151

CHAPTER-6

GROWTH AND CHARACTERIZATION OF STOICHIOMETRIC PbS

THIN FILMS

This chapter presents the details of sample preparation and characterization of

stoichiometric thin films lead sulphide (PbS). In this chapter, we present the detailed

investigations on the characterization of PbS thin films during the course of research

work. X-ray differection (XRD), UV-Visible spectroscopy, scanning electron microscopy

(SEM) with EDAX, Atomic force microscopy (AFM) and I-V measurements have been

used to investigate the optical, structural, surface morphology and electrical studies of

vacuum evaporated PbS thin films deposited without and with H2S atmosphere.

152

CHAPTER-6 GROWTH AND CHARACTERIZATION OF STOICHIOMETRIC PbS THIN FILMS

6.1 Introduction:

The binary IV-VI compounds formed from Pb and group VI elements like S, Se

and Te are among the oldest known semiconducting materials and have been used for

many years for electronic & optoelectronic device applications. The first ever reported

solid state diode was made from single crystalline PbS and its rectifying properties were

exploited in early radio receivers. Later on, interest in IV-VI semiconductors shifted to

mid-infrared optoelectronic device applications such as photon detectors operating in the

3-14 µm wavelength range, taking advantage of the narrow band gap between valance

and conduction band of the IV-VI compounds. Recently IV-VI multi-quantum well

structures have also attracted a lot of attention for their potential as efficient thermo-

detective devices [1].

Lead sulphide (PbS) is unique interesting semiconductor due to its technological

importance in I-R field sensitive devices widely used as infrared sensor due to its 0.4eV

direct band gap [2-4]. The large excitation Bohr radius of PbS (i.e.18nm) [5], results in

strong quantum confinement of both electrons and holes in nano-sized structure, so that

the value of the band gap can be controlled by modifying particle size according to the

effective mass model [6]. This material has also been used in many fields such as

photography [7]. This property of PbS makes it desirable and attractive for new

applications such as solar cells [8,9] In addition, PbS has been utilized as photoresistance,

diode lasers, humidity and temperature sensors, decorative and solar control coatings

[10,11] fabricated near infrared (NIR) active solar cells based on PbS quantum dots and a

conventional conjugated polymer [12]. Thin films of PbS have been prepared by different

153

workers using various techniques such as spray pyrolsis [13], chemical vapor deposition

[14], chemical bath deposition [15-18], successive ionic layer and reaction (SILAR) [19,

20], atomic layer deposition [21], and vacuum evaporation [22]. The structural, electrical

and optical properties of vacuum deposited thin films of sulphide semiconductors are very

sensitive to the deposition conditions [23]. Stoichiometry can be restored by several

techniques as by, co-deposition of sulphur together with PbS [24] and depositing the film

in a controlled hydrogen sulphide atmosphere [25]. The deposition of sulphide

semiconductors in a controlled H2S ambient atmosphere yields better crystallinity,

orientations and pin-hole free films, which would be of great importance in device

fabrication.

The present chapter deals with the deposition of PbS thin films by evaporation of

powdered PSb material without and with H2S atmosphere under vacuum. The

compensation the sulphur deficiency in vacuum evaporated PbS thin films has been done

by exposing the film to a H2S ambient atmosphere during deposition in same manner as

in case of vacuum evaporated CdS and ZnS thin films as discussed in chapter 4 and

chapter 5 respectively. The higher reactivity of hydrogen sulphide will ensure a better

conversion of the dissociated cations (Pb ions) into compound sulphide semiconductors

(PbS) and also will not produce any excess of sulphure at the substrate.

6.2 Sample preparation:

In the present work the thin films of lead sulphide have been deposited by thermal

vacuum deposited technique onto highly cleaned glass and quartz substrates. For

comparison, films of PbS are deposited without and with H2S atmosphere. For sample

preparation lead sulphide powder (99.9%) of sigma Aldrich Company was used to

evaporate in deep mouthed molybdenum boat. The deposition takes place in a vacuum of

the order of 10-5 torr. H2S atmosphere was obtained by controlled thermal decomposition

154

of thiourea inside the vacuum chamber. For ambient atmosphere of hydrogen sulphide a

borosil test tube was used for the thermal decomposition of thiourea at 150ºC, it was

separated from the PbS molybdenum boat by a stainless steel heat shield. Before

deposition keeping the substrates at an elevated temperature of about 200ºC helps to eject

any sulphur atoms deposited due to thermal decomposition of PbS during evaporation.

The lead ions promptly recombined with the H2S it give better stoichiometry of the

deposited films. The general detailed summarized flow diagram of above used modified

thermal vacuum deposition technique for deposition of stoichiometric sulphide

semiconductors films has been discussed and illustrated in figure 2.5 of chapter 2 of the

thesis.

6.3 Sample Characterization:

The optical properties of as-deposited films especially absorption and transmission

have been evaluated at room temperature by spectro-photometric examination. Structural

analysis has been done by X-ray diffraction (XRD) patterns. The surface morphology was

examined by scanning electron microscope (SEM) with EDAX and atomic force

microscope (AFM). Electrical properties have been studied by measurement of I-V

characteristics of the films using electrometer.

6.4 Optical Properties:

The optical properties of vacuum evaporated PbS thin films deposited on quartz

substrates both without and with H2S atmosphere were studied by the absorption and

transmission spectra taken at room temperature with the help UV-vis-NIR

spectrophotometer (Varian cary 5000) as shown in figure 6.1 and figure 6.2 respectively.

The vis-NIR optical absorption spectra of both films deposited without and with H2S

atmosphere have not shown any appreciable change in the spectral dependence

absorbance in the spectral range 400 – 1500 nm.

155

400 600 800 1000 1200 14000.0

1.5

3.0

4.5

Abso

rptio

n

W avelength (nm )

b a

a. PbS without H 2S atm osphereb. PbS w ith H 2S atmosphere

Figure 6.1: Absorption spectra of vacuum evaporated PbS thin films deposited without and with H2S atmosphere on quartz substrate.

300 600 900 1200 15000

10

20

30

40

50

60

70

% T

W avelength (nm )

a. PbS w ithout H2S atmosphere

b. PbS w ith H 2S atm osphere

b

a

Figure 6.2: Transmission spectra of vacuum evaporated PbS thin films deposited

without and with H2S atmosphere on quartz substrate.

156

Both samples have low transmittance in the ultraviolet (UV) region below 400 nm

due to the strong absorbance in this region of wavelength. Thereafter, transmission

increased with increasing wavelength towards near-infrared (NIR) region. For low

wavelengths, there is no transmission because all the light is absorbed, while the steady

state in NIR regions resembles the absorption spectra [26].

6.4.1 Energy band gap:

To energy band gap of vacuum evaporated PbS films (for both without and with

H2S atmosphere) has been determined by Tauc’s plot for allowed direct transition. The

direct energy gap value of 1.59 eV for the vacuum evaporated PbS thin film (for both

without and with H2S atmosphere) was obtained by extrapolating the linear portion of the

(αhυ)2 versus hυ plot in figure 6.3. The large excitation Bohr radius of PbS (18 nm) [27],

results in strong quantum confinement of both electrons and holes in nano-sized structure.

The increased band gap of vacuum evaporated PbS thin film from 0.41 eV to 1.59 eV is

due to strong quantum confinement effect in nanocrystalline PbS thin films [15,28,29].

The value of Eg of PbS thin films deposited with H2S atmosphere can then be used to

calculate the value of n from the slope of plot of ln((αhν) vs ln(hν-Eg) as shown in figure

6.4. The slope of linear region of this plot comes out n value ~ ½, which indicated

allowed direct transition in as-deposited PbS film material.

157

0 1 2 30

2

4

6

8

10

(h

h

PbS thin film s w ith H 2S atm osphere

Eg =1.59 eV

Figure 6.3: Plot of (αhν)2 Vs hν for vacuum evaporated PbS film deposited with H2S atmosphere.

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

0.5

1.0

1.5

2.0

ln(hv-Eg)

ln(

h

Figure 6.4: Graph between ln(hν-Eg) and ln(αhν) of vacuum evaporated PbS thin

films deposited with H2S atmosphere.

158

6.5 Structural Properties:

The crystallinity and phase of the vacuum evaporated PbS thin films deposited

without and with H2S atmosphere on glass substrates were characterized by X-ray

diffraction (XRD) measurement using an x-ray diffractometer with CuKα radiation.

6.5.1 XRD:

X-ray diffraction patterns of the PbS thin films deposited on glass substrates

without and with H2S atmosphere with 2θ ranging from 20° to 80° are shown in figure

6.5. The XRD pattern of vacuum evaporated PbS/glass thin film deposited without H2S

atmosphere as shown in figure 6.5 (marked ‘a’) had a strong and high intensity peak at 2θ

value about 30° corresponds to the cubic (200) crystalline plane with low intensity cubic

(311) peak at 2θ value about 51° and cubic (400) peak at 2θ value about 62.5°. It is

observed that the preferred orientation growth along the (200) direction for PbS films

deposited without H2S atmosphere. While XRD pattern of vacuum evaporated PbS thin

film deposited with H2S atmosphere as shown in figure 6.5 (marked ‘b’) revealed that the

crystallography of the film is good and characterized by five principle peaks at 2θ values

of about 25.98°, 30°, 43.10°, 51°, 53.49° corresponding to cubic (111), (200), (220),

(311) and (222) orientations respectively. Along with these peaks some small (low

intensity) peaks at 2θ values of about 69°, 71° and 79° corresponding to cubic (331),

(420) and (422) orientations respectively were also observed. It is clear that PbS films

deposited with H2S atmosphere has the preferential orientation along cubic (111) plane.

By comparison with the standard data from JCPDF card No. 78-1901, all diffraction

peaks in both samples can be indexed as a cubic structure of PbS. The crystallite size (d)

using (111) peak was calculated by using Scherrer formula [30] for PbS films deposited

with H2S atmosphere and comes out as 29.79 nm.

159

20 30 40 50 60 70 80

2

Inte

nsity

(a.u

.)

a

b

b. PbS with H2S atmospherea. PbS without H

2S atmosphere

(400

)

(111

)

(200

)

(220

)

(311

)(2

22)

(331

)(4

20)

(422

)

(311

)

Figure 6.5: XRD patterns of vacuum evaporated PbS thin films deposited without and with H2S atmosphere.

6.6 Surface Morphology:

The Surface Morphology of vacuum evaporated PbS thin films deposited without

and with H2S atmosphere was examined by scanning electron microscopy (SEM) with

EDAX and atomic force microscopy (AFM).

6.6.1 Scanning Electron Microscopy (SEM) with EDAX:

Scanning electron microscopy (SEM) with Energy dispersive X- ray analysis

(EDAX) is a suitable technique to study the microstructure and composition of the as-

deposited thin films. The SEM micrographs (at different magnification 50,000X and

1,00,000X) of vacuum evaporated PbS thin films deposited without and with H2S

atmosphere are shown in figure 6.6 and 6.7 respectively. The SEM micrographs show

typical tightly adherent PbS films on highly cleaned glass substrates. It is cleared that the

160

surface of PbS films deposited without H2S atmosphere is rough and grains are not

distributed uniformly.

Figure 6.6: SEM micrograph of vacuum evaporated PbS thin film deposited without H2S atmosphere at different magnifications (i) at 50,000X and (ii) at 1,00,000X.

Figure 6.7: SEM micrograph of vacuum evaporated PbS thin film deposited with H2S atmosphere at different magnifications (i) at 50,000X and (ii) at 1,00,000X.

(i) (ii)

(ii) (i)

161

On the other hand the surface of PbS film deposited with H2S atmosphere has fine

grains which are more uniformly distributed. So, the films deposited in H2S atmosphere

are homogeneous, without any crack, rather dense and exhibit almost complete coverage

of the substrate. This shows that the better surface morphology is achieved in the films

grown in controlled H2S atmosphere.

EDAX analysis was performed for the elemental compositional analysis of the

film. Figure 6.8 and figure 6.9 shows the EDAX spectrum of PbS films deposited without

and with H2S atmosphere on glass substrates. Electron beam induced inner-shell

ionization and subsequent emission of characteristic fluorescence are analyzed in order to

obtain the composition. The peaks for Pb and S were found in the spectrums (figure 6.8

and figure 6.9) confirm the presence of the Pb and S as the components of the as-

deposited thin films of PbS. The Si peak appears in EDAX is due to the glass substrates

used in the deposition of film material. The element weight% and atomic% of Pb and S in

EDAX spectroscopy of vacuum evaporated PbS thin films deposited without and with

H2S atmosphere are presented in Table 6.1 and Table 6.2 respectively. The atomic

percentage of Pb and S shows excess of Pb in the vacuum evaporated PbS thin films. The

average atomic percentage of Pb:S was found to be 52.11:47.89 in PbS thin film

deposited without H2S atmosphere whereas it is found 50.87:49.13 in PbS thin film

deposited with H2S atmosphere. These results shows that S is significantly increasing in

vacuum evaporated PbS thin film deposited in H2S atmosphere which indicates that the

PbS films deposited with H2S atmosphere have better stoichiometry in comparison to PbS

films deposited without H2S atmosphere.

162

Figure 6.8: EDAX analysis of vacuum evaporated PbS thin films deposited without H2S atmosphere.

Table 6.1: EDAX analysis of vacuum evaporated PbS thin films deposited without H2S atmosphere.

Element Wt% At%

SK 12.44 47.89

Pb M 87.56 52.11

Matrix 100.00

163

Figure 6.9: EDAX analysis of vacuum evaporated PbS thin films deposited with H2S atmosphere.

Table 6.2: EDAX analysis of vacuum evaporated PbS thin films deposited with H2S atmosphere.

Element Weight% Atomic%

S K 12.95 49.13

Pb M 87.05 50.87

Totals 100.00

164

6.6.2 Atomic Force Microscopy (AFM):

The 2D and 3D atomic force microscopy (AFM) images and histogram

distribution of vacuum evaporated PbS thin films deposited on glass substrate without and

with H2S atmosphere are show in figure 6.10 (i), (ii), (iii) and figure 6.11 (i), (ii), (iii)

respectively. All the AFM images were taken for an area of 1000 x1000 nm orders show

that the particles are closely bonded. The AFM images of the vacuum evaporated PbS

film deposited on glass substrate with H2S atmosphere revealed that the grains are more

spherical in shape and are homogeneously distributed over the whole surface in

comparison to the PbS film deposited on glass substrate without H2S atmosphere. The

average grain sizes are observed to be increased in PbS films deposited with H2S

atmosphere. The average roughness also increases in vacuum evaporated PbS films

deposited with H2S atmosphere. The average grain size & roughness of PbS films

deposited without and with H2S atmosphere comes out 12 nm (grain size) & 2.6602

(roughness) nm and 14 nm (grain size) & 3.39607 nm (roughness) respectively. PbS film

with H2S atmosphere show cluster of particles with highly dense structure with high

packing density and have advanced surface and typical columnar structure with highly

dense grains.

165

Figure 6.10: (i) 2D and (ii) 3D AFM images of vacuum evaporated PbS thin film deposited

without H2S atmosphere of an area 1000 x 1000 nm orders.

Figure 6.10: (iii) Histogram distribution of AFM image of vacuum evaporated PbS thin film

deposited without H2S atmosphere of an area of 1000 x 1000 nm orders.

(i) (ii)

(iii)

166

Figure 6.11: (i) 2D and (ii) 3D AFM image of vacuum evaporated PbS thin film deposited with H2S atmosphere of an area 1000 x 1000 nm orders.

Figure 6.11: (iii) Histogram distribution of AFM image of vacuum evaporated PbS thin films deposited with H2S atmosphere of an area 1000 x 1000 nm orders.

(i) (ii)

(iii)

167

6.7 I-V measurements:

Schottky barrier junction:

Rectifying metal–semiconductor contacts, also known as Schottky barrier, are the

basic devices in the technology of semiconductors. When a metal is brought into contact

with a semiconductor, there is usually a redistribution of charges, which results in the

formation of depletion layer in the semiconductor. This deformation of the band edge at

the interface is called a Schottky barrier. The potential barrier, which forms when a metal

is contacted with a semiconductor, arises from the separation of charges at the metal–

semiconductor interface such that a high resistance region devoid of mobile carriers is

created in the semiconductor. The barrier results from the difference in the work functions

of the two substances. The current flows in a Schottky barrier diode because of charge

transport from the semiconductor to the metal or in the reverse direction. There are four

different mechanisms by which the carrier transport can occur: (1) thermionic emission of

electrons over the barrier, (2) quantum mechanical tunneling of electrons through the

barrier,(3) carrier recombination (or generation) in the depletion region, and (4) carrier

recombination in the neutral region of the semiconductor which is equivalent to the

minority carrier injection. Process (1) is usually the dominant mechanism in Schottky

barrier junctions and leads to the ideal diode characteristics. The standard Schottky

barrier theory should explain the saturation current JS of the general current–voltage (I–V)

characteristics as a function of temperature T [31,32].

퐽 = 퐽 [exp (푞푉 푘푇) − 1]⁄ … … … … … … … … … . . (6.1)

where J is the current density, V is the voltage, n is the ideality factor, q is the

electronic charge, and k is the Boltzman constant.

In the Schottky theory, JS (T) is mainly determined by the barrier height ФB and

the effective Richardson constant A*

168

퐽 퐴∗푇 exp (−푞∅ 푘푇) … … … … . . … … … … … … … (6.2)⁄

A*=4πm*qk2h-3 is the effective Richardson constant [33] for thermionic emission

corresponding to the electron effective mass m* in the semiconductor and h is the Planck

constant. The barrier height may be written as

∅ = (푘푇 푞)⁄ ln (퐴∗ 푇 퐽 ) … … … … … … … … … … … … . (6.3)⁄

The diode ideality factor (n) is given as

푛 = (푞 푘푇)⁄ [푑(ln 퐽) 푑푉⁄ ] … … … … … … … … … … … . . (6.4)

The ideality factor, n; is very close to unity at low doping and high temperature.

However, it can depart (increases) substantially from unity when the doping is increased

and temperature is lowered. For an ideal Schottky barrier, where the barrier height is

independent of the bias and current flows only due to thermionic emission, n= 1. Factors

which make n larger than unity are the field (bias) dependence of barrier height, electron

tunneling through the barrier, and the carrier recombination within the depletion region. A

plot of ln J versus V gives a straight line. The saturation current density JS can be

obtained by extrapolating the straight line to V=0. Knowing saturation current density JS,

Richardson constant A* and the temperature T, the barrier height ФB can be determined.

The ideality factor n is determined by using the slope of the plot of ln J versus V.

The barrier height and ideality factor of the junction were investigated by means

of current–voltage measurements. The I–V characteristics of the junction formed are

shown in figure 6.12 (i) & (ii) for vacuum evaporated PbS thin films deposited without

and with H2S atmosphere respectively and can be explained by diode rectifier theory.

Both contacts were of vacuum deposited aluminum on the same side of the sulphide films

with the gap of same side about 1mm between them. The I–V characteristics of the

junction can be analyzed in terms of the thermionic emission model of Schottky barrier

current transport as given by equation (6.1) and (6.2).

169

-20 -10 0 10 20

-0.0003

-0.0002

-0.0001

0.0000

0.0001

0.0002

0.0003

Cur

rent

(

V in (Volts)

PbS without H 2S atmosphere

-20 -10 0 10 20

-0.0000005

0.0000000

0.0000005

Cur

rent

(

V in Volts

PbS with H 2S atmosphere

Figure 6.12: Current–voltage characteristics of vacuum evaporated PbS Schottky junction without and with H2S atmosphere.

(i)

(ii)

170

0 5 10 15 20 25

-8

-12

-16

-20

lnJ F

VF(in Volts)

PbS without H 2S atmosphere

Figure 6.13: (i) Plot of ln JF versus VF for vacuum evaporated PbS film depossited without H2S atmosphere.

0 5 10 15-12

-14

-16

-18

-20

-22

-24

lnJ F

V F(in Vo lts)

PbS w ith H 2S atm osphere

Figure 6.13: (ii) Plot of ln JF versus VF for vacuum evaporated PbS film deposited with H2S atmosphere.

(i)

(ii)

171

Figure 6.13 (i) & (ii) shows a plot between the forward current density ln JF and

forward voltage VF for metal–semiconductor contact PbS thin films without and with H2S

atmosphere respectively. The extrapolated value of current density JF to zero voltage

gives the saturation current density JS, (JS -15.46 and -20.63 without and with H2S

atmosphere respectively) The barrier height of the PbS Schottky junction is obtained by

using equation (6.3) and has the value 0.35 eV and 0.34 eV without and with H2S

atmosphere respectively.

172

References:

1. G. Bauer, G. Springholz, Semiconductor Materials: Lead Salt, Encyclopedia of

Modern Optics (Edited by- B.D. Guenther, Elsevier Ltd.) (2005), 385.

2. X. Lui, M. Zhang, International Journal of Infrared and Millimeter Waves 21 (2000)

1697.

3. J.L. Machol, F.W. Wise, R.C. Patel, D.B. Tanner, Phys. Rev. B 48 (1993) 2819.

4. P. Gadenne, Y. Yagil, G. Deutscher, J. Appl. Phys. 66 (1989) 3019.

5. O. Madelung, Semiconductor: Data handbook, Springer, (2004).

6. M.A. Rafea, N. Roushdy, Philosophical Magazine Letters, 90 (2010) 113.

7. P.K. Nair, O. Gomezdaza, M.T.S. Nair, Adv. Mater. Opt. Electron. 1 (1992) 139.

8. D. Kumara, G. Agarwal, B. Tripathi, D. Vyas, V. Kulshrestha, Journal of Alloys and

Compounds, 484 (2009) 463.

9. A. Guchhait, A.K. Rath, A.J. Pal, Solar Energy Materials & Solar Cells, 95 (2011)

651.

10. P.K. Nair, V.M. Garcia, A.B. Hernandez, M.T.S. Nair, J. Phys. D: Appl. Phys. 24

(1991) 1466.

11. Ileana Pop, Cristina Nascu, Violeta Ionescu, E. Indrea, I. Bratu, Thin Solid Films

307 (1997) 240.

12. H. Moreno-Garcia, M.T.S. Nair, P.K. Nair, Thin Solid Films 519 (2011) 7364.

13. B. Thangaraju, P. Kalinnan, Semicond. Sci. Technol. 15 (2000) 849.

14. G.P. Kothiyal, B. Ghosh and R.Y. Deshpande, J. Phys. D, Appl. Phy. 13 (1980) 869.

15. R. Das, Rajesh Kumar, Materials Research Bulletin 47 (2012) 239–246

16. M.M. Abbas, A. Ab-M. Shehab, N-A. Hassan, A-K. Al-Samuraee, Thin Solid Films

519 (2011) 4917.

173

17. J.A. García-Valenzuela, M.R. Baez-Gaxiola, M. Sotelo-Lerma, Thin Solid Films

534 (2013) 126.

18. S. Thangavel, S. Ganesan, K. Saravanan, Thin Solid Films 520 (2012) 5206

19. Tapio Kannicinen, Seppo Lindros, Jarkko Ihanus and Markku Leskela, J. Mater.

Chem. 6 (1996) 161.

20. J. Puiso, S. Lindroos, S. Tamulevicius, M. Leskela and V. Snitka, Thin Solid Films,

428 (2003) 223.

21. Erja Nykanen, Jutta Laine-Ylijoki, Pekka Soininen, Lauri Niinisto, Markku Leskela

and Liliane G. Hubert-Pfalzgraf, J. Mater. Chem. 4 (1994) 1409.

22. Sushil Kumar, T.P. Sharma, M.Zulfiquar, M. Husain, Physica B, 325 (2003) 8.

23. R.C. Tyagi and Rajendra Kumar, Thin solid Films, 25 (1975) S21-S24,

24. N.F. Foster, J. Appl. Phys. 38 (1967) 149.

25. Beer Pal Singh, Virendra Singh, R.C. Tyagi, T.P. Sharma, Applied Surface Science,

254 (2008) 2233.

26. N. Suriyanarayanan, S. Prabahar, S. Srikanth, V. Balasubramanian, D. Kathirvel,

Archives of Physics Research 1 (2010) 81.

27. O. Madelung, Semiconductor: Data Handbook, 3rd edition, Springer, 2004.

28. Y. Gulen, M. alanyalioglu, K. Ejderha, C. Nuhoglu, A. Turut, Journal of Alloys and

Compounds 509 (2011) 3155.

29. A.S. Obaid, M.A. Mahdi, Z. Hassan, M. Bououdina, Materials Science in

Semiconductor Processing 15 (2012) 564.

30. H.P. Klug & L.E. Alexander, X-ray diffraction procedures for polycrystalline and

amorphous materials, John Wily and Sons, New York, 491 (1954).

31. E.H. Rhoderick, Metal–Semiconductor Contacts, Clarendon Press, Oxford, 1978.

174

32. B.L. Sharma, Metal–Semi conductor Schottky Junctions and their Applications,

Plenum Press, New York, (1984).

33. L.P. Deshmukh, G.S. Shahane, Int. J. Electron. 83 (1997) 341.