Limitations of surface photovoltage measurementsAmal K. Ghosh, Joel I. Haberman, and Tom Feng Citation: Journal of Applied Physics 55, 280 (1984); doi: 10.1063/1.332843 View online: http://dx.doi.org/10.1063/1.332843 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/55/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Local ultra-violet surface photovoltage spectroscopy of single thread dislocations in gallium nitrides by Kelvinprobe force microscopy Appl. Phys. Lett. 101, 252107 (2012); 10.1063/1.4772538 Surface photovoltage measurements in μc -Si:H: Manifestation of the bottom space charge region J. Appl. Phys. 92, 2323 (2002); 10.1063/1.1495895 Microscopic surface photovoltage spectroscopy Appl. Phys. Lett. 80, 2586 (2002); 10.1063/1.1468275 Detection of copper contamination in silicon by surface photovoltage diffusion length measurements Appl. Phys. Lett. 74, 278 (1999); 10.1063/1.123280 Surface photovoltage spectroscopy of a GaAs/AlGaAs heterojunction bipolar transistor Appl. Phys. Lett. 73, 650 (1998); 10.1063/1.121936

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Limitations of surface photovoltage measurements Amal K. Ghosh, Joel I. Haberman, and Tom Feng Exxon Research and Engineering Company, Corporate Research Laboratories, Annandale, New Jersey 08801

(Received 3 August 1983; accepted for publication 20 September 1983)

Surface photovoltage measurement used to measure the diffusion length of minority carriers in solar cells does not yield the correct value even when the cell thickness is much greater than the diffusion length. Under the best conditions the measured diffusion length is at least 10% lower than the actual value. The discrepancy increases as the ratio of diffusion length to thickness increases.

PACS numbers: 72.40. + w, 84.60.Jt

Surface photovoltage (SPY) measurements have been used by many to measure the diffusion length L of minority carriers in solar cells. 1-5 Although aware of the fact that the thickness H of the cell has to be larger than the diffusion length L, most workers have paid very little attention to this restriction when doing the experiment. As long as the plot of light intensity rp (for a contant signal strength) versus 1/a, where a is the absorption constant, resulted in a straight line, it was assumed that the measured diffusion length was cor­rect. Bullis and Baroddy6 have concluded from their experi­mental results that as long as H> 1.2L, the L values mea­sured by the Spy method are essentially independent of H.

On the other hand, Phillips 7 has shown that as long as H?4L, the measured diffusion lengths are accurate. The present analysis indicates that the Spy technique is not very accurate for determining the diffusion length even when H> 4L. For L - 50/-lm, Spy measurement will give a diffu­sion length at least 10% lower than the actual value even for wafers ? 400 /-lm. The discrepancy increases as the ratio of diffusion length to thickness increases. Further theoretical analysis indicates one could get a straight line for ¢> vs 1/ a plot even if H <4L.

The short-circuit photocurrent J sc for the base region of aN /P solar cell is given by the following equations:

I

qF(1 - R )aLn J sc = exp[ - a(XJ. + WI]

(a 2L;, -1)

{

S L [H' ] H' } _,, __ n cosh - - exp( - aH ') + sinh - + aLn exp( - aH ') Dn Ln Ln

X aL" - , S L H' H' _n __ n sinh - + cosh-

D" Ln Ln

1 ¢>= 1 +-.

aLn

(1 )

(5) where R is the reflectance, a the absorption coefficient, ~ the junction depth, W junction width, H 'the total cell thick­ness H minus the junction depth Xj and the depletion width W, S the surface recombination velocity, q the electronic charge, and F the incident photon density per second per unit band width at wavelength A..

Thus, a plot of ¢> vs 1/a should give a straight line. The intercept at ¢> = 0 should give

Equation (1) can be reduced to the form used in SPY measurements by assuming the following: (a) exp[ -a(Xj + W)]~I;(b)exp( -aH')<lsuchthat,relative to other terms, exp( - aH') andaLn(exp - aH') can bene-

H' H' glected; (c) sinh -~cosh-.

Ln Ln

Under such conditions,

qF(1 - R )aLn J sc = (aLn - 1),

a 2L;, - 1

qF(1 - R )aLn

aLn + 1

qF(I-R)

1

¢> 1 ' 1+­

aLn

(2)

(3)

(4)

Ln = - 1/a. (6)

8 Ln = 3OOl'm

7 H L

6 100 54 .- 5 350 181 c ::> 600 229

/ .c 4 850 240 ~

g 3 ::2 ,/

/. . 2

"'~ 0

-300 -200 -100 0 100 200

1/a(l'm)

FIG. 1. Simulated Spy Data. The different lines are for a diffusion length L of 300 ~m and thicknesses of 100, 350,600, and 850 )1-m.

280 J. Appl. Phys. 55 (1), 1 January 1984 0021-8979/84/010280-02$02.40 © 1983 American Institute of Physics 280

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1 I 1.0 --------------t----.j.--- --------------- -----

1 I

0.9 ~i' ~=::~======= 0.8

0.7

..:r 0.6 ::J

0.1

I I 1 1 1

1 1

~{ Range of Solar i v-r Cell Thickness La = 1051'm : :

o 100 200 300 400 500 600 700 800 900

Thickness (I'm)

FIG. 2. Theoretical plot of L / Lo vs thickness. Here, L represents the mea­sured (simulated) diffusion length and Lo the actual diffusion length.

If the approximations (a), (b), and (c) are correct one should be able to plot 1/Jsc vs 1/a (assuming Rand Fare constant) and extract L from such a plot. Figure 1 shows theoretical plots of 1/ J sc vs 1/ a for several hypothetical pin junction cells having a diffusion length of 300 Jim and var­ious values of wafer thicknesses H. Jsc was calculated theor­etically using Eq. (I). Straight lines were obtained for all the thicknesses considered, but none of the lines gave the correct diffusion length . The deviation increases with decreasing wafer thickness. This is because requirements (b) and (c) are not fully satisfied. Even if condition (c) could be satisfied, requirement (b) still remains a problem for the range of a values necessary to carry out the experiment. Similar com­putations were made for other diffusion lengths and the re­sults are summarized in Fig. 2.

281 J. Appl. Phys., Vol. 55, No.1, 1 January 1984

There may be additional limitations with the experi­mental data because of the variation of a and R with surface preparation conditions and also from reflections from back surface for Iowa values. To show the validity of the data, comparison is often made between SPY and photoconduc­tive decay (peD) measurements. A carrier lifetime is deter­mined from peD measurement. Knowing the minority car­rier mobility, the diffusion length can be estimated. The peD data, however, also have limitations. For example, for a wafer thickness of 300-400 Jim, the measured lifetime is mainly due to surface recombination.9

'E. Y. Wang, C. R. Baraona, and H. W. Brandhorst, Jr., J. Electrochem. Soc. 121, 973 (1976).

2T. L. Chu and E. D. Stokes, J. Electron. Mater. 7,173 (1978). lE. D. Stokes and T. L. Chu., Appl. Phys. Lett. 30, 625 (1977). 4A. Pogany, Proceedings of the 14th IEEE Photovoltaic Specialists Confer­ence (IEEE, New York, 1980), p. 410. ~A. K. Sood, G. M. Freedman, R. O. Bell, and F. V. Wald, Proceedings of the International Symposium on Solar Energy, edited by J. B. Berkowitz and I. A. Lesk (Electrochemical Society, Princeton, New Jersey, 1976), p. 227.

6W. M. Bullis and T. J. Baroddy, Jr., MBS Tech. Notes, 555, 9 (1970). 7W. E. Phillips, Solid-State Electron IS, 1097 (1972). sH. J. Hovel, Semiconductors and Semimetals, Vol. II, Solar Cells (Aca­demic, New York 1975).

"T. Tiedje, J. I. Haberman, R. W. Francis, and A. K. Ghosh, J. Appl. Phys. 54,2499 (1983).

Ghosh, Haberman, and Feng 281

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