# Homework Help: Drift velocity of electrons in n-doped silicon

1. Feb 5, 2009

### Stef42

1. The problem statement, all variables and given/known data
"A cylinder of n-doped silicon is 10mm long, has a diameter of 5 mm and is known to have a mobility $$\mu$$=0.15 m2V-1s-1. The resistance of the block measured along its length is 255 $$\Omega$$

a) What is the resistivity of the silicon block?
b) Estimate the electron carrier density in the silicon
A current of 1mA is passed along the length of the block
c)What is the electric field inside the block?
d)What is the drift velocity of the electrons?

2. Relevant equations
[1] Resistivity $$\rho=RA/l$$ ; R= resistance, A= cross sectional area, l= length
[2] $$\frac{1}{\rho}=\mu ne$$ ; mu= mobility, n=electron carrier density, e=charge of electron
[3] E=V/x ; E=electric field, V= voltage, x= length of cylinder
[4] Vd=$$\mu$$E ; Vd=drift velocity,

3. The attempt at a solution

Right so first I got resistivity= (255x(2.5x10-3)2pi)/10x10-3= 0.5

Then using [2], I get n = 8.3x1019 (which to me seems too high?)

By using [3] and saying that the voltage=0.255 and x= 10mm, I get E= 25.5

Finally using [4] I get velocity= 3.825 ms-1 which seems pretty fast. I can't see where I could have gone wrong, thoughts? thanks for the help!

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