In this paper the dependence of the band structure and the electron scattering mechanisms on the molar fraction x are studied in Hg1-xFexSe. The crossover from the zero-gap band to the open band-gap configuration at x 0.08 is predicted. We explain the drop of the electron mobility for x &gt; 0.002 by the alloy scattering mechanism

B Witkowska&apos

C Skierbiszewskia

J Kossutb

T Suskia

Z Wilamowskib

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Vol. 82 (1992) 	 ACTA PHYSICA POLONICA A 	 No 5
Proceedings of the XXI International School of Semiconducting Compounds, Jaszowiec 1992
ELECTRON SCATTERING
AND THE BAND STRUCTURE
OF MIXED CRYSTALS Hg1-xFexSe*
C. SKIERBISZEWSKIa, Z. WILAMOWSKIb, T. SUSKIa,, J. KOSSUTb
AND B. WITKOWSKA'
°High Pressure Research Center, Polish Academy of Sciences
Sokołowska 29/37, 01-142 Warszawa, Poland
bInstitute of Physics, Polish Academy of Sciences
Al. Lotników 32/46, 02-668 Warszawa, Poland
In this paper the dependence of the band structure and the electron
scattering mechanisms on the molar fraction x are studied in Hg1-xFexSe.
The crossover from the zero-gap band to the open band-gap configuration
at x 0.08 is predicted. We explain the drop of the electron mobility for
x > 0.002 by the alloy scattering mechanism.
PACS numbers: 72.10.Fk, 72.20.Fr, 72.80.Jc
1. Introduction
HgSe:Fe is a suitable material for studies of the effects associated with the
spatial correlation of charged centers [1, 3-5]. The correlation of the localized
charges influences the electron concentration n e and the electron mobility μ at
low temperatures. The theoretical description of the experimental results for the
concentrations of iron nFe smaller than 2 x 10 19 cm-3 is satisfactory only when the
correlations between Fe+ centers are taken into account [2, 3]. On the other hand,
the mobility drop observed for Fe > 2 x 10 19 cm-3 has not yet been explained
[6]. Also, the details of the composition dependence of n e on x are not completely
understood, particularly in view of disagreements concerning the energy gap vs.
x variation [7]. In ths paper we put emphasis on determination of the changes
of the energetic positions of the band edges with composition of the crystal. As
pointed out by Kossut [8], the same two parameters V and W which describe in
the linear approximation the Γ6 and 8, respectively, band edges variation with
x can also be used to estimate the scattering rate of the conduction electrons by
chemical disorder (the alloy scattering mechanism). Therefore, the analysis of ne
and μ can provide an independent information related to the band stucture of
mixed crystals.
*This work is supported in part by the Coininittee for Scientific Research under grant
2 0483 91 01.
(809)
810	 C. Skierbiszewski et al.
2. Experimental results and analysis
We performed measurements of the conductivity and the Hall effect at T =
4.2 K in seven samples of HgSe with different amount of Fe. The results, together
with the literature data, are shown in Figs. 1 and 2. An initial increase in ne
Electron Scattering and the Band Structure ... 811
(Fig. 1) followed by a decrease in its values reflects changes of the energy gap as well
as the relative position (with respect to the conduction band edge) and the width
of the impurity Fe level. To reproduce experimental data the standard procedure
— discussed in detail in [9] — involving the solution of the neutrality equation was
extended by introducing an additional parameter D to describe the broadening σ
of the Fe level. A linear dependence σ(x) = Dx and a Gaussian shape of this level
were assumed. The enhancement of the mobility observed for nFe > 4 x 10 18 cm 3
(Fig. 2) originates, as mentioned, from the spatial correlations of charged centers
[2, 3]. The effect can be described with sufficient accuracy within the short range
correlation model (SRC) — as shown by line labeled 1in Fig. 2 [3]. For comparison,
the electron mobility calculated for random distribution of scattering ions is shown
by the line labeled 3 in this figure [10]. Both lines were evaluated neglecting the
alloy scattering. Surprisingly, for nFe > 2 x 10 19 cm-3 , in spite of more favorable
conditions for the correlation between charged centers to occur, the decrease in
the mobility is observed. We will show that this decrease can be interpreted as
due to the additional scattering mechanism — the alloy scattering. To describe
quantitatively the experimental results we carried out a fitting procedure with 3
fitting parameters: V, W and D. We find out, however, that these parameters
are not independent. Only the difference V - W can be reliably found from μ(x)
dependence. To evaluate the remaining parameters we assumed additionally that
the energetic position of Fe is constant. With this assumption, which corresponds
to Langer-Heinrich ideas [11], we can determine the ratio V/W. The best fitting
parameters: V - W = 3.7 ± 0.5 eV; V/W = -0.1 ± 0.1; D = 0.5 ± 0.2 eV were
obtained in this way. The dashed line in Fig. 2 shows the mobility due to the
alloy scattering obtained for values of V and W corresponding to the best fit,
namely, V = 3.3 eV and W = -0.4 eV. Lines 2 and 4 show the total mobility
taking into account the alloy and ionized impurity scattering for correlated system
(SRC theory) and randomly distributed centers, respectively. Let us stress that the
alloy scattering depends mainly on the difference V - W and, within the accuracy
of determination of V - W of 0.5 eV, leads to a reasonable agreement with the
experimental data. The difference between the experimental values of the mobihty
and the theoretical predictions of the SRC theory together with alloy scattering
(see line 2 in Fig. 2) for 2 x 10 19 cm-3 < nee < 4 x 10 20 cm-3 indicates that an
additional broadening of the impurity level must occur and that it contributes to
an impairment of the spatial correlation in the system of ionized impurities if it
exceeds the value of the Coulomb gap. The following conclusions can be drawn
from our analysis:
a) the drop of the mobility as a function of x observed at low temperatures
for x > 0.002 is due to chemical disorder (alloy scattering);
b) it is necessary to assume that the Fe related impurity level broadens
considerably as x is increased (d-band formation).
c) the crossover from the zerogap band to the open band-gap configuration
takes place at x 0.08 and the extrapolated energy gap in hypothetical FeSe
(x =1) is 3.5 eV.
812 	 C. Skierbiszewski et al.
References 	.
[1] Α. Mycielski, Ρ. Dzwonkowski, Β. Kowalski, B.Α. Orłowski, Μ. Dobrowolska, M.  Ar
-ciszewska, W. Dobrowolski, J.M. Baranowski, J. Phys. C 19, 3605 (1986).
[2] J. Mycielski, Solid State Commun. 60, 165 (1986).
[3] Ζ. Wilamowski, K. Świątek, Τ. Diet!, J. Kossut, Solid State Commun. 73, 883
(1990).
[4] W. Dobrowolski, K. Dybko, Α. Mycielski, J. Mycielski, J. Wróbel, S. Piechota,
M. Palczewska, Η. Szymczak, Ζ. Wilamowski, in: Proc. 18th Int. Conf. Phys. Semi-
cond., Stockholm 1986, Ed. O. Engström, Worłd Scientific, Singapore 1987, ρ. 1743.
[5] F. Poo!, J. Kossut, U. Dębska, R. Reinferberger, Phys. Reu. B 35, 3900 (1987).
[6] I. Kuleev, Ι. Lyapilin, V. Karyagin, Phys. Status Solidi B 163, 449 (1991).
[7] S.Yu. Paranchich, L.D. Paranchich, V.N. Makogónenko, S.V. Lototskaya, Fiz. Tekh.
Poluprovodn. 24, 225 (1990).
[8] J. Kossut, Phys. Status Solidi B 86, 593 (1978). .
[9] C. Skierbiszewski, Ζ. Wilamowski, J. Kossut, in: Proc. 7th Int. Conf. Narrow Gap
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[10] Τ. Dietl, W. Szymańska, J. Phys. Chem. Solids 39, 1041 (1978).
. [11] J. Langer, Η. Heinrich, in Ref. [4], pa. 175.


ELECTRON SCATTERING AND THE BAND STRUCTURE OF MIXED CRYSTALS Hg 1 -x FexSe*

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ELECTRON SCATTERING AND THE BAND STRUCTURE OF MIXED CRYSTALS Hg 1 -x FexSe*

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