Electronics 1 2 Silicon is doped with 5 x 10 16 arsenic atom

Electronics 1 (2)

Silicon is doped with 5 x 10 16 arsenic atoms/cm3: (a) Is the material n- or p-type? (b) Calculate the electron and hole concentrations at T 300K. (c) Repeat part (b) for 350K

Solution

1 ) as it will have majority charge electron it will become N type ,arsenic has more valence electrons than silicon.

2 ) fOR T= 300 k Nd >> ni

n = Nd = 5x10¹⁶ cm-3

( CONSIDERING ni =1.5 x 10¹⁰ cm-3 )

p = ni ² /n = (1.5 x 10¹⁰ cm^-3 ) ² / 5 x10¹⁶ cm-3 ( CONSIDERING ni =1.5 x 10¹⁰ cm-3 )

p = 4.5 x 10³ cm-3

3 ) fOR T= 350 k Nd = ni

n= Nd /2 + Nd /2 (1 + 4 ni ² / Nd ² ) ^1/2

= (5x10¹⁶ cm-3 /2 ) + 5x10¹⁶ cm-3 / 2 ( (1 + 4 ni ² / Nd ² ) ^1/2   

= (5x10¹⁶ cm-3 /2 ) + 5x10¹⁶ cm-3 / 2 ( (1 + 4 *1   ) ^{1/2 because} ( ni= Nd)

=   (5x10¹⁶ cm-3 / 2 ) + 5x10¹⁶ cm-3 / 4.47

= (2.5x10¹⁶ cm-3 ) + 1.11 x10¹⁶ cm-3

n   = 3.61 x10¹⁶ cm-3

p = ni ² /n =(5x10¹⁶ cm-3 )² /   3.61 x10¹⁶ cm-3  

  (5x10¹⁶ cm-3 ) X   (5x10¹⁶ cm-3 )   /   3.61 x10¹⁶ cm-3   

= 6.92 x10¹⁶ cm-3