Position of Fermi level versus temperature n = Ne -(Ec-Ef)/kT E₂ = E₂+kTh no N p = N₁₂e (E -(E₁-E₁)/kT E=Ev -kTln Po N₁₂ EF Ec + Ev 2 3 KBTln me mn. Inela 0.6 0.4 0.2 me* >mn Si Er [ev] 1.4 1.2 0.8 1 0.4 0.2 * me*

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Position of Fermi level versus temperature
n = Ne
-(Ec-Ef)/kT
E₂ = E₂+kTh
no
N
p = N₁₂e (E
-(E₁-E₁)/kT
E=Ev -kTln
Po
N₁₂
EF
Ec + Ev
2
3
KBTln
me
mn.
Inela
0.6
0.4
0.2
me* >mn
Si
Er [ev]
1.4
1.2
0.8
1
0.4
0.2
*
me* <mn*
100 200
300
400
500 600 700 800 900 1000
T[K]
100
200 300
400
500
GaAs
Red line
shows the
middle of
the bandgap
600 700 800 900 1000
T [K]
In intrinsic semiconductors, in a broad temperature range, the Fermi level remains
close to the middle of the bandgap.
Position of Fermi level
1. Calculate position of Fermi level in Si, Ge and GaAs at
temperatures -20°C, 20°C (room temperature) and 120°C.
2. Estimate the temperature at what Fermi level in these
semiconductors would cross Ę, or Ev.
Transcribed Image Text:Position of Fermi level versus temperature n = Ne -(Ec-Ef)/kT E₂ = E₂+kTh no N p = N₁₂e (E -(E₁-E₁)/kT E=Ev -kTln Po N₁₂ EF Ec + Ev 2 3 KBTln me mn. Inela 0.6 0.4 0.2 me* >mn Si Er [ev] 1.4 1.2 0.8 1 0.4 0.2 * me* <mn* 100 200 300 400 500 600 700 800 900 1000 T[K] 100 200 300 400 500 GaAs Red line shows the middle of the bandgap 600 700 800 900 1000 T [K] In intrinsic semiconductors, in a broad temperature range, the Fermi level remains close to the middle of the bandgap. Position of Fermi level 1. Calculate position of Fermi level in Si, Ge and GaAs at temperatures -20°C, 20°C (room temperature) and 120°C. 2. Estimate the temperature at what Fermi level in these semiconductors would cross Ę, or Ev.
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