(adsbygoogle = window.adsbygoogle || []).push({}); 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 [tex]\mu[/tex]=0.15 m^{2}V^{-1}s^{-1}. The resistance of the block measured along its length is 255 [tex]\Omega[/tex]

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 [tex]\rho=RA/l[/tex] ; R= resistance, A= cross sectional area, l= length

[2] [tex]\frac{1}{\rho}=\mu ne[/tex] ; mu= mobility, n=electron carrier density, e=charge of electron

[3] E=V/x ; E=electric field, V= voltage, x= length of cylinder

[4] V_{d}=[tex]\mu[/tex]E ; V_{d}=drift velocity,

3. The attempt at a solution

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

Then using [2], I get n = 8.3x10^{19}(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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# Homework Help: Drift velocity of electrons in n-doped silicon

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