Fundamentals of Semiconductor physics

Exercise n°1

Intrinsic semiconductor

Consider an intrinsic semiconductor in which the effective density of states is N C in the conduction band and NV in the valence band.

Question

Give the expressions of the electron density n (hole density p) in the conduction band (valence band, resp.).

Solution

Question

Use previous result to derive the intrinsic density ni and the position of the intrinsic Fermi level EFi.

The semiconductor considered here is Silicon, with an energy gap Eg=1,1eV and with NC=2,7.1019cm-3 and NV=1,1.1019cm-3.

Solution

Question

Calculate the intrinsic density and the Fermi level position for the following temperatures: 27°C, 127°C and 227°C. Hint: at 300K, kT=0.026eV; the energy reference will be taken at the highest occupied level of the valence band (EV=0eV).

Solution

Extrinsic semiconductor

Silicon is doped with phosphorus atoms (column V of Mendeleev table) with a concentration of 1018cm-3.

Question

What is, at 27°C, the electron density in doped Si ? Use this result to derive the hole density. Which type of semiconductor is obtained ?

Solution

Question

Calculate, at 27°C, the position of the Fermi level E F and plot the band diagram.

Solution

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