The current flowing in silicon bar is 2.02 [tex]\times[/tex] 10^-12 A.
Explanation:
Length of silicon bar, l = 10 μm = 0.001 cm
Free electron density, Ne = 104 cm^3
Hole density, Nh = 1016 cm^3
μn = 1200 cm^2 / V s
μр = 500 cm^2 / V s
The total current flowing in the bar is the sum of the drift current due to the hole and the electrons.
J = Je + Jh
J = n qE μn + p qE μp
where, n and p are electron and hole densities.
J = Eq (n μn + p μp)
we know that E = V / l
So, J = (V / l) q (n μn + p μp)
J = (1.6 [tex]\times[/tex] 10^-19) / 0.001 (104 [tex]\times[/tex] 1200 + 1016 [tex]\times[/tex] 500)
J = 1012480 [tex]\times[/tex] 10^-16 A / m^2.
or
J = 1.01 [tex]\times[/tex] 10^-9 A / m^2
Current, I = JA
A is the area of bar, A = 20 μm = 0.002 cm
I = 1.01 [tex]\times[/tex] 10^-9 [tex]\times[/tex] 0.002 = 2.02 [tex]\times[/tex] 10^-12
So, the current flowing in silicon bar is 2.02 [tex]\times[/tex] 10^-12 A.
