NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Using Measurements of Fill 

Factor at High Irradiance to 

Deduce Heterobarrier Band 

Offsets

Preprint

J. M. Olson, M. A. Steiner, and A. Kanevce

Presented at the 37th IEEE Photovoltaic Specialists Conference 

(PVSC 37)

Seattle, Washington

June 19-24, 2011

Conference Paper

NREL/CP-5200-50737

July 2011
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1

USING MEASUREMENTS OF FILL FACTOR AT HIGH IRRADIANCE TO DEDUCE 

HETEROBARRIER BAND OFFSETS

J.M. Olson, M.A. Steiner, and A. Kanevce

NREL, Golden, CO

ABSTRACT

Using a 2D device simulation tool, we examine the high 

irradiance behavior of a single junction, GaAs concentrator 

cell as a function of the doping in the back surface 

confinement layer. The confinement layer is designed to 

be a barrier for both holes and electrons in the base of the 

solar cell. For a p-type base we show that the FF of the 

cell at high concentrations is a strong function of both the 

magnitude of the valence band offset and the doping level 

in the barrier. In short, for a given valence band offset 

(VBO), there is a critical barrier doping, below which the 

FF drops rapidly with lower doping. This behavior is

confirmed experimentally for a GaInP/GaAs double 

heterostructure solar cell where the critical doping 

concentration (at 500 suns) in the back surface 

confinement layer is ~1e18 cm-3 for a VBO of 300 meV.

INTRODUCTION

It is well known that the fill factor and efficiency of a 

concentrator cell under high irradiance is a sensitive 

function of its series resistance, Rs. The Rs of the 

emitter/top contact of the cell usually receives the most 

attention. However, in III-V multijunction solar cells, 

heterobarriers, normally required for minority carrier 

confinement, can also be significant sources of Rs. This 

series resistance is associated with the reverse-bias, 

transport of majority carriers over the barrier. These 

barriers, if not properly designed, can reduce the FF and 

efficiency of the device, particularly at high irradiance 

levels. This problem is not unknown to the community[1, 

2] but there is very little quantitative guidance available to 

the cell designer. In this paper, we focus on the back 

surface field (BSF) layer of a n-on-p GaAs solar cell. The 

key parameters in this effort are the valence band offset 

VBO between the base of the cell and the BSF layer and 

the doping in the BSF layer. Experimentally the VBO is 

fixed by the choice of the BSF layer material, e.g. 

AlGaInP, GaInP, or AlGaAs. While there is much known 

about the AlGaAs/GaAs heterointerface, our 

understanding of the GaInP/GaAs heterointerface is far 

from complete. It is complicated by the tendency of GaInP 

to order[3] and difficulties with forming an abrupt interface 

with GaAs.[4, 5] However, with the aid of 2D, finiteelement, device simulation tool Apsys from Crosslight

Software, Inc., we can numerically vary the value of the 

VBO and, in combination with the level of doping in the 

BSF layer, study its effect on the FF and efficiency of the 

device under concentrated illumination. In the following we

show that by comparing the simulated results with 

experimental data we can deduce the magnitude of the 

VBO between GaInP and GaAs.

GaAs Cell Structure

A schematic of the GaAs device is shown in Figure 1. The 

BSF layer is nominally Zn-doped Ga0.52In0.48P with a band 

gap of 1.88eV. The doping in the window and emitter 

layers are set at 2e18 cm-3

. The doping in the base is set 

at 1e17 cm-3

. The emitter and BSF layer thicknesses are 

0.1μm and the base is 2.5 μm think. The active area of a 

cell (total area less busbar area) is 0.100 cm2

. Grid width 

and pitch are 10 μm and 150 μm respectively. Cells are

simulated/measured without antireflection coating. Details 

of the simulation conditions are similar to those published 

previously.[6]

The simulation of the device in Figure 1 assumes

thermionic transport of carriers across the heterojunction 

barriers. The composition and doping profiles at the 

interface between the p-GaAs base layer and the P-BSF 

layer are assumed to be abrupt. In practice abrupt 

interfaces are difficult to achieve. Without special 

precautions, the interface can be smeared or graded and 

the effective barrier height, which controls the carrier 

transport, can be substantially different compared to the 

ideal case. For this study, we use two techniques to 

mitigate this problem. First, we grow the GaAs solar cells

(by MOCVD) in the inverted configuration[7] so that the 

last two layers grown are the P-BSF layer and the P-GaAs 

back contact layer. The total growth time for these two

layers is less than 10 min. The growth temperature during 

this time is limited to less than 620 ̊C. These conditions

Figure 1 Schematic of a GaAs concentrator cell with 

back surface field layer.

p-GaAs 1e17 cm-3 2.5μm 

P-BSF layer 0.1μm

N-GaAs 2e18 cm-3 0.1μm

P-GaAs

N-GaInP2e18 cm-3 0.02 μm
2 

lead to less interdiffusion of the chemical constituents 

compared to the non-inverted case where the interface 

would be subjected to higher temperature (e.g. 650 ̊C) for 

longer times (30 min or more).[4] Second, the interface 

between the base and BSF layer is formed using a simple 

stop growth procedure, where at the end of the base layer 

the Ga-source is first switched off to cease all growth for a 

total of 9 seconds. For the first 6 s of this stop growth, only 

the arsenic source (AsH3) is flowing to the reactor. For the 

remaining 3 s only PH3 and the p-type doping source 

(diethyl zinc) are flowing to the reactor. At the end of the 9-

s stop growth, the Ga and In sources are introduced to 

initiate the growth of the GaInP BSF. This sequence 

ideally yields an interface layer of As-rich GaInAsP about 

1 monolayer thick.[5] 

The devices were processed in a manner described by 

Geisz et al.[7] The hole concentration in the BSF layers 

was determined from a set of Zn-doped calibration layers 

grown under similar conditions and deduced from 

electrochemical capacitance voltage measurements. The 

concentrator measurements were made using a 

Spectrolab HIPSS at 25 ̊C. 

RESULTS 

Simulated IV Curves and Fill Factor 

The JV curves of a GaAs heteroface solar cell at 500 suns 

(Jsc = 13 Acm-2) were simulated as a function of the doping 

in the BSF layer and the VBO of the BSF layer with 

respect to the base of the GaAs cell. An example of a 

simulated JV curve is shown in Figure 2. Here the BSF 

interface is abrupt, the VBO is set at 300 meV and the 

doping in the BSF is set at NA = 4.9e17 cm-2. Figure 2 also 

includes a JV curve for the isolated GaInP/GaAs 

heterobarrier, a JV curve for a GaAs cell with a low VBO 

at the BSF interface. The curve labeled “composite” is the 

superposition of the first two. The JV curve of the 

heterobarrier exhibits a roughly linear behavior for 

|ܬ ൏ |6 ܣܿ݉ିଶ. For larger positive currents (which 

correspond to hole transport from the base to the BSF), 

the effective resistance of the heterobarrier becomes 

much larger which is also reflected in the FF of the 

composite JV of the GaAs cell. 

In Figure 3 we show a contour plot of FF vs hole 

concentration and VBO. (Here, to conserve computation 

time, we consider 1D current flow only. Hence there are 

no emitter resistance effects and the FFs are 

unreasonably high.) It shows that for a given VBO, there 

exists a critical hole concentration in the BSF layer below 

which the FF decreases rapidly with decreasing hole 

concentration. Above this critical concentration, the FF 

increases much more slowly with increasing hole 

concentration. 

Figure 2 JV curves for an isolated GaInP/GaAs 

heterobarrier, a GaAs pn junction with a low VBO at 

the BSF interface and a composite of the two. 

Figure 3 Contour plot of fill factor at 500 suns 

(Jsc = 13 Acm-2) of a GaAs solar cell versus the hole 

concentration in the BSF layer and its VBO with 

respect to GaAs. 

Experimental 

The IV characteristics of the four GaAs devices with 

different Zn doping levels in the GaInP BSF were 

measured as a function of irradiance. The results at ~400 

suns (Jsc = 11 Acm-2) are shown in Figure 4. It is clear 

that the FF decreases, at first slowly and then more 

rapidly, with decreasing BSF layer doping. In Figure 5 we 

plot of the FF of the four GaAs devices (interpolated to 

Jsc=13 Acm-2) as a function of the doping in GaInP BSF 

layer along with three simulated curves for VBOs equal to 

275, 300 and 325 meV. The experimental curve lies 
3

roughly between the curves for VBOs of 275 and 300 

meV. The agreement between simulation and experiment 

is not perfect (compare the JV curves in Figure 3 and 

Figure 4). The simulated IV curves for the two lowest hole 

centrations only agree qualitatively with the measured IV 

curves. And the device with the lowest hole concentration 

in BSF layer has a higher FF (it is closer to VBO=275 meV 

than the other three samples). But the VBO that one infers 

from the experimental data would suggest that the VBO 

between GaAs and GaInP is close to 300 meV. This is 

consistent with most other reports.[8, 9]

Figure 4 I-V curves of four GaAs solar cells with 

variable Zn doping in the GaInP BSF.

Figure 5 Modeled and measured fill factor of a 

GaInP/GaAs heteroface solar cell at ~500 suns and a 

function of the hole concentration in the GaInP BSF 

and its VBO with the GaAs base.

DISCUSSION

Knowledge and control of heterojunction band offsets are 

important for the design of high efficiency solar cells.

Traditional methods of measuring the band offsets at a 

semiconductor heterojunction include direct measurement 

of carrier transport using current-voltage measurements, 

capacitance-voltage profiling[10], and deep level transient 

spectroscopy[8, 11]. These all involve the fabrication of 

special (albiet relatively simple) test structures that may or 

may not represent the situation in actual solar cells. These 

methods are not totally consistent yielding band offset 

values for a given materials combination that vary widely.

One can also measure the IV curve of an illuminated cell 

as a function of temperature. In general one expects the 

effective resistance of any heterointerface to decrease 

exponentially with increasing temperature. The limitation 

of this technique is that the temperature dependence of 

the heterobarrier transport is confounded with that of other 

temperature dependent processes or parameters.

Due to the nonlinear behavior of the transport over the 

barrier, these effects are not necessarily observable at low 

current densities or in the dark. (See Figure 2.) At low 

current densities (near Voc or at low irradiance levels) the 

barrier behaves like a simple resistor. This implies that 

the FF or maximum power loss associated with a 

heterobarrier cannot be deduced from a low current 

measurement of the effective resistance such as that 

proposed by King et al.[12] In the dark the majority carrier 

transport across the barrier is in the opposite/forward 

direction and not representative of the limiting mechanism 

under illumination.

The approach we use in this study is quite different: we 

use numerical simulation and experimental measurements 

of the FF as a function of dopant concentration on full 

devices to deduce the band offsets. The effect is isolated

to the heterojunction where the doping is being altered 

and is not confounded by the doping level in other parts of 

the cell.

There are, however, several limitations of this technique:

• For low VBO, the critical dopant concentration may be 

lower than the background carrier concentration of the 

BSF layer. One can always try high irradiance levels, 

but this too will have its limits.

• The diffusion of the dopant, particularly at high 

concentrations, across the interface can promote 

interdiffusion of the heterobarrier constituents and a 

smearing or grading of the interface. This can 

artificially lower the critical dopant concentration. [13]

• As noted above, the simulations assume an abrupt 

interface between the BSF and base of the cell and 

special precautions were taken to achieve these 

conditions experimentally. Indeed, we find that simply 

growing the interface without a stop growth largely 

eliminates the large FF loss at low dopant 

concentrations. Such measures can introduce other 

problems. For example the “graded” layer between 

GaInP and GaAs may not be lattice matched and 

depending on “switching” time constants for the 

individual source gases it is possible to have a graded 
4

layer that is “InGaAs”-rich leading to a low band gap 

region that could trap minority carriers.

• The technique requires the availability of device 

simulation software that can accurately treat 

heterobarrier transport.

CONCLUSIONS

We have presented an alternative method for measuring 

the band offsets associated with barrier layers in a single 

or multijunction solar cell. The method involves comparing 

simulated and measured JV curves at high irradiance 

levels as a function of doping level in the barrier layer. The 

techniques was applied to the valence band offset 

between GaInP and GaAs which forms the back surface 

field of a GaAs solar cell. We deduce a value for the VBO 

between GaInP and GaAs of ~300 meV that is reasonably 

consistent with literature values.

ACKNOWLEDGEMENT

This work was supported by the U.S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with 

the National Renewable Energy Laboratory.

REFERENCES

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layers for GaAs-based single-junction or 

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[2] S. J. Wojtczuk, et al., "Comparison of Windows 

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