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ФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИ
PHASE ANALYSIS AND ENERGY SPECTRUM OF InGaTe2
Gojaev E.M.,
Doctor physico- mathematics sciences, professor, Azerbaijan Technical University Gulmammadov K.J., Candidate physico- mathematics sciences, Azerbaijan Technical University Osmanova S.S., Candidate physico- mathematics sciences, Azerbaijan Technical University Rehimov R.S., Candidate physico- mathematics sciences, Azerbaijan Technical University Alieva P.F. Doctor of philosophy of physics, Azerbaijan Technical University
Abstract
Single-crystals of InGaTe2 compounds have been grown by Bridgman-Stockbarger method. Surface microrelief was studied, surface and volume images of single crystals were obtained by atomic force microscopy. It is revealed that the crystal is well formed and their surface does not require additional processing for optical investigations. The type of crystal structure and the parameters of the InGaTe2 unit cells are determined by X-ray phase analysis methods. It is revealed that this phase crystallizes in tetragonal system with lattice parameters -0 0
a = 8.463 A, C = 6.981 A, the space group D\l(14/mcm), the number of formula units 4. Theoretically,
the parameters of the elementary cells InGaTe2 were calculated by minimizing the total lattice energy, and it was found that the experimental and theoretical calculated values of the lattice parameters of this compound -
0 0
a = 8.409 A , C = 6.871 A are practically the same. Using the pseudopotential method, the band structure of InGaTe2 was calculated, the origin of the valence and conduction bands were determined, and the width of band gap was determined. It was found that InGaTe2 is a direct-gap semiconductor. Using the results of the band structure calculations, tensors of the effective masses of electrons and holes were calculated. It is revealed that the tensors of the reciprocal effective mass of electrons and holes both have a diagonal form and therefore the constant-energy surfaces are described by rotational ellipsoids, which corresponds to the symmetry of crystal.
Key words: InGaTe2 compounds, surface microrelief, X-ray phase analysis, band structure, lattice parameters, Murnaghan equations, effective mass tensors.
INTRODUCTION
For a modern explanation, the change in conductivity, both elementary substances and complex compounds, requires more specific ideas about the nature of the forces acting in crystal lattices. In this regard, the issues of crystal chemistry, based on structural studies, are very important. After revealing the decisive role of short-range order in the physicochemical features of solids and semiconductors in particular, the role of structural studies creating the experimental base of crystallochemistry became apparent.
As is known, the complex of physical properties of solids is determined by the chemical composition and spatial arrangement of the constituent atoms, although the nature of the electronic interaction between them is determined by the position of the constituent elements, but all this clearly appears only within the framework of a particular crystalline structure. Thus, the solution of one of the specific problems of physics and chemistry of semiconductors can in many ways
also be determined with the specification of the specific relationships of the physical features of semiconductors with the chemical composition of the crystal structure and the nature of the bond. However, at present, the study of new complex semiconductors is carried out unilaterally, it is often limited to the identification and study of their physical features, and for the study of crystal lattice structure is not given due attention. Despite the fundamental importance of the crystal structure, only a few complex type semiconductors have been deciphered quite fully [1-3].
The purpose of this paper is the phase analysis and the energy spectrum of the ternary compound InGaTe2.
EXPERIMENTAL PART
For the synthesis, the elements were used in purity In, Te, Ga-99.996 wt %. The ampoules were first purified by a mixture of HF with distilled water. After chemical cleaning, the ampoule was filled with highly purified elements. The mixture InGaTe2 was aged for
24 hours at 9700C. During the synthesis process, the ampoules were often shaken out in order to better mix the constituents. Further, the ampoule with the substance at a rate of 1.33 mm per hour was transferred from the high-temperature zone to the crystallization zone with an appropriate temperature of 7000C. Dif-fractograms were taken on DRON-1 in the filtered ra-
0
diation CuKa (X — 1.54056 A ). The lattice parameters were determined by extrapolation from the least-squares function
^cos2в sin в
+
cose в
\
It is known that scanning probe microscopy is one of the powerful modern methods of studying morphology and local properties of a solid body surface with high spatial resolution [4].
We investigated the microrelief of the surface of an InGaTe2 single crystal by the scanning probe microscope in the atomic-force regime.
43
To obtain an image by this method, a specially organized sample scanning process was carried out. When scanning, the probe first moved above the sample along a certain line, while the magnitude of the signal on the actuating element was proportional to the surface relief and was recorded in the computer's memory. Then the probe returned to the starting point and went to the next scan line, and the process was repeated again.
RESULTS AND DISCUSSION
The results of X-ray phase analysis showed that the compound InGaTe2 crystallizes in tetragonal sys-
0
tem with lattice parameters a — 8.463 A,
0
C — 6.981 A, space group D\l (14/mcm). The results of X-ray phase analysis are given in Table 1.
№ e sine 0 d exp,A 0 dрасч'A I h k l № e sine 0 dexp,A 0 dрасч'A I h k l
1. 10°29' 0.1819 4.2340 1.2310 470 2 0 0 15. 3203' 0.5306 1.4516 1.4513 33 5 3 0
2. 12°27' 0.2157 3.5709 3.4901 146 0 0 2 16. 3303' 0.5449 1.4135 1.4105 126 6 0 0
3. 130 19' 0.2002 3.345 3.327 998 2 1 1 17. 3501' 0.5739 1.3421 1.3401 101 5 3 2
4. 14055' 0.2574 2.9926 2.9921 689 2 2 0 18. 35050' 0.5854 1.3158 1.3141 130 3 3 4
5. 16044' 0.2876 2.6782 2.6762 331 3 1 0 19. 36016' 0.5916 1.3020 1.3028 46 5 2 3
6. 21025' 0.3653 2.1268 2.1237 640 3 1 2 20. 3802' 0.6161 1.2501 1.2494 27 6 2 2
7. 22048' 0.3876 1.9872 1.9821 181 2 2 3 21. 39047' 0.6398 1.2038 1.2149 70 5 1 4
8. 23058' 0.4062 1.8963 1.8923 360 4 2 0 22. 4205' 0.6702 1.1492 1.1492 26 5 4 3
9. 25012' 0.4259 1.8083 1.8092 72 4 0 2 23. 43053' 0.6932 1.1112 1.1112 20 7 3 0
10. 26011' 0.4412 1.7459 1.7450 28 0 0 4 24. 48039' 0.7507 1.0263 1.0263 34 8 2 0
11. 27022' 0.4526 1.6758 1.6752 128 1 1 4 25. 46018' 0.7230 0.9974 0.9973 38 6 6 0
12. 28027' 0.4769 1.6152 1.6132 19 2 0 4 26. 64054' 0.9055 0.8506 0.8569 40 7 5 4
13. 30019' 0.5051 1.5249 1.5331 86 5 2 1 27. 65035' 0.9101 0.8463 0.8463 15 8 6 0
14. 310 0.5151 1.4952 1.4960 76 4 4 0
As is known, experimental studies of lattice pa- using the first-principles theoretical calculations (ab in-rameters of crystals are laborious enough. Therefore, itio), the parameters of elementary cells of the compound InGaTe2 were determined [5].
0.2 0.4 0.6 0.8 1.0 1.2 MKU 0.2 0.4 0.6 0.8 1.0 мкм q.2 0.4 0.6 0.8 1.0 1.2 мкы 0.2 0.4 0.6 0.8 1.0 1.2
Fig.L Microreliefs of the surfaces InGaTe2 in a 2D scale for different directions.
Fig.2. Microrelief of the surfaces InGaTe2 in 3D scale.
AFM surface images InGaTe2 in 2D and 3D scales and for different directions are shown in Fig. 1 and 2. From this it follows that the crystal has a well-formed smooth surface and is very convenient for carrying out various studies without additional treatments.
It is known that when crystal is exposed foreign influence, it undergoes deformations. Then the lattice parameters and the parameters which determine the position of atoms (their coordinates) change. Therefore, the calculation of these parameters for a given value of the deformation is an important task. It is at constant entropy the pressure is determined by the derivative of
D (SE)
the total energy than pressure P = —777 , at constant
dP
B ' =
at small changes of pressure. If we take
У T
B' = B'0, thenB = B0 + B'0P determined. From here the following equation is determined: dV dP
V
Bo + B'0P
When integrating this expression, we obtain:
PV )=Br
Bo
\
v \B
-\ -1 V )
Whence
W Js
temperature bulk modulus is determined derivative of
(dP }
volume than pressure B = —V - . In the exper-
\dV JT
iment, the derivative of bulk modulus is determined as
V (P) = v0
f p\ 1 + B0 —
v °Bo )
determined.
1800 1900
V (a.u.)3
Fig.3. Dependence of the total energy on the volume of the unit cell InGaTe2.
As is known, solids have a certain volume of equilibrium of the unit cell, and with a change in this volume by a small amount, the total energy of the crystal increases. Murnaghan equation of state [6] describes
the dependence of the total energy E of the change in the volume V of the unit cell.
To determine the lattice parameters of we have calculated suitable values of total energy by changing
volume of unit cell ± 8% .The parameters in the equation of state Murnaghan were chosen so that the dependence of total energy from the cell volume ( Fig.3 ), obtained from equation (illustrated in Fig.3 Solid line) passes through the computed points. According to the
eV )=E + 9VB 16
V13 -1
results of calculations of the unit cell volume at equilibrium is V = 1664.0971 a.u., bulk modulus B =
35.9321 GPa, its pressure derivative B' = 4.1770. There is good accordance between these calculations results and Birch - Murnaghan equation [6] (Table 2).
"l2r
B0, +
3 -1
V
6 - 413
1
14703.6
Since the volume V = a2 C of the unit cell is equal to and the resulting volume of the equilibrium
state Vo = 1664.1829 a.u, calculations allow one to find the lattice parameters.
Table 2 Parameters of the equations of state of Murnaghan and Birch-Murnaghan.
Parameter InGaTe2
Murnaghan Birch-Murnaghan
Vo (a.u.) 1664.0971 1664.1829
Eo (Ry) -85685.005625 -85685.005625
B (GPa) 35.9321 35.9648
B' 4.1770 4.0662
3
2
The parameters of the crystal lattice and the coordinates of the atoms in the unit cell calculated by us are in good agreement with the literature data [6].
Table 3 Calculated parameters of chalcogen and In-GaTe2 lattice.
Parameter InGaTe2
LAPW EXP.[5]
a, Â 8.409 8.412
c, Â 6.871 6.875
X 0.174 0.173
It should be noted that the results obtained make it possible to calculate subsequently the phonon spectrum
and to study the effect of deformation on the electronic and optical properties.
It is known that calculations of the energy band of crystals constitute a basis for a theoretical study of the physicochemical properties of materials. In the present paper, the band structure of the InGaTe2 semiconductor compound has been calculated by the pseudopotential method. The electronic spectrum of this phase was calculated using the density functional method, using the ABINIT software package, using the Troiler-Martins pseudopotentials in the basis of plane waves. In the expansion of the wave function, we used plane waves with a maximum kinetic energy of 60 Ry. The lattice parameters were determined by minimizing the total energy, and the parameters of the structure were
Fig. 4 band structure of InGaTe2
optimized with the aid of the Gelman-Feynman forces. The process of minimizing forces was carried
out as long as the force modules
F
mRy
<3 --. To cal-
a.u.
culate the band structure of InGaTe2, the optimized lattice parameters a = 8.3945 A, c = 6.8352 A, the chalco-gen parameters x = 0.1730.
The calculation of the electronic spectrum of In-GaTe2 was carried out at symmetrical points of Г, Т, N, P, and also along lines connecting these points. The results of calculating the band structure are shown in Fig. 4.
As can be seen from the figure, the InGaTe2 valence band consists of three subbands. The lower subband consisting of four zones is distant from the others by a wide energy gap of the order of ~ 6 eV. Group theoretical analysis shows that these lower valence bands located about -10 -H1 eV are due to their origin of the 5s-states of Te. The next group of four valence bands located at an energy level of about -5 eV occurs mainly from the ¿--states of In and Ga atoms.
The remaining large group of ten zones with a width of 5 eV is derived from the p states of the In, Ga, and Te atoms. In [6], where the X-ray photoemission spectrum of InGaTe2 is shown, it is revealed that the photoemission spectrum consists of three distinct regions. These authors attribute a peak at -11.5 eV to 5s-states of Te, a peak of about -4 eV to Ga-Te bonds, and
~h(k0 + G')
a complex of features about -5^0 eV to Ga-Ga and GaTe bonds, which agrees well with our calculation of the band spectrum and group-theoretical analysis.
The components of the inverse effective mass tensor were determined by the formula
mn
m
= Sj +
2
m
z
(n, к 0| P\n', к 0)( n, к 0| P\n, к 0) En (к 0) - En, (к 0)
mo- electronic mass of substance: Kraneker-
u
triangular symbols, < n, k |FP|n', k > is the matrix
5
element of the momentum operator P — —ih- at
dxi
the extremal point k0 n and n' - electronic band, | n, k > - the wave function of electrons is equal to
(n,k0pn1k0} = 1 K0 (r)P,Pn>k0 (r)d"r
V X
V - the volume of a unit cell, En(k>) and (p*n^ (r)
are the energy and wave functions determined from the Schrodinger equation for k0,
z
2m„
S^ + V k + G,K + G )
<pn k + G ) = EnkÇn k + G)
V+ Gk + G ) - Fourier transform of the
pseudopotential.
Calculation of InGaTe2 zone structure shows that both maximum of valence and minimum of conductivity zones are located at point T of high symmetry ko=0.5bi-0.5b2+0.5b3 (bi, b2, bs). Here bi, b2, bs - are the vectors of the reciprocal lattice transfer.
In our calculations components of tensor of inverse effective mass of electron were measured with an accuracy mo 0.0i.
^3,09 0 0 ^
^ mc ^
v mn y
3,09 0
0 4,59
The components of the inverse effective mass tensor of holes are determined by the formula
*
v m* y
- 2.31 0 0 0 - 2.31 0 0 0 - 0.11
As can be seen, the tensors of the reciprocal effective mass of both electrons and holes have a diagonal form and therefore the constant-energy surfaces are described by rotational ellipsoids, what corresponds to the symmetry of crystal.
Literature
1. H.Hahn, B. Weltman Üder ternare chalko-genide des Thalliums mit Gallium und Indium, Naturwissenschaften, 1967. V. 54. №2. P.42.
2. D.Müller, G. Eulenberger und H. Hahn Über ternare Thalliumchalkogenide mit thalliums-selennid-struktur, Z. anorg. allg. chem.1973. V. 398. №2. P. 207220.
3. E.M. Gojayev. Structure, electronic and thermal properties of complex semiconductors on the basis of sp and 4f elements. Diss. for Doctor of Phys.-Math. science, Baku, institute of physics of academy Science of Azerbaijan.1985, 361p.
4. V.L. Mironov. Basics of scanning probe microscopy / A manual for students of senior courses of higher educational institutions. Russian Academy of Sciences, Institute of Physics of Microstructures. Nizhny Novgorod, 2004 - 114 p.
5. X.Gonze, J.M.Beuken, R.Caracas et al. First_Principles Computation of Material Properties: the ABINIT Software Project, Allan. Comput. Mater. Sci.2002. V. 25. P. 478-492.
6. M. Mobarak, H. Berger, G. F. Lorusso, V. Capozzi, G. Perna, M. Ibrahim and G. Margaritondo, "The growth and properties of single crystals of GaInTe2, a ternary chalkogenide semiconductor," Journal of Physics D: Applied Physics, Vol. 31, No. 12, 1998,p.1433-1437
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