Ž .Journal of Non-Crystalline Solids 227–230 1998 259–262

Lateral photovoltage in hydrogenated amorphous silicon

Alok Srivastava, S.C. Agarwal )

Department of Physics, Indian Institute of Technology, Kanpur 208 016, India

Abstract

The variation in the potential difference, observed between two coplanar electrodes on hydrogenated amorphous siliconŽ .a-Si:H films upon illumination with a laser beam, is studied as a function of the position of illumination, and thetemperature of a-Si:H. The results are analysed in the light of diffusion of photogenerated carriers and yield the ratio of thediffusion lengths of electrons and holes. q 1998 Elsevier Science B.V. All rights reserved.

Keywords: Hydrogenated amorphous silicon; Lateral photovoltage; Dember effect; Diffusion length

1. Introduction

As most of the applications of device qualityŽ .hydrogenated amorphous silicon a-Si:H rely on its

optical properties such as photoconductivity, thephysical parameters such as mobility and lifetime ordiffusion lengths of the photocarriers remain impor-tant subjects of fundamental as well as applied re-search. There have been numerous experimentalstudies to reveal the nature of the transport of photo-carriers and to estimate the values of diffusion

w xlengths, mobility and lifetime of these carriers 1,2 .In this paper we show that the diffusion of photocar-riers in a-Si:H films can be studied by measuring

Ž .lateral photovoltage LPV on partially illuminateda-Si:H films and the results can be analysed to yieldinformation about the diffusion lengths of electronsand holes.

) Corresponding author. Fax: q91-512 250 260; e-mail:sca@iitk.ernet.in.

2. Experimental

Device quality a-Si:H thin films are deposited byw xthe standard glow discharge method 3 using silane

gas, onto Corning 7059 glass substrates, held at atemperature of about 3008C. The films are about 1

Ž .mm thick and the current–voltage I–V and con-Ž .ductivity s T are measured between 300 K and 480Ž y6 .K in vacuum ;10 torr . The I–V characteristics

in the dark are found to be linear in the range ofŽ"100 V. The room temperature conductivity s 300

. y9 y1 y1K in the dark is 2=10 V cm with activa-tion energy of 0.87 eV, whereas the photoconductiv-ity under uniform white light illumination of inten-sity nearly 100 mW cmy2 is found to be about 10y3

Vy1 cmy1, indicating a change of nearly six orders

of magnitude in the conductivity upon illumination.The intensity dependence of photoconductivity fol-

Ž . glows s F AF with gf0.8. The sub-gap ab-phw xsorption measurements 4 give the density of lo-

Ž . 16 y3calised states N to be below 10 cm and thedŽ .slope of valance band tail E less than 50 meV.ov

0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII: S0022-3093 98 00064-7

( )A. SriÕastaÕa, S.C. AgarwalrJournal of Non-Crystalline Solids 227–230 1998 259–262260

Ž .Fig. 1. Setup for the measurements of LPV, I – V and s T . Darkbands are Teflon coated metal strips covering nichrome electrodes1 and 2 to avoid contact photovoltage.

These compare favorably with those reported on thew xdevice quality films in literature 5 .

Ž .For the lateral photovoltage LPV measurements,Ž .two coplanar nichrome electrodes about 6 mm long

at a separation of 20 mm are evaporated on top ofthe film. The LPV measurements are carried out in avacuum chamber equipped with a quartz windowand heating arrangement.

When light from a 635 nm diode laser is focusedŽ .to a spot on the sample, a lateral photovoltage LPV

is detected between the electrical contacts 1 and 2Ž .Fig. 1 . An electrometer was used to record thisLPV as a function of the position of the light spot.The measurements are performed at temperatures inthe range of 390 K to 450 K. LPV measurementsbelow 390 K are not reported as these are too noisybecause of the high impedance of the sample. Thetemperature is uniform over the entire sample toavoid thermoelectric voltages. This uniformity is en-sured by observing zero open-circuit voltage in thedark at each temperature before recording LPV.

Fig. 2. Position dependence of the LPV at different temperatures.x is measured from the centre of the film. Lines drawn are guides0

to the eye.

Fig. 3. Temperature dependence of LPV at a fixed x sy5 mm0

from the centre of the film. Line shown is a guide to the eye.

Moreover, the electrical contacts are kept in the darkusing Teflon-coated metal strips as shown in Fig. 1to prevent the generation of any contact photovolt-age.

3. Results

For the LPV measurements, we have used a low-Ž . Ž .power -5 mW semiconductor diode laser red .

This is mounted on a travelling microscope and thelaser beam is focused on the surface of the film. Thevalue and sign of LPV depends on the distance ofthe spot x from the centre of the film and it0

undergoes a sign reversal as the light spot travelsfrom one electrode to the other; the changeover in

Ž .sign occurs at the centre of the film x s0 . The0

position dependence of LPV at different tempera-tures is shown in Fig. 2. We observe that the LPVfollows a systematic trend and undergoes a signreversal at the centre of the film. Moreover, LPVdecreases in magnitude as the temperature of thesample is increased from 394 K to 448 K. Fig. 3shows temperature dependence of LPV for a fixed

Ž .position x sy5 mm of the light spot. For TG4000

K, LPV decreases almost linearly with increasingtemperature.

4. Discussion

The observed LPV can not be caused by thermo-electric emfs, as we have not detected them when thesample is in the dark. Also, the temperature differ-ence between the electrodes during illumination is

( )A. SriÕastaÕa, S.C. AgarwalrJournal of Non-Crystalline Solids 227–230 1998 259–262 261

too small, for the intensity of the light used, to givethe LPV. Further, we have ruled out the contactphotovoltage as the cause of LPV by keeping theelectrodes in the dark during the experiment. We

w xsuggest the Dember Effect 6 as being responsiblefor the observed phenomenon. The electron and holediffusion coefficients differ greatly in a-Si:H givingrise to different gradients of electrons and holesalong the length of the sample, resulting in theobserved LPV. We present our model for the ob-served phenomenon. The continuity and Poisson’sequations are solved for the experimental conditionsto obtain an estimate of the ratio of the carrier

Ž e h .diffusion lengths L rL in a-Si:H.D D

To calculate the observed photovoltage, we beginby calculating the spatial profiles of the electronsand holes during illumination by the laser spot, in thesteady state. For one-dimensional case we can writethe continuity and the Poisson’s equations for the

w xsystem as 7

E E nGyR q nm EqD s0, 1Ž .e e ež /E x E x

E E pGyR y pm EyD s0, 2Ž .h n hž /E x E x

E E es pyn . 3Ž . Ž .

E x e

Here G is the generation rate of photocarriers, De

and D are the diffusion coefficients of electronsh

and holes respectively and R and R are theire h

respective recombination rates. e is the permittivityof a-Si:H and n and p are the total number ofelectrons and holes at a distance x from the point ofillumination x in the steady state. More explicitly,0Ž . Ž . Ž . Ž .n x sn qd n x and p x sp qd p x where n0 o 0

and p , are the thermally generated carriers in theoŽ . Ž . Ž .dark independent of x and d n x and d p x are

the excess carriers and depend on x. The termsinside the parentheses in each equation represent thegradients of the drift and diffusion components ofthe current density respectively.

The observed LPV is generated by the diffusionof photogenerated excess carriers in the absence ofan external electric field. Therefore, we neglect the

Ž .drift component from the third term in Eqs. 1 andŽ .2 , keeping only the diffusion component, which

determines the charge redistribution in the thin film.Assuming the recombination to be independent of

Ž Ž . . Ž Ženergy, we take R s nyn rt and R s pye 0 e h. . w xp rt 8,9 . This gives0 h

en x sA exp y xyx rL qB qGt qnŽ . Ž .1 0 D 1 e 0

4Ž .hp x sA exp y xyx rL qB qGt qpŽ . Ž .2 0 D 2 h 0

5Ž .

where Le and Lh are the diffusion lengths of elec-D De hŽ . Žtrons and holes defined as L s D t and L(D e e D

.s D t respectively and x is the distance of the( h h 0

spot of illumination from the centre of the sample.The constants A , A , B and B are determined1 2 1 2

from the boundary conditions. When x is far awayŽ . Ž .from the spot of illumination, both n x and p x

must tend to their thermal generation values n and0

p respectively. This gives B syGt and B s0 1 e 2

yGt . On the other hand, at x sx , i.e., at theh 0

spot of illumination, nsn qn and psp qp ,0 ph 0 ph

where n and p are the photogenerated carriers atph ph

this position. The constants A and A are both1 2

taken to be equal to the total number of photogener-ated carriers, i.e., A sn and A sp .1 ph 2 ph

The diffusion profiles of the excess carriersŽ Ž . Ž . . Ž Ž . Ž . .d n x sn x yn and d p x sp x yp are,0 0

therefore, given by following equationsed n x sn exp y xyx rL 6Ž . Ž .Ž .ph 0 D

hd p x sp exp y xyx rL . 7Ž . Ž .Ž .ph 0 D

The Poisson equation is now solved with theabove charge profiles to obtain the potential differ-

Ž .ence LPV between two points situated asymmetri-Žcally to the charges as a function of x the position0

.of the light spot . The calculated LPV is plottedalong with the experimental data in Fig. 4. We find areasonably good fit for Le rLh s7. This ratio is inD D

good agreement with the estimates available in theliterature from other experiments. However, the val-ues of n , p and Le needed to give the requiredph ph D

magnitude of LPV are much larger than expected.We note that we have taken into account only themobile carriers in our analysis, whereas the trappedcharges will also contribute to the LPV. The spatialdistribution of trapped charges is expected to besimilar to the free charges. Therefore, their inclusion

( )A. SriÕastaÕa, S.C. AgarwalrJournal of Non-Crystalline Solids 227–230 1998 259–262262

Fig. 4. Theoretical fit to the experimental data at T s431 K withLe s1 mm and Le rLh s7.D D D

will increase the area of the charge distributionsŽ .without any change in shape. Further, we have

ignored the band bending at the top and bottomsurfaces of a-Si:H in our analysis. If one of the bandsis bent up on one surface and down on the other, theundoped a-Si:H film will behave like the p–i–n

w xstructures of Martins et al. 10 which show LPV.These considerations may account for the magni-tudes of the parameters needed to explain the magni-tude of the LPV.

The temperature dependence of LPV may becaused by the change in the diffusion coefficients

w xD , D of electrons and holes 7 . These changese h

result in a change in the charge profiles of electronsand holes, which gives a smaller LPV at highertemperatures.

5. Conclusions

We have measured the lateral photovoltage ona-Si:H films by nonuniform illumination as a func-tion of temperature, analysed the results based on thediffusion of photocarriers in the thin film, and have

estimated the ratio of the electron to hole diffusionlength Le rLh by measuring lateral photovoltageD DŽ .LPV in undoped a-Si:H. The position dependenceof LPV gives Le rLh to be about 7 which is inD D

reasonably good agreement with the values reportedin the literature.

Acknowledgements

We thank Drs. Avinash Singh, V.N. Kulkarni, A.Mookerjee, Pratima Agarwal,G. Lucovsky, K.Weiser, M. Vieira, S. Koynov and W. Beyer foruseful discussions. The help of Mr. Manu Bajpai isduly acknowledged. This work is partially supportedby DST and CSIR, New Delhi, India.

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