equation treatment for a conventional 
planar-junction cell. Simplifying assumptions necessary to 
obtain analytic solutions to the problem were made. The 
model was then applied to real materials. silicon (Si) and 
gallium arsenide (GaAs) (GaAs results are not included 
here - see [3] for details), using a 100 mW/cm2, AM15 
spectrum, to obtain quantitative comparisons of the two 
geometries. Cell efficiencies, open-circuit voltages, short- 
circuit currents, and fill factors were calculated as a 
function of cell thickness (which is the same as the rod 
length in the nanorod case), nanorod radius, and electron 
diffusion length, at fixed emitter and base doping levels (or 
core and sheath dopings in the nanorod case) and 
window-layer thickness. Two regimes were considered - 
first the trap density was assumed to be the same 
throughout the material and thus the quasi-neutral region 
and depletion region lifetimes were coupled. and secondly 
!he depletion region trap density was held fixed at 10' cm- 
, so that depletion region lifetimes T,,o, i p a  = 1 ps, while the 
quasi-neutral region trap density was allowed to vary 
independently. Thus the relative impact of traps in the 
depletion- and quasi-neutral regions could be seen. 
0-7803-8707-4/05/$20.00 02005 IEEE. 55 
The model for the radial pn junction nanorod solar cell 
was constructed by extending the analysis of the planar 
cell geometry [4j to a cylindrical geometry. The pn 
junction in the nanorod was assumed to be abrupt, and 
the depletion approximation was assumed to be valid. 
The emitter layer (i.e. the exterior "shell" of the nanorod) 
was n-type, while the base (i.e. the interior 'core" of the 
nanorod) was p-type. Light was normally incident on the 
top face of the nanorod. Recombination was assumed to 
purely be due to Shockley-Read-Hall recombination from a 
single trap level .at mid-gap [ti]; other recombination 
processes such as Auger remm bination were neglected. 
Surface recombination effects were, however, included. 
To simplify the analysis and to allow for analytic 
solutions, carrier transport was taken to be purely radial. 
Hence, each cross-sectional "slice" of the rod was treated 
separately, and the resulting flux was integrated over the 
fength of the rod. This approximation is valid when the 
carrier motion in the z-direction is much less than the 
carrier motion in the r-direction, which is the case when 
the carrier concentration gradient andlor the electric field 
in the rdirection is much greater than in the z-direction. 
This condition is appropriate for materials that are 
collection-limited, because the length scale associated 
with carrier transport will be much shorter than that 
associated with light absorption. 
No correction was made for 'iess than 100% 
packing density. In practice light will not be incident truly 
normal to the rods, but rather at some angle. At small 
angles from normal incidence, light that is incident on the 
top of a rod will remain within the rod due to total internal 
reflection, while light that is not incident on the top of a rod 
is likely to pass through many rods while traversing the 
cell, due to the high aspect ratio of the rods. The precjse 
details await further study. 
Detailed results of this modeling are presented 
elsewhere [3]. herein is a summary of the most important 
findings. It was found that this novel design shows large 
improvements overthe planar geometry so long as two 
conditions are satisfied: a) a planar solar 'cell made from 
the same material is collection limited, i.e. the diffusion 
length of minority carriers is too low to allow for collection 
of most or all of the light-generated carriers in the 
conventional planar geometry, and b) recombination in the 
depletion region is not too high, or, equivalently, the 
lifetime of carriers in the depletion region is not too short. 
For Si, this means that the lifetime of carriers in the 
depletion region lifetimes must be greater than -10 ns, or, 
equivalently, that the trap density in the depletion region 
must be less than - c m q  If condition (a) is satisfied 
but not (b). then the radial cell outperforms the planar cell 
only slightly. 
The short-circuit current density in the Si nanorod cell 
is essentially independent of the trap density in stark 
contrast to the ptanar cell, indicating that the radial pn 
junction design overcomes the problems of carrier 
collection that are present in the conventional planar 
geomehy- 
- 
. 
a) si PI" Cell 
Fig. 2. Efficiency vs. cell thickness L and minority electron 
diffusion length Ln, for (a) a conventional planar pn 
junction Si cell, and (b) a radial pn junction hanorod Si cell. 
In both cases the top surface shown in the plot has the 
depletion region trap density fixed at cmd, so that 
depletion region lifetimes T,,o, ~ p o  = 1 ps, while the bottom 
surface has depletion region trap density equal to the trap 
density in the quasi-neutral region, at each value of L. In 
the radial pn junction nanorod case, the cell radius R is set 
equal to Ln, a condition that was found to be near-optimal. 
- 
The degree to which the open-circuit voltage varied 
with the trap density depended most strongly on the trap 
density in the depletion region, for both the radial pn 
junction case and for the planar case. A low trap density 
in the depletion region produced a relatively high open- 
circuit voltage even if the quasi-neutral region tra density 
was relatively high. A high trap density (> - 10' cm3) in 
the depletion region inevitably led to a low open-circuit 
voltage. 
. 
.P 
Taken together, this means that the efFiciency of a 
radial pn junction nanorod solar cell citn remain high 
despite a high quasi-neutral region trap density. provided 
that the depletion region trap density is not too high (Fig. 
2). In Si with very low diffusion lengths (L,=lOO nm), 
56 
extremely large efficiency. gains (from 1.5% to 12%) are 
possible by exploiting the radial pn junction nanorod 
geometry, provided that the trap density in the depletion 
region is held fixed at a relatively low level (e -5 x I O l 5  
cmm3). Even at higher depletion region trap densities (2.5 x 
10'' ~ m - ~ ) ,  in Si with Ln=l pm efficiency gains from 4.2% 
to 13% are predicted. These increases are atttibuted to 
the greatly enhanced carrier collection that is possible in 
the radial pn junction nanorod cell, and is computational 
verification of the principle of exploiting geometry to 
extract carriers from optically thick, low diffusiowlength 
solar cell materials. 
An optimally designed radial pn junction nanorod cell 
should be doped as highly as possible in both n- and p- 
type regions, have a narrow emitter width, and have a 
radius approximately equal to the diffusion length of 
electrons in the p-type "core" (in qualitative agreement 
with [6]). If light trapping techniques are nct employed the 
nanorod length should be approximately equal to the 
'optical thickness" of the material, defined as the thickness 
of material required to absorb 90% of the power due to 
above-bandgap photons, which is 125 pm for Si. 
This large value for optical thickness is one reason 
that Si is a good candidate material for the nanorod cell. 
Si's large optical thickness implies that Si used in a 
conventional planar pn junction cell must have a large 
minority-carrier diffusion length in the base region. 
EXPERIMENTAL 
In order to realize a radial pn junction nanorod solar 
cell experimentally. routes to the fabrication of densely- 
packed. well-oriented arrays of nanorods, with diameters 
in the range IOOnm - 1 pm, and lengths - 100 pm 
(potentially less with light trapping). are of interest. Of 
particular interest is the Vapor-Liquid-Solid (VLS) method 
to fabricate Si nanorods on a 4 11> Si substrate 17 [8]. A 
thermal Chemical Vapor Deposition (CVD) system was 
used, with silane (Sib) as the vapor-phase reactant, and, 
in some experiments, hydrogen (H2) as a carrier gas. 
Metal seed particfes were created either lithographically 
using a lift-off process, or by simple evaporation of a thin 
(5nm) layer of metal that dewetted from the substrate 
during deposition to form an array of nanoparticles. 
In choosing a catalyst particle to seed nanorod 
growth, one has to take many factors into account. 
particularly if one is concerned with making devices. 
Previously, gold (Au) has been used to seed the growth 
[Q]. However, Au is known to form a deeplevel trap state 
within the band-gap of Si [IO]. Although Au has a 
relatively low solubility in the growing nanorod 
(segregation coefficient 2.5 x [4]), this nonetheless 
implies that Au concentrations of -10" cmd will be 
present in nanorods (segregation coefficient 2.5 x lob x 
solubility of Au in Si at eutectic point 0.814 [ll] x 5.0 x 
IOp Si atoms cm4 [lo]). This can create a high enough 
trap density to seriously degrade the electronic 
performance of Si, leading to sub-nanosecond lifetimes 
r 101. 
We have explored alternative catalysts that do not 
have such adverse effects on the minority carrier lifetime 
of Si. In searching for a catafyst one must take the 
following issues into account: 
4 
b 
0 
0 
b 
0 
0 
Rod growth must be thermodynamically favorable 1121 
The catalyst should not form a deeplevel trap state 
within the band-gap of Si 
Si should be highty soluble in the liquid catalyst 
The catalyst should have low solubility in solid Si 
The catalyst-Si eutectic temperature should be 
matched to the vapor precursor decomposition 
kinetics 
The catalyst should not form an oxide, which would 
impede VLS nanorod growth 
The catalyst should have a low vapor pressure at the 
eutectic temperature, so that catalyst is not lost to the 
vapor phase 
The catalyst-Si binary phase diagram should not- 
include solid intermediate phases, which could 
interfere with VLS growth of Si nanorods 
The catalyst should be inert to the chemical reaction 
products 
Taking these considerations into account. aluminum 
(A), indium (In), and gallium (Ga) have been explored as 
catalysts for the VLS process. These elements have the 
advantage over Au of not forming deeplevel traps within 
the band-gap of Si. The major disadvantage of these 
catalysts is their relatively higher solubifity in solid Si 
(segregation coefficients for AI, In and Ga are 0.002, 
0.0004, and 0.008, respectively [4]). However, since a p- 
type Si nanorod is ultimately desired this may not be a 
significant problem, since these impurities all form 
relatively shallow acceptor states near the valence band in 
Si [IO]. 
Representative images of our fabrication results from In 
catalysts are shown in Fig. 3. The rod density as well as 
the range of rod diameters (-1OOnm to > I  pm) are in the 
size range desired for nanorod solar cell applications - 
positive signs for the use of In as a catalyst. 
To date Al catalysts have yielded thin shells at the 
edges of the seed particles rather than nanorods. Also, 
the growth is much slower than typically seen in the VLS 
process. This is attributed to the aluminum oxide that 
forms very rapidly on the AI surface and acts as a barrier 
to VLS growth [ 131. 
In order to fabricate the device pictured schematically 
in Fig. 1, control of nanorod density and orientation must 
be much better than has been achieved to date. If precise ' 
control of nanorod position via a template-less growth 
mechanism proves challenging, it may be possible to use 
porous alumina to template VLS growth of a nanorod array 
[I41 I15J. To do this, a porous alumina layer of thedesired 
thickness could first be grown on top of silicon, then seed 
particles deposited within the pores, and then Si nanorods 
grown in the pores by the VLS process. Having fabricated 
a well-oriented, dense array of p-type nanorods. radial pn 
57 
junctions could be formed for example by phosphorus 
diffusion doping. 
Fig. 3. Si nanorods grown' from In seed paticles. at 
pressure P=l Torr, SiHr flow of 40 sccm, and temperature 
T=500 C. 
CONCLUSIONS 
Radial pn junction nanorod cells a k  a novel approach 
to the creation of high efficiency solar cells using low 
lifetime materials. To attain high efficiency in this new 
geometry it is essential that the depletion region trap 
density is not too high (< cmJ). The trap density in 
the quasi-neutra! regions can be higher than this with little 
detrimental effect. 
Fabrication of a radial pn junction nanorod solar cell 
requires creating a dense array of well-oriented Si 
nanorods, each with a radial pn junction, as well contacts 
to both the p- and n-type regions. Si nanorods have been 
grown by the VLS method using In catalyst particles, a 
step towards the fabrication of a nanorod solar cell. , 
ACKNOWLEDGEMENTS 
The authors would like to thank 3P Solar and NREL 
for their financial support. 
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Radial pn junction nanorod solar cells: device physics principles and routes to fabrication in silicon

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Radial pn junction nanorod solar cells: device physics principles and routes to fabrication in silicon

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