Chapter 3 Experimental Results
3.3 Hall measurement
3.3 Hall measurement
Carrier concentration plays an important role to discuss the complicate resistivity behavior. In this section, we will discuss hall measurements and the carrier concentration.
Figure 3.13 Hall effect measurement
Figure 3.14 Temperature dependence of Carrier concentration
0 100 200 300
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voltage wires. By applied the field, carrier would accumulate into one hand side so that we could measure the Hall voltage (VH). This kinds of material has large magneto-resistance. This results include the sum of the magneto-resistance and the Hall resistance (RH). In the positive and negative field, the Hall resistance are RH+ = RMR + RH and RH- = RMR - RH, respectively. We suppose the magneto-resistance was symmetry in field, the Hall contribution can calculate from subtracting RH+ - RH- and dividing by 2.This result shows a semiconductor behavior, the magnitude in 300 and 2 K are about 1018 and 1015 1/cm3, respectively (Figure 3.14). The main carriers are electron which call n-type and was double checked by Seebeck measurement. The magnitude of carrier concentration decrease as temperature decrease from 300 to 50 K. It can easily correspond to resistivity increase. According this two results, we could know that the semiconductor behavior is leaded by electron carriers.
Figure 3.15 Se concentration dependence of Carrier concentration singular point
1.1 1.2 1.3 1.4 1.5 1.6 1.7
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Figure 3.16 Temperature dependence of Hall resistance
For each results, an unusual phenomenon was observed. They show singular points in the carrier concentration curve. Figure 3.16 shows temperature dependence to Hall Resistance. It can be observed that the RH is cross through the zero point. Besides, the RH results are smooth so we are not preferred to be measurement mistakes.
According to Equation 2-17, we can know that carrier concentration is inverse proportion to the Hall resistance. As RH comes to zero point, the carrier concentration would diverge and bring out the singular points.
To find out the reason, we started from the Hall resistance. Figure 3.16 shows the RH are cross from negative to positive. This phenomena was already published in Bi2Te2Se3 bulk. Figure. 3.17 shows an imagination electron structure. At 0 K, the dominate carriers are electron holes. Unusually, it has to be noticed that there is a donor
0 50 100 150 200 250 300
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level closed to the conduction band with thermal activation energy. When the temperature raises, the donor level starts to generate electrons to the conduction band.
When the electron amounts are larger than electron holes and become to dominate, it transforms to n-type material. At the meanwhile, the electron amounts are equal to holes, the RH values are zero and the carrier concentration will be diverging and becoming to a singular point.
Figure 3.17 Band structure of Topological insulator and donor level
In the singular point area, high resolution scanning was done. As well as the resistivity’s inflection point, we also observed that singular points have correlation to Selenium concentration. In Figure 3.15, blue points showed the singular temperature dependence of the Se dopants. We could confirm that singular points are dependent to the Se doped concentration.
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Carrier Concentration @2K (1015 /cm3 ) Bi
1.5Sb0.5Te3-ySey
Figure 3.18 Carrier concentration at 2 K
Carrier concentration decreases as Selenium dopant decrease. As the temperature below about 50 K, carrier concentration values are constant and independent on temperature which could correspond to low tempertaure resistivity behavior. Figure 3.18, it shows Selenium concentration dependence of carrier concentration at 2 K and resistivity results also show the same trend at 2K.
Figure 3.19 shows the combination of singular points and inflection points. It could be observed that they had direct correlation between resistivity and carrier concentration. We can calculate thermal activation from resistivity by Arrhenius Law and Arrhenius function is defined by
σ = 𝜎0exp (−𝐸𝑎
𝑘𝐵𝑇) (Equation 3-1)
Where σ is conductivity, 𝐸𝑎 is thermal activation, 𝑘𝐵 is Boltzmann constant and 𝑇 is temperature. Figure 3.20 shows thermal activation is about 20-100 meV and the
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energy gap in Bi2Te2Se was known by 300meV from published lecture. We could conjecture that thermal activation is caused from donor level and conduction band.
Thermal activation is increase with Selenium dopant increase and directly effecting carrier concentration singular point. Each part of carrier concentration behaviors can correspond to different resistivity behaviors and correlation between carrier concentration and resistivity could be established.
Figure 3.19 Resistivity inflection point and Carrier singular point
1.1 1.2 1.3 1.4 1.5 1.6
0 40 80 120 160 200
Hall Singular point RT Inflection point
Temperature (K)
Se doped concnetration
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Figure 3.20 (a) Thermal activation
Figure 3.20 (b) Arrhenius function fitting
0.01 0.02 0.03 0.04
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3.4 Magneto-resistance
This kind of materials have a large magneto-resistance. The magneto resistance was also measured by four-terminal method with PPMS. It was expect to observe Weak anti localization (WAL) and Shubnikov–de Haas oscillation. This two kinds phenomena could lead to analysis the surface state effect. The WAL was known from spin-orbital interaction and let it could be a spintronic material.
Figure 3.21 Resistance at 9T and zero field
Figure. 3.21 shows the temperature dependence of resistance results under magnetic field. The MR behaviors are different in different temperature. It is observed
0 100 200 300
0 700 1400 2100 2800
Resistance ()
Temperature (K)
9 Tesla
Zero field
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started to increase. When it goes down to 2 K, the MR raises rapidly. We will discussthose phenomena separately.
Figure 3.22 Magneto-resistance
Figure 3.22 shows the field dependence of MR with different temperature. In the 50 to 100 K, the results show a typical MR behavior which the MR is nearly proportional to B. The particular behavior was observed below 50 K and have a sharp deep. This phenomena is more obvious at low temperature, 2 K results was deliberated.
At the low field area, MR increased very rapid until to about 3 tesla. This low temperature at low field MR behavior was called Weak Anti-Localization (WAL). It leads to the deep of MR in low field in this material. In publish lectures, WAL comes from the surface electron’s spin-orbital interaction and is a characteristic of 3D
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topological insulators. When it goes to high temperature area, the bulk effects raise and cover the surface behavior. Causing that we could not observe the WAL at high temperature.
Figure 3.23 shows magneto-resistance results with different composition at 2 K.
We could not observe the WAL difference with different composition at low field area.
At high field, different results are also getting the same value. Our explanation is that WAL doesn’t come from the bulk effect but is contributed to surface electrons so that it could be independent on Selenium dopant.
Figure 3.23 Magneto-resistance at 2K
9 6 3 0 -3 -6 -9
0.0 0.2 0.4 0.6 0.8
Magneto-resistance @2K (R/R 0)
Magnetic Field (Tesla) MF20 MF16 MF19 MF17