CH274 - Electrons in Solids and Materials Exercise 3.2
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CH274 - Electrons in Solids and Materials
Exercise 3.2 – electron density in the CB versus temperature
Determine the electron density in the CB for Si at:
room temperature (Eg = 1.12 eV)
一100 °C (Eg = 1.14 eV)
+100 °C (Eg = 1.09 eV)
+500 °C (Eg = 0.95 eV)
Assume a temperature-independent effective density of states, NC ~ 1025 m-3 .
Model answer
The concentration of conduction electrons for an intrinsic semiconductor (pure material) is given by the formula:
n = NC e一Eg / 2kT ,
where Eg is the semiconductor band gap and NC is the effective density of states which we assume to be temperature-independent with a value of ~ 1025 m-3 .
As a consequence, for Si we can write:
nSi,RT = 1025 
e一1. 12/(2
0.0256) = 3. 16
1015 m-3,
nSi,-100oC = 1025 
e一1. 14
1.6
10一19 /(2
1.38
10一23 
173) = 2.57
108 m-3,
nSi,100oC = 1025 
e一1.09
1.6
10一19 /(2
1.38
10一23 
373) = 4.39
1017 m-3,
nSi,500oC = 1025 
e一0.95
1.6
10一19 /(2
1.38
10一23 
773) = 8.05
1021 m-3 .
In conclusion, since the conduction electron concentration n depends exponentially on temperature, even relatively small variations in temperature generate massive variations in n.
2022-09-17