Question

What is the forbidden energy gap for germanium crystal at $0\;K$?
A. $0.071\;eV$
B. $0.71\;eV$
C. $2.57\;eV$
D. $6.57\;eV$

Answer 1

For each semiconductor there will be a certain value of the forbidden energy gap. At the temperature of $0\;K$, the energy level of the electron in the semiconductors are in the normal state. Thus, the forbidden energy gap is low compared to that of the excited states.

Complete step by step answer:
(i) Germanium:
Germanium is a type of semiconductor in the periodic table group IVA. The atomic number of germanium is $32$, an atomic weight of it is$72.59\;u$, and a density of $5.5\;gc{m^{ - 3}}$. Its melting temperature is $937.4{\;^ \circ }C$. The electronic configuration of germanium is $\left( {Ar} \right){\left( {3d} \right)^{10}}{\left( {4s} \right)^2}{\left( {4p} \right)^2}$ and the atomic radius is $0.137\;nm$.
Germanium has the diamond cubic crystal structure, an fcc lattice with two germanium atoms as basis, one at $\left( {0,0,0} \right)$ and the other one at $\left( {\dfrac{1}{4},\dfrac{1}{4},\dfrac{1}{4}} \right)$ in units of the cube edge. It is also shown as two percolate fcc lattices of germanium atoms with their origins displaced by $\left( {\dfrac{1}{4},\dfrac{1}{4},\dfrac{1}{4}} \right)$ .

(ii) Forbidden gap:
The forbidden energy gap of the semiconductor is defined as the difference in the conduction energy band and the valency energy band.
The forbidden energy gap of the germanium crystal based on the structure at $0\;K$ is $0.71\;eV$.

Hence, option (B) is correct.

Note:
The forbidden energy gap of a semiconductor is completely based on the structure of the crystal atoms and also based on the temperature of the crystal. The temperature plays a major role in determining the forbidden energy gap by changing the excitation level of the atoms.