in the temperature range 10 – 800k

ADV. MAT. SCI. & TECH.
Received:
Vol. 2, Nº 1 pp. 09-14, 1999
Accepted:
OPTICAL ABSORPTION MEASUREMENTS ON MnIn 1.6Ga 0.4S 4 IN THE TEMPERATURE RANGE 10 – 800K
ISSN 1316-2012
Published:
DEPÓSITO LEGAL pp 96-0071
© 1999
12-06-99
25-06-99
31-08-99
CIPMAT
OPTICAL ABSORPTION MEASUREMENTS
ON MnIn1.6Ga0.4S4
IN THE TEMPERATURE RANGE 10 – 800K
GRIMA GALLARDO P.(a); E. OROZCO(a); M. MUÑOZ(a); L. NIEVES(b) & J.A. HENAO(c)
<peg@ciens.ula.ve>
(a)
Centro de Estudios en Semiconductores (C.E.S.)
(b)
Dpto. Física. Fac. Ciencias.
Universidad de Los Andes.
Mérida. Venezuela
(c)
Laboratorio de Cristalografía.
Universidad Industrial de Santander.
Bucaramanga. Colombia
ABSTRACT
Optical absorption measurements in the temperature range 10-800K had been performed on
single crystal samples of MnIn1.6Ga0.4S4 and the optical energy gap, Eg, had been obtained as a
function of temperature, T. The behavior of Eg with T had been analyzed in terms of usual theoretical
models. From these analysis we found a Debye temperature of 268 ± 24K and a variation of the
optical energy gap with temperature, dEg/dT = - 8.25 x 10-4 eV/K.
Key Words: Semiconductors, Optical Absorption, Optical Energy Gap.
MEDIDAS DE ABSORCIÓN ÓPTICA EN MnIn1.6Ga0.4S4
EN EL RANGO TEMPERATURA 10-800K
RESUMEN
Medidas de absorción óptica en el rango de temperatura 10-800K han sido realizadas en muestras
monocristalinas de MnIn1.6Ga0.4S4, obteniéndose la brecha de energía Eg en función de la temperatura.
El comportamiento de Eg con T ha sido analizado en términos de los modelos teóricos usuales. De
este análisis se encontró una temperatura de Debye de 268 ± 24 K y una variación del gap con la
temperatura dEg/dT = -8.25 x 10-4 eV/K.
Palabras Clave: Semiconductores, Absorción Óptica, “Optical Energy Gap”.
cation Mn in the compound under study may introduce
interesting magneto-optical and magneto-electrical
properties [8].
INTRODUCTION AND THEORY
MnIn1.6Ga0.4S4 is a laminar semiconductor material from
the general alloy composition MnIn2(1-x)Ga2xS4, with x=0.2
[1-3]. This alloy belongs to the most general family of IIIII2-VI4 materials, where ZnIn2S4 is one the most studied
example [4-6]. The laminar character (or bidimensionality)
of these materials produces important anisotropy in their
properties; for example, it has been reported that the
electric conductivity in ZnIn2S4 is four times higher in the
perpendicular direction to the axe c, than in the parallel
direction [7]. In addition, the presence of the paramagnetic
The aim of this work is to analyze the variation of the
optical band gap with temperature, in the high temperature
range (T>300K), of the compound MnIn1.6Ga0.4Se4, using
the basic model relations for temperature dependencies
of optical energy gaps in semiconductors. Recently, Pässler
[9] has discussed and compared these models using GaAs
high precision Eg (T)-data given by Grilli et al. [10] but in
the low temperature range (T<280K).
FICHA:
9
GRIMA GALLARDO P.; E. OROZCO; M. MUÑOZ; L. NIEVES & J.A. HENAO.ADV. MAT. SCI. & TECH. 2(1):09-14, 1999.
OPTICAL ABSORPTION MEASUREMENTS ON MnIn 1.6 Ga 0.4 S 4 IN THE
TEMPERATURE RANGE 10 – 800K.
GRIMA GALLARDO P.; E. OROZCO; M. MUÑOZ; L. NIEVES & J.A. HENAO.-
One of these models is the Varshni [11] relation:
Eg (t) = E0 - α T / (T+ ß)
2
EXPERIMENTAL TECHNIQUES
AND RESULTS
(1)
where α and ß are fitting parameters characteristic of a
given material. The theoretical basis of this much-used
relation is unfortunately rather weak, since ß, which is
supposed to be related to the Debye temperature [11,12],
may in certain cases be negative. Moreover, at low
temperature, this equation predicts quadratic temperature
dependence, whereas experiments find approximate
temperature independence. The parameter a represents
the T → ∞ limit of the slope dEg (T)/dT.
Single-crystals of MnIn1.6Ga0.4S4 were obtained by
chemical vapor transport using I2 as transport agent and
a temperature gradient of 80K [20]. Samples show yelloworange color, laminar character, irregular shape, 5-10 mm
diameter and ~ 0.5 mm thin.
Scanning Electron Microscopic (SEM) analysis
indicates that orange samples are slightly deficient in S
and the relative In/Ga ratio is slightly shifted towards
lower values with respect to the stoichiometric values,
which implies In defect and Ga excess [20].
Another empirical approach had been suggested by
Viña et al [13] who considered a Bose-Einstein statistics:
Eg (T) = EB – aB (1+ 2 / exp ( /T) – 1)
X-ray diffraction measurements (RIGAKU, mod. D/Max
III-B) gives spectra which indexes in the rhombohedral
system (space group R3m, Z = 3), with lattice parameters
a = 3.8580 ± 0.0005 Å and c = 37.126 ± 0.005 Å when
hexagonal axes were used (Table I). This structure is similar
to that found for the politype 12R4 of ZnIn2S4 and may be
represented by distorted compact packing of sulfur atoms
with cations occupying the tetrahedral and octahedral
sites. In the perpendicular direction to the axe c, there are
twelve layers of sulfur atoms following the sequence hcch
in the Jagodzinski notation [18]. These layers could be
separated in three groups of four layers, each one with
three layers of cations: two with the cations in tetrahedral
coordination and one with octahedral coordination.
(2)
Where the T → 0 gap limit, Eg (0), is given by EB - aB and
the effective phonon energy ω is represented by a
corresponding phonon temperature = ω / k.
A qualitative difference between these two models
arises at low temperatures and has been discussed by
Pässler [9]. We will not repeat here the details but the
conclusion: when they are applied to the high precision
Eg (T)-data given for GaAs: Varshni’s formula (eq. 1)
overestimate the measured temperature dependence
whereas Viña’s et al alternative (eq. 2) underestimate. In
order to overcoming this situation Pässler [9] proposed
the expression:
Eg (T) = Eg (0) – (α /2) [[1+ (2T/ )p ]1/p –1 ]
Figure 1 shows Differential Thermal Analysis (D.T.A.)
spectra obtained in a Perkin-Elmer DTA-7 equipment. It is
observed two transitions in the heating, at temperatures
of 1194 and 1248K, whereas in the cooling, three transition
temperatures can be observed, at 1274, 1246 and 1188K.
The transition at 1274K is somewhat spurious at it is seems
to be too high to be the solidification point compared
with the value of 1248K obtained for the melting point in
the heating. The value of 1246K seems to be more
adequate for the solidification point and the transition at
1274K could be attributed at some kind of impurity formed
at high temperature or due to a drift of the base line
produced by repositioning of the liquid drop into the
quartz ampoule.
(3)
where p = ν + 1, and ν is the coefficient of the spectral
function f ( ) ∝ ν in consideration. The parameter α has
the same meaning than in Varshni’s model. The
corresponding application of this expression to Grilli et
al. data gives a fine fit (Figure 1 of ref. [9]) of the
experimentally observed behavior.
Finally, we will try to fit our data with a simplified form
of the Manoogian-Leclerc expression [14,15], that has been
extensively used [16-19]:
Eg = E0 – U Tx - V Θ [coth (Θ/2T) – 1]
(4)
The first term of the equation describes the effect of
thermal expansion or lattice dilation on the band gap and
the second term represents the contribution from electronphonon coupling, with acoustic and optical terms being
averaged. The parameter Θ = hν/k is the usual mode
energy expressed as a temperature. This equation, with
four parameters to fit is rather difficult to use and obtain
physical meaning for the parameters.
Slices obtained by cleavage, 20-30 mm in thickness were
used for standard light transmission measurements in the
temperature range 10-800K. We used a fully automated
CARY –17I spectrophotometer with a non-polarized
tungsten lamp as a light source, a cryostat (Air Products)
cooled by helium gas for low temperatures (10-300K) and
a homemade furnace for high temperatures (300-800K).
10
OPTICAL ABSORPTION MEASUREMENTS ON MnIn 1.6Ga 0.4S 4 IN THE TEMPERATURE RANGE 10 – 800K
Line
hkl
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
003
006
009
101
102
00 12
107
108
00 15
10 11
10 13
10 14
00 18
110
113
10 17
00 21
119
10 19
201
202
204
208
11 15
10 22
10 23
11 18
00 27
10 25
10 26
11 21
20 19
20 20
216
10 28
218
dobs
dcal
[Å]
[Å]
12.405
6.197
4.126
3.326
3.287
3.095
2.827
2.712
2.475
2.374
2.171
2.077
2.063
1.929
1.907
1.828
1.767
1.747
1.686
1.668
1.663
1.645
1.572
1.521
1.506
1.453
1.409
1.375
1.358
1.313
1.303
1.269
1.242
1.237
1.232
1.218
12.374
6.187
4.125
3.327
3.288
3.093
2.827
2.711
2.475
2.374
2.171
2.077
2.062
1.929
1.906
1.828
1.768
1.747
1.686
1.669
1.664
1.644
1.572
1.521
1.506
1.453
1.409
1.375
1.357
1.313
1.303
1.270
1.242
1.237
1.232
1.218
| dobs – dcal |
I/I0
For light detection, a Ge photodiode connected to a LockIn amplifier (Princeton Research mod. 5208) was used.
[%]
0.032
0.011
0.001
0.001
0.001
0.002
0.000
0.001
0.000
0.000
0.000
0.000
0.001
0.000
0.001
0.000
0.001
0.000
0.000
0.001
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.001
0.000
0.000
0.000
0.000
In figure 2 we show a plot of It / I0 vs energy for 10,200,
400 and 700K (the other temperatures has been omitted
for clarity). We observe a shift towards lower energies
with temperature increases as it was expected. The
normalized transmitted light decreases and the oscillations
due to interference disappear at high T, these effects may
be attributed to surface oxidation since the experiments
are carried out at ambient atmosphere. Energy gap values
were obtained by extrapolation of the It/I0 function to the
minimum transmission value, as it was show in figure 3 for
T=10K.
9
3
100
4
4
1
1
7
5
2
8
2
4
6
2
10
5
3
1
1
1
1
1
1
1
1
1
1
4
2
1
1
1
3
1
1
In table II we show the energy gap values as a function
of temperature and the respective plot in figure 4. The circles
are the experimental values and the lines the fitting with
equations (1) to (4). The first observation is that all the
models reproduces well the behavior observed in the entire
temperature range. Although our data has not the accurate
precision of Grilli et al data (in our case the experimental
error is approximately of the order of the size of the circles
in the plot), in the insert we are amplified the low temperature
range. We can clearly observe that the model of Viña
reproduces very well the experimental plateau, whereas
the others models overestimated the values.
T [K]
10
15
20
25
30
40
50
75
100
Table I. Miller indices, observed and calculated lattice
spacing, and relative intensity of diffracted lines obtained
for MnIn1.6Ga0.4S4.
Eg [eV]
T [K]
Eg [eV]
2.69
2.69
2.69
2.69
2.69
2.69
2.69
2.69
2.67
150
200
250
300
400
500
600
700
800
2.64
2.61
2.58
2.55
2.47
2.39
2.31
2.22
2.10
Table II. Optical energy gap values as a function of
temperature
Model
Eg
[eV]
Θ
[K]
α
[eV/K]
p
U
[eV/K]
V
[eV/K]
Norm
Varshni
Eq. 1
2.694
246
9 x 10-4
—
—
—
0.0156
Viña
Eq. 2
2.690
269
—
—
—
—
0.0145
Pässler
Eq. 3
2.692
291
8 x 10-4
2.20
—
—
0.0143
Manoogian
Eq. 4
2.692
261
—
—
1.2 x 10-5
3.0 x 10-4
0.0128
Table III. Comparative fitting parameters obtained with equations (1) to (4).
11
GRIMA GALLARDO P.; E. OROZCO; M. MUÑOZ; L. NIEVES & J.A. HENAO.-
Figure 1. DTA of MnIn1.6Ga0.4S4.
Figure 2. Optical Transmission, It/I0 vs Energy for MnIn1.6Ga0.4S4 at 10, 200, 400 and 700K.
12
OPTICAL ABSORPTION MEASUREMENTS ON MnIn 1.6Ga 0.4S 4 IN THE TEMPERATURE RANGE 10 – 800K
Figure 3. Optical Transmission for T=10K showing the criteria for obtaining the optical energy gap value.
Figure 4. Optical Energy Gaps vs Temperature for MnIn1.6Ga0.4S4. Circles: Experimental values; Solid line: Varshni’s model
(Eq. 1); Dashed line: Viña’s model (Eq. 2); Dotted line: Pässler’s model (Eq. 3); Dotted-Dashed line: Manoogian’s model (Eq. 4)
13
GRIMA GALLARDO P.; E. OROZCO; M. MUÑOZ; L. NIEVES & J.A. HENAO.-
For the fit, the value of Eg at 800K has not been taken
into account because the transmitted light has been
drastically reduced at this temperature (less than 5%) and
the Eg value is not reliable. In table III we compare the
fitting parameters obtained by application of theoretical
models. From this table we obtain that Eg (0) = 2.69 ± 0.01
eV, Θ = 268 ± 24 K and α = (8.5 ± 0.5) x 10-4 eV/K.
AKNOWLEDGEMENTS
This work has been suported by CDCHT - Universidad
de Los Andes by grant C-949-99-05-B.
REFERENCES
The value p = 2.2 (Pässler’s model) is in very good
agreement with typical values (2.2 to 2.6) obtained for
semiconductors with bandgaps ranging between 0.3 and
3 eV [9]. Also, the values of U and V parameters in the
Manoogian-Leclerc model are in the range usually
observed [19, 21-23].
In order to test the value obtained for the Debye
temperature (268 K) we can calculated Θ from the model
of Oshcherin [24]:
Θ = (cont/α1/3) Tm1/2 d1/3 / M5/6
(5)
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N.N. Niftiev, A.G. Rustamov, O.B. Tagiev and G.M.
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V. Sagredo, L. Nieves and G. Attolini. Inst. Phys. Conf.
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F. Hulliger. Structural Chemistry of Layer-type Phases.
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[5]
H. Haeuseler and M. Himmrich. Z. Anorg. Allg. Chem.
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N. Berand and K.J. Range. J. Alloys and Comp. 205, 295
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A. N. Anagnostopoulos and J. Spyridelis. Phys. Stat. Sol.
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E. Infante. Master Thesis, Universidad de Los Andes,
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R. Päessler. Phys. Stat. Sol. (b) 200, 155 (1997).
1/3
Where (cont/α ) depends of the crystal structure (174,
151 or 189 for f.c.c., b.c.c. or diamond structures,
respectively); Tm is the melting point in K, d is the density
and M is the mean atomic weight per lattice site. Using
the respective atomic weight of the elements, the
experimental lattice parameters (x-ray measurements) and
the experimental melting point (DTA) we obtain Θ = 255 K
with (cont/α1/3) = 189 and Θ = 235 K with (cont/α1/3) = 174,
in good agreement with the experimental value of
Θ = 268 K, obtained before. Unfortunately we don’t have
the value of (cont/α1/3) for the structure observed for
MnIn1.6Ga0.4Se4 but it would be not very different to the
values of the f.c.c. or diamond structures.
[10] E. Grilli, M. Guzzi, R. Zamboni and L. Pavesi. Phys. Rev.
B45, 1638 (1992).
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[12] C.D. Thurmond. J. Electrochem. Soc. 122, 1133 (1975).
Taking account only the high temperature range
(300K<T<700K) the slope dEg/dT = (-8.25± 0.5) x 10-4 eV/
K was calculated. This value would be compared with
dEg/dT = (-4.23± 0.5) x 10-4 eV/K, dEg/dT = (-5.16± 0.5) x
10-4 eV/K and dEg/dT = (-5.2± 0.5) x 10-4 eV/K reported for
MnIn1.2Ga0.8S4 [3], MnIn0.8Ga1.2S4 [3] and MnInGaS4 [1],
respectively. It seems that dEg/dT values for
MnIn 1.2 Ga 0.8S 4 , MnIn 0.8 Ga 1.2 S 4 and MnInGaS 4, are
underestimated because of the temperature range used
(T < 300K) where dEg/dT have a non-linear behavior.
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1979 (1984).
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CONCLUSIONS
[19] A. Rivero, M. Quintero, Ch. Power, J. González, R. Tovar
and J. Ruiz. J. Elect. Mater. 26, 1428 (1997).
Optical absorption measurements had been performed
on MnIn1.6Ga0.4S4 single crystals in the temperature range
10-800K. DTA measurements show that there are not
phase transitions in this temperature range. The behavior
of the optical bandgap with the temperature was adjusted
using the theoretical models of Varshni [11], Viña [13],
Päessler [9] and Manoogian [14,15]. All the models fit
well in the entire temperature range. From these fittings
we obtained a Debye temperature of 268 ± 24K and dEg/
dT = (-8.25 ± 0.5) x 10-4 eV/K.
[20] L. Nieves. Lic. thesis. Universidad de Los Andes. 1998.
Unpublished.
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2739 (1989).
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Woolley and B.R. Pamplin. J. Can. Phys. 60, 10 (1982).
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70, 1451 (1991).
[24] B.N. Oshcherin. Phys. Stat. Sol. (a) 35, K35 (1976)
14