Diffusion length measurements of thin amorphous silicon layers

~

Solld State Commmuntcattons, Vol. 69, No. 8, pp.807-810, 1989.

0038-1098/89 $3.00 + .00

Printed in Great Britain.

Pergamon P r e s s p l c

DIFFUSION LENGTHMEASUREMENTS OF THIN AMORPHOUSSILICON LAYERS J.C. van den Heuvel, R.C. van Oort, M.J. Geerts Faculty of Electrical Engineering, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands (Received 18 November by B. MQhlschlegel)

A new method for the analysis of diffusion length measurements by the Surface Photovoltage (SPV) method is presented. I t takes into account the effect of the reflection of l i g h t from the back contact in thin layers and the effect of a f i n i t e bandwidth of the used interference f i l t e r s . The model was found to agree with experiments on thin amorphous silicon (a-Si:H) layers. I t is shown that in the region were these effects are negligible this method is equivalent to the standard method.

I.Introduction

2.Theory

The Surface Photovoltage technique is often used to obtain the diffusion length of minority carriers in semiconductors. A transparent Schottky barrier contact is used in this technique. When this transparent rectifying contact is illuminated with monochromatic l i g h t , a photovoltage is developed between the contact and the bulk due to the diffusion of generated minority carriers to the contact. In the method presented by GoodmanI the l i g h t intensity at each wavelength is adjusted to give a constant photovoltage and the following relation can be applied:

The sample is assumed to be one dimensional, divided into the space-charge region, O
I = const ( I/e + Ld )

(I) G(x) = q e I (I-R) exp(-ex)

In this equation I is the incident photon flux, e the absorption coefficient, and LA is the diffusion length. The diffusion length can be obtained from the intercept on the I/o axis of the straight line in the plot of I versus I/e. The v a l i d i t y of Eq.(1) depends on two sets of inequalities:

(4)

where R is the r e f l e c t i o n of l i g h t from the surface, and x is the position in sample. The formula given by Moore for the photon f l u x i s : I -

const (l/~+Ld) 41 (]/e+L d) 42 - 41(]/~)exp(-~W)

(5)

W<< Ld << d

(2)

41 = ( 1 + VT#n/VcF1 ) F1

(6)

W << 1/~ << d

(3)

42 = ( I + VT#n/VcF2) F2

(7)

where W is the width of the space charge region and d is the sample thickness. The two sets of inequalities mean that we imagine the sample to be i n f i n i t e l y thick, thus disposing of the boundary at the back. In the present work a new method is presented to obtain the diffusion length from Surface Photovoltage measurements. This method takes into account the reflection of l i g h t from the back contact in thin layers and the effect of a f i n i t e bandwidth of the used interference f i l t e r s . A comparison with the method of Goodman and Moore2 as well as a comparison with experiments is presented.

In these equations is VT the thermal voltage kT/q, #. the mobility of electrons, vc is the surface"recombination velocity, and FI and F2 are integrating factors which lead to this result. Eq. (5) tends to Eq. (1) for small values of W i . e . W<
807

(8)

808

DIFFUSION LENGTH MEAStIREMENTS OF THIN AMORPHOUS SILICON LAYERS

111e photon f l u x used to obtain a constant photovoltage is: I = const / J

(g)

We can evaluate Eq.(8) and Eq.(g) using Eq.(4) for the generation in the case of an i n f i n i t e sample thickness. We obtain for the photon flux: I =

const (I/a+Ld) (I/a+Ld) - (I/a) exp(-aW)

(I0)

This equation is equivalent to Eq.(5) in the case of a negligible surface recombination. In this case v, tends to zero and the factors @l and ~2 t end~to VylL./v,. Since the l a t t e r factor appears both in th~ n~merator and denominator the result is equal to Eq.(10). In our experiments we found that the surface recombination can be disrecarded. At short wavelengths there was no decrease in the photovoltage which is the case for a high surface recombination because of the generation close to the surface due to the high absorption. In the case of a f i n i t e sample thickness we have to replace the generation given by Eq.(4) with the following equation:

it12

G(x) = Go(x). non-~1

l-r,r(exp(-2i~d)l+r'exp(-2i6(d-x))12 11a)

Go(x) = q • I exp(-ex)

(11b)

6 = 2x (nl- i k l ) / ~

(11c)

where no, n~ and n2 are the refractive indices, r( , r2 and tz are the Fresne] coefficients, is the wavelength, and kz is the extinction coefficient. The indices refer to the notation used by Heavenss and the optical system that is depicted in Fig. 1. To obtain the diffusion length i t is no longer possible to use the simple graphic method

Vol. 69, No. 8

based on Eq.(1). We used equations (8), (9), and (11) to calculate the curve of ! versus ~ and adjusted L~ to obtain the best f i t to the experimental photon f l u x . 3.Experimental Coming 7059 glass coated with tin-oxide, with a sheet resistance of 120 Q/o, was used as a substr"ate. The amorphous s i l i c o n was deposited in a stainless steel reactor by means of RF (13.56 MHz) glow discharge decomposition of silane (SiH4) diluted up to 55 vol.% in hydrogen. The deposition conditions were: a substrate temperature of 523 K, a total flow rate of 100 sccm and an RF power of 36 mW/cmz. After the i n t r i n s i c layer an n-doped layer of 500 A was deposited by decomposition of SiH4 containing 1% PH3. The samples were then removed from the reactor chamber and ohmic contacts were made on top by evaporation of chromium followed by photolithography. The size of the dots on the substrates varied from 0.25 nTn= to 2 m z. The absorption c o e f f i c i e n t as a function of the wavelength and the layer thickness were obtained from the optical r e f l e c t i o n and transmission of samples deposited in the same run on an uncoated Coming 7059 glass substrate. The thickness of the combined i- and n-layer was 0.568 #m. The transparent Schottky barrier is formed at the tin-oxide/a-Si:H interface. We used two methods to obtain the photon flux as a function of the wavelength. In the f i r s t method we used a monochromator to obtain monochromatic l i g h t in the wavelength region between 550 nm and 640 nm. The short-circuit current was held constant by adjusting the photon flux. In the second method we used a set of interference f i l t e r s with wavelengths of 520, 560, 600, 620, and 640 nm with a bandwidth of 10 nm. In this measurement we held the photovoltage constant by adjusting the photon flux. We used red bias l i g h t with a wavelength of 700 nm at several intensities to reduce the space charge width. 4.Results

incident~

~r,

/t,r=t; /t lrar;r2t~

/< /

Ro

\

nl--lk I '

n2- I k=

t,r=/

\

/

/~ \_ /~t'r~'l'r" I ,~--Si:HI

I chr°mium I

Fig. 1. The optical system that was used to calculate the generation. The arrows indicate the light rays which are transmitted and reflected at the interface between the different media.

The photon flux versus the reciprocal absorption is shown in Fig.2. These values were obtained by keeping the short-circuit current constant while changing the wavelength of the l i g h t . The interference effects caused by the reflection from the back contact can be easily seen. In Fig.3 we show the calculated generation as a function of position in the layer for a wavelength of 590 nm and a wavelength of 610 nm. The s h i f t in the position of the peaks cause the interference effects in the photon flux. We used equations (8), (9), and (11) to calculate the photon flux. As can be seen from Fig.4 the calculated curve agrees well with the measured curve for a diffusion length of 0.12 ~m and a space-charge width of 0.19 pm. These are not unique solutions so we used red bias l i g h t as suggested by Moore4 to reduce the space charge width. To obtain a sufficient intensity of the probe l i g h t in the case of bias l i g h t , we had to use a set of interference f i l t e r s with a bandwidth of 10 nm instead of a monochromator. The bandwidth was taken into account by adding the

Vol. 69, No. 8

DIFFUSION LENGTH MEASUREMENTS OF THIN AMORPHOUS SILICON LAYERS

~5

2,5

y

2.0

X

0 0

809

1.5

2.0 l,/'

1.5 X ZJ cO 1.0 o (13.

1.0

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0.5

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0.1

I

I

I

I

I

0.2

0.3

0.4

0.5

0.6

0.O 54(

0.7

I

I

I

I

I

560

580

600

620

640

1/absorption (micrometer)

wavelength

Fig.2. The 'Goodman" p l o t of the measured photon f l u x versus the reciprocal absorption of the a-Si:H.

660

(nanometer)

Fig.4. Comparison of the calculated photon f l u x (dashed l i n e ) with the measured photon f l u x ( s o l i d l i n e ) . The calculated results were obtained for a diffusion length of 0.12 #m and a space-charge width of 0.19 Im.

3.0

3.0

2.5

2.5

~. I

×

|

2.0 t

v

tt l I

c

._o

1.5

4-,

v

¶I ~ l lf ^

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,, rI

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!

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,,,v ',l,/i\

@ ~

,-v

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,,

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;~/,~ I

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f

~,

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0.5 I

: ',VIv ~:11;1\~ '~ ~ l

"

1.5

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iV il : / t : 0.0 0.0

2.0

(micrometer)

Fig.3. Calculated generation as a function of p o s i t i o n in the a-Si:H layer. The s o l i d curve corresponds to a wavelength of 590 nm, the dashed curve to a wavelength of 610 nm.

0.0 500

.

.

.

.

a

.

550 wavelength

.

.

.

,

•

600

I

,

,

650

(nanometer)

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Fig.5. Comparison of the calculated and measured photon f l u x in the case of l i g h t obtained from narrow band pass f i l t e r s . The calculated data are indicated by closed c i r c l e s , the experiment a l data by a s o l i d line connecting the measured points. The calculated results were obtained f o r a d i f f u s i o n length of 0.12 lUn and no spacecharge width.

810

DIFFUSION LENGTH MEASUREMENTS OF ~ I N

calculated generation of several wavelengths within the bandwidth. This is an advantage of our method over that of Moore since there is no p o s s i b i l i t y to account for a deviation from monochromatic l i g h t in Eq.(5). Figure 5 shows the measured photon flux at a red bias l i g h t intensity of approximately one sun compared to simulation using a diffusion length of 0.12 #m and a negligible space-charge width. As can be seen from the figure the measured points and the calculated points correspond accurately. In conclusion we have presented a new

AHOI~HOUS SILICON LAYERS

Vol. 69, No. 8

method for the analysis of Surface Photovoltage measurements. I t takes into account the effect of the reflection from the back contact in thin layers and the effect of a f i n i t e bandwidth of the used interference f i l t e r s . We showed theoret i c a l l y that in the region where these effects are negligible this method is equivalent to the standard method by Goodman and Meore. We also compared the model with experiments and found that i t agrees well with the measurements and can be used to obtain the diffusion length of a-Si:H in the case of thin layers.

References

1. 2. 3. 4.

A. Goodman, J.Appl.Phys. 32, 2550 (1961). A.R. Moore, J.Appl.Phys. 54, 222 (1983). J. Reichman, Appl.Phys.Lett. 38, 251 (1982). A.R. Moore, Semiconductors and Semimetals, Vol.21C, p.239. Academic Press, New York

(1984).

5. O.S. Heavens, Optical Properties of Thin Solid Films. Butterworths Scientific Publications, London (1955).