Corresponding author: Tatyana G. Yugova ( p_yugov@mail.ru ) © 2021 Tatyana G. Yugova, Aleksandr G. Belov, Vladimir E. Kanevskii, Evgeniya I. Kladova, Stanislav N. Knyazev, Irina B. Parfent'eva.
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Citation:
Yugova TG, Belov AG, Kanevskii VE, Kladova EI, Knyazev SN, Parfent'eva IB (2021) Comparison between results of optical and electrical measurements of free electron concentration in n-InAs specimens. Modern Electronic Materials 7(3): 79-84. https://doi.org/10.3897/j.moem.7.3.76700
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A theoretical model has been developed for determining the free electron concentration in n-InAs specimens from characteristic points in far IR reflection spectra. We show that this determination requires plasmon-phonon coupling be taken into account, otherwise the measured electron concentration proves to be overestimated. A correlation between the electron concentration Nopt and the characteristic wavenumber ν+ has been calculated and proves to be well fit by a third order polynomial. The test specimens have been obtained by tin or sulfur doping of indium arsenide. The electron concentration in the specimens has been measured at room temperature using two methods: the optical method developed by the Authors (Nopt) and the conventional four-probe Hall method (the Van der Pau method, NHall). The reflecting surfaces of the specimens have been chemically polished or fine abrasive ground. The condition Nopt > NHall has been shown to hold for all the test specimens. The difference between the optical and the Hall electron concentrations is greater for specimens having polished reflecting surfaces. The experimental data have been compared with earlier data for n-GaAs. A qualitative model explaining the experimental data has been suggested.
indium arsenide, electron concentration, Hall effect, reflection spectrum, plasmon-phonon coupling
The information value of experimental data increases greatly if the target parameter can be measured using different methods. It is recommendable to compare the different measurement data taking into account that each method has its specific features. For example the free carrier concentration in semiconductor specimens is typically measured using the Hall effect, either its classic six-probe variant or the more convenient four-probe Van der Pau modification.
Along with the Hall method the free carrier concentration in heavily doped semiconductors is often measured using the so-called plasma reflection method which is contactless and nondestructive unlike the Hall one. The spectral dependence of the reflection coefficient is recorded in the far IR region and the free carrier concentration is determined from the positions of the characteristic points.
It should be noted that free carrier concentration data obtained by electrical measurements represent the whole specimen bulk while those obtained by optical measurements only refer to the narrow superficial layer of the specimen. For this reason data obtained with these methods may differ. It was shown [
By analogy with the cited work [
The measurements were conducted for 21 n-InAs specimens 16 of which were sulfur-doped and 5 were tin-doped. The specimens were in the form of plane-parallel 6–10 mm side square wafers 1.03–2.26 mm in thickness (Table
No. | Doping impurity | d (mm) | ν+ (cm–1) | N opt (1018 cm–3) | N Hall (1018 cm–3) | δ (%) |
1 | S | 1.30 | 369 | 0.660 | 0.564 | 14.5 |
2 | S | 1.50 | 457 | 1.19 | 1.04 | 12.6 |
3 | S | 1.74 | 491 | 1.43 | 1.28 | 10.5 |
4 | Sn | 1.03 | 496 | 1.48 | 1.27 | 14.2 |
5 | S | 2.26 | 532 | 1.78 | 1.59 | 10.7 |
6 | S | 1.90 | 538 | 1.83 | 1.59 | 13.1 |
7 | S | 1.77 | 545 | 1.89 | 1.79 | 5.3 |
8 | S | 1.93 | 573 | 2.15 | 1.93 | 10.2 |
9 | Sn | 1.43 | 591 | 2.34 | 2.14 | 8.5 |
10 | S | 1.39 | 600 | 2.43 | 1.95 | 19.8 |
11 | Sn | 1.24 | 617 | 2.63 | 2.32 | 11.8 |
12 | S | 1.01 | 635 | 2.84 | 2.44 | 14.1 |
13 | S | 1.57 | 639 | 2.89 | 2.50 | 13.5 |
14 | S | 2.12 | 656 | 3.09 | 2.79 | 9.7 |
15 | S | 1.47 | 668 | 3.25 | 2.95 | 9.2 |
16 | S | 1.75 | 673 | 3.31 | 3.11 | 6.0 |
17 | Sn | 1.10 | 677 | 3.36 | 2.98 | 11.3 |
18 | S | 2.17 | 678 | 3.38 | 3.05 | 9.8 |
19 | S | 1.79 | 683 | 3.44 | 3.09 | 10.2 |
20 | S | 1.92 | 684 | 3.46 | 3.13 | 9.5 |
21 | Sn | 1.32 | 684 | 3.46 | 2.92 | 15.6 |
The contact material for electrical measurements was indium. Two specimens were placed on a holder one at each side and tinned copper contact wires were soldered to the holder outputs. The holder with the specimens was placed in the gap between electric magnet core poles perpendicularly to the magnetic field induction vector. The measurements were conducted at magnetic induction B = 0.5 Tl and a 200 mA current passing through the specimen. Then the electrical resistivity ρ, the free electron concentration NHall and the electron mobility μ were calculated. The relative random error of NHall measurement was within ± 10 %.
N
opt was calculated from far IR reflection spectra (plasma resonance) [
More detailed information on Nopt determination from the reflection spectrum was reported earlier for n-GaAs [
Band gap Eg, eV 0,36 [
HF dielectric permeability ε∞ 11,6 [
Wavenumber at longitudinal optical phonon frequency νLO, cm–1 243 [
Wavenumber at transverse optical phonon frequency νTO, cm–1 219 [
Valence and conduction band interaction matrix element Pcv, eV · cm 8.7 · 10–8 [
As a result the electron concentration vs characteristic wavenumber calibration curve was plotted (Fig.
N opt = 1.05 · 1010(ν+)3 – 3.15 · 1012(ν+)2 + 3.22 · 1015(ν+) – 6.27 · 1017. (1)
Here Nopt is in cm–3 and ν+ is in cm–1.
We show that the plasmon-phonon coupling being disregarded, Nopt proves to be overestimated but this difference near the edge of the Tensor-27 Fourier spectrometer operation range is within 10% and decreases further with an increase in ν. Note that the respective differences are 20% for n-GaAs [
Table
As can be seen from Table
Figure
N Hall = 0.9002Nopt – 0.0309. (2)
When doing RMS linear approximation one should estimate the quality of the fit between the experimental points and the linear function. The criterion is the parameter R2: the closer R2 to unity the better the approximation. In the case considered R2 = 0.9896 as calculated by the software along with the other approximation parameters.
It can be seen from Fig.
One can therefore safely assure that there is a difference between NHall and Nopt and this difference is unilateral, i.e., NHall anis always lower than Nopt. The random factor (scatter about a certain mean value) is also absent.
As noted above the result was different for n-GaAs: NHall could be lower or higher than Nopt. The concentrations measured by the two methods were equal at Neq = 1.07 · 1018 cm–3 [
This difference in the behavior of doping impurities in GaAs and InAs single crystals can be accounted for by the difference in the homogeneity ranges of these compounds. Excess gallium or indium controls the bulk concentration of arsenic vacancies. As reported earlier [
The lower arsenic vacancy concentration determines the smaller fraction of the electrically neutral doping impurity in the bulk which forms complexes with arsenic vacancies. During Hall measurements the magnetic field destroys these complexes to transfer the impurity to an electrically active state thus increasing the NHall concentration [
As we showed earlier [
It is a well-known practice for optical measurements to thoroughly polish the reflecting surface of the test specimen to a mirror-like condition. The question arises, what if the quality of the reflecting surface is intentionally degraded, i.e., the specimen is abrasive ground so the reflecting surface becomes matted? How strongly will the optical properties of the specimen and hence Nopt change?
With this task in mind, we conducted the following experiment: we ground the reflecting surfaces of four specimens out of those listed in Table
Figure
As can be seen from Fig.
Table
It can be seen from Table
Furthermore the Nopt concentration in all the test specimens decreases after surface grinding and becomes closer to the NHall concentration (Table
Thus one can assert that there is a systematic difference between the Nopt and NHall concentrations, the former concentration always being higher. This difference is smaller for ground specimen surface.
Note that this study was undertaken in order to explore the possibility of transition from the conventional Hall method of free electron concentration measurement to a more convenient optical one. The experimental results reported in this work should be taken into account.
Hall vs optical electron concentration: white circle is sulfur-doped specimens and blue circle is tin-doped specimens.
Optical and electrical measurement data on electron concentration for polished and ground reflecting surfaces of specimens
No. | Reflecting surface treatment | d (mm) | ν+ (cm–1) | N opt (1018 cm–3) | N Hall (1018 cm–3) | ΔN (1017 cm–3) |
1 | Polished | 1.30 | 369 | 6.60 | 5.64 | 0.96 |
Ground | 1.14 | 364 | 6.35 | 5.67 | 0.68 | |
10 | Polished | 1.39 | 600 | 2.43 | 1.95 | 4.8 |
Ground | 1.42 | 597 | 2.40 | 2.21 | 1.9 | |
14 | Polished | 2.12 | 656 | 3.09 | 2.79 | 3.0 |
Ground | 2.05 | 639 | 2.89 | 2.69 | 2.0 | |
18 | Polished | 2.17 | 678 | 3.38 | 3.05 | 3.3 |
Ground | 2.00 | 667 | 3.24 | 3.05 | 1.9 |
A theoretical model was developed for determining the free electron concentration in n-InAs specimens (Nopt) from characteristic points in far IR reflection spectra. We showed that Nopt determination requires plasmon-phonon coupling be taken into account, otherwise the measured Nopt electron concentration proves to be 10% overestimated. A correlation between the electron concentration and the characteristic wavenumber was calculated and proves to be well fit by a third order polynomial.
The free electron concentration in the specimens was measured using two methods: based on reflection spectra (Nopt) and using the conventional Van der Pau method (NHall), for different treatment of specimen reflection surface: chemical polishing and fine abrasive grinding. The condition Nopt > NHall was shown to hold for all the test specimens. The difference between the optical and the Hall electron concentrations proved to be greater for specimens having polished reflecting surfaces.
The experimental data were compared with earlier data for n-GaAs. A qualitative model explaining the experimental data was suggested.