MODELING Cu MIGRATION IN CdTe SOLAR CELLS UNDER DEVICEPROCESSING AND LONG-TERM STABILITY CONDITIONS 

Glenn Teeter and Sally Asher

National Renewable Energy Laboratory • Golden, CO 80401

Abstract Diffusion-Segregation Model: Pseudo-Binary Diffusion Couple Formulation

Migration Potential Near a PseudoBinary Diffusion Couple InterfaceDevice-Processing Simulation Results: 

High-Diffusivity Case

Device-Processing Simulation Results: 

Low-Diffusivity Case

Survey of Cu Diffusivities 

and Solubilities in CdTe 

and CdS

Long-Term Stability Simulation 

Results: High-Diffusivity Case

Long-Term Stability Simulation 

Results: Low-Diffusivity Case

The information contained in this poster is subject to a government license.

2008 33rd IEEE Photovoltaic Specialists Conference • San Diego, CA • May 11–16, 2008 • NREL/PO-520-43265

An impurity migration model for systems

with material interfaces is applied to Cu

migration in CdTe solar cells. In the model,

diffusion fluxes are calculated from the Cu

chemical potential gradient. Inputs to the

model include Cu diffusivities, solubilities,

and segregation enthalpies in CdTe, CdS

and contact materials. The model yields

transient and equilibrium Cu distributions in

CdTe devices during device processing

and under field-deployed conditions.

Preliminary results for Cu migration in

CdTe PV devices using available diffusivity

and solubility data from the literature show

that Cu segregates in the CdS, a

phenomenon that is commonly observed in

devices after back-contact processing

and/or stress conditions.

= ∑[( ) + ( ) ]

i

i

p

i

i p

i

Cu

i A niX Cu μ n X μ

i

i

i

i p

i

i

p X

X H kT

X

A

n Cu

Cu

CuCuCu- 1

ln 1

− = ∆ +∂

∂

μ =

( ) i

p

i

D

i ∆HCu- p

= − E +φCuFigure 1. Schematic illustration of the ideal-solution Cu

migration potential near a hypothetical material

interface.

Hseg= ∆HCu- p − ∆HCu- p'

x

J MC p

∂

∂

= − CuCu Cu

μ

C0

C

kT

D M p

=

















∂

∂ − ∂

∂ −















∂

∂ − ∂

∂

=

x

C

C

C

x

C D

x

D C

kT x

DC

C

C

J p p 0

0

Cu0

φ

x

J

t

C

∂

∂

= − ∂

∂

J = −D(∂C ∂x)

CdTe:Cu diffusivity data

D0 (cm2 s-1) ED (eV)

Ref. SC or

PX

Diffusion

mode

1.70E-06 0.24 [1]

6.65E-05 0.57 [2] SC low

7.30E-07 0.33 [3]

1.30E-06 0.29 [4] PX high

8.20E-08 0.64 [5]

3.70E-04 0.67 [6]

9.57E-04 0.7 [7]

CdTe:Cu solubility data

C0 (cm-3) Ea (eV) Ref.

1.56E+23 0.55 [2] SC low

~2E+17 ~0 [4] PX high

3.73E+24 0.68 [8]

CdS:Cu diffusivity data

D0 (cm2 s-1) ED (eV) Ref.

1.20E-02 1.05 [9] SC

2.10E-03 0.96 [10] SC

1.60E-03 0.77 [11] SC

— 0.95 [12] SC

6.00E-09 0.5 [13] PX

— 1.0 [14] SC

CdS:Cu solubility data

C0 (cm-3) Ea (eV) Ref.

8.00E+21 0.27 [13] PX

6.60E+22 0.505 [10] SC

REFERENCES 

[1] B. O. Wartlick, C. Blanchard, and J. F. Barbot, "Study of silver and copper diffusion in p-type Hg/sub 0.3/Cd sub 0.7/Te and CdTe by capacitance measurements," Materials Science & Engineering B (Solid-State Materials for Advanced Technology), vol. B71, pp. 254-257, 2000.

[2] E. D. Jones, N. M. Stewart, and J. B. Mullin, "The diffusion of copper in cadmium telluride," Journal of Crystal Growth, vol. 117, pp. 244-248, 1992.

[3] T. D. Dzhafarov, S. S. Yesilkaya, N. Y. Canli, and M. Caliskan, "Diffusion and influence of Cu on properties of CdTe thin films and CdTe/CdS cells," Solar Energy Materials and Solar Cells, vol. 85, pp. 371-383, 2005.

[4] R. A. Enzenroth, K. L. Barth, and W. S. Sampath, "Transient ion drift measurements of polycrystalline CdTe PV devices," Conference Record of the 2006 IEEE 4th World Conference on Photovoltaic Energy Conversion (IEEE Cat. No. 06CH37747), pp. 4 -4, 2006.

[5] H. Mann, G. Linker, and O. Meyer, "Diffusion processes at the Cu-CdTe interface for evaporated and chemically plated Cu layers," Solid State Communications, vol. 11, pp. 475-479, 1972.

[6] H. H. Woodbury and M. Aven, "Some Diffusion and Solubility Measurments of Cu in CdTe," Journal of Applied Physics, vol. 39, pp. 5485-5488, 1968.

[7] O. E. Panchuk, V. I. Grytsiv, and D. P. Belotskii, "Diffusion of Cu in CdTe," Inorganic Materials, vol. 11, pp. 1510-1512, 1975.

[8] A. V. Vishnyakov, V. N. Zubkovskaya, and T. V. Kukleva, "Solubility of copper in cadmium telluride," Inorganic Materials, vol. 25, pp. 502-505, 1989.

[9] J. L. Sullivan, "An ultrasonic investigation of the diffusion of noble metals in CdS," Journal of Physics D (Applied Physics), vol. 6, pp. 552-559, 1973.

[10] J. L. Sullivan, "Diffusion and Solubility of Cu in CdS Single Crystals," Physical Review, vol. 184, pp. 796-805, 1969.

[11] R. L. Clarke, "Diffusion of Copper Cadmium Sulfide Crystals," Journal of Applied Physics, vol. 30, pp. 957-960, 1959.

[12] L. V. Borkovskaya, B. R. Dzhumaev, L. Y. Khomenkova, N. E. Korsunskaya, I. V. Markevich, and M. K. Sheinkman, "About the nature of diffusion anisotropy in CdS crystals," Semiconductor Physics Quantum Electronics & Optoelectronics, vol. 3, pp. 282-286, 2000.

[13] E. B. Kaganovich, I. K. Ostrovskaya, Y. S. Pilipyuk, and E. M. Pochtar, "Diffusion and solubility of copper in photoconductive CdS films precipitated from aqueous solution," Inorganic Materials, vol. 24, pp. 1236-1238, 1988.

[14] L. V. Borkovska, L. Y. Khomenkova, N. E. Korsunska, I. V. Markevich, and M. K. Sheinkman, "Some peculiarities of impurity diffusion in CdS crystals," Physica Status Solidi B, vol. 229, pp. 269-273, 2002.

Figure 2. Device-processing simulation of Cu migration in

CdTe PV device for the high-diffusivity case.

Figure 3. Device-processing simulation of Cu

migration in CdTe PV device for the low-diffusivity

case.

Figure 4. Long-term stability simulation of 

Cu migration in CdTe PV device for the 

high-diffusivity case.

Figure 5. Long-term stability simulation of Cu

migration in CdTe PV device for the lowdiffusivity case.

SIMS Depth Profile

Figure 6. Typical SIMS profile of a

ZnTe:Cu back-contacted device after

back-contact processing.

Free Energy

Chemical Potential

Migration Potential

Segregation Enthalpy

POhenomenological Flux Eq. Mobility

Migration Flux

Continuity 

Equation

Fick’s 1st Law