Semiconducting Devices Question 31

Question: The typical ionisation energy of a donor in silicon is

[IIT-JEE 1992]

Options:

A) $ 10.0eV $

B) $ 1.0eV $

C) $ 0.1eV $

D) $ 0.001eV $

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Answer:

Correct Answer: C

Solution:

When donor impurity (+5 valence) added to a pure silicon (+4 valence), the +5 valence donor atom sits in the place of + 4 valence silicon atom.

So it has a net additional + 1 electronic charge.

The four valence electron form covalent bond and get fixed in the lattice.

The fifth electron (with net - 1 electronic charge) can be approximated to revolve around + 1 additional charge.

The situation is like the hydrogen atom for which energy is given by $ E=-\frac{13.6}{n^{2}}eV $ .

For the case of hydrogen, the permittivity was taken as e0.

However, if the medium has a permittivity er, relative to e0, then $ E=-\frac{13.6}{\varepsilon _{r}^{2}n^{2}}eV $ For Si, er = 12 and for n = 1, $ E\tilde{}0.1eV $



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