Question

2. An N-type sample of silicon has uniform density (Nd = 1019/cm–3 ) of arsenic, and a P-type silicon sample has a uniform density (Na = 1015 /cm–3 ) of boron. For each sample, determine the following: (a) The temperature at which the intrinsic concentration ni exceeds the impurity density by factor of 10.

Answer 1

Answer: The temperature at which the intrinsic concentration exceeds the impurity density by factor of 10 is 636 K.

Explanation:

The given data is as follows.

         $N_{d} = 10^{19} per cm^{-3}$

         $N_{a} = 10^{15} per cm^{-3}$

As we are given that $n_{i}$exceeds impurity density by a factor of 10.

Therefore,   $n_{i} = 10N_{d}$

   $10^{20} = 3.87 \times 10^{6} \times T^{\frac{3}{2}}e^({\frac{-7014}{T}})$

$T^{\frac{3}{2}}e^({\frac{-7014}{T}}) = \frac{10^{20}}{3.87 \times 10^{6}}$

          T = 1985 K

Also,  $n_{i} = 10N_{d}$

       $10^{6} = 3.87 \times 10^{16} \times T^{\frac{3}{2}}e^({\frac{-7014}{T}})$

                T = 636 K

Thus, we can conclude that the temperature at which the intrinsic concentration exceeds the impurity density by factor of 10 is 636 K.