Modeling the temperature dependence of the discrete Landau levels in electronic semiconductors Abstract

Т, К	p-Bi0,7Sb1,3Te2,93Se0,07	p-Bi0,7Sb1,3Te2,93Se0,07		p-Bi0,6Sb1,2Te2,91Se0,09		p-Bi0,5Sb1,5Te2,91Se0,09
	For Eg, eV		Eg, eV		Eg, eV		Eg, eV
100	0,213	0,93	0,214	0,80	0,216	0,64	0,217
120	0,209	0,94	0,210	0,81	0,213	0,64	0,214
140	0,205	0,98	0,205	0,86	0,208	0,66	0,210
160	0,200	1,03	0,200	0,91	0,202	0,69	0,206
180	0,196	1,10	0,193	0,96	0,197	0,74	0,200
200	0,191	1,18	0,186	1,01	0,191	0,79	0,195
220	0,186	1,27	0,179	1,07	0,184	0,81	0,190
240	0,181	1,37	0,171	1,12	0,178	0,85	0,184
260	0,176	1,46	0,163	1,16	0,171	0,88	0,178
280	0,172	1,52	0,156	1,17	0,166	0,90	0,173
300	0,167	1,52	0,150	1,12	0,162	0,91	0,168

As can be seen from the table, a change in the effective mass of the density of states significantly affects the band gap. For example, for the p-Bi_0.7Sb_1.3Te_2.93Se_0.07 solid solution, the change in the band gap due to the change in the effective mass at T = 100 K is equal to . With an increase in temperature to T = 300 K, a change in the band gap due to a change in the effective mass of the density of states is

.

From this it can be seen that a decrease in the band gap due to a change in the effective mass with an increase in temperature from 100K to 300K can increase by more than an order of magnitude. Fig.3 shows graphs of the temperature dependence of the band gap for p-Bi_2-xSb_xTe_3-ySe_y solid solutions taking into account changes in the effective mass of the density of states taken from Fig.4. Thus, changes in the effective mass of the density of states with temperature can strongly affect the temperature dependence of the width of the forbidden zones.

Conclusion

A model of the distribution of discrete Landau levels in the conduction band with allowance for the cyclotron effective mass is constructed. Based on the constructed model, a computer program for calculating Landau levels at various temperatures was created. The temperature dependence of the density of energy states of semiconductors in InAs is studied taking into account the dependence of the effective mass on energy in a strong quantizing magnetic field. The temperature dependence of the density of energy states was obtained taking into account changes in the cyclotron effective mass in a strong magnetic field. Using numerical experiments, it was shown that at temperatures T> 120 K, a change in the effective mass of the density of states with increasing T significantly affects the temperature dependence of the band gap.

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