5 A bar of Ge is doped with phosphorous at a concentration o

5. A bar of Ge is doped with phosphorous at a concentration of 10^16cm^-3. It is exposed to light so that electron-hole pairs are generated throughout the volume of the bar at the rate of 10^19/s·cm^3. The recombination lifetime is 2us. Find p0 , n0 , p’, n’, p , n, and the np product.

A bar of Ge is doped with phosphorous at a concentration of 10^16cm^-3. It is exposed to light so that electron-hole pairs are generated throughout the volume of the bar at the rate of 10^19/s-cm^3. The recombination lifetime is 2mus. Find p_0, n_0, p\', n\', p, n, and the np product.

Solution

a)

equilibrium hole concentration

p_o=N_a=10¹⁶ cm^-3

b)

For Ge n_i=2*10¹³ cm³

equilibrium electron concentration

n_o=n_i²/p_o = (2*10¹³)²/10¹⁶ =4*10¹⁰ cm^-3

c)

In steady state ,the rate of regeneration is equal to rate of recombination

p\'/T =10¹⁹/s cm³

p\' =10¹⁹*2*10^-6

p\' =2*10¹³ cm^-3

d)

n\'=p\'=2*10¹³ cm^-3

e)

p=p_o+p\' =10¹⁶+2*10¹³=1.002*10¹⁶ cm^-3

f)

n=n_o+n\' =4*10¹⁰ +2*10¹³ =2.004*10¹³ cm^-3

g)

np=(1.002*10¹⁶ )(2.004*10¹³)=2.008*10²⁹ cm^-6