Host Semiconductors suitable for DMS...

CHAPTER 2

Host Semiconductors suitable for DMS compounds


47

Chapter 2

2.1 Introduction

The choice of the appropriate semiconductors as a base for DMS is the

primary requirement. The semiconductors which are used as a DMS compounds

should have excellent thermal conductivity, easy to fabricate, good electrical,

mechanical and thermal properties. There is large variety of semiconductors

available today with quite different properties from each other. There are some

elementary semiconductors as Si, Ge and Sn, which all are usually referred as

group IV semiconductors. Another group element is carbon, which solidifies into

two structures, diamond and graphite. Sn also exists in two phase’s β-Sn which is

metallic and semiconducting α-Sn. The last element of this group is Pb, which is

metallic. One can also combine two different elements of the group IV to obtain

compound materials such as SiC or SiGe. These materials are investigated for

high-temperature electronic applications. The elements of group III (II) can be

combined with group V (VI) elements to form new compound semiconductors

such as III-V and II-VI.

Group I elements in conjunction with group VII elements lead to wide

energy gap insulators, since these materials are formed by ionic bonds and not by

covalent bonds as III-V and II-VI semiconductors. This is due to the reason that

ionic bonding is most likely to exist when the elements envolved have wide

difference in electronagetivity, e.g. an electropositive alkali atom plus an

electronegative halogen atom such as NaCl. Most of the III-V semiconductors

such as GaP, GaAs etc exist in the zinc blende structure, which is a cubic lattice.

Some exists in the wurtzite structure such as AlN, GaN, InN etc, which

corresponds to a hexagonal lattice. GaAs is well known and technologically best

developed III-V compound semiconductor since the middle of the 1950’s due to

its use in most of the electronic devices such as monolithic microwave integrated

circuits, infrared light emitting diodes, laser diodes and solar cells. In contrast to

Chapter 2

48

Si, GaAs and many other compound semiconductors are direct band gap

semiconductors so that optical applications of these systems are very common.

One can obtain ternary and quartnary semiconductors such as AlxGa1-xAs and

InxGa1-xAs1-yPy, respectively, from III-V semiconductor, which are mixed crystals.

However, in contrast to group IV semiconductors, III-V semiconductors exhibit a

certain degree of ionic bonding. Other well known materials are the II-VI type

semiconductors. These II-VI compounds typically exhibit a large degree of ionic

bonding than III-V compounds, since the respective elements differ more in the

electron affinity due to their location in the periodic table.

I-VII compounds can also form semiconductors which can exhibit a very

large ionicity. The energy gap is considerably larger than that in many III-V

compounds. Most important materials of this type are AgCl and AgBr in the fcc-

NaCl structure but differ from the zinc blende structure. There are other

elementary semiconductors such as Se and Te from group VI-the chalcogens.

Since the group VI elements have only two missing valence electrons to be shared

with neighboring atoms, these materials have a tendency to form chain structures.

Other compound semiconductors include the IV-VI compounds such as PbS, PbSe

etc. One of the elements, oxygen of this group shares their electrons with the

group IV element to form dioxide materials such as SiO2, GeO2, SnO2 and PbO2.

These materials have very interesting electronic properties. The properties of this

class of compounds vary widely from insulating to magnetic and metallic

behavior. There are more combinations of group V and VI or II and V which can

also be possible. Further there is one more class of ternary semiconductors which

belongs to the chalcopyrite structure, named after the mineral chalcopyrite CuFeS2

I−III−VI2 and II−IV−V2 compounds. These ternary compounds are equivalent to

the diamond structure, in which every atom is bonded to four first-neighbors in a

tetrahedral structure. The chalcopyrite structure can be obtained by doubling the

zinc-blende structure along the z-axis and filling the lattice sites. Some important

rare earth oxides like CeO2 and PrO2 are studied to replace SiO2 to overcome the


49

current tunneling problem because these semiconductors have large dielectric

constants.

The electronic properties of these semiconductor compounds have been

studied extensively from both, experimentally and theoretically by the large

number of research groups in order to predict the electronic band gap. But, still

there exists large discrepancy between the experimental and theoretical band gap

of many of the semiconductors. From theoretical front, most of the researchers

usually use the DFT method with LDA and GGA to calculate the band gap of

semiconductors. But, these two approximations widely underestimate the band gap

of the semiconductors or insulators from experimental values. Some also some

alternative methods are also there to improve the band gap; like DFT+U [1]

method, but these can only be applied to correlated and localized electrons, e.g. 3d

or 4f in transition metal intermetallics and rare-earth oxides. Another possibility is

to use Hybrid functionals (e.g., HSE)) [2], LDA +DMFT [3] and GW [4]

approximation, but these methods need very expensive computational work. We

apply a semilocal modified Becke Johnson (mBJ) potential in which mBJ

exchange term is coupled with LDA correlation. The resultant XC potential

(mBJLDA) could catch the essentials of orbital dependent potentials (hybrid

functionals) and predicts the energy bands more accurately such that calculated

band gaps of the materials comes out in good agreement with experiments. Hence,

in this chapter, we have started with natural choice to calculate the electronic

properties of some semiconducting compounds which are best suited to make new

DMS compounds after doping with some TMs. This chapter is divided in to two

sections:

(i) IV-VI semiconductors: RO2 (R = Si, Ge, Sn and Pb) compounds in

rutile structure.

(ii) II-VI-V2 semiconductors: ABAs2 (A = Zn, Cd; B = Ge, Sn) in

chalcopyrite structure.

Chapter 2

50

All the oxide materials of IV-VI group are stable in the rutile type structure.

This structure is the simplest and most common type of structure and is adopted by

the transition-metal/rare-earth compounds: TiO2, VO2, VF2, CrO2, MnO2, MnF2,

FeF2, CoF2, NiF2, ZnF2, RuO2, TaO2, PdF2 and IrO2, and by the main-group (IVA)

oxides: SiO2, GeO2, SnO2, PbO2. The properties of this class of compounds vary

widely from insulating to metallic behavior, a variation which is a challenge to

theorists. Among these compounds, the most of the IVA-based dioxide materials

having high dielectric constant and suitable band gap are of general attention for

the next generation gate oxides for silicon based electronics [5-8] and as a host

matrices for non volatile flash memory applications [9,10]. These materials are of

great interest to the research community due to their outstanding mechanical,

chemical and high temperature properties [11]. These compounds are also

important from the geophysical point of view [12] and their electronic properties

vary widely from insulating to metallic nature. The single crystals of the rutile

type polymorph of SiO2, GeO2 and SnO2 were prepared by Yamanaka et al. [12]

and they studied the bond character of these compounds using X-ray diffraction.

Among the RO2 series, silicon dioxide (SiO2) exists in variety of

polycrystalline forms or glassy phases as well as in amorphous structure. As many

as 40 crystalline polymorphs have been well described and studied in the literature

[13]. Out of these forms, only α- and β-quartz, α- and β-cristobalite, coesite and

stishovite have a temperature density field of thermodynamic stability for

chemically pure silica [14-16]. Stishovite, is the first known form of high pressure

polymorph of silica and occurs in the rutile structure. It is the one of the most

common transparent materials in nature and its band gap is 8.9 eV [17] which is

largest among the known dioxides materials. Silica (SiO2) based ceramics are

good electrical and thermal insulators. SiO2 has attracted much attention because

of its potential application in ceramic and glass industries, in optical fibers,

catalysis, microelectronics and provide low-loss dielectric waveguides in the field

of integrated optics [5,6]. Especially, SiO2 plays an important role in Si/SiO2


51

interface of Si-based technology; the conventional technology of the

semiconductors. From last decade, this wide band gap material also has gained

much interest due to its use in the nanocrystal devices [7]. There exists a lot of

experimental studies such as X-ray emission spectra, X-ray and ultraviolet

photoelectron spectra (XPS and UPS), photoconductivity, optical reflectivity [18-

22] etc. which reveal the detailed analysis of bandstructure and density of states

(DOS) of SiO2 with a prediction of large band gap in the DOS at the Fermi level

(EF). The XPS measurements [21] showed that the band gap in crystalline state of

SiO2 is larger than the amorphous state. On the other hand, the reflectivity spectra

[23] of both states showed that the band structures are quite similar. The several

theoretical efforts such as Orthogonalized Linear Combination of Atomic Orbitals

(OLCAO) method [25,26], simple Tight Binding method [27], Linearized

Augmented Plane Wave (LAPW) method [28] and Plane Wave basis

Pseudopotential method [11] have also been made in order to calculate the energy

bands at the symmetry points and total DOS of SiO2. Moreover, Sato et al. [29]

have performed the first principle calculation for the investigation of electronic

structures of with and without TM doped SiO2 using Korringa–Kohn–Rostoker

coherent potential approximation (KKR-CPA). They suggests that this material

exhibits HMF after doping with some TMs and useful for spintronic applications.

Although germania (GeO2) is a chemical and structural analog to silica and

exists in three phases: crystalline, glass and liquid. The crystalline germania has

two stable polymorphs: one low density phase with a α-quartz (hexagonal)

structure and high density phase with rutile (tetragonal) structure. The rutile

structure is stable at ambient temperature and pressure whereas the quartz

structure is stable above ~ 1300 K at ambient pressure [30]. It has been studied

experimentally by X-ray diffraction, neutron scattering, spectroscopic techniques

such as X-ray absorption spectroscopy (EXAFS/XANES), Raman spectroscopy,

NMR spectroscopy and IR spectroscopy in order to find phase stability by varying

pressure [31-37]. On the other hand, the several theoretical calculations to study

Chapter 2

52

the band structure [11,38,39], elastic properties [40], thermal expansion [41] and

melting phenomenon [42] of germania also exist in literature.

SnO2 (stannic oxide) is a very attractive semiconductor material which

finds great interest due to its outstanding electrical, optical and electrochemical

properties. It also shows room temperature ferromagnetism (FM) after suitable

doping with transition metal ions which is an interesting property from spintronics

point of view [43-45]. For these reasons, there are a large number of reports on

electronic properties of SnO2 both, theoretically [43,46] and experimentally

[17,47], which studied its bandstructure and DOS in details and found that it is

direct and wide band gap semiconductor with a band gap at the centre of Brillouin

Zone (BZ). Moreover, SnO2 is also a key functional material which presents

special properties such as transparency or remarkable chemical and thermal

stabilities with direct applications for photodetectors, catalysts for oxidation and

hydrogenation, solar cells, semiconducting gas sensors, liquid crystal displays,

protective coatings, and starting materials for indium-tin oxide films used as

transparent conducting electrodes.

The last compound of RO2 series is the PbO2, has attracted considerable

attention owing to its use as the active material for storage of chemical energy in

lead acid batteries. It exists in two structures: α-PbO2 (orthorhombic - columbite

structure) and β-PbO2 (tetragonal - rutile structure) with space group Pbcn (Vh14)

and P42/mnm (D4h14), respectively. Under the normal conditions, β-PbO2 is more

stable structure [48]. The studies of photoemission spectroscopy, X-ray absorption

and emission spectra for β-PbO2 [49] show that conduction and valence band

touch at EF and after convolution with a broadening function, these bands appear

to merge. Therefore, this compound is best described as a semimetal. Payne et al.

[49] studied the electronic structure of β-PbO2 using Vienna ab-initio Simulation

Package (VASP) within GGA formalism and predicted it as a semimetal.

Robertson [50] calculated the electronic structures of rutile phase of SnO2, GeO2,

PbO2, TeO2 and MgF2 using tight binding method and discussed the formation of


53

band gap in terms of two centre interactions: P = pσ (cation-p, anion-p) and Q = sp

(cation-s, anion-p).

On the other hand, Ternary AIIBIVCV2 semiconductors represent part of

pnictides family which crystallize in the chalcopyrite structure and show important

optical, electrical and structural properties [51]. These materials have great

technological interest to the research community due to their nonlinear optical

properties [52]. In particular, their narrow band gaps make them suitable in

photovoltaic applications such as infrared detectors, light emitting devices, visible

light semiconductor lasers and in solar cells [51,53,54]. Recently, some of these

compounds show room temperature ferromagnetism (FM) and half metallicity

after suitable doping with transition metal ions which is an interesting aspect from

spintronics point of view [55,56]. These II-IV-V2 compounds resemble with the

III-V zinc blende binary semiconductors but contain two different cations instead

of one in binary. The former structure is logical extension of the latter with some

interesting structural anomalies [57,58]. First of all, Goodman [59] investigated

the II-IV-V2 compounds and reported chalcopyrite (CuFeS2) structure for these. A

room temperature photoluminescence found in ZnGeAs2 [60] proved its

significant device potential and boosted the research activities in this type of

compounds. Shay et al. [61] analyzed the electroreflectance spectra of CdSiAs2

and CdGeAs2. They characterized these compounds by large built in compressions

and internal displacement of As anions due to difference in the cation covalent

radii (rCd > rSi, rGe) and found a direct band gap for both.

On the theoretical front, Continenza et al. [57] calculated the structural and

electronic properties of some II-IV-V2 type chalcopyrite compounds using the

FPLAPW and ab-initio pseudopotential methods and examined the variation of

band gap with internal distortion parameter (u). Zopal et al. [62] predicted the

structural, thermodynamic and electronic properties of CdGeAs2 using linear

combination of atomic orbitals (LCAO) method and studied the effect of pressure

on electronic band structure. Limpijumnong et al. [63] carried out the first

Chapter 2

54

principle calculation of CdGeAs2 using Linear muffin tin orbital (LMTO) method

in full potential (FP) and atomic sphere approximations including spin orbit

coupling. The main emphasis of that study was to predict the band gap and energy

band splitting near the fundamental gap. The band structure calculation of CdBC2

(B = Si, Ge, Sn; C = P, As) pnictides at ambient pressure and its variation with

pressure using LMTO and projector augmented wave (PAW) methods with in

LDA and Generalized Gradient Approximation (GGA), respectively, were

reported by John [64]. She showed that band gap decreases on increasing pressure

which is due to the reduction in p-d interaction between Cd and B atom.

The most of the calculations reported in the literature to predict the

electronic properties of these materials have been carried out using two

approximations, LDA and GGA. However, as we discussed earlier, these two

approximations underestimate the band gap with respect to experimental values.

In the first section, we have focused on the trends observed in electronic

properties by changing R atom along group IVA in present RO2 compounds. To

find the accurate band gap of present semiconductors, the bandstructures have

been calculated using semilocal XC mBJLDA potential such that mBJ exchange

term is coupled with LDA correlation. These results are also compared to those

obtained from GGA and EV-GGA to test the accuracy with experiments. In the

second section, we have investigated the electronic properties of ZnGeAs2 and to

access the effect of changing local environment on these properties by substituting

cation (Zn or/and Ge) with corresponding next group element. The main aim of

the present study is to predict the accurate band gap of the rutile structure type

RO2 (Si, Ge, Sn and Pb) and Chalcopyrite structure type ABAs2 (A = Zn,Cd; B =

Ge,Sn) semiconductors. These studied compounds have excellent thermal

conductivity, easy to fabricate, good electrical, mechanical and thermal properties

are best suited to make DMS compounds.


55

2.2 Details of the calculations

The RO2 (R = Si, Ge, Sn and Pb) compounds crystallize in rutile structure,

a structure with tetragonal (P42/mnm) symmetry [17,48] such that the unit cell

contains two formula units (six atoms) as shown in Fig. 2.1. In this structure, each

R-atom is coordinated by six oxygen atoms in an octahedral configuration whereas

each oxygen atoms is bounded by three R-atoms. In RO2 compounds, the R atom

is present at (0,0,0) and O atom is located at (u,u,0). The internal parameter u is

0.307 [65] for RO2 (R = Si, Ge and Sn) and 0.310 for PbO2 [66] which represents

the relative displacement between R and O atoms.

The unit cell of ternary ABAs2 (A = Zn, Cd; B = Ge, Sn) (ABC2 type)

compounds in chalcopyrite structure (space group, I42d ) contains two formula

units (eight atoms), shown in Fig. 2.2 such that the A atom is present at (0,0,0), B

atom is at (1/2,1/2,0) and C atom is situated at (u,1/4,1/8). Here the parameter u

represents the displacement of anions from the ideal tetrahedral site. Each cation

(A or B) is connected by tetrahedron of anion (C) whereas each anion (C) is also

associated to four similarly arranged cations (two A and two B).

Fig. 2.1 Unit cell (left side) and IBZ for rutile crystal structure of RO2.

The symmetry k-points are shown on IBZ.

The first principle calculations of the electronic structure of present

compounds as well as for those in following chapters have been performed using

Chapter 2

56

the relativistic all electron full potential linearized augmented plane wave

(FPLAPW) method as implemented in the WIEN2k code [67]. The calculations

are based on the density functional theory (DFT) [68] in which the exchange and

correlation (XC) effects were taken into account using the three approximations:

GGA, EV-GGA [69] and mBJLDA [70] for RO2. Due to semimetallic nature of

PbO2, we have used only GGA formalism for predicting its ground state

properties. The parameterization of Perdew–Burke–Ernzerhof (PBE) [71] has been

used to construct the exchange-correlation potential for GGA formalism. The

radius of MT spheres (RMT) values for Si, Ge, Sn, Pb and O atom were taken to be

1.80, 2.0, 2.35 and 2.45 and 1.50 a.u., respectively.

Fig. 2.2 Unit cell (left side) and IBZ for Chalcopyrite crystal structure

of ABAs2. The symmetry k-points are shown on IBZ.

In the second section, the XC effects were taken into account using the

mBJLDA potential. The radius of MT spheres (RMT) values for Zn, Cd, Ge, Sn,

and As atom were taken to be 2.2, 2.5, 2.3, 2.5 and 2.3 a.u., respectively. The

plane wave cut off parameters were decided by RMTkmax = 8 (where kmax is the

largest wave vector of the basis set) and Gmax = 14 a.u.-1 for Fourier expansion of

potential in the interstitial region. The k-space integration has been carried out

using the modified tetrahedron method [72]. For RO2 (rutile structure) the self

consistency is obtained by 189 k-points in the irreducible brillouin zone (IBZ)


57

while for the ABAs2 compounds, a mesh of 405 k-points in the IBZ has been used

such that the total energy converges to less than 10-4Ry.

2.3 Results and Discussion

We have summarized from the literature some important ground state

properties in Table 2.1 for overview of experimental studies performed for present

compounds.

Table 2.1: list of experimental crystallographic and ground state properties of

Rutile RO2 (R = Si, Ge, Sn and Pb) and ABAs2 (A = Zn, Cd; B= Ge, Sn)

chalcopyrite compounds.

Compounds Expt.

Crystal

Structure

Ground state Expt.

Band

gap

(eV)

Characterization

Techniques

RO2

SiO2 Tetragonal Insulating 8.90 XPS and UPS,

photoconductivity

GeO2 Tetragonal Semiconducting 4.68 EXAFS/XANES,

Raman spectroscopy,

X-ray diffraction

SnO2 Tetragonal Semiconducting 3.60

PbO2 Orthorhombic

and tetragonal

Semi-metallic

Semi-metallic

- X-ray absorption

emission spectra

ABAs2 ZnGeAs2 Tetragonal Semiconducting 1.07,

1.15

Optical transmission,

electroreflectance

ZnSnAs2 Tetragonal Semiconducting 0.76,

0.75

Electroreflectance,

epitaxial layers

CdGeAs2 Tetragonal Semiconducting 0.66,

0.57

Electroreflectance,

hall effect

CdSnAs2 Tetragonal Semiconducting 0.32,

0.26

Electroreflectance

Chapter 2

58

2.3.1 Ground state properties

2.3.1.1 Rutile RO2 compounds

The electronic structure calculations of present RO2 compounds have been

performed at corresponding experimental lattice constants [12,66] as listed in

Table 2.2.

2.3.1.1.1 Density of States (DOS): First of all, the total and partial density of

states (DOS) of RO2 (R = Si, Ge, Sn and Pb) compounds have been analyzed in

energy range -10 eV to 10 eV as shown in Fig. 2.3. We have seen from the Fig.

that the nature of the DOS depends on the R atom. The total DOS increases in the

vicinity of EF with increase in the size of R atom among present compounds.

Fig. 2.3 Calculated total and partial DOS of RO2 (R = Si, Ge, Sn and

Pb) compounds. EF corresponds to Fermi level.


59

The valence band (VB) is filled upto EF in all these compounds. The total

DOS have similar characteristics in all but the band gap goes on decreasing with

increase in atomic size of R atom. Ultimately, the band gap becomes negligible for

the last compound PbO2 due to the slight overlap of the DOS in VB and

conduction band (CB) at EF.

Table 2.2: Experimental Lattice constants of RO2 (R = Si, Ge, Sn and Pb)

compounds, calculated band gap and its deviation from experimental values

( )cal exptg g gE E E∆ = − of these compounds (except PbO2) using three approaches:

GGA, EV-GGA and mBJLDA.

Compounds Lattice Const. (Å) Eg (eV) ∆Eg (eV) SiO2 a = 4.181

c = 2.662 (a) This Work: GGA EV-GGA mBJGGA Others: Expt.

5.69 6.25 7.66 5.61(c) 5.15(d) 8.90(h)

-3.21 -2.65 -1.24 -3.29 -3.75 -

GeO2

a = 4.402 c = 2.865 (a)

This Work: GGA EV-GGA mBJGGA Others: Expt.

1.91 2.39 4.10 3.13(c) 1.80(e) 4.68(i)

-2.77 -2.29 -0.58 -1.55 -2.88 -

SnO2

a = 4.74 c = 3.19(a)

This Work: GGA EV-GGA mBJGGA Others: Expt.

1.27 1.90 3.35 1.70(f) 0.65(g) 3.60(j)

-2.33 -1.7 -0.25 -1.9 -2.95 -

PbO2 a = 4.93 c = 3.36(b)

- - -

(a) Ref. 12, (b) Ref. 66 , (c) Ref. 11, (d) Ref.26, (e) Ref. 39, (f) Ref. 43, (g) Ref.

46, (h)Ref. 17 (i) Ref. 33, (j) Ref. 47.

Chapter 2

60

The observed decrease in band gaps is due to an increase in the atomic

radius of R-atom in RO2 compounds which results in poorer orbitals overlap of R

and O atoms and thus, leads to formation of longer and weaker bonds. This poorer

overlap produces a decrease in separation between valence and conduction bands.

Therefore, we observe a progression from SiO2, an insulator, to GeO2 and SnO2,

both semiconductors, and finally to PbO2, a semimetal.

In order to check the contribution of individual atoms we have analyzed the

total DOS (TDOS) in terms of partial DOS (PDOS). In VB, the main contribution

towards TDOS comes from O-p states throughout the entire energy range with

noticeable contribution from R-s and R-p states. The bottom of the CB is mainly

contributed by R-s states with small admixture of R-p and O-p sates. The O-s

states have negligible contribution in both, VB and CB. As, PbO2 exhibits a very

small DOS at EF (shown in inset of Fig. 2.3) such that there is no gap in VB and

CB. Therefore, it can be described as semimetal.

The calculated band gap for present RO2 compounds (except PbO2) using

three approaches: GGA, EV-GGA and mBJLDA are listed in Table 2.2 and Fig.

2.4. It is clear that mBJLDA results represent the energy bands more accurately

such that calculated band gaps of present compounds are in good agreement with

corresponding experimental values. Among the present compounds, SiO2 has

highest band gap of 7.66 eV within mBJLDA. We have predicted a larger value of

band gap than as calculated by Sevik et al. [11] Similar trends are also predicted

for GeO2 and SnO2 where our calculated band gaps using mBJLDA are much

better and close to actual experimental value [17,33,47] than other calculated

values [11,26,39,43,46]. On the other hand, EV-GGA results for band gaps (Eg)

are better than those obtained from GGA but still, there exists large discrepancy

from corresponding experimental values. In order to show the deviation

( cal. expt.g g g∆E = E - E ) from experimental band gap, we have plotted the theoretical vs.

experimental band gap in Fig 2.4. This deviation is smallest for SnO2 within

mBJLDA formalism.


61

Fig. 2.4 Calculated vs. experimental band gaps of RO2 (R = Si, Ge and

Sn) compounds.

In general, it is relatively larger for all studied compounds using GGA and

EV-GGA as compared to that obtained in mBJLDA formalism. The magnitudes of

deviation from experimental value obtained in our study and that of other

calculated results are listed in Table 2.1. The agreement of band gaps is rather

poorer in other calculations as compared to ours within mBJLDA formulism.

2.3.1.1.2 Electronic charge density: In order to understand the electronic states

of RO2 compounds, we have constructed the valence electronic charge density

maps (in the units of e/a.u.3) in Fig. 2.5 along the [110] plane. A detailed

description of charge densities within FPLAPW method was presented by Blaha

and Schwarz [73]. Starting from SiO2, the bonding has a significant covalent

character due to sharing of charge between Si and O atoms. Moreover, the charge

transfer occurs mainly from Si atom towards O atom. We have noticed that the

Chapter 2

62

nearest neighbor distance between R and O atom increases from 3.31 (in SiO2) to

4.04 a.u. (in PbO2) which leads to longer bonds along the series. Thus, the

electron density in the interatomic region between R and O atoms decreases with

increase in size of R atom such that covalent character decreases. In other words,

the ionicity of R-O bond increases along the series SiO2 → PbO2.

Fig. 2.5 Calculated valence charge density, n(r) along the [110] plane

in units of e/a.u.3 for (a) SiO2, (b) GeO2, (c) SnO2 and (d) PbO2

compounds.

2.3.1.1.3 Bandstructure: After analyzing DOS, charge densities and predicting

band gap, we have plotted the bandstructures of all these compounds in Fig. 2.6.

The common features of these structures (except PbO2) include the observation of

direct band gap along the Γ- Γ direction and existence of valence band maximum

at EF. We have chosen EF as the reference energy level for all. Firstly, we show the

band structure of SiO2 along the high symmetry directions of the Brillouin zone in

Fig. 2.6 (a). A band gap of 7.66 eV governs the insulating nature for this

compound. In SiO2 and GeO2, the manifold-bands which are ranging from -10 eV


63

to 0 eV in the VB is due to O-p states mainly with a small contribution from R-s

and R-p states. The O-p states are extended upto EF. Above EF, the bands at E > 8

eV in case of SiO2 and at E > 4 eV in GeO2 arise from empty R-s, R-p and O-p

states.

Fig. 2.6 Calculated bandstructures and total DOS of (a) SiO2, (b) GeO2,

(c) SnO2 and (d) PbO2 compounds. Horizontal line at E = 0 eV

marks the Fermi level EF.

Due to the overlapping of R-s and O-p states, the bonding (in VB) and

antibonding (in CB) states are formed, resulting the band gap in the compound.

SiO2 has the strong and short covalent bond which results of excellent orbital

overlap due to small size of Si. This overlap produces greater separation between

Chapter 2

64

bonding and antibonding states. Similarly, we may predict the semiconducting

band structure of GeO2 and SnO2.

In last, as we move from SiO2 to PbO2, overlap of atomic orbitals in PbO2

becomes poorest due to its largest size among present compounds. This overlap

leads to no separation between bonding and antibonding states. Thus, PbO2 may

be classified as semimetal. For the semimetallic PbO2, the valence band manifold

in the range from -8.0 eV to 0 eV may be described as O-p derived bands with Pb-

s and Pb-p derived bands dispersing through. The band at and above EF are

generally of mixed O-p and Pb-s character mainly. Finally in Fig. 2.7, we compare

the bandstructure of one of the compounds under investigation SnO2, as obtained

by three different XC potentials: GGA, EV-GGA and mBJLDA.

Fig. 2.7 Comparison of energy bands of SnO2 within GGA, EV-GGA

and mBJLDA formalism.

As we have fixed EF and also the top of VB to E = 0 eV, thus, the shifting

of bands is expected only in CB with in all formalisms. It is observed that the

mBJLDA potential produces better band splitting. Therefore, the VB and CB shift

downwards and upwards, respectively, in energy as compared to energy bands in


65

GGA, such that the difference between CB minimum and VB maximum increases.

In this way, the band gaps come closer to corresponding experimental values with

mBJLDA.

No doubt that EV-GGA [74] also produces the larger band splitting and the

agreement of band gap w.r.t experimental value is better than those obtained from

GGA but still it is not favorable to use. As the EV-GGA formalism reproduces the

exchange potential well but at the expense of poor agreement in the exchange

energy (EX). Therefore, as a result, it is not possible to reproduce those physical

quantities which directly depend on EX, such as bulk modulus and equilibrium

volume. In other words, optimization of lattice constants with EV-GGA gives

incorrect results.

2.3.1.2 Chalcopyrite type ABAs2 compounds

In order to investigate the effect of changing cation(s) in ZnGeAs2, the first

principle calculations of present ternary ABAs2 (A = Zn, Cd; B = Ge, Sn)

compounds have been performed at corresponding experimental lattice constants

[51,75] as listed in Table 2.3.

2.3.1.2.1 Density of states (DOS):

First of all, calculated TDOS of these compounds with available XPS

spectra are presented in Fig. 2.8. Here, TDOS of ZnGeAs2 and CdSnAs2

compounds are in accordance to the measured XPS data [76,77]. The TDOS of all

compounds are generic in nature and show a band gap at Fermi level (EF). A

general observation from the Fig. is that the band gap decreases with the

substitution of either one or both cations (i.e. Zn or/and Ge) in reference

compound, ZnGeAs2. For deep analysis and comparison of the trends observed in

DOS by changing cations accordingly, the muffin-tin projected partial DOS for

parent (ZnGeAs2) and cation substituted compounds are shown in Figs. 2.9 – 2.11.

In ZnGeAs2 (Fig. 2.9), Zn-d states are localized deeper in valence band along with

Chapter 2

66

Ge-s states from -7.5 eV to -5.6 eV, showing no effective role to decide the

magnitude of semiconducting band gap.

Table 2.3: Experimental Lattice constants (a,c) in Å with internal parameter (u) of

ABAs2 (A = Zn, Cd; B = Ge, Sn) compounds and their band gap (Eg) using

mBJLDA formalism. The accuracy of band gaps [∆Eg1(eV) = Eg(theo.) - Eg(Expt.1)]

and [∆Eg2(eV) = Eg(theo.) - Eg(Expt.2)] with respect to two experiments is also

mentioned.

Compounds (a,c) Eg ∆Eg1 ∆Eg2

ZnGeAs2 a = 5.671(a)

c = 11.151

u = 0.25

This work

Others

Expt.1

Expt.2

1.27

0.03 (b)

1.07 (d)

1.15 (e)

0.20

-1.04

-

-

0.12

-1.12

-

-

CdGeAs2

a = 5.945(a)

c = 11.212

u = 0.28

This work

Others

Expt.1

Expt.2

0.69

0.32(c)

0.12(c)

0.66 (d)

0.57 (e)

0.03

-0.34

-0.54

-

-

0.12

-0.25

-0.45

-

-

ZnSnAs2 a = 5.851(a)

c = 11.702

u = 0.232

This work

Others

Expt.1

Expt.2

0.84

0.18 (b)

0.76 (d)

0.75 (e)

0.08

-0.58

-

-

0.09

-0.57

-

-

CdSnAs2 a = 6.10(a)

c = 11.92

u = 0.262

This work

Others

Expt.1

Expt.2

0.51

0.12(c)

0.10(c)

0.32 (d)

0.26 (e)

0.19

-0.20

-0.22

-

-

0.25

-0.14

-0.16

-

-

(a)Ref. 51, (b) Ref. 76, (c) Ref. 64, (d) Ref.77, (e) Ref. 51


67

Fig. 2.8 Calculated total DOS of ABAs2 (A = Zn, Cd; B = Ge, Sn)

compounds (solid lines) and comparison with the available

experimental XPS data (small triangles).

The next manifold band from -5.2 eV to valence band maxima (VBM) is

mostly derived from As-p and Ge-p states with a small contribution of Zn-s and -p

states. The conduction band minimum mainly contains Ge-s and p states

hybridized with As-p states. The Zn-s and As-s states have negligible contribution

in both VB and CB. ZnGeAs2 has the strongest overlap of s and p states of cations

(Zn and Ge) and anion (As), respectively due to small size of Zn and Ge atoms as

compared to cations in other compounds.

Chapter 2

68

Fig. 2.9 Calculated partial DOS of AGeAs2 (A = Zn, Cd) compounds.

The solid and dotted lines show the contributions of individual

states of ZnGeAs2 and CdGeAs2 Compounds, respectively.

To access the effect of local environment by substituting cation(s) in

ZnGeAs2, we have analyzed the DOS as follows:


69

(i) Substitution of cation (Zn) by Cd (next group element): This substitution

results in CdGeAs2 compound. No significant difference in magnitude of total

DOS is observed in the vicinity of EF by this substitution (Fig. 2.9). The Cd-d

states are shifted lower in energy by ~ 2.0 eV than Zn-d states in ZnGeAs2. The

width of manifold band in the vicinity of EF is reduced by 0.3 eV w.r.t. reference

compound. Like in ZnGeAs2, the upper VB is mainly dominated by Ge-p and As-

p whereas CB is constituted by Ge-s,p and As-p states in CdGeAs2. The CB

minimum shows blue shift in energy scale as Ge-s and As-p states lie nearer to EF

in CdGeAs2. Thus, a decrease in band gap of this compound is observed w.r.t.

ZnGeAs2.

(ii) Substitution of cation (Ge) by Sn (next group element): The DOS of

resultant compound (ZnSnAs2) in VB is energetically favorable and no qualitative

changes are exhibited as shown in Fig. 2.10. But the width of the manifold band in

upper VB is 0.2 eV smaller in energy than that in ZnGeAs2.The d-bandwidth

remains unaltered as d-states are originated from common Zn atom in both

compounds. The contribution of cation, Sn-s states increases considerably in VB

at lower energy than that in ZnGeAs2. The blue shift observed in CB minimum by

this substitution is smaller than that in CdGeAs2 (case i). Again, this shifting is due

to presence of As-p and Sn-s states in CB at relatively lower energies.

(iii) Substitution of both cations (Zn and Ge) by Cd and Sn, respectively: Fig.

2.11 shows the comparison of total and partial DOS of ZnGeAs2 and CdSnAs2

(resultant compound). In this case, the general shape stays rather unaffected. The

width of the manifold band in VB reduces by maximum amount (0.7 eV) in

CdSnAs2 as compared to previous two cases. The contribution of Sn-s states

becomes more significant. The shifting of d-states towards lower energy is smaller

than that in case (i) due to the different local environment established by heavy

Sn-atom. Moreover, the blue shift in the CB minimum becomes largest, predicting

the lowest band gap for CdSnAs2.

Chapter 2

70

Fig. 2.10 Calculated partial DOS of ZnBAs2 (B = Ge, Sn) compounds.

The solid and dotted lines show the contributions of individual

states of ZnGeAs2 and ZnSnAs2 compounds, respectively.


71

Fig. 2.11 Calculated partial DOS of ABAs2 (A = Zn, B = Ge and A =

Cd, B = Sn) compounds.The solid and dotted lines show the

contributions of individual states of ZnGeAs2 and CdSnAs2

compounds, respectively.

Chapter 2

72

2.3.1.2.2 Electronic charge density:

The cations and anions in present compounds are linked with each other by

sp3 hybridization. In these compounds, the characteristics of two bonds, A-As and

B-As vary with the change of anyone or both cations (A and B) by their next

group element.

Fig. 2.12 Total valence electron charge density, n(r) in a (1 1 0) plane in

units of e/˚A3 for ABAs2 (A = Zn, Cd; B = Ge, Sn)

compounds.


73

The electronic charge density contours have been investigated in the (110)

crystallographic plane of ABAs2 (A = Zn, Cd; B = Ge, Sn) compounds to analyze

the origin of chemical bonds between all atoms as shown in Fig. 2.12. The contour

plot shows tendency of ionic/covalent character for A-As/B-As bond which

depends on Pauling electro-negativity difference of the atoms, As (2.18), Ge

(2.01), Sn (1.96), Cd (1.69) and Zn (1.65). It is found that majority of charges are

accumulated on As-atom and the distribution of electronic charge is spherical

which results in the bonding between A-As and B-As atoms. Among the present

compounds, Zn-As bond has highest electron negativity difference which governs

the strongest ionic tendency for this bond. This ionic character reduces for Cd-As

bond slightly. On the other hand, the charge density is largest in between the

atoms for Ge-As bond which shows the strong overlap and governs the covalent

character. The covalency also decreases by replacing Ge with Sn to form Sn-As

bond. Moreover, these plots show that valence electrons from Zn, Ge, Sn and Cd

atoms are transferred to As atom.

The calculated band gap for present ABAs2 compounds using mBJLDA are

listed in Table 2.3. Due to the accurate representation of the energy bands, the

calculated band gaps of present compounds come out to be in good agreement

with corresponding experimental values [51,77]. Even the accuracy of our

calculated band gaps w.r.t experiment is very high as compared to other theoretical

results [64,77] for all compounds. The band gaps for studied compounds are found

in range 0.51 eV to 1.27 eV. Thus, these ternary compounds are characterized as

narrow band gap semiconductors and may be very promising for nonlinear optics

and optoelectronics particularly upto mid IR range [79,80].

2.3.1.2.3 Bandstructure: The band structures of all these compounds are

presented in Fig 2.13. The common features of these compounds include the

observation of direct band gap along the Γ- Γ direction and existence of valence

band maximum at EF. In the band structure of reference compound, ZnGeAs2

Chapter 2

74

(upper left panel of Fig. 2.13), the manifold- bands ranging from -4 eV to 0 eV in

the VB is due to As-p and Ge-p states mainly with a small contribution from Zn-p

states.

Fig. 2.13 Calculated bandstructures of ABAs2 (A = Zn, Cd; B= Ge, Sn)

compounds. The horizontal line at E = 0 eV marks the Fermi

level (EF).

The As-p states are extended upto EF. Above EF, the bands at E > 3 eV arise

from empty As-p and Ge-p states. The overlapping of cations (Zn and Ge)-s and

anion (As)-p states, produces the bonding and antibonding states in VB and CB,


75

respectively, resulting the band gap in the compound. ZnGeAs2 has the greatest

separation between bonding and antibonding states among present compounds due

to the excellent orbital overlap as discussed earlier. Similarly, we can elucidate the

semiconducting band structure of other three compounds. Further, the substitution

of cation(s) in ZnGeAs2, results in poor overlap of atomic orbitals due to the larger

size of substituted cation(s) involved. This leads to smaller separation between

bonding and antibonding states which is responsible for lowering the band gap

from its initial value in reference compound, ZnGeAs2.

2.4 Conclusions

We have demonstrated the electronic band gap of RO2 (R =Si, Ge, Sn and

Pb) and ABAs2 (A = Zn, Cd; B = Ge, As2) compounds. In the first section, the

physical state of RO2 series has been altered with the change of R atom down the

same group. Using FPLAPW method, we have observed that the ground state of

the present compounds of RO2 series have been changed from insulator (SiO2) to

semi-metal (PbO2). We have predicted the large direct band gap of all the

semiconductors (except PbO2) which is in very good agreement with the

experimental value. We have noticed that the mBJLDA is flexible to reproduce

accurately both, the XC energy and its charge derivative. Thus, the band gaps with

mBJLDA come out to be very close to experimental values. On the other hand,

GGA and EV-GGA formalisms underestimate the band gap. The covalent

character of the R-O bond decreases with increase in size of R-atom. As the size of

R atom increases which results in poorer orbitals overlap of R and O atoms and

thus, leads to formation of longer and weaker bonds responsible for the semi-

metallic nature of PbO2. This poorer overlap produces a decrease in separation

between valence and conduction bands. This overlap between R and O atom is

strong in case of SiO2. The valence band maximum is contributed by O-p, R-s and

R-p states whereas conduction band minimum is dominated by R-s states mainly.

The semimetallic nature of PbO2 is governed by the partial occupation of lowest

Chapter 2

76

part of strongly hybridized conduction band at EF. We have also observed that the

charge transfer occurs mainly from R atom towards O atom. As we change the R

atom down the series, the electron density in the interatomic region between R and

O atoms decreases. This is due to the reason that the nearest neighbor distance

between R and O atom increases from 3.31 a.u. (in SiO2) to 4.04 a.u. (in PbO2)

which leads to longer bonds along the series. In other words, the ionicity of R-O

bond increases along the series SiO2 → PbO2.

In the second section, the first principle calculations has been performed to

calculate the electronic properties of ABAs2 (A = Zn, Cd; B = Ge, Sn) compounds

to see the effect of changing local environment. We have observed that the band

gap of the reference compound ZnGeAs2 change significantly by substituting

cation(s) with corresponding next group element. We predict a direct band gap in

all these compounds this gap decreases with the change of either one or both

cations in ZnGeAs2. The calculated band gaps are in better agreement with

corresponding experimental ones as compared to other calculations. The electronic

band structure is analyzed in terms of contributions from various electrons and the

covalency or ionicity of two bonds, A-As and B-As has been discussed with

respect to the substitutions. This covalent/ ionic character depends on Pauling

electron-negativity difference of A, B and As atoms. These compounds are

characterized as narrow band gap semiconductors with a maximum gap (1.27 eV)

for ZnGeAs2. A good agreement of band gaps with experiments indicates that mBJ

functional is best suited for calculating electronic structure of semiconductors and

insulators.

The agreement between theoretical predictions and experimental obsevation

for electronic properties allows a deep understanding of these compounds in terms

of their band structures and DOS. This study could be very useful to provide a

strong basis for the development of new DMS compounds for spintronic

applications.


77

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