Question

The product of the hole concentration and the conduction electron concentration turns out to be independent of the amount of any impurity doped. The concentration of conduction electrons in germanium is 6 × 10¹⁹ per cubic metref conduction electrons increases to 2 × 10²³ per cubic metre. Find the concentration of the holes in the doped germanium.. When some phosphorus impurity is doped into a germanium sample, the concentration o

Answer 1

We know that for an intrinsic semiconductor, the concentration of electrons is equal to the concentration of holes.
The product of electron hole pair concentration always remains constant.
i.e. Number of holes ×  Number of conduction electrons = Constant
Initially, the number of conduction electron per cubic metre = 6 × 10¹⁹
We know,
Number of holes per cubic metre  = Number of electrons per cubic metre
∴ Number of holes per cubic metre = 6 ×10¹⁹
After doping,
Number of conduction electrons per cubic metre = 2 × 10²³
Now,
Let the number of holes per cubic metre be x.
As the product of electron hole pair concentration always remains constant,

\[(6 \times  {10}^{19} )(6 \times  {10}^{19} ) = (2 \times  {10}^{23} )x\] 

\[ \Rightarrow x = \frac{6 \times 6 \times {10}^{19 + 19}}{2 \times {10}^{23}}  \] 

\[ \Rightarrow x = 18 \times  {10}^{15}  = 1 . 8 \times  {10}^{16}\]