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THE FOURIER MOBILITY SPECTRUM ANALYSIS APPLICATION TO
BI-SN SUPERDILUTED ALLOYS
Alexander Fedotov1 , Sergey Perevoznikov1,2 , Uladzislau Humennik1
1 Physics
2 Research
Faculty of Belarusian State University
Institute for Physical Chemical Problems of the Belarusian State University
[email protected]
The Bi-Sn system is the promising basic compound for thermoelectrical p-type materials at low and medium temperatures [1].
The presence of several types of charge carriers (light electrons, light and heavy holes) encourages the researchers
for the search of suitable galvanomagnetic methods for electronic properties characterization. Standard formulas for
magnetoresistance and Hall coefficient are not applicable, so we propose the approach based on Fourier Mobility Spectrum
Analysis (FMSA) technique.
We choose doping level of Bix -Sn1−x small enough (x ≤ 0.08 at. %) to keep dispersion law and electronic bands
shape of Bi unchanged. The rapid solidification method allows the cheap synthesis of uniform polycrystalline samples (30
µm thickness, less than 1% surface roughness). We measured magnetoresistance and Hall coefficient (see Fig.1(a)) in temperature range 4−300 K tunder magnetic fields up to 8 T. Then, we determined magnetoconductivity tensor components
from galvanomagnetic data for usage as the input to the FMSA code.
The FMSA code was implemented with Fourier-space fitting algorithm in addition to standard iterative fitting in
direct-space and including derivatives to mean squared error [2]. Several versions of the code were made in different
languages. The Fortran version of code proved itself to be the fastest, Fig.1(b).
The concentrations, mobilities and Fermi level temperature dependences were estimated for the studied range of Bi
doped with Sn for the first time. For the He temperatures the comparison between our result and Fermi level found from
the Shubnikov-de Haas oscillations [3] showed good coincidence (see Fig.1(c)).
The presented technique allowed us to extract not only low-temperature position of Fermi level but all the temperature
range dependence of Fermi level. It was found that temperature dependences do not match with the Sommerfeld expansion
due to significant relative changes in Fermi level values with temperature.
-6
1 10
H
-6.0x10
-9.0x10
-6
2 10
4 10
-6
6 10
-1.2x10
-5
8 10
0
100
200
T, K
(a)
-2
-2
-2
-2
-2
300
Shubnikov-de Haas effect analysis
Our analysis
160
, meV
Pure Bi
10
1
120
h
-6
3
R , m /C
0.0
-3.0x10
200
Time spent
Time for 1000 iteration, hours
3.0x10
80
0.1
40
0
Wolfram
Python 2.7
Mathematica 10.4 SciPy, NumPy
(b)
Cython
Intel Fortran 2015
0.00
0.02
0.04
0.06
0.08
x, at. %
(c)
Fig. 1. (a) - temperature dependence of low-field Hall coefficient RH (B ≈ 10−2 T) (b) - the comparison of time required
for 1000 iteration on the same computational problem, (c) - the comparison of concentration dependences of Fermi level
ξT h counted from the top of T-point for our analysis (round dots) and literature data (squared dots)
We thank the Belarusian Republican Foundation for Fundamental Research for the financial support given to project
F16M-067 which made this research possible.
[1] Sung Hoon Park, Seungki Jo, Beomjin Kwon et al., High-performance shape-engineerable thermoelectric painting, Nature Communications 7,
13403 (2016).
[2] I. Vurgaftman, J. R. Meyer, C. A. Hoffman et al., Improved quantitative mobility spectrum analysis for Hall characterization, Journal of Applied
Physics 84 , 4966-4973 (1998).
[3] A. Nikolaeva, D. Gitsu, T. Huber et al., Thermoelectric properties of quantum Bi wire doped with Sn and electron topological transitions induced
by stretch and doping, Reviews on Advanced Material Science 8, 73-78 (2004).