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

  1. Feb 5, 2009 #1
    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 m2V-1s-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] Vd=[tex]\mu[/tex]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!
  2. jcsd
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