[12%] Silicon is an industrially important semiconductor with the cubic unit cell shown below (Si at — Solid State Chemistry Chemistry Question
Problem Context
[12%] Silicon is an industrially important semiconductor with the cubic unit cell shown below (Si atoms represented as black spheres):
How many Si atoms are contained in this unit cell?
Model Answer
There are 8 Si atoms in the unit cell.
The length of the edge of the unit cell is 0.543 nm. Calculate the density of silicon in g cm –3.
Model Answer
V = (0.543 10 -7 cm) 3 = 1.60 10 -22 cm 3
mass = 8 (28.09 g mol -1 )/(6.022 10 23 mol -1 ) = 3.73 10 -22 g
density = 3.73 10 -22 g/1.60 10 -22 cm 3 = 2.33 g cm -3
Semiconductors like Si have an electronic structure characterized by a band of nominally filled orbitals (the “valence band”) separated from a band of nominally empty orbitals (the “conduction band”) by an energy gap called the “band gap” of the semiconductor. Conduction arises in a pure semiconductor when there is thermal promotion of an electron from the valence to the conduction band; both the electron in the conduction band and the vacancy (“hole”) in the valence band are efficient carriers for electrical conduction.
Diamond, silicon, and germanium all have the same structure, but the band gap decreases in the order C (diamond) >> Si > Ge. Explain the trend in the size of the band gap.
Model Answer
The filled valence band consists of -bonding orbitals, while the empty conduction band consists of -antibonding orbitals. Thus, the stronger the bonding, the larger the band gap. The smaller elements form shorter, stronger bonds (C–C >> Si–Si > Ge–Ge), so the band gaps also decrease in this order.
Substituting just a few parts per million of B into Si results in a dramatic increase of electrical conductivity compared to ultrapure Si. Explain why.
Model Answer
Replacing a Si atom (with 4 valence electrons) with a B atom (3 valence electrons) decreases the electron count by one without changing the number or type of orbitals. Thus each B atom leads to a vacancy in the valence band. These "holes" are good charge carriers, and so even a small number of boron atoms lead to a relatively large number of charge carriers (and hence high conductivity) compared to pure Si, where the only charge carriers arise from thermal excitation.