Question

A Ge specimen is doped with Al. The concentration of acceptor atoms is ${{10}^{21}}$ atoms/\[{{m}^{3}}\]. Given that the intrinsic concentration of electron-hole pairs is ${{10}^{19}}$ atoms/\[{{m}^{3}}\], the concentration of electrons in the specimen is
(A) \[{{10}^{17}}/{{m}^{3}}\\ \]
(B) \[{{10}^{15}}/{{m}^{3}}\\ \]
(C) \[{{10}^{4}}/{{m}^{3}}\\ \]
(D) \[{{10}^{2}}/{{m}^{3}}\\ \]

Answer 1

Hint: -
Doping is done in a semiconductor to increase the conductivity of the semiconductor. We are given with Ge being doped with Al. We need to find the concentration of the electron specimen in the sample.

Complete Step by Step Solution:
Let \[{{N}_{e}}\]represents the number of electrons, \[{{N}_{h}}\]represents the number of holes and \[{{N}_{i}}\]be the number of an initial number of atoms. We know the relationship between them is given as \[{{N}_{e}}.{{N}_{h}}=N_{i}^{2}\]
Here \[{{N}_{e}}\]=?\[{{N}_{h}}\]=\[{{10}^{21}}\], \[{{N}_{i}}={{10}^{21}}\]
Substituting the values, we get
\[
   {{10}^{21}}\times {{N}_{e}}={{10}^{19}}\times {{10}^{19}} \\
  {{N}_{e}}=\frac{{{10}^{38}}}{{{10}^{21}}}={{10}^{17}}{{m}^{-3}} \\
\]
Hence, the correct option is (A)

Additional Information:
Doping means the addition of impurities into a semiconductor to define modification of conductivity. Two of the most important materials with which silicon can be doped with, are boron which has 3 electrons in its outermost shell and phosphorus which have 5 electrons in its outermost shell. Other materials that are commonly used are aluminium, arsenic, antimony etc. For p-doped semiconductors, the acceptor energy level is close to the valence band. And for n- doped semiconductors the donor energy level is close the conduction band

Note:
Elements with 3 valence electrons are used for p-type doping and elements with 5 valence electrons are used for n-type doping. P-type semiconductors have holes as their majority charge carriers and n-type semiconductors have electrons as majority charge carriers.