Optical properties of ZnxCd1 − xSe films

Thin Solid Films 260 (1995)

75 85

Optical properties of Zq, Cd, _ .r Se films P. Gupta,

B. Maiti, A. B. Maity, Received

S. Chaudhuri,

I I February 1994: accepted I5 November

A. K. Pal

1994

Abstract Zn, Cd, ~Se films (0 < 1.O) were deposited by the hot wall evaporation technique onto glass substrates. The optical band gap (~7,) in the Zn, Cd, , Se films showed a bowing effect, with a bowing parameter of about I .26. Microstructural information was obtained from X-ray diffraction and transmission electron microscopy (TEM) measurements, which indicated a predominant wurt7lte structure for .Y < 0.5 and a zinc blende structure for .Y > 0.7. The grain size. determined from scanning electron microrcopy and TEM. was observed to decrease with increasing zinc content in the films. The films were highly resistive and polycrystalline in nature, with partially depleted grains. An optical method. developed on the basis of the model of Dow and Redfield. was used to determine the barrier height and the density of trap states at the grain boundary region, along with the carrier concentration of the polycrystalline films. The variation of the electric field within the grains also was studied. The cff‘ective mass of the carriers varied with Y and indicated a bowing effect K~WCVY/~S: Grain

boundary:

Optical

properties;

Semiconductors

1. Introduction

Zn, Cd,

,Se is considered

to be a very important of’ its various applications in optical devices utilizing the visible range of the spectrum. The material in thin film form has great potential in the fabrication of superlattice structures [I] and phosphor materials for television screens [2]. In addition the material with .Y < 0. I is important for nuclear detector applications [3]. Also, it is known from earlier studies that the absorption edge of the material varies from 710 to 463 nm with x varying from 0 to 1. Although the electrical properties of Zn, Cd, _ ,. Se mixed crystals have been reported [4], there seems to have been no notable study of this important material in thin film form. Therefore, the objective of the present work is to carry out a detailed study of the preparation and characterization of Zn, Cd, _ ~ Se films in thin film form.

material because

2. Experimental

details

The Zn, Cd, ~.,. Se films were prepared by coevaporating CdSe and ZnSe powders (99.999%) from two quartz crucibles placed inside a specially designed cylin0040-6090/95/$9.50 SSDI

0040.609()(

(‘

1995

94)0646

Elsevier I -X

Science S.A. All rights

reserved

drical graphite heater [5]. Two distinct temperature zones around 900 K and 1000 K could be located inside the graphite heater, in which to place the crucibles containing CdSe and ZnSe respectively. The films were deposited at a system pressure of 10 ’ Pa with a substrate temperature of about 480 K. The thicknesses of the films ranged between 1 and 2 pm. The compositions of the films were determined by energy-dispersive X-ray (EDX) measurements. Microstructural information was obtained from scanning electron microscopy (SEM), transmission electron mciroscopy (TEM) and X-ray diffraction (XRD) studies. The optical reflectance vs. wavelength traces of the films were recorded using a spectrophotometer (Hitachi, U-3410) in the range 400- 1200 nm. 3. Results and discussion General, for analysis of the optical data of a semiconducting film, the film is required to have a perfectly smooth ideal surface bounded by plane parallel faces. However, in practice, there are always surface and volume imperfections present in the film, which significantly affect the optical porperties. Both physico-chemical and geometrical imperfections may be present in a thin film.

76

P. Gupk~ et (11.1 Thin Solid Films 260 (1995) 75-X.5

The deviations from stoichiometry in a semiconducting film, along with changes in the composition resulting from adsorption and/or doping by foreign atoms, are considered as the physico-chemical imperfections. In turn, the surface roughness, grain boundaries and

pores present in the volume of the film are the rical imperfections. Thus, to derive unflawed mental parameters, the defect states arising out imperfections, along with the surface roughness, be considered in analyzing the optical data in

-J

n

Fig. 1 (a)-(f)

geometexperiof these should a semi-

II

Zn,

Cd,_,

Se

0 :SEM .

: Reflectance

0.13

E 2 0.12 1-J 0.11I-

O.lClFig.

l.(a),(b)

SEM

images of two representative

Zn, Cd,

, Se films

(c), (d) the corresponding SEMs ( :J) and reflectance ( 0)

for (a) .x = 0.66 and (b) s = 0.09:

distrubu-

tion of grains ohtained

measure-

ment\.

(e)

corresponding

(f)

from

TEM

images

ditfraction

(magnification

patterns

of

films

x 19 920) for

(e)

and

0.0sIL

0

the

.x = 0.37.

(0

., = 0.9I and (g) .i = 0.66.

conducting film. In the present study, we have considered the effects, of grain boundaries and roughness on the optical properties. SEM and TEM images of representative films of Zn, Cd, _ , Se are shown in Fig. 1. SEM (Figs. l(a) and (b)) of the films indicated columnar grains with a rough

Zn,

Cdl_x

of grain size L with

SEM

reflectance results.

d

.2 > ,-

0

(a) I 0.2

c\ I 0.4

I Se films:

f .

(111) -F

=

v for Zn, Cd,

7

-0.685 0

results: 0.

surface. The average grain size and the distribution of the grains were evaluated from both SEM images and optical reflectance measurements [6]. The distributions of the grains, evaluated as above, for two representative films are shown (Figs. l(c) and l(d)) along with the corresponding micrographs (Figs. I (a) and I(b)).

Se

.0.4

X

Fig. 2. Vartation

Q. (a) -0.70 ‘---a_<,

C 3

0.z

OI 0.6

I

0.6 6

x zo.91

PT

” (111I x =0.66 r

X

(311)

vl C

50I

a,

(002)

I

x =0.09

C

2 8 (deg.) Fig. 3. X-ray constant

diffractron

traces of three representative

with .x, for the zmc blende (

--

films with (a) x = 0.09 (b) A = 0.66 and (c) .\- = 0.9

) and wurtzite

(-

) structures.

I:

inset shows the vartation

of the lattice

78

P. Gupta et ul. / Thin Solid Films 260 (1995) 75-85

0.16 5

O!I-

6k0.2.2-

5 1.2

1.4

1.6 hJ

0.2t3: 3.1

1.8

0.10 2.0

(eV I

14Zn,Cdl_,

12Fig. 4. Plot of In(R,,/R) vs. l/i.’ for a representative Zn,Cd, ~..Se film with x = 0.91; inset shows a plot of surface roughness u,, vs. s.

(hJ

Se

= 1.81 eV

)

JO(b) 8The polycrystalline texture of Zn, Cd, _ .~Se films was revealed by TEM (Figs. l(e) - l(g)) studies. The TEM diffraction pattern indicated a wurtzite structure (Fig. l(e)) for x < 0.5 and a zinc blende structure (Fig. l(f)) for x > 0.7. Mixed phases were observed (Fig. l(g)) for films with 0.5 < x < 0.7. The average grain size L, estimated from the SEM and TEM images, was found to decrease with increasing x in the Zn, Cd, __, Se films (Fig. 2). .L obtained from the optical measurements [6] is also shown in Fig. 2, along with those values obtained from the SEM measurements. There are several reports [7-lo] on the structural properties of Zn,Cd, -%Se. These structural studies on Zn, Cd, ~_~Se indicated that single-crystal Zn, Cd, _~Se is obtained in a wurtzite (hexagonal) or cubic (zinc blende) structure, depending on the x value. Bassam et al. [7] reported that for x < 0.5, the structure is hexagonal and becomes cubic for x > 0.5. However, Nasibov et al. [8] obtained cubic single crystals for 0.7 < x < 1.0, which changed to hexagonal modification for 0 < x < 0.5, and the interval 0.5
6-0, 0

I 0.2

0.4

0.6

0.8

11

X

Fig. 5(a). Variation of refractive index n (0) and extinction coefficient k (A) of Cd,,4zZn, sxSe film with photon energy (hv). (b) Variation of dielectric constant E with x for Zn, Cd, , Se film with hv = 1.81eV.

structure [lo] but, in films both wurtzite and zinc blende structures were obtained. Cerdeira et al. [IO] reported a zinc blende structure for CdSe thin films on glass substrates. A zinc blende structure of CdSe on mica and GaAs was also reported by other workers [ I 1, 121. ZnSe has a zinc blende structure both in bulk and thin film forms [13, 141. In the present study, it was observed that the zinc blende structure is the most preferred structure for Zn, Cd, _~Se on glass substrates for x > 0.7, while the wurtzite structure is favoured for x < 0.5. The above observation is in agreement with the XRD studies (Fig. 3) of Zn, Cd, _ ~ Se films, which indicated a predominant wurtzite structure below x < 0.5 and changed to a predominant zinc blende structure for x > 0.7. The existence of a mixed structure was observed for 0.5
P. Gupiu ef (11./ Thin Solid Films 260 (1995) 7S- 85

Znx Cdl_xSe

o-

2.5-

Experimental

-

14.0

Best

fit

Points curve

(bz1.261 13.9 7

13.8 <

d

m = 0.2

c

_bI;-: :;:

I

JT

l;Jooy@y , 2.0

2.2

2.4

2.6 h3 (eV)

2.8

I.511 0

0.2

0.4

0.6

0.8

1.

X

3.0

Fig. 7. Variation of band gap I?,(.\-) of Zn, Cd, , Se films with I; experimental points; -~-, best tit curve: h = 1.36.

b.

Fig. 0. Plot of In n vs. hv for a representative Zn,Cd, ~, Se film (x = 0.91); inset shows the corresponding plot of In(rhv) vs. In(hl, - E,).

zinc blende and wurtzite structures respectively. The variation of the lattice constants was estimated from the XRD traces and is shown in the inset in Fig. 3. A sharp change in the lattice constant may be observed at x = 0.5, which is similar to the observations of other workers [7-91. 3.1. Measurements

of surface roughness

For reflection from a rough surface, the reflection coeflicient R of light reflected in the specular direction from a surface which has a Gaussian distribution of the heights of it irregularities may be written as [6, 151 $=erp[(-FIr]+{l

x {l -erp[

-exp[-cy)2]}

-Z!(~~]~

(1)

where R,, is the reflection from a perfectly smooth surface, (r,) and u are the r.m.s. height and r.m.s. slope of the irregularities in the surface, respectively, L is the wavelength of the incident radiation, and LX,is the half acceptance angle of the instrument. R,, may be taken to be equal to R + R,i,, with Rdlft being the diffused part of the reflectance. The first term on the right-hand side of Eq. ( 1) describes the coherent part of the reflectance, while the second term describes the incoherently reflected light, as recorded by the spectrophotometer. If 3, is small, the incoherent term can be neglected, and we may write

(2)

where C is a constant arising from the spatial fluctuation of the optical constants. Thus, the slope of the plot of ln(R,/R) vs. l/i2 (Fig. 4) will give the surface roughness of the film. The roughness (T(,values evaluated in this way for the Zn, Cd, _ , Se films were in the range 9- 13 nm for 1 > .Y > 0. It may be seen from the inset in Fig. 4 that the values of (T() decreased with increasing X, i.e. with increasing zinc content in the films. Thus, from Figs. 2 and 4. it is evident that the roughness increases with increasing grain size and decreasing Zn content in the Zn, Cd, _ , Se films. 3.2. Determination

of the optical constants clnd thp hand

@P The optical constant of the Zn., Cd, ~, Se films were determined from the reflectance vs. wavelength traces recorded from both air-film (R) and glass-film (R,) sides of the films. The diffused part of the reflectance (R,;,) also was recorded. The refractive index n and the extinction coefficient k were estimated from [ 161

(n,*-

n,‘)(R

+ R, - RR, - 1)

’ = 2[(n, + n,)(R - R,) + (n, - n,,)(RR, k2

=

(n, -

nj2-R,h t n)’ R, - 1

- li

(3)

(4)

where n, and n, are the refractive index of air and glass respectively. The values of 12 and li were obtained as indicated above, and the variations of n and k with hv for a representative film are shown in Fig. 5(a). It can be seen that the refractive index showed an initial increase with an increase in the photon energy, before showing a sharp fall with further increase in the photon energy near the band gap. However the extinction coefficient k

80

P. Gupta et al. / Thin Solid Films 260 (199s) 75-85

indicated a sharp rise with the incident photon energy at the band gap. The real part of the dielectric constant E in the Zn, Cd, _ _~Se films, calculated from E = n 2 - kZ, could be seen to increase from 5 to 14 with increasing x (Fig. 5(b)). The absorption coefficients x in the Zn, Cd, ,.Se films were obtained from c( = 4zk//l. The optical transitions in the films were studied [ 161from the variation of In a with Izv. We have that ahv is related to the band gap energy by ahv = Ci B,(hv - EJ”,

(5)

where B, is a constant which is different for different types of transition, as indicated by different values of mi, and Egi is the corresponding band gap. A plot of In c( vs. hv indicated (Fig. 6) a sharp fall at the band gap energy. The value of E, obtained in this way for a representative Zn, Cd, _-_,Se film with x = 0.9 1 corresponds to an m value of 0.4 (inset in Fig. 6), which is slightly lower than that expected for the direct transition (i.e. 0.5). It may be noted that the Zn, Cd, _ ,.Se films studied here indicated direct transitions for all the compositions. The variation of E,(x) with the composition indicated a non-linear behaviour, showing a bowing phenomenon (Fig. 7) in the Zn,Cd, _,Se films. The band gap E,(x) can be fitted to the expression [ 17- 191 E,(x) = E, + (E, - E, - b)x + bx2

(6)

where E, and E, are the band gaps of ZnSe (X = 1.0) and CdSe (x = 0), respectively, and b is the bowing parameter. The value of b obtained from the fit of the experimental data is 1.26. 3.3. Determination

of intercrystalline

barrier height

The Zn,Cd, _,Se films studied here have a polycrystalline texture. Therefore, the grain boundary scattering will play a dominant role in describing the electron transport processes in the films. Because the films were highly resistive, measurement of the Hall mobility at low temperatures to generate data for analysis of the grain boundary effects were extremely difficult. The carrier concentration N, the intercrystalline barrier height E,, and trap state density Q, in the Zn, Cd, _ ~ Se films were determined by an optical technique [20] which utilizes a modified version of the Dow-Redfield model [21, 221 and has been briefly described here. The excess absorption in a polycrystalline semiconductor at energies less than the band gap energy is described by the Franz-Keldysh effect arising out of the built-in electric field in the material. The FranzKeldysh effect may be described by using the model of Dow and Redfield [21, 221, which was modified by Bujatti and Mercelja [23] for spherical grain distribution. In Zn, Cd, ~.~Se films, we have columnar grains,

\ \

0.2

o - Experimental

points

_---

Theo. with

cXE

-.-.-

Theo.with

AM

-

Theo.with

total

‘1

I 0.05

0

Eg-

(X

I 0.10

hJ(eV)

Fig. 8. Plot of r/cc0 vs. (E, - hv) for a representative film (x = 0.37): 0, experimental points, -, theoretical best fit with K = 0.32 nm-’ and F,=2.94 x IO’Vcm~ (considering both uE and r”); .-.-, plot with only tiE. theoretical plot with only a”; -~ -, theoretical

which may be assumed to be made of stacked circular discs. The electric field F(r) within the crystallites may be assumed to vary exponentially and, considering the presence of a depletion region with a width of about 1, at the surfaces of the circular discs of radius L, the electric field within the grains may be represented by F(r) = F, exp[ -(L

- r)K]

(7)

where K is the inverse of the Debye length (1,) and F, is the field present at the surface of the grain. We have that F, is independent of the crystallite size and is given by

F,& E

where E is the static dielectric constant, K is the inverse of the Debye screening length (&), Q, is the density of trap states at the grain boundaries and q is the electronic charge. This form of field distribution is a generalized form with which one can describe both partially and fully depleted conditions of the grains. The depletion at the grain boundary regions results in the band bending and, as a consequence, it would affect the optical absorption below the band edge. Following Bujatti and Marcelja [23], the total absorption A(hv) at a photon energy hv (considering the region hv < E,) normalized to the total absorption at the band gap (A,) may be expressed as

P. Gupra et 01. / Thin Solid Films -760 (I 995) 75 OX_5

0

0

assuming columnar grains of radius L and of equal height Where, P(L) is the probability of a crystallite having a radius L. It can be noted here that a in Eq. (9) is a function of both the photon energy and electric field in the crystallites. Thus, ar(F, kto) may be expressed in its generalized form as -I#‘? rA”(F, h(Q) = I(F, h(lI)L~

(10)

_I’< =

;’

.I“7= I,, = I

with

(11) In

=

81

m. Q(.& + Z4C,) m. 1 12(E, + 2A,,/3) (--IT?‘. 1

(12)

Here. IVES,m, and m,, are the free and effective masses of an electron and a hole, respectively, A0 is the spin-orbit splitting factor, n is the refractive index and c is the velocity of light. The subscript zero indicates quantities at the energy gap (f&). To include the contribution of different grain sizes to rx, we have assumed a distribution of grains [6] given by P(L) = (L - L ,,,,,,1 (L,,,

- L) exp -$ (

1

(13)

where L,,, = L + (5, L,,, = L - 6, c = (L,,, + L,,,)/2 and zi( = 0.76L) is the half-width of the distribution of L. This probability function P(L) increases rapidly for small values of L and then decreases with a Gaussian tail for large values of L. Using Eqs. ( 10) -( 13) the final form of Eq. (9) becomes A

24’(ho)

A,-

30t’

(:)[($ -

or

(15)

“‘(yF,)~“‘(E,-~w) ;, 113K-2/i(Es _ fit,])113 at hco = E,

It may be observed (Fig. 8) that Eq. ( 15) alone cannot describe the experimental observations. This would mean that contributions from additional sources to the absorption coefficient have to be taken into account to describe the experimental data accurately. Thin films are generally characterized by the presence of a large number of defects and the existence of high stress. Therefore, in addition to the grain boundary electric field effect considered above, the mechanical stress resulting from lattice dilation at the grain boundary regions should be considered, which may cause permanent lattice disorder (in the grain and grain boundary region) and temperature lattice disorder. Thus, the stress will affect the electronic structure and, hence, the optical absorption processes below the band edge, in general. The effect of the mechanical stress in the grain boundary region of polycrystalline films had been associated with the electrostatic fluctuations of the band edge by several authors [24-261. To calculate the abosrption resulting from the mechanical stress, we first consider the variation of E, in various sites of the specimen. using the distribution function [25] D(E,)

= exp[lw’j

(16)

where (r2 = E,’ A.‘, ii’ z u/4L,, with L, being the characteristic length over which Eg is assumed to be constant, and u is the average lattice constant. For polycrystalline materials, L, is approximately the same as the dimension of the microcrystallite i.e. L, z 2L, with L being the average radius of the crystallites. Physically, the parameter A is a relative local and thermal fluctuating dilation constant, and depends on the grain size and shape of the polycrystalline film and its lattice temperature [25]. We have that the general form of the absorption coefficient r M (tzc,~) resulting from mechanical stress may be expressed as

P. Guprcret al./ Thin SolidFilms 260 (1995) 75-85

82

s x

a”(ho)

-

10'8

KW(E,)

dE,

Zn,

(17)

/I,,,

where D(E,) dE, is proportional to the number of microcrystallites per unit volume, and P(E) is the probability of indirect transitions within the region of the sample in which the energy gaps are between Eg and

Cdl-x

Se

O-From

optical

A-From

TEP 0 0

;

Eg+dEg.

A

A

0

OA

A

By assuming the form of P(E) as given by Szczyrobowski [25], i.e.

00

A

A

P(E) = P,, exp[(hwi

“‘1

(18)

where

and substituting Eq. ( 16) in Eq. ( 17), the final form of CIM(h~) after simplification becomes

a”(ho) = cdpexprs

E”)] @(ho)

(19)

0

0.2

0.4 X

0.6

0.8

1.

Fig. 9. Plot of carrier concentration N as a function of x in Zn,Cd, _, Se film: 0. from optical studies; A, from TEP measurements.

where $’ is the value of cr”(Am) at E,, E,, = E, - c~‘/ 2E’ and @(ho) is a slow varying function written as i* @(ho) = Eg-’ {exP[-(&)]dE,

(20)

It has been%entioned earlier that direct transition was observed in our Zn, Cd, _ .~Se films for all the compositions for tiw 3 i$,, with & being the average value of the fluctuating Eg values in the grain and grain boundary regions. However, in the photon energy region tzw GE,, besides the allindirect transitions also owed direct transition, may occur simultaneously in these polycrystalline films. Then, the function @(ho) in Eq. (20) may be assumed to be almost constant and its explicit form is

-II rntn

x exp( -x213) dx

(21)

with x,,,,,, = 6m, ho/h2K2 and xmax= 6m, Eg/h2K2. In a real situation, the inclusion of a finite grain size distrubution, as given by Eq. ( 13). will modify the expression of a”(ho), i.e. Eq. (19), as cc”(ho) = a? exp[(hw - E,)/C,,]B(L)@(L,ho)

where

E

bll,x

B(L) z

(22)

The inclusion of the grain distrubution has been found to modulate this function over a very negligible order. Using Eqs. ( 15) and (22), one can obtain the total absorption below the band edge (c( = ~1~+ a”) and, hence, Z/CX~resulting for grain boundary effects. The best fit of this simple theoretical model to the experimental points will provide meaningful information on the grain boundary potential E,,, density of trap states (Q), carrier concentration N, etc., in the polycryslline films. Thus, a/a0 was evaluated numerically as a function of hv, by adjusting the parameters K and F,. The experimental plot of a/cc0 vs. hv is shown in Fig. 8 for a representative film, along with the theoretical plots. The effect of strain in the film is evident from the significant difference between the theoretical plots drawn considering only electrical (cz”) and total (aE + a”) values. The best fit obtained in this way considering both CC~and aM gives the values of K and F,. The values of the barrier height Eb and trap state density Q, may be obtained from h

=yF,

exp( - Xo)L2 dL Q, =:

K

(23)

83

P. Guptu et al. 1 Thin Solid Films 260 (1995) 75 85

Table 1 Values of the barrier height Ehq density of trap states Q,, average grain size L and Debye length i, for different Zn,Cd, ~_, Se films Sample no.

.Y

o.o!,

CZS-3 CZS-4 czs-8 czs-9 czs-I czs-I czs- I I

0.37 0.52 0.5X 0.66 0.70 0.9 I

*d

(cm-2)

(nm)

(nm)

0.64 0.95 1.10 2.80 0.82 0.90 0.70

142 123 120 114 III 116 108

3.73 3.13 2.99

Q, x

(eV) 0.062 0.092 0.102 0.131 0.056 0.035

0.028

lo-l2

L

4,

Zn, Cdt_x

0.17 0.16t

Se

0

From

Eg

A-

From

Eb

I .58 2.26 1.28 1.38

X

Fig. 11. Variation optical band gap men&.

of m,/m, vs. .Y for Zn, Cd, , Se films: r>. from measurements; .I, from barrier height measure-

,g 2.0 " 2

1.6

-3 'z 1.2 L: 0.8

0

0

0.02

0.04

0.06 0.08

0.10

0.12 0.14

r-(/urn) Fig. 10. Variation of electric field F within grains for three representative Zn, Cd, ~, Se films with (a) x = 0.09, (b) x = 0.37 and (c) x=0.91: 0. L=O.l08pm; A, L=O.l25pm: 0, L=O.l40pm.

The values of & and Qt for different x values, obtained from Eqs. (23) and (24), are given in Table 1. It may be noticed that E,, varies in the range 0.030.1-I eV for different x values in Zn, Cd, _-xSe films, whereas Q, varies from 7 x 10” to 2.7 x lOI cmd2. 3.4. Determination

qf the

carrier density

For highly resistive films, such as Zn, Cd, _ _~Se, the determination of the carrier concentration N from Hall measurements is practically difficult and uncertain. The density of charge carriers may be determined from the value of the Debye length Ad, obtained from optical measurements by using the relationship (25)

where k is the Boltzmann constant and E is the dielectric constant, q being the electronic charge. The values of the Debye length 1, in our films are shown in Table 1 for different values of x. The carrier concentration (N) values obtained from these I, values are shown in Fig. 9. We also have determined the carrier concentration for the Zn,Cd, _ r Se films from thermoelectric power (TEP) measurements, by considering the effect of the grain boundary barrier height on the TEP data, similar to the corresponding effect reported earlier for CdS, Te, ~, films [27]. Our results showed good agreement with those obtained from the optical measurements (Fig. 9). It may be noted from Fig. 9 that N varied between 5 x IOih and 3 x lO”cmwith an increase in x. We also have studied the variation of the built-in electric field Fin the film. We have that the variation of the electric field F within a grain depends on the value of Ad. Using Eq. (7), we can determine the value of Fat different distances r from the centre of a grain. Fig. 10 shows a plot of the variation of F with r for three Zn,Cd, _,Se films with different grain sizes. It may be observed from this figure that the field F increases sharply at the grain boundary for different x (or zinc content) values of the Zn., Cd, ~Se films. The average grain size t values for different values of x (obtained from SEM, TEM and optical studies) are given in Table 1. It may be noted that L >>i, in our films, which indicated partially depleted grains. 3.4. Determination

of’ eflective

mass qf‘ the carriers

The barrier height Eb in a polycrystalline film is given by [211

84

P. Gupta et al. / Thin Solid Films 260 (1995) 75-85

lop)“2($$

Eb = 2.58 x

where (27) so that the effective mass ratio (m,/m,) may be obtained if B is determined from the intercept of the plot of In(&) vs. In(hv - E,) using Eq. (5) for direct transitions. The values of m, for Zn, Cd, _ x Se films, obtained as above, are plotted in Fig. 11 as a function of x. It is interesting to note that the values of m,, deduced from the above consideration, may be fitted to the empirical relation m,(x) = m,, + (me2 - m,, - b&c + b2x2

(&1 0

f(m,)

(29)

where f(m,) = me/( 1 - m,). For materials with m, <<1, .f(mJ = m,, so that m, values also may be generated from E, for all the films studied here (Fig. 11). The values of m, generated from Eb and Eg values tally closely with one another, showing that f(m,) z m, is valid in these films. Thus, the effective mass bowing parameter b, may be related to the optical band gap bowing parameter b by b2 =

b (p2Pme)

served.

Acknowledgment

Two of us (P. G., B. M) wish to thank the C.S.I.R., Government of India, for awarding fellowships during the tenure of this research programme.

(28)

showing a bowing phenomenon in m,(x). The value of 6, generated from this plot (Fig. 11) is about 0.053. We have that the band gap Eg may be expressed in terms of the effective mass m, as

Ed=

the grain boundary parameters, i.e. barrier height E,, trap state density Q, and carrier concentration N, in the Zn, Cd, _ r Se films were obtained from optical measurments, by considering the columnar growth pattern. The effect of mechanical stress on the absorption coefficient was considered along with that resulting from the built-in electric field within the grains. A significant contribution resulting from stress in the film was ob-

(30)

This relationship was observed to be valid for several other ternary semiconductors 1281.

4. Conclusions The optical properties of Zn, Cd, _-r Se films were determined for different x values. The optical band gap E,(x) and the effective mass of an electron m,(x) showed bowing effects, with bowing parameters which indicated good agreement with each other, although these bowing parameters were slightly higher than those reported earlier for single-crystal Zn, Cd, _ x Se. SEM of the films indicated a rough surface. The roughness was found to vary within 9-13 nm. The films have a predominantly wurtzite structure for x < 0.5 and a zinc blende structure for x > 0.7, while a mixed structure was observed in the range 0.5 < x < 0.7. The grain boundary effect in the Zn, Cd, _ x Se films was analyzed by a modified version of the Dow-Redfield model, and

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