CHAPTER IV

OPTICAL STUDIES ON INDIUM OXIDE, TIN OXIDE AND INDIUM TIN OXIDE

THIN FILMS

4.1 Introduction

Optical thin films are widely used in opto-electronic devices such

as solar cells, electrodes in liouid crystal displays, and transparent heating

elements. Reflection, transrr~ission and absorption and their relations to

optical constants are matters of interest for experimental and theoretical

investigations. The optical parameters like absorption coefficient, optical

band gap and refractive index can be determined from transmittance as

well as absorbance measurements. The deposition conditions and post

deposition annealing treatments are the factors that determine the optical

properties of transparent conducting oxides. '" In this chapter the optical

properties of indium oxide, ;in oxide and indium tin oxide thin films are

dealt with.

4.2 Theory

The optical properties mainly depend on the refractive index of the

material and thickness of the film. In the case of an absorbing material the

refractive index which is a complex quantity is given by N = n+ik, where n

is the real quantity of refractive index and k is the extinction coefficient.

The physical significance of k is that on traversing a distance in the

medium equal to one vacuum wavelength, the amplitude of the wave

decreases by the factor exp (-21cik). There are different methods to

measure n and k, which are given by Heavens. 4,

Manifacier et proposed a simple method for the determination

of the optical constants n, k and thickness t of a weakly absorbing film. An

absorbing medium bounded 3y two transparent media with refractive

indices no and nl is shown in Figure 4.1. The amplitude of the transmitted

wave is given by

t , t , exp(-i2nnVh) A =

1 + r,r, exp (-i4x nVh"

In which t,, t2 r,, and r2 are tr;insmission and reflection coefficients at the

front and rear faces respectively. The transmission is given by

In the case of weak absorptioj? k2 << (n-no) and k2<<(n-n,)2

Where c, = (n+no) (n+nj), c2 := (n-no) (nl-n) and

a, = exp (-4xkktlh) = exp (-at) ------------ (4.4)

where a is the absorption coefficient of the thin film. Outside the region of

fundamental absorption, the dispersion of n and k are not very large. The

maximum and minimum of T in equation (4.3) occurs for

where m is an integer.

The extreme values of the transmission are given by

Fig. 4.1 Reflection and iransmission of light by a single thin film

no A

V +a

N= n-ik

w 11 1

v

Considering T,, and Tmi, as continuous functions which are the

envelopes of maxima T,,(ht and the minima Tmi,(h) in the transmission

spectrum as shown in Figure 4.2. The ratio of the equations (4.6) and

(4.7) gives

Substituting equation (4.8) in equation (4.6) gives

2

where N= + 2nO1t, ;- T,,, - T,, 2 ,rnX TI""

From equation (4.9) n is aetermined knowing T,,, Tmi, and no at the

same wavelength.

The thickness t of th~s film can be calculated from the two maxima

or minima from equation (4.5).

Fig. 4.2 Plot of Percentage of transmission as a function of wavelength for tin oxide film of thickness 350 nm.

Where m is the number of os;cillations between two consecutive maxima

and minima. hl, n (XI) and h2, n(h2) are the corresponding wavelengths

and refractive indices.

Knowing n and t, wr? can determine a using equations (4.4)

and (4.8).

For a film of thickness t, a is given by

where T is the transmittance and A ,the absorbance.

Using the values of a and t, we can calculate k from equation (4.4).

Care should be taken in using the above method: (1) The samples must

be homogeneous and parallel faced, (2) The variation of n and k with the

wavelength should be small; this condition fails in the vicinity of

fundamental absorption in short wavelength region, (3) The effective band

width of the spectrometer should be kept smaller than the half width of the

interference maximum.

4.3 Determination of Energy Band Gap

The most direct method for probing the band structure of thin film

semiconductors is the st~rdy of the optical transmission/absorption.

From the frequency dependerice of it, we can determine the energy gap

of the material.

The absorption and dispersion of a plane electromagnetic wave is

described by the complex refractive index N = n + ik, where n is the real

refractive index and k is the extinction coefficient. The plane wave can

be represented by

where K is the propagation wzve vector K = K1 + iK2

Equations (4.13) and (4.14) form a solution of Maxwell's equation

for the electromagnetic field i r~ a medium of magnetic permeability unity, if

K. K = W'E /c2

where c is the velocity of light.

The complex dielectric: constant E which includes the effects of the

conduction and displacemem: current is defined as

2 . . The complex refractive index N is also defined by E = N glvlng

E~ = o / m 0 = 2 nk

In the case of homogene3us plane waves

K, = n d c

K2 = k&

Substituting in equation (4.13), we get

Ex = Eo exp [io(nx/c -t] exp (-d<x/c) ........ (4.17)

This equation represents a wave with a velocity c/n which is

attenuated by exp(-okxlc) travelling in x-direction. The absorption

coefficient a, defined by the relative decrease of the intensity per unit

distance in the direction of propagation is

In the case of direct band transition the valence band maximum

and the conduction band minimum appear at the same point in the

Brillouin zone at k = 0. Figure 4.3 shows the direct vertical optical

transition near the fundamental absorption edge.

The direct band gap is estimated from the relation7

Fig. 4.3 Direct transition frorn the valence band to the conduction band.

where a is the absorption coefficient of the photon of energy hv and C

A =-; A being a constant. Ttie procedure consists of plotting a2 vs hv

hv

and extrapolating the linear region to the energy axis; the intercept

being identified with the bancl gap.

When a transition requires a change in both energy and

momentum, a double transition process is required because the photon

cannot provide a change in momentum. This situation is overcome with

the emission or absorption cd phonons. Momentum is conserved via a

phonon interaction as illustratt?d in Figure 4.4.

The indirect band gap is determined from the relation

There is a shift in the band gap towards higher energy for the film

having higher carrier density This shift is due to the filling of the states

near the bottom of the condm~ction band and is known as the Burstein-

~ o s s ' , ~ shift and is illustrated in Figure 4.5. The shift is given by the

relation.

where Ego is the intrinsic band gap and A E ~ ~ is the BM shift. The shift is

related to the carrier density as

Fig. 4.4 Indirect transition from the valence band to the conduction band

l a )

undoped l b )

heavlly doped

Fig. 4.5 Illustration of Burstein-Moss shift.

where m* is the reduced effective mass.

4.4 Indium Oxide

Indium oxide thin film:; are evaporated using the vacuum coating

unit from a tantalum boat. The details of the plant are described in

Chapter 2 (Section 2.13). Spectroscopically pure indium procured from

the Nuclear Fuel Complex, Hyderabad is used as the source material. It is

evaporated from the tantalum boat. A base pressure of 2 x 10 .~ mbar is

obtained using the rotary ancl diffusion pumps. Pure oxygen is admitted in

to the chamber using the needle valve of the plant. The evaporation is

carried out at different constant oxygen partial pressures. Glass slides

have been used as the substrates.

The glass slides have been cleaned using the cleaning procedure

described in Chapter 2 (Section 2.15). The substrate temperature is

varied using a substrate heater and the temperature is measured using a

previously calibrated chrcmel alumel thermocouple. The rate of

evaporation and thickness of the films are controlled by using a quartz

crystal thickness monitor. The thickness of the films are counter checked

by using the multiple beam interference techniquei0. The rate of

evaporation is 13-1 5 nmlmin.

The samples are annealed in a furnace for 30 minutes at 300°C.

The UV-visible spectrum of the sample is recorded using the double beam

spectrophotometer (Shimadzu 160 A).

4.4.1 Results and Discussion

Figure 4.6 is the plot of percentage of transmission as a function of

wavelength for indium oxide thin films of thickness 250 nm. It is observed

from the transmission spectrum that the film is highly transparent

throughout the visible region. For wavelength below 400 nm, the

transmission falls rapidly due to the band-to-band absorption. The

average transmittance in the visible region is above 80%.

Using the equation (4.9), the refractive index in the visible region is

calculated as a function of wavelength for indium oxide films. Figure 4.7

shows the refractive index and extinction coefficient of the film as a

function of wavelength.

The transmission treasurements are carried out for different

samples and the interference patterns are found sensitive to the thickness

of the film. In order to (observe interference pattern the extinction

coefficient k of the film sbould be small enough to allow the light to

transverse the sample several times. For these films k is small in the

visible region and it increases as the absorption edge is approached.

Therefore, the determinatior~ of the refractive index is limited to the visible

region only.

Fig.

Wavelength (nm)

4.6 Plot of percentage of transmission as a function of wavelength for indium oxide film of thickness 250 nm.

Fig 4.7 Plot of n and k vs h for indium oxide thin film

~ o l z e n " observed variation of refractive index with wavelength

and annealing conditions and obtained a refractive index 2 at 550 nm.

~ i s u h a s h i ' ~ obtained the refractive index as 1.96 and extinction

coefficient as 0.13 at 500 nm. ~ a s e e m ' ~ also reports the value of

refractive index as 2.0.

The transmission spectrum of samples deposited at different

oxygen partial pressures are obtained. The thickness of samples are

120 nm each. Oxygen partial pressures has a prominent role in

transmittivity. Using the assumption that the transition probability

becomes constant near the absorption edge and neglecting reflection,

the absorption coefficient fo' the direct allowed transition is determined

from the relation.14

where T is the transmission and t is the thickness of the film.

Figure 4.8 shows the dot of a2 vs photon energy for indium oxide

films deposited at a substrate temperature of 2 0 0 ' ~ and at different

oxygen partial pressures. Extrapolation of the linear region of the graph

gives the band gap. The values are given in Table 4.1.

Fig. 4.8 Plot of a2 vs hv for indium oxide thin films deposited at various qsures. oxygen partial pre.

Table 4.1. Variation of direct band gap with oxygen partial pressure for indium oxide films

For the indirect band transition the photon energy dependence of the

absorption coefficient near the absorption edge is given by a = C(hv - E,)'.

Figure 4.9 shows the plot of a'" vs photon energy. The linear portion is

extrapolated to zero absorption to obtain indirect band gap. It is given in

Table 4.2.

Oxygen partial pressure (xlo4 rnbar)

Table 4.2 Variation of indirect band gap with oxygen partial pressures for indium oxide thin films

Direct band gap (eV)

3.12

3.67

3.79

3.90

It is difficult to give a satisfactoly explanation for the high

absorption because oxygen vacancies and occupying atoms are

Oxygen partial pressure (x104 mbar) Indirect band gap (eV)

2.45

2.56

2.63

2.80

Fig. Plot of vs hv for indium oxide thin films deposited at various oxygen partial pressures

responsible for light absorption. Still it may be due to the polycrystalline

nature of the sample.

With the increase of substrate temperature, the tranmissivity shows

improvement. Table 4.1 shorn's the values of direct optical band gap for

indium oxide films deposited at various oxygen partial pressures. The band

gap is found to increase with oxygen partial pressure. When the oxygen

partial pressure is increased, transformation of In0 to ln203 is accelerated.

The variation of o12 vs hv of annealed samples (300°C for one hour)

are plotted in Figure 4.10. The variation of optical band gap is determined

and is tabulated (Table 4.3).

Table 4.3 Variation of Direct band gap with oxygen partial pressures (annealed)

The variation of indirect band gap with thickness is shown in Figure

4.1 1. The values obtained are given in Table 4.4.

Fig. 4.10 Plot of or2 vs hv of annealed samples of indium oxide thin films For different partial pressures of oxygen

Fig.4. 11 Plot of vs hv for different thicknesses for indium oxide thin films at a constant substrate temperature of 200' C.

Table 4.4 Variation of lndirect band gap with thickness

The variation of a2 with photon energy for indium oxide annealed

for different intervals of tirrie keeping the annealing temperature (TA)

constant at 350 '~ is studied. (Figure 4.1 2) The direct band gap is found in

each case and is given in Table 4.5.

Thickness (nm)

140

150

Table 4.5 Variation of Direct band gap with annealing time

Indirect band gap (eV)

2.39

2.47

2.59

2.63

el ling ham'^ reports ?hat the absorption coefficient a depends on

the details of the matrix elements and of the band structure, which are still

not fully known.

Annealing time (minute!;)

As deposited

40

The improved transmissivity with increase in substrate temperature

is due to the disappearance s~f non-stoichiometric disordered structure.

Direct band gap (eV)

3.55

3.72

3.81

3.96

Fig. 4.12 Plot of a2 vs hv for indium oxide thin films annealed for different intervals of time at constant thickness of 120 nm.

4.5 Tin Oxide

Spectroscopically pure tin powder is procured from Nuclear Fuel

Complex, Hyderabad which is used as the source material for evaporation.

In the vacuum coating unit a vacuum of 2 x mbar is obtained with the

help of a rotary vacuum pump and 12 inch diffusion pump. Oxygen is

admitted through the needle valve. Tin is evaporated in an oxygen

atmosphere. The substrates are glass slides. The substrate temperature is

varied using a substrate heater. The temperature is measured using a

calibrated chromel-alumel thermocouple, which is attached to the

substrate. Evaporation is controlled within the range 7-8 nmlmin.

The thickness of the films and rate of evaporation are controlled by

using the quartz crystal thickness monitor and are counterchecked by the

multiple beam interference technique. The films are subjected to post

deposition annealing in air. A double beam spectrophotometer (Shimadzu

160A) is used for recording tlie UV-visible spectrum.

4.5.1 Results and Discussion

Figure. 4.13 represents the variation of the % transmission with

wavelength for a typical tin oxide thin film of thickness 250 nm.

The refractive index and extinction coefficient for the film deposited

at 275OC and having thickness 250 nm are calculated in the visible region

using equations (4.9) and (4.4). Figure 4.14 is the plot of refractive index

and extinction coefficient as a function of wavelength.

100 _ _ _ _ _ ----- / , , _ _ _ _ - - - - - - - -

80

s r 60 0 .- 3 .-

40 c ? C

20 PA, 200 300 400 500 600 700 800 900

Wavelength (nm)

Fig. 4.13 Plot of percentage of transmission as a function of wavelength for tiri oxide film of thickness 250 nm.

Wavelength (nm)

Fig.4.14 Plot of n and k vs h for tin oxide thin film

Figure 4.15 is the plot of o12 vs hv for the samples deposited at

substrate temperatures 200,225, 250 and 2 7 5 ' ~ and annealed in air for

30 minutes at 3 0 0 ~ ~ . Extrapolating the linear portion of the graph gives

the direct band gap. The values of direct band gap obtained are listed in

Table 4.6.

Table 4.6 Variation of direct band gap with substrate temperature for tin oxide thin films

Substrate temperature (OC) Direct band gap(eV)

3.86

275 3.97

Figure 4.16 represen1:s the variation of band gap with oxygen

partial pressure for films annealed at 3 0 0 ' ~ for 30 minutes. The values of

band gap are given in Table L..7.

Table 4.7 Variation of direct band gap with oxygen partial pressure for tin oxide thin films

Oxygen Partial Pressure (XI o4 mbar) 1 Direct band gap(eV) I

Fig. 4.15 Plot of a2 vs hv for tin oxide thin films deposited at various substrate temperatures and annealed

Fig. 4.16 Plot of a' vs hv for tin oxide thin films annealed at 300°C for minutes.

The indirect band gap of the sample is calculated using the relation

CL = C(hv - E~)'. Figure 4.17 shows the variation of a"' with photon

energy. Extrapolating the linear portion yields the values of indirect band

gap. Table 4.8 gives the values of indirect band gap.

Table 4. 8 Variation of indirect band gap with oxygen partial pressure for tin oxide thin films

Oxygen Partial Pressure (x104 mbar) / Indirect Band gap(eV) I

The high absorption coefficient observed for the tin oxide thin films is

due to the polycrystalline natk~re of the sample, which is evident from the

X-ray studies.

The direct band gap 0.' tin oxide reported by spenceI4 is 4.3 eV.

Reddy and Chandorkar have obtained a value of 3.leV for the band

gap. Sundaram and ~hagava t '~ report the direct band gap as 3.95 eV.

Band gap of 3.93 is obtained by Summit." In the present study, the direct

band gap obtained is 3.79 e\ l at an oxygen partial pressure of 2x10

mbar. The variation of band gap with substrate temperature is due to the

Burstein-Moss shift.

opp = l x l 0 ~ ' n b a r 7 " 2 "

" 4 "

A " 5 "

Fig. 4.17 Plot of vs hv for tin oxide thin films deposited at different oxygen partial pressures

Many workers have reported the indirect band gap of tin oxide.

Sundaram and ~hagava t ' ~ have obtained a value of 3.27 eV and Tarey

and !3aju2' report the value as 3.415 eV. spence14 has obtained a value

of 2.7 eV.

For single phonon eneIFgy a"' vs hv plot has two straight-line

regions corresponding to indirect band gap (Eg + Eph) and (Eg - Eph).

~~n iho t r i " obtained EPl, as 0.005 eV. The transition is assisted by 11

optical modes and many accou:;tic modes.

4.6 Indium Tin Oxide

Indium tin oxide films have been prepared using the vacuum

coating plant by reactive thermal evaporation using a tantalum boat.

The details of the plant have been given in Chapter 2 (Section 2.13).

The procedure of making alloy of indium and tin is given in Chapter 3

(Section 3.5.1).

Cleaned glass slides have been used as the substrate onto which

a calibrated thermocouple is attached. The substrate temperature is

varied using a substrate heater. Thickness and rate of evaporation are

controlled using the quartz crystal thickness monitor. The rate of

evaporation is 13-15 nmlniin. The UV-visible spectrum of the

sample has been recorded using the UV-visible double beam

spectrophotometer (Shimadzu 160A).

4.6.1 Results and Discussion

Figure 4.18 is a typical graph representing the variation of

percentage of transmission vs wavelength for indium tin oxide thin film

having thickness of 200 nm.

Figure 4.19 shows the variation of refractive index and extinction

coefficient of the above sample with wavelength.

It is observed from the transmission spectra that the film is

transparent throughout the visible region. The average transmittance

in this region is above 80%. For wavelength below 400 nm the

transmission falls rapidly. The transmission is found to increase with

annealing.

The direct band gap of the films can be calculated from the

transmission data in the lower wavelength region. By extrapolating the

linear portion of the u2 vs photon energy graph gives the direct band

gap of the sample. Figure 4.20 is the plot of a2 vs hv from which the

direct optical band gap is calculated. The optical band gap (E,) for a

film annealed at 3 5 0 ' ~ for 20 minutes is 3.86 eV. Table 4.9 gives the

values of direct band gap for different annealing time.

Wavelength (nrn)

Fig. 4.18 Plot of percentage of transmission as a function of wavelength for IT0 thin films of thickness 200 nm.

Wavelength (nm)

Fig. 4.19 Plot of n and k vs h for IT0 film

. tm= 10% da120nm I a s deposhed

a annealed for20 mts at 3 5 0 ' ~

30 "

40 "

0

Fig 4.20 Plot of a2vs hv for indium tin oxide thin films with 10 % tin concentration

The indirect band gap of the fillns are calculated using the relation

Table 4.9 Variation of direct band gap with annealing time.

a = C (hv-E,)

Extrapolation of the linear portion of the $h vs hv graph (Figure

4.21) gives the indirect band gap. The indirect band gap obtained for the

samples is given in Table 4.1 Ci.

Annealing time (minutes)

40

Table 4.10 Variation of indirect band gap with annealing time for IT0 films

Direct band gap(eV)

3.77

3.86

3.93

3.97

The effect of doping of tin is studied. The results are shown in

Figure 4.22. Films of thickness 100 nm are used for the study. The doping

Annealing time (minutes)

As deposited

20

percentage is varied. (5%, lo%, 15% and 20% of tin). The band gap

Indirect band gap (eV)

2.18

2.31

Fig 4.21 Plot of a0.5vs hv fcr indium tin oxide thin films with 10% tin concentration

h v (eV)

Fig 4.22 Plot of a2vs hv for indium tin oxide thin films having different tin concentrations

calculated for these samples is given in Table 4.1 1. A band gap of 3.85

eV is obtained for indium tin oxide film at a doping of 5% tin.

Table 4.11 Variation of direct band gap with doping.

Doping %(Tin) Direct band gap (eV)

Weijtens and anl lo or?^ obtained the band gap of 3.53 eV. Wu 23

has reported a value of 3.57. Ray obtained the direct band gap 3.8eV

for IT0 films. Indirect band gap of 1.80 eV is reported by Weijtens and

anl loon.^^ Thilakan and Kumar obtained a value of 3.83 eV for direct

band gappg.

Studies on the direct band gap show an increase in band gap with

doping percentage.

The refractive index shows an increase in wavelength while the

extinction coefficient shows decrease with the wavelength. wup3 obtained

the refractive index and extinction coefficient as 2 and 10.~. 0esterleinp4

reports the value of refractive index 2 for IT0 films. Pommier et abp5

obtained a value of 1.8. The refractive index is not an intrinsic property of

IT0 but depends on the deposition conditions. Martin et a/." report the

refractive index and extinction coefficient as 1.8 and 0.025 respectively for

IT0 films. Habibi and Talebian report a value of 1.61 for refractive index

of IT0

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