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Contract No. DE-AC36-99-GO10337 

S. Kurtz, J.F. Geisz, D.J. Friedman, and A.J. Ptak

National Renewable Energy Laboratory 

R.R. King, D.C. Law, and N.H. Karam 

Spectrolab, Inc. 

Prepared for the 31st IEEE Photovoltaics Specialists 

Conference and Exhibition 

Lake Buena Vista, Florida 

January 3–7, 2005 

February 2005 • NREL/CP-520-37157 

Collection of Photocarriers in 

GaxIn1-xNyAs1-y Solar Cells 
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COLLECTION OF PHOTOCARRIERS IN GaxIn1-xNyAs1-y SOLAR CELLS 

Sarah Kurtz, J.F. Geisz, D.J. Friedman, A.J. Ptak, R.R. King,1

 D.C. Law,

1

 and N.H. Karam1

National Renewable Energy Laboratory, 1617 Cole Blvd., Golden, CO 80401 1

Spectrolab, Inc., 12500 Gladstone Avenue, Sylmar, CA 91342 

ABSTRACT 

Collection of photocarriers in GaxIn1-xNyAs1-y solar 

cells is limited by the poor quality of the GaxIn1-xNyAs1-y.

Some reports have shown collection of photocarriers 

outside of the depleted layer in annealed GaxIn1-xNyAs1-y,

but the key to achieving the higher collection has been 

unclear. In this paper, we attempt to quantify the diffusion 

and collection lengths that contribute to the photocurrent in 

GaxIn1-xNyAs1-y solar cells. The data imply that the 

effective μτ product for the lightly doped GaxIn1-xNyAs1-y

material may vary when a field is applied. We conclude 

that the fields present in most of our best GaxIn1-xNyAs1-y

cells are large enough to aid collection of photocarriers. 

 

BACKGROUND 

A four-junction solar cell using GaInP/GaAs/X/Ge, 

where X is a 1-eV material, has the potential for a 40% 

efficiency [1]. The addition of nitrogen to GaAs 

dramatically reduces the bandgap. A GaxIn1-xNyAs1-y alloy

(hereafter, GaInNAs) has been demonstrated with a 1-eV 

bandgap and with a lattice constant matched to that of 

GaAs, implying that it is a possible candidate for the 

desired 1-eV material. Unfortunately, attempts to use the 

GaInNAs in a solar cell show that its material quality is 

poor, resulting in inferior performance [2,3]. However, lowcurrent GaInNAs cells can be used effectively in a 5- or 6-

junction solar cell [4]. 

The optimization of solar-cell performance usually

requires optimization of both the material quality and the 

device structure. Measurements of GaInNAs have shown 

reduced electron mobility, minority-carrier lifetime, and 

minority-carrier diffusion lengths relative to those of GaAs. 

Annealing GaInNAs has improved its photoluminescence 

and device performance, but the mechanism for the 

improvement is not completely understood. There is a 

large body of evidence showing that defects are removed 

from GaInNAs by certain types of anneals [5-7]. There is 

also clear evidence that annealing changes the net carrier 

concentration [8-10]. In a previous study, we showed that 

improved performance in our GaInNAs solar cells was 

correlated with type conversion of the top part of the active 

GaInNAs layer [10]. We have also shown that a GaInNAs 

layer grown without any intentional doping can show ~1017

cm-3 acceptors as grown, but ~1017 cm-3 donors after 

annealing [9]. The observed acceptors and donors are, 

apparently, related to point defects associated with the 

nitrogen and unintentionally added impurities. Lower 

background carrier concentrations can be achieved by

reducing the carbon and hydrogen, as is described in this 

proceedings [11]. 

The intentional addition of dopants to GaInNAs can 

lead to the intended p- or n-type behavior of GaInNAs, but 

it is our experience that GaInNAs is sometimes highly

compensated. For one set of growth conditions, we added 

more than 1018 cm-3 of Se to convert the as-grown

GaInNAs to n-type, despite that the background acceptor 

concentration without Se was only ~1017 cm-3. This result 

is not unexpected because the formation energy of 

acceptors is usually reduced in n-type material and vice 

versa. Thus, in many cases, GaInNAs is highly

compensated and the net acceptor or donor concentration 

is difficult to predict. 

Other researchers have also described compensated 

GaInNAs for which the background carrier concentration 

changes after annealing. For example, researchers at 

Sandia National Laboratories described a GaInNAs solar 

cell with an n-type (2 X 1017 cm-3, Si doped) emitter and a 

p-type (4 X 1016 cm-3, unintentionally doped) base made 

from layers with residual carbon contamination of 6-8 X 

1017 cm-3 [3]. Given that the carbon concentration was 

higher than both the net acceptor and donor concentrations, their GaInNAs was compensated in both the 

base and the emitter. They reported that the GaInNAs cell 

had a depletion width of 0.15 μm before annealing and 

0.26 μm after annealing, implying that the net acceptor 

and/or net donor concentrations changed after the anneal, 

affecting the device structure as well as the material 

quality.

Thus, the normal process of first optimizing the 

material quality, then the device design, becomes 

confused when GaInNAs cells are studied. In this paper, 

we seek to determine how the presence of an electric field 

affects the performance of the solar cell. We model the 

solar cells and determine the observed minority-carrier 

diffusion length depending on the estimated junction 

depth. Assuming that the minority-carrier mobility and 

lifetime are independent of field, we then compare the 

probable diffusion and collection lengths and propose that 

fields in the emitter and/or base layers enhance 

photocarrier collection. 

EXPERIMENTAL METHOD 

The fabrication and measurement of the GaInNAs 

solar cells and materials have been described elsewhere 

[9,10]. Briefly, the GaInNAs is grown by atmospheric1
pressure metal-organic chemical-vapor deposition in a 

hydrogen carrier gas. No intentional doping was added to 

the GaInNAs layers reported here; the background 

acceptor concentrations varied depending on the growth 

conditions and the annealing conditions. A 2-μm-thick

GaInNAs layer was grown between p-type and n-type 

GaInP layers. Thus, the structure is nominally a p-i-n 

structure with the n-type layer (emitter) on top. However, 

the junction depth moved as the background doping of the 

GaInNAs varied. A 1-μm-thick GaAs layer was added on 

top to confine the cell’s response to the approximate 

spectral region of interest. 

GaInNAs CELL PERFORMANCE AND STRUCTURE 

A first question asked in optimizing performance of a 

new material is whether a change in growth conditions can 

give improved results. We selected a range of growth 

conditions (e.g., growth rate, V/III ratio) that were known to 

give differing levels of carbon and hydrogen 

contamination. Using these, we fabricated GaInNAs solar 

cells, reoptimizing the anneal conditions for each. (In the 

undoped structure, the optimal anneal has been shown to 

cause formation of an n-type emitter of optimal thickness 

[10].) The resulting quantum efficiency curves are shown 

in Fig. 1. The compositions of the samples varied slightly, 

but in each case an internal quantum efficiency of ~0.8 

was obtained near the GaAs bandedge. The similarity of 

the results implies that the growth conditions and 

background impurity levels are unimportant relative to the 

importance of defining the optimal structure of the 

background-doped cell by using an optimal anneal. 

0.8

0.6

0.4

0.2

0.0 Internal quantum efficiency

1.0 1.1 1.2 1.3 1.4

Photon energy (eV)

 Baseline (MD217)

 Low growth rate (MD216)

 High growth rate (MD252)

 Low C (MD253)

 Low H (MD261)

Fig. 1. Internal quantum efficiency curves for GaInNAs 

cells grown under a variety of growth conditions and 

annealed for an empirically optimized time. 

A second way of studying the importance of the 

device structure is to compare the doping profiles of highand low-performing cells. Starting with measurements for 

about one thousand GaInNAs solar cells, we selected 

those with high (> 8 mA/cm2

) and low (< 5 mA/cm2) 

current densities. The absolute current densities for these 

cells are meaningless because the GaAs window allowed 

transmission of some light with energy above the GaAs 

band. The data were screened, removing data for 

samples that were shorted, resistive, or irrelevant for some 

other reason. For example, some of the samples had 

junctions located toward the back of the devices, resulting 

in poor photocurrent collection. Capacitance-voltage data 

for all of the rest of the samples are summarized in Fig. 2. 

The data are clumped in two groups: those with low

photocurrents show narrow depletion widths; those with 

higher photocurrents show wider depletion widths. This 

result is not surprising because it has been reported that 

GaInNAs has poor minority-carrier properties. However, 

excellent GaAs cells can be grown with 1017 cm-3 doping 

(narrow depleted layer). Of greater importance to this 

study, we note that most of the better cells show a trend 

toward increasing carrier concentration with depth, 

implying the presence of an electric field that could aid the 

collection of photocarriers. This field is caused when the 

p-type, as-grown GaInNAs converts to n-type from the top 

down. The details of why the top surface converts first are 

unknown, but there is evidence that injection of hydrogen 

from the ambient contributes. 

10 8

15

2

4

6

10 8

16

2

4

6

10 8

17

2

Carrier concentration (cm

-3

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Depletion width (μm)

These cells showed low photocurrents

These cells showed

higher photocurrents

Fig. 2. Comparison of capacitance-voltage profiling for 

samples with relatively small (< 5 mA/cm2

) and large 

photocurrent densities (> 8 mA/cm2

). 

DIFFUSION AND COLLECTION LENGTH 

The minority-carrier diffusion, Ld, and collection, Lc, 

lengths are usually related to the mobility, μ, and lifetime, 

τ, by

Ld = (μτ kT/e)0.5; Lc = μτE (1) 

where k is Boltzmann’s constant, T is the temperature, e is 

the electric charge, and E is the electric field. These 

equations assume that μ and τ are independent of E and 

Fermi level. The addition of a small amount of nitrogen to 

GaAs introduces states that are localized on the nitrogen 

[12]. Addition of more nitrogen lowers the conduction 

band dramatically, but the conduction band retains some 

localized character, implying that GaInNAs will not behave 

like a traditional semiconductor material [12]. Thus, μ and 

τ may not be independent of electric field; we will 

reexamine this question later in the paper. 

Electron mobilities as high as 500 cm2

/Vs have been 

reported for GaInNAs [9], but more commonly the electron 

and hole mobilities have been reported near 300 cm2

/Vs 

[13]. It is not clear that the majority-carrier mobility

measured by Hall is relevant to the minority-carrier 

mobility. Nevertheless, if the carrier mobility is ~300 

cm2

/Vs and the lifetime is about 0.3 ns, then the μτ

product is ~10-7 cm2

/V. The collection and diffusion 

lengths were calculated using Eq. 1 and μτ products within 

a factor of 10 of 10-7 cm2

/V. (See Fig. 3.) 

2
0.01

0.1

1

10

100

1000

Diffusion/collection length (μm)

0.01 2 3 4 5 6 70.1 2 3 4 5 6 71 2 3 4 5 6 710

Electric field (V/μm)

Diffusion

μτ = 10-6 cm2/V

μτ = 10-7 cm2/V μτ = 10-8 cm2

/V

Collection

High

field

Low

field

Fig. 3. Collection length expected from diffusion (thin 

lines) or collection (bold lines) as a function of electric field 

and μτ product calculated using Eq. 1 (μτ = 10-8 cm2

/V 

solid lines; 10-7 cm2

/V dotted lines; 10-8 cm2/V dashed 

lines). 

MODELED SOLAR-CELL PERFORMANCE 

The absorption coefficient of GaInNAs is similar to 

that of GaAs except that the bandedge is shifted and 

shows an exponential tail [10]. We have assumed that the 

solar cells can be modeled as three layers: emitter (top), 

depleted layer, and base [10] with all photocarriers 

collected in the depleted layer, and the collection in the 

other two layers determined by an effective minority-carrier 

diffusion length and surface-recombination velocity. The 

equations are given in ref. [10]. The assumption that the 

emitter and base are uniform layers is an approximation, 

and leads to an effective diffusion length, Leff, that reflects 

both diffusion and field-aided collection. 

Modeling of these devices is complicated because the 

junction depth is unknown. In a standard solar cell, the 

emitter thickness can be estimated by measuring the 

emitter sheet resistance and electron concentration. 

Thus, we might estimate the junction depth from the sheet 

resistance of the type-converted, n-type emitter layer after 

removal of the n-type GaInP layer. Before removal of the 

GaInP layer, the sheet resistance is dominated by

conduction in the GaInP layer. After removal, the cells 

with optimal performance show a sheet resistance on the 

order of MΩ/square. Depth profiling (capacitance-voltage 

profiling), as shown in Fig. 2, implies that the donor 

concentration is < 1016 cm-3. The data in Fig. 2 reflect 

widening of the depleted layer both toward the front and 

toward the back of the device. Thus, it is not clear 

whether the carrier concentration measured in Fig. 2 

reflects the net donor concentration, acceptor 

concentration, or a combination of both. Modeling of 

reverse-biased cells implies that the reverse-bias data in 

Fig. 2 include depletion of the emitter, giving confidence 

that the donor concentration is < 1016 cm-3. For an 

electron mobility of 300 cm2

/Vs, an electron concentration 

of 3 X 1015 cm-3, and a sheet resistance of ~1 MΩ/square, 

we expect a thickness of ~0.07 μm for the conducting 

layer. However, the free surface is known to pin the Fermi 

level in the middle of the gap of a GaAs-like material. This 

causes a second depleted layer that may be comparable 

to the first: ~0.4 μm wide. A measurement of the sheet 

resistance of the bare layer will be increased because 

carriers are found only in the part of the emitter that isn’t 

depleted by the free surface. Thus, we anticipate that the 

probable junction depth is ~0.07 μm plus the probable 

width of the depleted layer, or 0.4 μm ± 0.4 μm. 

Given the uncertainty of the junction depth, we treat 

the junction depth as a fit parameter. The width of the 

depleted layer is measured by capacitance-voltage 

profiling. If photocarriers are collected only in the depleted 

layer, a low response is expected, as shown for an 

illustrative example by the lowest curve in Fig. 4. The poor 

fit of the low curve implies that additional holes are 

collected from the emitter and/or electrons are collected 

from the base. Two additional fits are shown in Fig. 4. 

One assumes that the junction is at the front of the cell 

and that all added collection is from the base. The other 

assumes that there is no collection from the base and 

varies the thickness of the emitter and effective diffusion 

length in the emitter to give an optimal fit. These two fits 

are both excellent, as shown in Fig. 4, implying that the 

data can be explained either by collection of holes or 

electrons. 

0.6

0.4

0.2

0.0

Internal quantum efficiency

900 950 1000 1050 1100 1150nm

Photon wavelength (nm)

 Measured for MC622

emit. t. Leff(elec) Leff(hole) (μm)

 0 0.39 0.01 0.45 0.01 0.77 0 0.01 0.01

Fig. 4. Internal quantum efficiency of GaInNAs cell, 

measured and modeled using a depletion width of 0.465 

μm and the indicated values for the emitter thickness and 

Leff for electrons and holes. 

Fundamentally, there are four possible mechanisms 

for collection outside of the depleted layer: 1) diffusion of 

holes from the emitter, 2) field-aided collection of holes 

from the emitter, 3) diffusion of electrons from the base, 

and 4) field-aided collection of electrons from the base. 

From the modeling shown in Fig. 4, it is impossible to 

differentiate these. From the observation that the 

formation of the n-type emitter increases the photocurrent 

[10], we are confident that holes from the emitter 

contribute to the photocurrent, but we can’t be certain that 

electrons from the base don’t also contribute. 

In the depleted layer, field-aided collection of both 

holes and electrons occurs. If the μτ product of either the 

holes or electrons were insufficient for collection in this 

field, then those carriers would build up in the depleted 

layer, causing the field to change. For the samples 

described in Figs. 2 and 4, the depletion width is on the 

order of 0.5 μm. The built-in field is less than the bandgap 

3
of the GaInNAs (~1.1 eV), yet greater than the open-circuit 

voltage observed for the cells (~0.4 V). Thus, if the built-in 

field is ~0.8 V, the strength of the field in the depleted 

layer is on the order of 1 V/μm. We observe that the 

photocarriers are efficiently collected for a depleted layer 

thickness of ~0.5 μm, implying that the collection length for 

both electrons and holes is at least 0.5 μm for a field of ~1

V/μm. Then, from Eq. 1, the μτ product for both holes and 

electrons is at least 5 X 10-9 cm2

/V. Assuming that μτ is 

independent of field, then the diffusion length for both 

carriers is at least ~0.1 μm. This is comparable to what 

we measure for holes in ~1017 cm-3, n-type GaInNAs (data 

not shown), but longer than what we have measured for 

electrons (too small to be measured, or < 0.05 μm). This 

discrepancy for the electron transport might be resolved if 

the addition of a field facilitates the emission of an electron 

from a localized state, increasing its mobility or lifetime in 

the presence of an electric field. An alternative 

explanation is that the transport is degraded by doping at 

the ~1017 cm-3 level. 

The lower lines in Fig. 2 show a change of about a 

factor of 2 to 4 in carrier concentration over a distance of 

about 0.5 μm. The change in Fermi level expected for a 

factor of 4 change in doping is kT ln(4) or 36 mV. Thus, 

we estimate that the low field outside of the depleted layer 

is ~0.04 V/ 0.5 μm, or ~0.1 V/μm. For this field, we model 

(Fig. 4) Leff = ~0.4 μm outside of the depleted layer. For 

μτ = 5 X 10-8 cm2

/V, the diffusion and collection lengths 

are both ~0.4 μm. Thus, the μτ product that provides an 

adequate diffusion length to explain the data also implies 

that field-aided collection is important in that same region. 

The diffusion lengths observed for a 

GaInNAs/aqueous junction imply lower μτ either because 

these layers were more highly doped, or because the μτ is 

field dependent. 

The observed μτ values are summarized in Table 1. 

Although these are very rough estimates, it is clear that 1) 

the observed μτ product varies with field, and 2) the ~0.1 

V/μm fields observed in the best GaInNAs samples are 

expected to lead to field-aided collection. Evidence of 

field-aided minority-carrier transport in transistors has 

been reported by Welser, et al. [14]. 

Table 1. Estimates of observations of μτ. The aqueous 

junction measurements were completed on uniform layers 

with donor concentrations of ~1017 cm-3. 

Carrier Field

(V/μm) 

μτ (cm2

/V) Collection from: 

Electrons ~ 1 > 5 X 10-9 Depleted layer 

Electrons ~ 0.1 < 5 X 10-8 Base 

Electrons ~ 0 < 1 X 10-9 Aqueous junction 

Holes ~ 1 > 5 X 10-9 Depleted layer 

Holes ~ 0.1 ~ 5 X 10-8 Emitter 

Holes ~ 0 ~ 5 X 10-9 Aqueous junction 

 

In summary, we have observed that the device 

structure is more important than the growth conditions for 

high-performance GaInNAs cells. The high-performing 

devices show wide depletion widths and an electric field 

outside of the depleted layer. Modeling of the GaInNAs 

solar cells shows collection outside of the depleted layer, 

but is ambiguous about whether the added collection is 

from the emitter or base. Various estimates of the μτ

product show that the μτ product may be field dependent 

or dependent on doping. The relevant μτ products are 

close to 10-8 cm2

/V. The analysis shows that field-aided 

collection in the emitter and/or base enhances the 

photocurrent of the solar cells. 

ACKNOWLEDGMENTS 

We thank C. Kramer and M. Young for the sample 

preparation. This work was funded, in part, under the Dual 

Use Science and Technology (DUS&T) program by the Air 

Force Research Laboratory, Space Vehicles Directorate 

(AFRL/VS), and, in part, by Spectrolab, Inc. This work 

was completed at the National Renewable Energy

Laboratory under DOE Contract No. DE-AC36-

99GO10337. 

 

REFERENCES 

[1] S.R. Kurtz, et al., "Projected performance of three- and 

four-junction devices using GaAs and GaInP," 26th IEEE 

PVSC, 1997, pp. 875-878. 

[2] D.J. Friedman, et al., "1-eV solar cells with GaInNAs 

active layer," J. Cryst. Growth 195, 1998, pp. 409-415. 

[3] S.R. Kurtz, et al., "InGaAsN solar cells with 1.0 eV 

band gap, lattice matched to GaAs," Appl. Phys. Lett. 74, 

1999, pp. 729-731. 

[4] R.R. King, et al., "Metamorphic III-V materials, 

sublattice disorder, and multijunction solar cell approaches 

with over 37% efficiency," 19th European PVSEC, 2004. 

[5] D. Kwon, et al., "Deep levels in p-type InGaAsN lattice 

matched to GaAs," Appl. Phys. Lett. 74, 1999, pp. 2830-

2832. 

[6] R.J. Kaplar, et al., "Deep levels and their impact on 

generation current in Sn-doped InGaAsN," J. Appl. Phys.

90, 2001, pp. 3405-3408. 

[7] P. Krispin, et al., "Nitrogen-related electron traps in 

Ga(As,N) layers (<=3% N)," J. Appl. Phys. 93, 2003, pp. 

6095-6099. 

[8] J.F. Geisz, et al., "Photocurrent of 1 eV GaInNAs 

lattice-matched to GaAs," J. Cryst. Growth 195, 1998, pp. 

401-408. 

[9] S. Kurtz, et al., "Annealing-induced-type conversion of 

GaInNAs," J. Appl. Phys. 95, 2004, pp. 2505-2508. 

[10] S. Kurtz, et al., "Modeling of electron diffusion length 

in GaInAsN solar cells," 28th IEEE PVSC, 2000, p. 1210. 

[11] A.J. Ptak, et al., "Enhanced-depletion-width GaInNAs 

solar cells grown by molecular-beam epitaxy," 31st IEEE 

PVSC, 2005. 

[12] P.R.C. Kent and A. Zunger, "Evolution of III-V nitride 

alloy electronic structure: The localized to delocalized 

transition," Phys. Rev. Lett. 86, 2001, pp. 2613-2616. 

[13] S.R. Kurtz, et al., "Minority carrier diffusion and 

defects in InGaAsN grown by molecular beam epitaxy," 

Appl. Phys. Lett. 80, 2002, pp. 1379-1381. 

[14] R.E. Welser, et al., "Minority carrier properties of 

carbon-doped GaInAsN bipolar transistors," J. Phys.: 

Condens. Matter 16, 2004, pp. 53373-53385. 

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Collection of Photocarriers in GaxIn1-xNyAs1-y Solar Cells 

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and N.H. Karam 

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14. ABSTRACT (Maximum 200 Words)

Collection of photocarriers in GaxIn1-xNyAs1-y solar cells is limited by the poor quality of the GaxIn1-xNyAs1-y. Some 

reports have shown collection of photocarriers outside of the depleted layer in annealed GaxIn1-xNyAs1-y, but the key 

to achieving the higher collection has been unclear. In this paper, we attempt to quantify the diffusion and collection 

lengths that contribute to the photocurrent in GaxIn1-xNyAs1-y solar cells. The data imply that the effective μτ product 

for the lightly doped GaxIn1-xNyAs1-y material may vary when a field is applied. We conclude that the fields present in 

most of our best GaxIn1-xNyAs1-y cells are large enough to aid collection of photocarriers. 

15. SUBJECT TERMS

PV; photocarriers; solar cells; photocurrent; capacitance-voltage; electron mobilities; field-aided collection; 

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