Zinc Sulphide Doped With Chromium. A Density Functional Theory Study

Bachelor Thesis, 2017

58 Pages, Grade: 4.00





1.1 Research Problem
1.2 Research Plan

Literature Review

3.1 Energy Band Theory
3.2 Semiconductors and their Characteristics
3.3 Direct/Indirect Band Gap Semiconductors
3.4 II-VI Compound Semiconductors
3.5 Zinc Sulphide
3.6 Exchange Interaction
3.6.1 Direct Exchange Interaction
3.6.2 Indirect Exchange Interaction Double Exchange Interaction
3.7 Jahn Teller Effect-
3.8 Techniques for Computational Study
3.9 Density Functional Theory
3.9.1 Many-Body Problems in Solids
3.9.2 Hohenburg-Kohen Theorems First Hohenburg Kohen Theorem Second Hohenburg Kohen Theorem
3.9.3 Kohan-Sham Equation
3.9.4 Exchange Correlational Functional
3.9.5 Local Density Approximation (LDA)
3.9.6 Local Spin Density Approximation (LSDA)
3.9.7 Generalized Gradient Approximation (GGA)
3.9.8 LDA and GGA with Hubbard Correction
3.9.9 Hybrid Functional
3.9.10 Tran-Blah Modified Becke Johnson Potential (TB-mBJ)
3.10 Basis Sets
3.10.1 Slater-Type Orbital (STO)
3.10.2 Gaussian-Type Orbital (GTO)
3.11 Amsterdam Density Functional (ADF)

4.2 Brief Introduction to ADF-BAND
4.2.1 Features of ADF-BAND
4.2.2 Operating System for ADF-BAND
4.2.3 Electronic and Structural Parameters using ADF -BAND
4.2.4 Construction of wurtzite ZnS structure with ADF -BAND
4.2.5 Construction of a unit cell of ZnS
4.3 Computational Aspect

5.1 Electronic Properties
5.1.1 Chromium Doped Zinc Sulphide: 16 atoms
5.1.2 Cr Doped ZnS: 32 atoms
5.1.3 Cr Doped ZnS: 64 atoms
5.2 Conclusion




Fig. 1.1: Stick and Ball Representation of ZnX Crystal Structures-

Fig. 3.1: Comparison of Conductors, Semiconductors and Insulators on the Basis of Band Gap-

Fig. 3.2: Electronic Distribution of Zinc and Sulphur

Fig. 3.3: Formation of Covalent Bond due to Transfer of Electrons from Zinc to Sulphur

Fig. 3.4: Double Exchange Interaction in Manganese Ions

Fig. 5.1: Total and Partial DOS for 16 Atoms of Cr doped ZnS with (a) GGA and (b) GGA+U Functionals

Fig. 5.2: 3d States of Chromium Atom with (a) GGA and (b) GGA+U

Fig. 5.3: Total and Partial DOS for 32 Atoms of Cr doped ZnS with (a) GGA and (b) GGA+U Functionals

Fig. 5.4: Cr-3d Plots for 32 Atoms of (a) GGA and (b) GGA+U

Fig. 5.5 Total and Partial DOS for 64 Atoms with (a) GGA and(b) GGA+U Functionals

Fig. 5.6 3d States of Chromium Atoms for (a) GGA and (b) GGA+U

Fig. 5.7: (a) Five-fold Degeneracy, (b) Crystal Field Splitting, (c) Jahn Teller Distortion, (d) pd-Hybridization, (e) S-3p States -

Table 3.1: Values of Lattice Constants and Band Gap for Zinc Blende, Wurtzite and Rock Salt Structures


The electronic and magnetic properties of Cr doped wurtzite ZnS were studied by means of most advanced theoretical approach density functional theory (DFT) using generalized gradient approximation (GGA) functional and its correction factor GGA+U. Calculations have shown that doping of chromium at cationic sites of wurtzite zinc sulphide results in formation of a p-type semiconductor. Addition of hubbard term in the system causes an increase in band gap value and creates a gap between spin up and spin down channels for 3d states of chromium atoms. Chromium doped ZnS possess half metallic character because of excess in majority spin carriers than minority ones. Hopping of electrons in anti-bonding states of chromium atoms refers to the ferromagnetic behavior of the material. Half metallicity and ferromagnetic nature of the chromium doped wurtzite zinc sulphide makes this material a best candidate to be used in the field of spintronics.



For past few decades, work in semiconductor field appears to be of substantial importance in industrial world and offers a new direction to upgrade the standards of life. This novel era of semi-conductors has remake the history of science with its groundbreaking technology and has proven to be an extensively emerging field to handle even single atoms and molecules for manipulation and fabrications. In the recent years, material science has open a new window towards applicability of semiconductor devices in electronics, spintronics and many other branches of science. Presently, II-VI materials have gain much value because of their broad range of applicability in advance fields of science [1]. These elements involve transition metals like zinc, cadmium and nonmetals like oxygen, sulphur, selenium, tellurium. Due to their wide band gap, these compounds possess shorter wavelength and used in optoelectronic devices [2]. II-VI compounds have been seriously investigated by researchers as they are cost effective to be used as photovoltaic devices. Photovoltaic methods are used to convert solar energy into electrical energy for power generation purposes [3]. II-VI semiconductors are widely used in electronics, photonics, sensors, nano devices and in optoelectronic devices because of their novel characteristics [4]. Since the suitability of material for a particular device is revealed by its overall electronic structure, II-VI compounds and their quantum wells have assumed tremendous importance in past few years because of applications of semiconductors in electronics and optical devices. Applications of II- VI semiconductors in optoelectronic devices have achieved a high experimental level during recent years [5]. Zinc monochalcogenides are prototype II-VI semiconductors. All these compounds are found to crystallize in zinc—blende, wurtzite structures and exist in rock salt phase at specific pressures [6].

Abbildung in dieser Leseprobe nicht enthalten

FIGURE 1.1 Stick and Ball Representation of ZnX Crystal Structures. (a) Cubic Rocksalt, (b) Cubic Zincblende, (c) Hexagonal Wurtzite. The Shaded Grey and Black Spheres Denote Zn and X (O, S, Se, Te) Atoms, respectively

(Kittel Charles, Introduction to Solid State Physics 7th-Edition)

Zinc Sulphide, a II-VI compound semiconductor is most used material for electroluminescent devices. ZnS can also be used to fabricate light emitting diodes and laser diodes operating in the UV region. ZnS presents three phases which are cubic zinc blende, hexagonal wurtzite and cubic rock salt. Each state possesses distinctive physical properties. Zinc blende is considered to be one of the well-balanced states at room temperature, whereas wurtzite structure exists above 1293K. On the other hand, rocksalt in stable form can be secured only at comparatively elevated pressures [7]. ZnS naturally appears in cubic Zinc blende state, commonly known as sphalerite. ZnS is also obtained in the form of mineral wurtzite, in which numerous tetrahedrally structured compound semiconductors crystallize [8]. Zinc blende phase of ZnS is the only composite that can be achieved through epitaxial growths. Fundamentally, electronic behavior of wurtzite structure is dissimilar to that for zinc blende ZnS [9]. ZnS exhibits high bulk refractive index and because of its lacking absorption capability in visible and near infrared regions, it is the most competent candidate to be used in inorganic compounds to refine their properties [10].

In this research, electronic and magnetic properties of II-VI semiconductor Cr- doped ZnS in bulk phase is studied with density functional calculations. Functionals involved are generalized gradient approximation and GGA+U in ADF-BAND. It can be examined that p-type semiconductor is formed when chromium is doped with wurtzite zinc sulphide. This newly formed p-type semiconductor has half metallic nature due to the presence of excess of majority spin carriers. From the electronic properties of chromium doped zinc sulphide, ferromagnetic behavior has been revealed. In between neighboring chromium atoms, hopping of electrons appear due to doubly exchange interaction. This double exchange interaction occurs between electrons having parallel spin, thus giving rise to ferromagnetic behavior. When material is treated with hubbard term U having a value of about 4.01 eV, then this increases the band gap value. Application of correction factor in the system optimize the value of band gap to some extent. The use of hubbard term increments the gap between spin up and spin down channels. The previously reported literature on chromium doped Zinc Sulphide lacks consistency and a serious research has not been done on this material. The results obtained from this research are very vital to demonstrate the dynamic behavior of Cr: ZnS and its role in spintronic devices.

1.1 Research Problem

Although II-VI compound semiconductors, because of their applications in many fields of science have become the favorite material for researchers, but there is no sufficient literature available for wurtzite ZnS with doped transition element chromium and no consistent research has been done on this material. The main motive of this research is to reveal the properties of chromium doped zinc sulphide in wurtzite phase. The basic purpose of this work is to explore those characteristics of the material which can be fruitful in the field of spintronics.

1.2 Research Plan

Thesis report on this research work is covered by five chapters. 1st chapter contains a brief introduction of the materials employed in this study and short description of their emerging applications in field of science.

2nd chapter demonstrates the research that has previously been done by the researchers on this material. Research on electronic properties of ZnS and Cr-doped ZnS is described in this section.

Chapter 3 gives a detailed description of our material, half metallic semiconductors, exchange interactions of electrons resulting in hopping and fundamentals of Density Functional Theory.

4th chapter demonstrates the techniques employed in this study to explore the electronic and magnetic properties of the chromium doped zinc sulphide.

Chapter 5 involves discussion on results obtained from our calculations while doping chromium atoms with wurtzite zinc sulphide. A technical analysis concluded that Cr: ZnS possess half metallicity and shows ferromagnetic behavior which can be a key point for this material to be used in spintronics. This chapter involves the detailed study of Cr: ZnS with different supercells.



ZnS has also a key role in photonics including lasers, sensors, LEDS. Electronic structure of ZnS can determine its optical properties as band gap energy is related to frequency as well as wavelength. Cardona et al examined electronic structure of zinc blende ZnS using VASP package with LDA functional. He reported a direct band gap of 2.19eV. Gap value obtained by GGA is 2.07eV less than that got by LDA. When ZnS is doped with Ag, then band gap of ZnS becomes narrow [8].

Taguchi et al found a band gap of 3.801 eV at 4.2 K for zinc blende ZnS and have grown thin films of ZnS using metal organic chemical vapor deposition (MOCVD) [11]. Abounadi et al get peaks between 3.799 eV and 3.8005 eV with low temperature reflective measurements. Trans et al faced difficulties while obtaining band gap value for bulk ZnS at room temperature. He faced this problem because good quality bulk ZnS was not commercially available. He observed band gap value in between 3.56 eV and 3.764 eV. Band gap obtained using absorption methods is about low as 3.56 eV, it is due to lack in accurate location of band edge and method of analysis. However, Cardona et al get a band gap of 3.74eV and 3.76 eV for bulk ZnS, using reflectivity and wavelength modulated reflectivity techniques respectively [12].

Ahmed et al observed a band gap of 3.5 eV-3.7 eV from sample growth by chemical co-precipitation. Ahmed et al also employed other measurement techniques like XRD and scanning electron microscope (SEM). Optical properties of nanocrystals of ZnS were studied by Mir. He used the UV-Vis spectroscopy technique and investigated a band gap of 3.7 eV at room temperature. Weidong et al developed pseudopotentials. Zakharov et al also used same technique as done by Weidong et al and adjusted d- character in valence band maximum. He did this adjustment by addition of short range attractive potential in non-local d states of Zn pseudopotentials. He obtained a band gap of 2.31 eV for ZnS in zinc blende phase and concluded that local density approximation (LDA) underestimated the band gap results by 30-40 % from its experimental findings. Weidong et al and Zakharov used Green function and screened Coulomb interaction (GW) to get a value of 3.98 eV (zinc blende) and 4.03 eV (wurtzite) respectively. Weidong et al found a band gap of 2.03 eV with generalized gradient approximation (GGA) functional while 3.27 eV with GGA+GW [13].

Willatzen et al worked for the correction of band parameters for semiconductors. On the behalf of nearest neighbor distance, bulk modulus of 90 GPa for ZnS was determined by Cohen. However, expression for bulk modulus was reported by Lam et al with total energy method [14]. Zakhorov et al found valence band energy of -12.36 eV [15].

Results obtained from Yeh, Wei and Zunger predicted large band gap for wurtzite phase than others phases. According to Bellotti et al, as ZnS wurtzite structure exhibits higher ionization transition rate and also possess high optical gain, thus it is best candidate for fabrication of electroluminescent devices. Ozaki and Adachi also studied optical spectra for zinc blende phase of ZnS. Findings of Ozaki, Adachi, Cardona and Harbeke reported that inter band transition peaks in real and imaginary part of dielectric shift towards lower energy of the system [9].

La porta calculated energy, geometry and change in phases of ZnS polymorphs by the application of pressure. He used periodic first principle calculations based on DFT. Calculations were performed with B3LYP-D hybrid functional having dispersion correction and a Gaussian basis set. Porta reported that wurtzite phase acts like a more concise state than zincblende phase, and a wurtzite phase develop a residual polarization in tetrahedral clusters as it encounters a lack of symmetry. Wurtzite structure is in hexagonal group P63mc having lattice constants a = 3.79 Å and c = 6.14 Å. c/a ratio comes out to be 1.621, diverges minutely for this phase. However octahedral clusters are created in rock salt phase, in which each atom of zinc is encompass by six atoms of sulphur.

Data analysis obtained from this, revealed that mixed bonding is present in ZnS phases. Nilsen observed Raman spectrum for Zinc blende structure and found two bands having transverse optic mode at 271 cm-1 and longitudinal optic mode at 352 cm-1

Band gap calculations reported by Porta et al showed that both wurtzite and zinc blende phases have a direct band gap of 4.14eV and 4.10eV respectively. However, rock salt phase possesses an indirect gap of 1.45eV. Difference of 6.3% in band gap calculations was because of use of dispersion factor. DOS results yield that upper valence band has 3p orbitals of sulphur in which 4s and 4p orbitals have less donation. Strong bonding b/w Zn and S atoms have been established due to 3d states of zinc in its valence band. Hybridization of 4s and 4p orbitals in zinc occurs in conduction band, also possessing a minute proportion of 3p orbitals of sulphur. Binding energies for zinc 3d orbitals comes out to be 7.43eV, 6.98eV and 7.67eV for zinc blende, wurtzite and rocksalt phases respectively [7].

Doping of transition metals and rare earth elements with II-VI semiconductors is one of the reliable method to adjust color of semiconductors. ZnS having a bulk band gap of 3.67 eV is a good choice as a host semiconductor for doping to obtain nanostructures due to its stability, low cost and low toxicity. It has also been proved to be a good option for room temperature dilute magnetic semiconductors.

Cr is a transition metal element with enormous electronic shell structures, and its ionic radius is nearly close to Zn, which implies that Cr can easily penetrate into ZnS lattice. Cr possess a high magnetic moment and it supports the aspect of ferromagnetism. Furthermore, Cr metal is antiferromagnetic. Cr doped ZnS nanoparticles exhibit room temperature ferromagnetism [16].

Theoretical research yields that transition metal doped II-VI compounds exhibit room temperature ferromagnetism because of exchange interaction b/w spin of doping atoms and carriers in host compound, which in turn expected to produce global ferromagnetic behavior in the entire lattice. Intensive research has been done on synthesis of materials with Room Temperature Ferromagnetism (RTFM) on dilute magnetic semiconductors [17].

The room temperature ferromagnetic behavior of Cr doped ZnS in magnetic field range from 0 to ±1.5T. The undoped samples exhibit diamagnetic behavior whereas Cr doped ZnS exhibit weak ferromagnetic or superparamagnetic behavior at room temperature. In spite of delicate experimental methods, computational methods have also been extensively used to explore the properties of compounds. Usually, GGA or LDA underestimate the band gap and failed to give optimized results [18]. Excitation wavelength of 334nm gave maximum intensity for ZnS and Cr doped ZnS nanoparticles. Cr doped ZnS samples exhibit hysteresis loop at room temperature for 2 atm% of Cr conc. This reveals that slightly doped Cr: ZnS shows good ferromagnetism that can be attributed to the presence of small magnetic dipoles which interacts with their nearest neighboring dipoles inside crystal [19].

XRD studies on pure and Cr-doped ZnS nanoparticles showed the cubic structure of ZnS and absence of any secondary phase. Optical measurements indicate blue shift in the absorption edge arising because to quantum confinement in nanostructures. A slight red shift with further increase in Cr concentration is attributed to sp-d type interactions. Ferromagnetic behavior is observed in Cr doped ZnS nanoparticles but it diminishes with increase in Cr concentration [20]

Cr in ZnS lattice provide unpaired spins for ferromagnetism rather than Cr clusters. So, ferromagnetism in Cr doped ZnS samples may be considered due to exchange interaction between localized spins and delocalized carriers. Increase in annealing temperature increases magnetization resulting in thermal energy but this leads to decrease in surface defects hence reducing magnetization with further rise in temperature. Above annealing temperature of 5000C, hysteresis loop becomes smaller, and cubic ZnS changed to hexagonal wurtzite structure of ZnO. However, magnetization decreases but coercivity increases with increasing temperature. DRS spectra revealed that increase in annealing temperature shift band gap to higher wavelengths [21].

Muliken charge analysis has been done to study bonding in pure and doped ZnS. Pure analysis demonstrates charge transfer of order 0.45e from Zn to S atoms. In doped ZnS analysis, there is a significant charge transfer of 0.15e to 0.67e. Binding energy increases with doping thus enhancing its structural stability [22]

Zeng et al notice room temperature paramagnetism and increase in PL intensity with increase in Cr doping in ZnS nanocrystallites. Amaranatha Reddy et al examined ferromagnetism and blue emission with quenching effect again with increasing dopant conc. in Cr doped ZnS nanoparticles. Palvinder et al reported significant ferromagnetism in Cr doped ZnS nanoparticles by co-doping nitrogen synthesized via precipitation method [16].

In 1988, Xu et al observed that integrated PL intensities from Eu3+ and Cu2+ doped ZnS nanocrystals are obviously stronger than that from Mn2+ doped ZnS nanoparticles. Sarkar et al have observed ferromagnetism in Mn-doped (2.5 nm) ZnS nanoparticles below 28K. Satio et al discovered room temperature ferromagnetism in ZnxCr1-xTe with Curie temperature of 300K. Droubay et al found that Cr-doped TiO2 film also exhibit room temperature ferromagnetism. Hu et al noticed that room temperature ferromagnetism could arise from Zn vacancies and can be increased by heavy Cr doping [18]. Pal et al observed structural and electronic properties of ZnS nanotubes by means of density functional tight binding method [23].

ZnS because of acting like host semiconductor for doping, has great significance in applications like light emitting diodes, field emitters and lasers. ZnS is a promising candidate for optoelectronic and luminescent device applications because of its wide band gap of 3.68 eV. Transition metal doped with II-VI semiconductors have also extensive applications in optoelectronic devices [18].

Density functional theory (DFT) serves as one of the most helping tool for determining the electronic and structural properties of the compound semiconductors. DFT is not a newly developed technique, research on this method has been done for decades and it holds a successful background [24]. To solve the many body problems, hartree approximations were introduced for the very first time in history in the late 1920s. Hartree introduced a Hartree Fock method to solve many-body problems, which was the oldest technique for evaluation of electronic wavefunctions. According to Hartree approximation, total electronic wave function which must be symmetric is the product of N-single particle orbitals, and the product is a Hartree product. This approach does not take into account the Pauli’s Exclusion principle thus neglecting electron spin, failed to satisfy antisymmetric behavior of electrons [25]. Lack of symmetry in Hartree approximation was noticed by Fock and Slater in 1930 [26]. To solve this problem, Slater’s determinant and an extension of Hartree method known as Hartree-Fock method were introduced in the recent 1930s [27]. But, the calculations done with Hartree-Fock method were complicated and took time for better understanding, so this method was not proved too useful [28]. In the late 1920s, Thomas Fermi model proposed by Thomas and Fermi was introduced to figure out the electronic and structural properties of many-body problems. However, this model was failed to determine many properties with high accuracy but it is considered as the ancestor of density functional theory [29]. Foundation of DFT rests mainly on two theorems proposed by Hohenberg and Kohen in 1964. According to these two theorems, ground states not only gives ground state density but it must minimize the energy [30]. DFT deals with electron density of the system, so instead of dealing with 3N variables (N indicates number of electrons, 3 spatial variables x, y, z) for many-body electron wavefunctions, electron density as a functional is used as it is just a function of 3 variables. Thus, to figure out the many electronic wave-functions by means of DFT calculations have become much easier [31].

Density functional Theory has proved to be a very important tool for studying the material characteristics and its use is increasing exponentially. In our research, we have done analysis of Cr doped ZnS.



Detailed description regarding background of density functional theory and its calculation techniques has been given. One of the main characteristics that determine whether the material is a conductor, insulator or a semiconductor is its band gap. Band gap is associated with energy band theory. its description is here.

3.1 Energy Band Theory

When an electron revolves around an isolated atom, it is under the influence of forces only within the atom. However, when we consider a whole material then as all the atoms are very close to each other, so electron will experience a force from other atoms too. Band may be considered as a collection of energy levels. In an atom, electrons in first orbital form an energy level and electrons in 2nd orbital form another energy level and so on. Energy levels of atoms in a solid split up into sublevels called states, which are formed due to the effect of forces exerted by atoms on each other.

In an atom, energy level associated with outer shell (valence) electrons is called valence band. Valence band is the highest occupied band. It may be completely filled or partially filled with electrons but never empty. Bands below valence band are normally completely filled and as such play no role in conduction. If electrons in the valence band gain sufficient energy, they become free electrons. Now, they can freely move about the entire material. Energy level associated with free electrons is termed as conduction band. Since free electrons are responsible for conduction, they are called conduction electrons. Conduction band may be empty or partially filled with electrons [32]. Extra energy required by a valence electron to move to the conduction band is forbidden energy. It is also known as band gap energy. On the basis of magnitude of this energy, we can decide whether a material is conductor, insulator or a semiconductor. Insulators have full valence band; empty conduction band means it has no conduction electrons and a large band gap of several electron volts. Conductors have plenty of free electrons for conduction. In conductors, there is no band gap as there is large overlapping of valence and conduction bands. There is no physical distinction between two bands which ensures the availability of a large number of free electrons. In contrast to insulators and conductors, semiconductors at room temperature have partially filled valence and conduction bands and have a very small band gap of the order of 1 eV.


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Zinc Sulphide Doped With Chromium. A Density Functional Theory Study
University of Gujrat
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It is verified that this thesis titled "DFT study of Cr doped wurtzite ZnS" contains sufficient material required for the award of degree of bachelor studies in physics. It is hereby solemnly declared that the data quoted in this thesis is based on original work, and has not yet been submitted or published elsewhere.
dft study, adf band theory, electronic and structural parameters, band gap, unit cell of ZnS, density of states, origin software, graph, five-fold degeneracy, cystal field splitting, Jahn Teller Disortion, p-type semiconductor, spin up and spin down
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SN Butt (Author), 2017, Zinc Sulphide Doped With Chromium. A Density Functional Theory Study, Munich, GRIN Verlag, https://www.grin.com/document/508622


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