Question

(a) Find the concentration of electrons and holes in a sample of germanium that has a concentration of donor atoms equal to 1015 cm?3. Is the semiconductor n-type or p-type? (b) Repeat part (a) for silicon.

Answer 1

Answer :- The intrinsic carrier concentration of Germanium, n_i = 2.4 x 10¹³ cm^-3 at 300 K . Given N_d = 10¹⁵ cm^-3 and N_a = 0. Thus the electron concentartion is-

So, n₀ = (0.5 x 10¹⁵ )+ (50.06 x 10¹³ ) cm^-3
n₀ = 100.06 x 10¹³ cm^-3 = 10¹⁵ cm^-3 .

Hence hole concentration, p₀ = (n_i)² / n₀ = 5.76 x 10¹¹ cm^-3 . Since n₀ > p₀ , so it is an n-type semiconductor.

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The intrinsic carrier concentration of Silicon, n_i = 1.5 x 10¹⁰ cm^-3 at 300 K . Given N_d = 10¹⁵ cm^-3 and N_a = 0. Thus the electron concentartion is-

So,  

Hence hole concentration, p₀ = (n_i)² / n₀ = 2.25 x 10⁵ cm^-3 . Since n₀ > p₀ , so it is an n-type semiconductor.

Also in both cases the dopant is donar i.e. petavalent material. So the semiconductor formed will be of n-type.