The Temperature Dependence of the Density of States in Semiconductors 219

1.050

1.070

1.090

1.110

1.130

1.150

1.170

1.190

0

50

100

150

200

250

300

350

400 450 500

Т, К

E

g

, eV

Experiment for Si [13]

calculations for the parabolic zone

calculation for the of Kane

Figure 4. The temperature dependence of the band gap of

Si.

0.3400

0.3500

0.3600

0.3700

0.3800

0.3900

0.4000

0.4100

0

50

100

150 200250300

T, K

E

g

, eV

0.4200

Experiment for InAs [14]

calculations for paraboliс zony

calculation for the model of Kane

Figure 5. The temperature dependence of the band gap of

InAs.

p-Bi2−xSbxTe3−ySey takes into account of the temperature

dependence of the effective mass of the density of states

in the valence band. The temperature dependence of the

band gap for the changes in the effective mass of the

density of states is obtained. The numerical experiments

show that at temperatures T > 120 K, change in the effec-

tive mass of the density of states by increasing T has sig-

nificant effect on the temperature dependence of the band

gap.

In this temperature range ([0, 300 K], [0, 500 K]),

mathematical modeling of the temperature dependence of

the band gap is satisfactorily described by a parabolic

dispersion law and the Kane model. The experimental

results of changing the band gap of silicon [13] and InAs

[14] within the accuracy of measurement is consistent

with the results of theoretical calculations. Comparison

of theory and experiment shows that the thermal broad-

ening of the energy levels with the GN function satisfac-

torily describes the process of the temperature depend-

ence of the band gap of Si and InAs.

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