Photoconductivity and recombination dynamics for a-Si:H at different thicknesses

Solar Cells, 25 (1988) 169 -179

169

PHOTOCONDUCTIVITY AND RECOMBINATION DYNAMICS F O R a-Si:H AT D I F F E R E N T THICKNESSES YA-GU JAMES YE and W. A. ANDERSON Department o f Electrical and Computer Engineering, State University o f New York at Buffalo, 217C Bonner Hall, Buffalo, N Y 14260 (U.S.A.) (Received November 23, 1987; accepted June 23, 1988)

Summary The photoconductivity oph of amorphous silicon (a-Si:H) of various thicknesses is described as a function of temperature, wavelength and light intensity. The room temperature aph is very dependent on the dark Fermi level and the sensitization is a consequence of a change in the energy band bending. Under illumination, the power dependence of oph on intensity K can be divided into several regions for all thicknesses. However, there are more variations in K when light is injected. The K value covers the range of 0.2 - > 1.0. This indicates that the slope of distribution of density of states in the gap varies considerably for the different cases. Different wavelengths of illuminating light also reveal a similar situation. The temperature dependence of oph and activation energy Ea for films of various thicknesses show the same trend. Both oph and E~ decrease with temperature. The rate of decrease for thin samples is less than that for thick ones. This result is analyzed and explained by means of a model.

1. Introduction The increase in photoconductivity oph as the Fermi level Ef is moved closer to the conduction band was first reported b y Anderson and Spear [1] and more recently by Bayer and Hoheisel [2]. Rose proposed a model for aph based on the assumption of an exponential distribution of traps and the direct power dependence on the characteristic energy slope of this distribution [3]. Mort, Fritzsche and Derch e t al. suggest that in a-Si:H almost all recombination traffic takes place by tunneling between localized states, and not only through extended states [ 4 - 6]. Shur and Hack [7] proposed a new model based on two exponential distributions of acceptor-like and donor-like traps that adequately explain both the change in oph and its power (K) dependence on the dark Fermi level E~o. The sensitization of aph is interpreted in terms of a change in occupation of these recombination centers which is also responsible for variations in the power dependence [8]. 0379-6787/88/$3.50

© Elsevier Sequoia/Printed in The Netherlands

170 The present work involves studies of the power dependence K on light intensity and the relations of Oph and activation energy E a - T for various thicknesses of a-Si:H. Under the same conditions, a study is also made of illumination of the samples using light of various wavelengths to determine the surface and bulk recombination. All the experimental data are explained using the Spear model for Oph based on a recombination model. This is then compared to the Rose and Fritzsche model on the assumption of an exponential distribution of traps. Finally, a study is made of the superlinearity of the dependence of Oph on light intensity for thin samples, with sublinearity observed at lower intensities.

2. The two models 2.1. R e c o m b i n a t i o n m o d e l In 1974, Spear showed that at r o o m t em perat ure the recom bi nat i on path (see Fig. 1) should be EA --+ E y and not Ec -~ E v . The deduced activation energy was n o t consistent with the Ec -+ E v values derived from Oph-T data [1, 9]. Under stronger light, the recombination path is E A - + E y , as shown in transition Rs of Fig. l(a). Under weak light, the recom bi nat i on path is EA -~ EFo --->E y , as shown in transition Rw of Fig. l(b). The excitation process for Oph is represented by

(1)

~=G+E--C

The r eco mb in at i on process for aph is represented by h A = C -- E -- R

(2)

where G is the rate of photocarrier generation, C the rate at which electrons in E c fall into a trap (C = CI + C2), E the rate of re-excitation of the trapped electrons, R the rate of recombination (Rs, Rw), n the density of electrons in the conduction band, and nA the density of electrons in trap EA. Also

R s = bsnA 2, for stronger light

(3)

R w = b w N F n A , for weaker light

(4)

E = eAn A

(5)

C 2 = CA(NA -- nA)n

(6) n

_

EC

]c_

G,

_•_ .

.

l-Z---I,,

EC

Io.. I .

EF

"

__E¥ EV EV (a) (b) Fig. 1. Excitation and recombination processes involved in photoconductivity in a-Si:H.

171 where bs is the recombination coefficient for stronger light, bw the recombination coefficient for weak light, ea the probability for re-excitation of trapped electrons, cA the probability that electrons at Ec will fall into the trap,/CA the density of centers in trap En, and NF the density of centers in E F . Since, at a steady state

h

= hA

C2

=

0

(7)

E

(8)

R =V

(9)

=

we can obtain the following equation:

nA =

(10)

where k = 1 for weaker light and 0.5 for stronger light.

2.2. Distribution of exponential band tail model Rose in 1978 and Fritzsche in 1983 assumed an exponential band tail model [4], as illustrated in Fig. 2. The density of states for an energy level in the band tail is given by

g(E) = go exp(--(Ec -- E)/kTo}

(11)

Since in a steady state the rate of recombination of electrons must equal their rate of generation G, and G is proportional to the intensity of light I, we obtain I

n -

(12)

Etn

f

g(E) dE

EFo

Starting with eqn. (11) and using eqn. (12) we find that n

I =

gokTo exp{--(Ec

f

- -

Etn)/kTo}

__

(l-f)=

Ev Et EFp

./ ,11 I EFIEtn Ec

Fig. 2. E x p o n e n t i a l b a n d - t a i l m o d e l o f a-Si:H.

(13)

172 Although EFn is always below Etn

i

Etn = EFn + k T in /'n +Pt \ n /

(14)

electron p h o t o c o n d u e t i o n is d o m i n a n t with EFn very close to Etn , and Etn ~ EFn

(15)

Substituting in eqn. (15) yields n =

I

gokTo e x p { - - ( E c -- EFn)/kTo}

(16)

with the definition of the quasi-Fermi level n = N c e x p { - - ( E c --

EFn)/kTo}

(17)

Assuming

a = T/To

(18)

this results in n =

g -

(19)

1 1+~

-

To

T+ To

(20)

In eqns. ( 1 1 ) - (20), go is the density of states for the band-tail model,

g(E) the density of states for energy level in the band-tail, To the logarithmic slope parameter of the band-tail of the do m i nant photocarrier, Etn the trap quasi-Fermi level for electrons, EFn the quasi-Fermi level for electrons, Nc the density of states in the c o n d u c t i o n band, K the ratio factor, and p the hole density.

3. Sample preparation and equipment All the samples were provided by the Solar Energy Research Institute. Deposition rate was 2.0 A s-l; deposition times were 180, 82, 40 and 10 min, corresponding to film thicknesses o f 2.16, 0.98, 0.48, and 0.12 pm respectively. Films were deposited consecutively at 250 °C substrate temperature, 90 sccm pure silane flow rate, 900 m T o r r chamber pressure, and an r.f. p o wer density of 25 mW cm -2. The intrinsic a-Si:H films were deposited on 25 × 25 × 1 mm 7059 glass. After deposition, the distance between the two coplanar electrodes was 2 mm with a length of 10 mm. The electrodes, made o f silver paste, were coated on the surface of the film to make a low resistance contact. P h o t o c o n d u c t i v i t y oph was measured using an ELH light

173

source, Keithley 223 power supply and Keithley 480 picoammeter. Voltage was set at 30 V across the samples during the measurement of dark current and photocurrent from which Od and Oph were calculated. The different wavelengths of light were derived by using filters having narrow band transmission at 4000 A and 5200 A. Temperature was measured by a thermocouple with heating of the sample during testing occurring in an air ambient. 4. Results and discussion

2.4. Intensity dependence First we consider thick samples with d > 1 ~m and Figs. 3 - 5. When the intensity of light I is less than 30 mW cm -2, the slope of the iph-I curves of 0.8 - 1.0 gives K = 1.0. For I greater than 30 mW cm -2 (see Fig. 3), iph is proportional to the square root of the light intensity I and K = 0.5. These results are consistent with eqn. (10) as suggested by Anderson and Spear. The former could be due to electron and hole formation of an exciton resulting in monomolecular recombination, because of the excitonformed field between electron and hole which is not broken under weak light. The latter would then indicate that the exciton is broken under a stronger light and that the recombination is bimolecular. The slope of iph-I, K = 1 also occurred under green and blue light conditions as shown in Figs. 4 and 5. 10 4 0.50 I 0 3_

0.8{ .'79 I0- ~

"-IOL. o

oi0.q o

Thickness

O-

v

0.98pro

~3 2 . 1 6 p r o o 0.48wm ~. O. 12pro

I 0-; 0_2

Ib-'

110 °

llO '

Ib 2

3

White Light Intensity, I ( m W / c m 2) Fig. 3. P h o t o c u r r e n t - l i g h t intensity curve for a-Si:H samples of various thicknesses under white light illumination.

174

o~ Thickness v 0.98pro [] 2.16pro

Jr

0 0.48pro

O.IZpm

°1 io~

/ "

,=o.~
~ .o_~

/o//

~2 =o

13-

D'

I ~0.. =

I '0-'

/

/

ll0 °

/ / ,

I~01

II02

l03

Blue (0.4pro) Light Intensity, I (rnW/cm=) Fig. 4. Photocurrent-light intensity c u r v e for a-Si:H samples of various thicknesses under blue light i l l u m i n a t i o n .

103

,°t

~I°I -~

OJ

.2

/

o

#_

Thickness

o/

v 0.98pro Q 2.16pm

o 0.4Spin z~ O. I 2pro I

0/0_ 2~

11(3.~

ilO o

i101

i'02

03

Green (0.52pro) Light Intensity, I (mW/cm2) Fig. 5. P h o t o c u r r e n t - l i g h t i n t e n s i t y c u r v e for a-Si:H samples o f various t h i c k n e s s e s u n d e r green light i l l u m i n a t i o n .

175

Next we consider thin samples having d = 0.48 pm and 0.12 pm. Firstly, we should notice that K > 1 does occur for thin samples under stronger light intensity. This was not found for thick samples. When the film thickness rapidly decreases, there occurs an increase in the bending of the band [10]. This causes a separation between electrons and holes that slows the recombination process and increases iph as shown in Figs. 3 - 5. Secondly, the content of superlinearity ( K > 1) rises significantly with reduced film thickness. The result confirms the increased spatial extent of band bending with decreasing thickness of film. The above mentioned condition is probably due to one additional set of gap states with different values of R = bn/bp: this was predicted by Fritzsche [4] and is shown in Fig. 6. The slope To of the distribution of density of states is not only changed: it also probably becomes negative with decreasing thickness of film due to the increased distortion of the crystal lattice. For very thin films, the distribution of the density of states is no longer a simple exponential curve and it is strongly influenced by surface conditions. Under very weak light intensity ( I < 10 °- 10 -~ mW cm -2) for short wavelength illumination, the iph--I curve shows a sublinearity K < 0.5 as indicated in Fig. 4. This might have several causes. Firstly, the quantity of photons absorbed by the film rapidly decreases due to the light absorbed in the surface layer when blue light injects. Secondly, sublinearity may be caused by a surface defect under low light intensity, where it produces a non-radiative recombination center. Thirdly, the thin sample contains more defects than a thick one; hence the sublinearity is significant, i.e. K = 0.2.

4.2. Temperature dependence When the temperature decreases, the quasi-Fermi level EFn of electrons moves away from E c. The probability of recombination of carriers increases and the carrier lifetime becomes smaller, causing oph to decrease as shown in Figs. 7 - 10. Also, the activation energy AE decreases with temperature because the slope of the distribution of states dg(E)/dE in the gap decreases, as illustrated in Figs. 7 - 10 and 11. In such a case, we employ the Fritzsche model as follows. According to eqns. (16) and (19), we can obtain

In[g(E)]

/KTo -I-I/KTo adding atate Energy

Fig. 6. Energy level model of one additional set of gap states.

176

16 4 d=O.98pm

E o

t

C v

i .+2_ ._> o

=

I

° o

Color

-~

[] Green

~L

O

White Blue

3x I ~6

2.3

2!5

~%

217 I OS/T

Fig. 7.

aph-T c u r v e

2~9 (K)"

3'.1

3!3

3.5

I

for a sample thickness of 0.98 ~m.

~16 5 d=O.4Bpm

,,-£ o I

C v

,g o o

,go Color

a.

z~ W h i t e o

Blue

[~ Green

2xi~ 6

2'.3

2~5 103/T

2L-t

2'.9

3.3

(K~ I

Fig. 8. G p h - T curve for a s a m p l e t h i c k n e s s o f 0 . 4 8 / / m .

177

~5 d=O. I 2pro

3 ~_

[] Green o Blue z~ White

~e 2~5

2.3

2~7 103/T

Fig. 9.

Oph-Tcurve for

2.L9 -I (K)

3~1

3:3

3.5

a sample thickness of 0.12 #m.

d = 2 . I 61Jm

o o o

a Blue

2L5

217

2.19

I 03/T

3~1

3'.3

3.5

(K3 I

Fig. 10. Oph-T curve for a sample thickness of 2.16 pro.

(~)

a

LkE

= exp

hT---o

Since 1/kT o decreases increased w i d t h o f t h e t e m p e r a t u r e situation, sample. This has b e e n

(21)

w i t h decreasing t e m p e r a t u r e , ~ increases and the band-tail results in a decrease in oph. U n d e r t h e same t h i c k samples have a o ~ higher t h a n t h a t o f a t h i n discussed in ref. 9. Nevertheless, f o r t h i c k e r samples

178 In

[g(E)]

:

,

dE

Etn2 #tn I Energy Fig. 11. V a r i a t i o n o f t h e d i s t r i b u t i o n o f gap states w i t h t e m p e r a t u r e w h e r e Tj > T2.

(d = 2.16 #m) there occurs an interesting problem. The aph-T curve has a flatter region at 370 - 320 K, i.e. AE = O. This indicates where the distribution of quasi-Ef states have a peak in density of states. 4.3. Wavelength dependence Light of different wavelengths was used to homogeneously illuminate the films with the light intensity carefully calibrated. The activation energy AE is wavelength dependent, even for the same thickness of film. This indicates that there exists a varying absorption of light over the sample due to a varying E F distribution in the gap. When considering photoconductivity, the influence of the surface layer is reduced and aph mainly depends on the thickness of film d. Thus, aph (thick) > Oph (thin). Besides, for thick samples the spectral response to white and green light is greater than that for blue in a-Si:H. Thus, aph (white) = aph {green)> Oph (blue). For thin samples, part of the white light is not perfectly absorbed and aph (green), aph ( b l u e ) > Oph (white). Considering spectral response, green light is still more effective than blue, such that aph {green) > aph (blue). This indicates the influence of an imperfect surface region. 5. Conclusions The dependence of Oph on light intensity, temperature, wavelength, and K shows a strong variation for amorphous silicon samples of various thicknesses. The different K values are related to the slope of the distribution of density of states in the gap. The thin samples behave significantly differently from the thicker ones because of the influence of the surface layer which contains defects not present in the bulk. Proper surface passivation could be helpful here.

Acknowledgment The authors wish to thank Dr. Y. S. Tsuo, of the Solar Energy Research Institute, for providing the samples and for reading the manuscript.

179

References 1 D. A. Anderson and W. E. Spear, Philos. Mag. B, 36 (1977} 695. 2 W. Beyer and B. Hoheisel, Solid State Commun., 47 (1983) 573. 3 A. Rose, Concepts in Photoconductivity and Applied Problems, Krieger, New York, 1978. 4 J. Mort and D. M. Pai, Photoconductivity and Related Phenomena, Elsevier, Amsterdam, 1976, pp. 199 - 204. 5 H. Fritzsche, Theory of Steady State Photoconductivity, lecture in Shanghai, China, 1983. 6 H. Dersch, L. Schweitzer and J. Stuke, Recombination process in a-Si:H, spin dependent photoconductivity, Phys. Rev. B, 28(15) (1983) 4678. 7 M. Shut and M. Hack, J. Appl. Phys., 55 (1984) 3831. 8 M. H. Brodsky, Topics in Applied Physics, 36, Springer-Verlag, Berlin, 1979, p. 139. 9 Y. H. Hai and Z. Y. Zhou, J. Electron. Sinica, 4(4) (1982) 248. 10 Y. G. Ye, W. A. Anderson and Y. S. Tsuo, Sol. Cells, 23 (1988) 191.