Chapter 29.1, Problem 15PP

To determine

To compute: the ratio of the doped carriers to the thermal carriers.

Answer to Problem 15PP

The ratio of doped carrier to the thermal carrier is 38.4.

Explanation of Solution

Given data:

Number of electrons in germanium = 1 million = $1\times {10}^6$ atoms

Number of arsenic atoms = 1

Number of electrons in germanium per centimeter cube ( e )= $4.34\times {10}^{22}$

Thermal carrier of germanium = $1.13\times {10}^{15}$

Formula used:

  $\text{Doped carrier=}\left(\frac{1\text{ Free electron}}{1\text{ Arsenic atom}}\right)\left(\frac{1\text{ Arsenic atom}}{1\times {10}^6\text{electrons}}\right)\left(e\right)$

Calculation:

  $\begin{array}{l}\text{Doped carrier=}\left(\frac{1\text{ Free electron}}{1\text{ Arsenic atom}}\right)\left(\frac{1\text{ Arsenic atom}}{1\times {10}^6\text{electrons}}\right)\left(e\right)\\ \text{Doped carrier=}\left(1\right)\left(\frac{1}{1\times {10}^6}\right)\left(4.34\times {10}^{22}\right)=4.34\times {10}^{16}\end{array}$

Required ratio,

  $\frac{\text{doped carriers}}{\text{thermal carriers}}=\frac{4.34\times {10}^{16}}{1.13\times {10}^{15}}=38.4$

Conclusion:

Hence, the number of arsenic atoms in per silicon atom is 38.4.