Question

A silicon sample is doped with 4.5 × 10¹⁷ cm^-3 boron atoms. Assume T= 300 K, n_i = 1.5 x 10¹⁰ cm^-3

^{What is the hole concentration and electron concentration?}

Answer 1

here is the solution of above problem:-

given :- concentration of donor items (N_d) = 4.510¹⁷ cm^-3

  intrinsic carrier concentration  (n_i) = 1.5 10¹⁰ cm^-3 T =300K

Solution:-

  The majority carrier electron concentration is given by

no = ½ {(Nd - Na) + ((Nd - Na) ² + 4n_i² ) ^1/2 }

assuming Na=0

n_o= ½ { ( 4.510¹⁷ - 0) + ( ( 4.510¹⁷ - 0 )² + (4 1.5 10¹⁰)² )^1/2

⁼   ½ { ( 4.510¹⁷) + ( ( 2.0.25   10³⁵ ) + ( 3.610²¹) ) ^1/2

=  ½ { ( 4.510¹⁷) + ( 4.5 10¹⁷ ))

=  ½ ( 9 10¹⁷)

majority carrier electron concentration is n_o= 4.5 10¹⁷

electron concentration n_o= 4.5 10¹⁷ cm^-3

The minority carrier hole concentration is given by : -

p₀ = ( n_{i i})² / n₀

= ( 1.5 10¹⁰ )² / 4.5 10¹⁷

minority carrier hole concentration ( p₀) = 500 cm^-3