A silicon bar is 2 micro meters long and has 100 micro meters squared cross sect

Question

A silicon bar is 2 micro meters long and has 100 micro meters squared cross section. It is doped with 1x10^17 cm^3 arsenic.

a) Find the current with 1V applied at room temperature
b) How long does it take for an electron to drift from one end of the bar to the other
c) If an excess of holes is somehow introduced into the center of the bar, describe the minority carrier distribution after a time roughly equal to the minority carrier lifetime
d) If the doping level was increased by a factor of 100, would the current also increase by the same factor?

Explanation / Answer

a) length of silicon bar L=2 *10^-6
area of cross section A=100 micrometers
doping concentration = 1*10^17 cm^3 =n
so,current I=J*A=nqV*A,where q=1.602*10^-19 c
V=mobiliy*electricfield=1300(silicon)*1 Volt

I=(1*10^17*10^-6) (1.602*10^-19)(1300*1)/(2*10^-6)
= (1.602*13*10^-4)/2
=1.041 mA

b) Time T=L/V=(2*10^-6)/(1300*1) where V=velocity of electrons
=1.538 ns(nanoseconds)
d) if doping level is increased by 100,current also inceases by yhe same factor..bcoz I n where I=nqV*A

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