Download Chapter 1 Existing information about transition metal

1
Chapter 1
Existing information about transition metal
dichalcogenides (TMDCs)
2
1.1 INTRODUCTION
Transition metal dichalcogenides characteristically contain layered crystal
structures. Number of researchers have fascinated by the motivating properties of the
compounds of this family. For the last few decade scientists are beginning to turn to
transition metal dichalcogenides shortly known as TMDCs. As their name suggests, these
are made up of transition metals such as molybdenum, tungsten or niobium linked with
chalcogens such as sulfur, selenium etc... They comprise a layer of transition metal atoms
sandwiched between two layers of chalcogen atoms. However, the atoms in these layers
are strongly held together by covalent bonds, whereas each layer sheet is only associated
to its neighbouring layer by weak van der Waals bonds, allowing individual sheets to be
separated from each other [1].
Transition metal dichalcogenides (TMDCs) are layered materials with strong in plane
bonding and weak out of plane interactions permits two dimensional layers of single unit
cell thickness. Although TMDCs have been studied for decades, recent advances in these
materials characterization and device fabrication have opened up new opportunities for
two dimensional layers of thin TMDCs in electronics and optoelectronics. TMDCs such
as MoS2, MoSe2, WS2 and WSe2 and some mix compounds of these materials have
valuable band gaps that change from indirect to direct in single layers, allowing
applications such as transistors, photo detectors and electroluminescent devices [1]. The
historical developments of TMDCs methods for preparing atomically thin layers, their
electronic and optical properties have been reviewed.
The compounds of Transition metal dichalcogenides group can be represented by
the formula of the type MX2 (where M is the transition metal group VIB and X2 is the
chalcogen element such as Se, S, Te etc...). TMDCs with various characters of metal,
semiconductor and magnetic substances have been studied widely. These materials are
considered structurally as strongly bonded two dimensional X-M-X layers loosely
coupled to one another by relatively weak Van der Waals type forces [1].
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In X-M-X sandwich layer the metal atom (M) is bonded to six nearest neighbour
atoms (X). Figure 1.1 shows the schematic diagram of two dimensional model of
transition metal dichalcogenides.
Fig.1.1 Schematic model of atomic layers of TMDCs
The optical and electrical properties of TMDCs have been investigated by several
researchers. The structural and bonding properties of transition metal have become an
important field in recent solid state research. It is well known that the electronic structure
of transition metal dichalcogenides is characterized by two types of states. First, there is a
strong interaction between the outer s/p orbital’s of the metal and outer p and s chalcogen
orbital. The electronic states resulting from this interaction form a broad bonding and a
broad anti bonding bond, commonly referred to as the valence and the conduction band.
Secondly, there is a much weaker interaction between the outer d orbital’s of the
transition metal and the outer p chalcogen orbital [2].
4
Ultrathin two-dimensional layered transition metal dichalcogenides (TMDCs) are
fundamentally and technologically intriguing. They are found to be chemically versatile.
Multi layered TMDCs are direct band gap semiconductors whose band gap energy, as
well as carrier type (n- or p-type), varies between compounds depending on their
composition, structure and dimensionality. They have been investigated as chemically
active electro catalysts for hydrogen evolution and hydrosulfurization, as well as
electrically active materials in opto-electronics devices. Their morphologies and
properties are also useful for energy storage applications such as electrodes for Li-ion
batteries and super capacitors.
Structure of these transition metal dichalcogenides can be described as solid
containing molecules which are in two dimensions extends to infinity and which are
loosely staked on top of each other to form three-dimensional crystals. Several layered
materials have promising semiconducting properties and have attracted attention as a new
class of solar cell materials. Very important optical energy, electrical energy and chemical
energy
conversion
efficiencies
have
been
obtained
in
photovoltaic
and
photoelectrochemical solar cells. The potential of this group of materials has not been
fully discovered yet. It appears to be limited mainly by the availability of appropriate
materials. Attempts have been made to produce good quality crystals and thin films of the
layered transition metal dichalcogenides for photovoltaic and photoelectrochemical solar
cells devices applications. Several approaches actively pursued to produce high quality
single crystals and thin films of layered transition metal dichalcogenides. The layered
transition metal dichalcogenides exhibit promising properties for quantum solar energy
conversion. Few of these properties are listed below.
The energy gap of TMDCs is largely fall in the range of 1 to 2 eV and therefore it is
ideal for the solar energy absorption.
Due to strong metal dichalcogenides hybridization the width of valance and
conduction band is of considerably high magnitude and because of this the charge
carrier mobility are sufficiently high.
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The absorption coefficients are found to be high for TMDCs materials. It largely falls
in the range of 105 cm-1.
Therefore solar energy conversion devices produced form TMDCs may be
considered as a bright option to more known solar cells. Out of the entire TMDCs family
single crystal of W0.9Se2, WSe2 and MoSe2 compounds, grown with direct vapour transport
technique are chosen for the present investigation. The advantages of crystal growth by
direct vapour transport technique are discussed in detail in chapter 2. The elemental
information about the material molybdenum (Mo), tungsten (W) and chalcogen element
selenium (Se) used in present investigation for the synthesis of W0.9Se2, WSe2 and MoSe2
single crystals are shown in Table 1.1.
Table 1.1 Elemental information of Molybdenum (Mo), Tungsten (W) and Selenium (Se)
Parameters
Mo
W
Se
Atomic Number
42
74
34
Atomic Weight (amu)
95.95
183.84
78.97
Group
6
6
16
Density(kg/ m3)
10280
19250
4810
Melting point (K)
2896
3695
494
Boiling point (K)
4912
6203
958
Electrical resistivity(× 10-8 Ω· cm )at RT
534
528
High
Thermal conductivity(W/m.K)
138
173
20
Molar specific heat (J/mol/K)
24.06
24.27
25.36
Heat of fusion (kJ/mol)
37.48
35.3
6.69
Heat of vaporization(kJ/mol)
598
774
95.48
Covalence radius (pm)
130
139
120
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1.2 MOLYBDENUM (Mo)
Molybdenum is a Group VI chemical element with the symbol Mo and atomic
number 42. Mo display body centered cubic structure at room temperature. There is no
confirmation for face changes up to 280 Gpa in experiments. It is likely that the
solid-solid phase transition found in shocked Mo is the bcc hcp transition. It forms hard,
steady carbides in alloys, and due to this reason most of world production of the element
is in making many kinds of steel alloys, including high strength alloys and super alloys
[3].
Fig. 1.2 The solid state structure of molybdenum.
The majority of molybdenum compounds have low solubility in water. Molybdenum
enclosing enzymes are by far the most general catalysts used by some bacteria to break
the chemical bond in atmospheric molecular nitrogen, allowing biological nitrogen
fixation. Owing to the diverse functions of the various auxiliary types of molybdenum
enzymes, molybdenum is a required element for life in all higher organisms in the
majority of the bacteria [3].
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1.2.1 Application of Molybdenum
Molybdenum is used in steel alloys for its high corrosion resistance and weld ability.
The ability of molybdenum to withstand extreme temperatures without significantly
expanding or softening makes it useful in applications that involve intense heat, including
the manufacture of armor, aircraft parts, electrical contacts, industrial motors and
filaments. Approximately all the high strength steel enclose Mo in amounts from 0.25 %
to 8 %. Molybdenum improves the strength of steel at high temperatures. It is used as
electrodes in electrically heated glass furnaces. It is also employed in nuclear energy
applications as well as for missiles and air craft applications. It is a valuable catalyst in
petroleum refining [4].
1.2.2 Electronic Configuration of Molybdenum
The following symbolize the electronic arrangement for the ground state neutral
gaseous atom of molybdenum. The pattern associated with molybdenum in its compounds
is not necessarily identical.
Ground state electron configuration
:
[Kr] 5s1 4d 5
Shell structure
:
2,8,18,13,1
Magnetic ordering
:
Paramagnetic
Crystal structural
:
Body Centered Cubic (BCC)
Element category
:
Transition metal
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1.3 TUNGSTEN
Tungsten is a chemical element with the chemical symbol W and atomic number 74.
Tungsten is a hard and rare metal under standard conditions and found naturally on Earth
only in chemical compounds. Tungsten exists in two major crystalline forms which are α
and β. The former has a body centered cubic structure and is the most stable form. The
structure of the β phase is called A15 cubic. Tungsten has the highest melting point
(3,422 °C) lowest vapor pressure (at temperatures above 1,650 °C) and the highest tensile
strength among all the elements. The density of tungsten is 19.3 times than that of water,
and about 1.7 times than that of lead. Tungsten has the lowest coefficient of thermal
expansion. The low thermal expansion and high melting point and tensile strength of
tungsten originate from strong covalent bonds formed between tungsten atoms by the 5d
electrons [5].
Fig. 1.3 The solid state structure of tungsten
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1.3.1 Application of Tungsten
Tungsten with minor amounts of impurities is found to be brittle and hard. Tungsten's
alloys have wide applications in incandescent light bulb filaments, X-ray tubes (as both
the filament and target), electrodes in TIG welding, super alloys, and radiation shielding.
Due to hardness and high density tungsten is widely used in military field. Tungsten
compounds are also often used as industrial catalysts. Tungsten alloys are sometimes used
in low temperature superconducting circuits. Tungsten with some percentage of
chalcogen elements found to have semiconducting nature. Semiconductor crystal of
tungsten dichalcogenides are used in PEC solar cell [5].
1.3.2 Electronic Configuration of Tungsten
The following correspond to the electronic arrangement of the ground state neutral
gaseous atom of tungsten. The pattern associated with tungsten in its compounds is not
necessarily identical.
Ground state electron configuration
:
[Xe] 4f14 5d4 6s2
Shell structure
:
2, 8, 18, 32, 12, 2
Magnetic ordering
:
Paramagnetic
Crystal structural
:
Body Centered Cubic (BCC)
Element category
:
Transition metal
10
1.4 SELENIUM (Se)
Selenium is a chemical element with symbol Se and atomic number 34. It is a
non-metal chalcogen element. It rarely occurs in its pure state in nature. Black selenium
converts in to gray selenium at the temperature of 180°C. The gray selenium is the most
stable and dense form of selenium. The gray selenium has hexagonal crystal lattice
consisting of helical polymeric chains. Gray Se is formed by slow heating of allotropes,
by slow cooling of molten Se, or by condensing Se vapours just below the melting point.
Red and black coloured Se are insulators while gray Se is a semiconductor showing
appreciable photoconductivity. It can resists process of oxidation by air and it is not
affected by non-oxidizing acids. The viscosity of selenium does not exhibit the unusual
changes at high temperature [6].
Fig.1.4 The solid-state structure of selenium
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1.4.1 Application of Selenium
The selenium exhibits photovoltaic and photoconductive properties. Due to that
selenium is used in photocopying, photocells, light meters and solar cells. Zinc selenide
was the first material used for blue LEDs. Cadmium selenide has recently played an
important part in the fabrication of quantum dots. Sheets of amorphous selenium convert
x-ray images to patterns of charge in xeroradiography and in solid-state, flat-panel x-ray
cameras. Selenium is a catalyst in some chemical reactions but it is not widely used
because of issues with toxicity. In X-ray crystallography, incorporation of one or more
selenium atoms in place of sulfur helps with multi-wavelength anomalous dispersion and
single wavelength anomalous dispersion phasing. Selenium is used in the toning of
photographic prints, and it is sold as a toner by numerous photographic manufacturers. Its
use intensifies and extends the tonal range of black-and-white photographic images and
improves the permanence of prints [6].
1.4.2 Electronic Configuration of Selenium
The following correspond to the electronic arrangement of the ground state neutral
gaseous atom of selenium. The configuration associated with selenium in its compound
form is not necessarily identical.
Ground state electron configuration
:
[Ar] 3d10 4s2 4p4
Shell structure
:
2, 8, 18, 6
Magnetic ordering
:
Diamagnetic
Element category
:
Polyatomic nonmetal
Crystal structure
:
Hexagonal
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1.5 APPLICATION OF TMDCs
Significant growth has been made in the application areas of semiconducting
TMDCs. Even a monolayer (thickness < 1 nm) semiconducting TMDCs can provide an
equivalent electrical performance to a 10 nm thick organic or amorphous oxide
semiconductor. Ultrathin TMDCs are particularly fine suited for transparent and flexible
electronics. The charge transport and scattering mechanisms have been recognized and it
is found to be useful in many electronic devices. This fundamental knowledge of TMDCs
has begun to convert into essential functional of an electronic circuit is well. The need for
developing an inexpensive and efficient method of converting solar energy into electrical
or chemical energy inspired fast development of semiconductor electrochemistry in the
past decades. The method of converting solar energy with the support of semiconductor
photo electrochemical cells has been advanced as an option to the well known energy
conversion method involving the use of solid state semiconductor solar cells. TMDCs
materials are used in optoelectronics, holographic recording systems, switching, infrared
generation and detection system [6].
Layered transition metal dichalcogenides MX2 (M = metal; X2= chalcogen atom) may
be considered as an ideal model system for the investigation of fundamental aspects of
semiconductor metal interface. The TMDCs appears to be an appropriate electrode for
solar energy conversion due to its ability to obtain relatively large photocurrents in
aqueous electrode. TMDCs have been used as cathode in the lithium electrochemical cell.
N type TMDCs can be used with p type WSe2 to form a heterojunction rectifier device.
These properties suggest its stable and efficient application in the photo electrochemical
solar cell [6].
Similarly, access to high-quality, large area substrates is rising with the entrance of
chemical vapor deposition grown materials, although improvements are needed for high
performance circuit applications. In the field of optoelectronics, methods for improving
light absorption, fluorescence and electroluminescence quantum yields in ultrathin
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materials will be desirable if they are to be feasible with conventional bulk
semiconductors. Finally, in the field of sensing applications, chemical fictionalization
methods are preferred, that impart high chemical selectivity and robustness without
unsettling the excellent electronic properties of the TMDCs semiconductor. However, the
chemical vapour deposition technique is the single identified method to obtain electronic
grade TMDCs over big areas. Similarly, solution based methods for arranging and
depositing TMDCs materials require large improvement, particularly for high
performance
electronic
and
optoelectronic
use.
While
many applications
of
semiconducting TMDCs are almost the same to other electronic materials, the atomically
slim nature of TMDCs presents exceptional opportunities [5]. By focusing genuinely on
such exclusive opportunities, the technological strength of semiconducting TMDCs can
be maximized.
1.6 OCCURRENCE AND SYNTHESIS
Since TMDCs single crystals are not identified to occur naturally and so they have to
be produce in the laboratory. For the growth of this crystal, a range of growth techniques
are accessible at present. These contain both, growth from the melt as well as growth
from the vapour. The well acknowledged methods over the years for the growth of binary
IV-VI compounds consist of Bridgman, direct vapour transport (DVT) and chemical
vapour transport (CVT) techniques. The VIB metal compounds have been originally
produced as single crystals by Kjekshus [7] and coworkers. Since then, a number of
research groups have deal with the growth of single crystals constantly from the vapour
phase. The compounds are always produced from the pure elements. The single crystals
are developed from the vapour phase either by conscious cooling creating sublimation or
by a mineralization. Chemical transport responses are frequently used to develop single
crystals of TMDCs. The developed crystals are stable in standard laboratory
circumstances [7].
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1.7 EXISTING INFORMATION REGARDING CHARACTERISTICS
OF TMDCs
1.7.1 Structural Investigation
Small dimensional crystals are of immense importance because of their exacting
properties associated to the crystalline anisotropy. Transition metal dichalcogenides that
crystallize in the form of parallel fiber represent a diversified family ranging from super
conductors to widespread band gap semiconductors. Diverse physical properties initiate
from minute difference of the X-X and M-M legend lengths, consequential in structures
possessing three different varieties of trigonal prismatic chains. Their essential structural
units are formed of MX6 trigonal prisms that distribute trigonal faces and made of chains
parallel to the hexagonal c axis. Same concept has been revealed in fig 1.5 and fig 1.6.
Every chain shifted with regard to two adjacent ones by half the lattice factor, all along
the c direction [7].
The chains are connected by metal-chalcogen bonds and shape layers are associated
by a lot weaker Van der Waals forces. Their structure formulates them beneficial for
battery cathode intercalation and photochemical cell purposes. These layered compounds
crystallize hexagonally in strong strands or filamentary strip created platelets. As shown
in figure 1.6, a linear sequence of metal atoms is parallel to the c axis (the growth axis),
and six chalcogen (X) atoms encircle via a metal atoms forming distorted trigonal prism.
The layer-type lattice has the metal ions in the middle of the distorted trigonal prisms
which distribute trigonal faces, consequently forming isolated columns. The columns
scuttle parallel to the crystallographic axis (c-axis) and are relocating from the
neighboring columns through one-half the unit cell along the c axis [7].
15
Fig. 1.5 Crystal structure of TMDCs
Fig. 1.6 Primitive cell of MoSe2 / WSe2 single crystal
The distance among metal atoms by the side of the b axis is a lot shorter than the
inter prism distance. This structure has the similarity with a bundle of metallic chains
each with an insulating covering. The Van der Waals selenium-selenium bonds are in
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plane perpendicular to the columns and the Van der Waals gap is almost vertical to the
c-axis. As an example structure of MoSe2 and WSe2 are shown in fig1.5 and fig 1.6.
The transition metal dichalcogenides (TMDCS), where M representing a transition
metal of group 4B, 5B and 6B and a chalcogen element such as S, Se, Te etc.., crystallise
in layered structures consisting of sandwiches of three hexagonally formed sheets of
atoms. The majority of group 4B and 6B (TMDCS) are semiconductors while group 5B
dichalcogenides are metallic and turn out to be superconductors at low temperatures. The
crystal formation of these materials can be separated into two central groups. Depending
on the crystal field symmetry about the metal atom, it can be octahedral or trigonal
prismatically coordinated by the six nearest neighbour chalcogens. The group 4B
dichalcogenides have octahedral structural symmetry, the group 6B dichalcogenides have
prismatic, while several group 5B compounds shows evidence of either or both structures
[7].
1.7.2 Electrical Properties of TMDCs
From the literature survey, it is found that TMDCs are diamagnetic. Every
characteristic of layer materials are found to be anisotropic. The magnitude of the
conductivity at 300K fluctuates widely from sample to sample, possibly because of
varying contamination concentrations. However, there is now noticeable proof that the
minimum indirect band gap in these semiconductors is higher than 0.3 eV and the
electrical conductivity in these materials is minimum at 300K. It has been found in the
current research work that electrical conductivity of TMDCs increases with the
temperature (chapter 4).
It is found from literature review that early studies were made by hicks.et.al in 1967
[5]. He has shown that the carrier concentration of both n and p type MoSe2 and WSe2
specimen were of the order of 1016cm-3 . An intensive study has been made on mobility of
charge carriers in the layered semiconductors by fivaz.et.al (1967) [8]. He has investigated
the temperature dependence of electrical conductivity and Hall coefficient of
17
semiconducting compounds e.g. MoS2, MoSe2, and WSe2. From the investigation he has
explain various scattering mechanisms involved in these materials. He also stated that in
these materials, the free charge carriers have a tendency to become localized within each
layer. Therefore they behave as if they are moving through a part of independent layers.
Moreover, it was investigated that this tendency is related by a strong interaction between
the free carriers and the optical phonons polarized vertically to the layers [8]. Table 1.2
and table 1.3 display the discovered electrical data of MoSe2 and WSe2 single crystal by
various researchers.
Table 1.2 Electrical data of Tungsten diselenide
SR.
Research
Carrier
NO.
scholar
type
Carrier
Hall
Hall
concentrations
mobility
coefficient
ρ(Ω.cm)
N(cm-3)
µ H (cm2/V.S)
RH(cm3/C)
Resistivity
Ref.
1
Hicks.et.al.
P
0.570
8 x1016
99
78
[5]
2
Fivaz.et.al.
N
1.23
1 x1017
100
---
[8]
3
Deshpande.et.al.
P
3.41
6.01x1015
304
1039.24
[9]
4
Lux-Steiner.et.al.
P
4.0
6 x1015
250
---
[10]
5
Spah. et.al.
N
080
7.4x1016
236
---
[11]
6
Mahalawy.et.al.
N
0.166
3.88 x1017
121.5
---
[12]
7
Present work
P
0.8635
6.429 x 1014
1561
9709
18
Table 1.3 Electrical data of Molybdenum diselenide
SR.
Carrier
Carrier
Hall
Hall
concentrations
mobility
coefficient
ρ(Ω.cm)
N(cm-3)
µ H (cm2/V.S)
RH(cm3/C)
Resistivity
Research scholar
NO.
type
Ref.
1
Hicks.et.al.
N
0.6
5.6 x1016
15
-110
[5]
2
Grant.et.al.
N
1
1.6 x1017
40
-0.78
[6]
3
Pathak.et.al.
N
0.1769
1.1 x1017
213
----
[13]
4
Agarwal.et.al.
N
11.5
1.78 x1016
30.3
-650
[14]
5
Hu.et.al.
N
2.5
3.5 x1016
31.4
-----
[15]
6
Sumesh.et.al.
N
47.51
1.74 x1017
75.58
-----
[16]
7
Present work
P
0.9635
8.13 x 1014
1452
7526
1.7.3 Optical Properties of TMDCs
The investigation of optical properties of TMDCs gives important information of the
electronic properties and band structures of the crystal. The wilson.et.al [1] have
investigated the optical spectra of transition metal dichalcogenides having trigonal
prismatic coordination. The transmission spectra and optical absorption of group VI A
materials have been investigated at liquid nitrogen temperature (77K) and room
temperature by frindt.et.al in 1965 [17], evans.et.al in1965 and 1968 [18], wilson .et.al in
1969 [1], hazelwoods.et.al in 1971 [19] and the transmission spectra of group VIA have
19
been investigated at liquid helium temperature by beals.et.al [20]. In the present
investigation optical band gap of WSe2, W0.9Se2 and MoSe2 single crystal have carried out.
Optical band gap of all the samples under investigation are found to be around 1.4eV.
The ennaoui.et.al (1986) [21] and huang .et.al (2000) [22] have reported the
application of MoSe2 as photovoltaic material. The curtist.et.al in 1986 have reported the
working of MoSe2 as dehydrosulfurization catalysts. Recent investigations have revealed
that the layer type semiconducting group VI transition metal dichalcogenides (TMDCs),
which absorb visible solar energy in the neighborhood of infrared light, are mainly
attractive materials for photoelectrochemical solar energy translation. Among TMDCs
family the most efficient systems turned out to be MoSe2 and WSe2. The latest uses of
these materials contain polymer based TMDCs solar cells.
It is seen from literature review that optical band gap of TMDCs material falls near to
maxima of solar radiation. It indicates that TMDCs material like MoSe2, WSe2 and mix
compound of both can absorb maximum of the solar radiation incident on it. This
increases the possibility of generation of photo electron hole pairs. Therefore TMDCs
material must be useful in photo sensitive application. Thus it is worth investigating the
use of TMDCs in PEC solar cell.
20
REFERENCES
[1]
J. A. Wilson and A.D. Yoffe,
J.Adv. Phys., 18 (1969) 193.
[2]
J. R. Lince and P. D. Fleischauer,
J. Mater. Res., 2 (1987) 827.
[3]
J. Gobrecht, H. Gerisher and H. Tributsch,
J. Electrochem. Soc., 125 (1978) 1086.
[4]
F. R. Fan, H. S. white, B. Wheeler and A. J. Bard,
J. Electrochem. Soc., 127 (1980) 518.
[5]
W.T.Hicks,
J. Electrochem Soc., 111 (1964) 1058.
[6]
A. J. Grant, T.M. Griffiths, G.D. Pitt and A.D. Yoffe,
J. Phys. C.: Solid State Physics, 8 (1975) L17.
[7]
Bratts. L and Kjekshus, A , Acta Cehm. Scand, 26 (1972) 3441.
[8]
R. Fivaz and E. Mooser,
Phys. Rev. B., 163 (1967) 743.
[9]
M.P. Deshpande, P.D. Patel, M.N. Vashi and M.K. Agarwal,
J. of Crystal Growth, 197 (1999) 833-840.
[10]
M. Ch. Lux- Steiner, R. Spah, M.Obergfell, E. Bucher,
1st IPSE Conference, Kobe, Japan, (1984) 259.
[11]
R. Spah, U. Elrod, M. Ch. Lux-Steiner, E. Bucher and S. Wagner,
Appl. Phys. Lett., 43 (1983) 79.
[12]
L.H. El Mahalawy and B.L. Evan,
Phys. Stat. Sol. (b), 79 (1977) 713.
[13]
V. M. Pathak,
Ph.D. thesis, Sardar Patel University, Vallabh Vidyanagar, (1990).
[14]
M.K. Agarwal, H.B. Patel and K. Nagi Reddy,
J. Cryst. Growth, 41 (1977) 84-86.
21
[15]
S.Y. Hu , C.H. Liang , K.K. Tiong and Y.S. Huang,
J. of Alloys and Compounds, 442 (2007) 249.
[16]
C. K. Sumesh,
Ph. D. thesis 2008, Sardar Patel University, Vallabh Vidyanagar.
[17]
R. F. Frindt,
J. Phys. Chem. Solids, 24 (1963) 1107.
[18]
B. L. Evans and P. A. Young,
Phys. Stat. Solidi, 25 (1968) 417.
[19]
B. L. Evans and R. A. Hazelwood,
Phys. stat. sol. (a) 4 (1971) 181.
[20]
A. R. Beal, J. C. Knights and W. Y. Liang,
J. Phys.C., 5 (1972) 3540.
[21]
A. Ennaoui, S. Fiechter, W. Jagermann and H. Tributsch
J. Electrochem.Soc,. 97 (1986) 133.
[22]
J. M. Huang and D. F. Kelley,
Chem. Mater., 12 (2000) 2825.
[23]
C. M. Fang, R. A. Degroot, and C. Haas,
Phys. Rev. B, 56 (1997) 4455.
[24]
H. Isomaki and J. Vonboehm,
J. Phys. C., 14 (1981) L75.
[25]
L. F. Mattheiss,
Phys. Rev. 8 (1973) 3719.
[26]
D. G. Clerc, R. D. Poshusta, and A. C. Hess,
J. Phys. Chem., 100 (1996) 1575.
[27]
C. Umrigar, D.E. Ellis, D. S. Wang, H. Krakauer, and M. Posternak,
Phys. Rev. B., 26 (1982) 4935.
[28]
R. A. Bromley , R .B. Murray and A. D Yoffe,
J. Phys .C., 5 (1972) 759.
[29]
V. L. Kalikhman and Ya Umanski,
Sov. Phys. Upeshki, 15 (1973) 728.