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Semiconductor doping

  1. Oct 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Si atoms get doped inside GaAs to a concentration of 1.5*10^8 . Assume that the silicon atoms are
    fully ionized and that 35percent atoms replace gallium and that 65% of the added
    atoms replace arsenic t=300k
    Fnd the acceptor and donor concentrations

    Calculate electron / hole concentrations and Ef-Efi
    2. Relevant equations
    (Nd-Na)/2 + sqrt((Nd-Na/2)^2+ni^2)
    (Na-Nd)/2 + sqrt((Na-Nd/2)^2+ni^2)

    3. The attempt at a solution
    Nd=.35*(7*10^15) =2.4*10^15
    Na=(.65)*(7*10^15)=4.5*10^15

    For the next part(assuming the above is correct), should I use ni of the GaAs or Si for the next part? Or the given value of 1.5*10^8?

    (2.4*10^15-4.5*10^15)/2 + sqrt((2.4*10^15-4.5*10^15/2)^2+1.5*10^8^2) =-8.99*10^14 = donor concentration

    (-2.4*10^15+4.5*10^15)/2 + sqrt((-2.4*10^15+4.5*10^15/2)^2+1.5*10^8^2)=1.2*10^15 = acceptor concentration
     
  2. jcsd
  3. Oct 10, 2015 #2

    mfb

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    Staff: Mentor

    You should explain what you are calculating. Where does the number 7*10^15 come from?

    Negative concentrations don't make sense.
    The material is still GaAs, so you needs its properties. Plus the new acceptors/donors.
     
  4. Oct 10, 2015 #3
    it's the effective density of states of GaAs

    Should I be using the intrinsic carrier concentration instead is 1.8*10^8 which I have not used yet.
     
  5. Oct 10, 2015 #4

    mfb

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    You do not replace .35 of your gallium atoms.
    .35 of the silicon atoms replace a gallium atom, but you have a tiny amount of silicon atoms compared to the gallium atoms.
     
  6. Oct 10, 2015 #5
    Is the concentration of silicon 1.8*10^8? 1.I thought the question was saying GaAs was at a concentration of 1.5*10^8 after the Silicon was added, am I reading it wrong?

    Si replacing GA > Nd=.35*1.5*10^8 = 5.25*10^7
    Si replacing As= Na=.65*1.5*10^8 = 9.75*10^7

    Or should I be using the intrinsic carrier concentration of GaAs, and calculating how much Silicon has changed it by, then getting a fraction of the result?
     
  7. Oct 13, 2015 #6
    Si replacing GA > Nd=.35*1.5*10^8 = 5.25*10^7
    Si replacing As= Na=.65*1.5*10^8 = 9.75*10^7

    Electron concentration
    n0=(Nd-Na)/2 + sqrt((Nd-Na/2)^2+ni^2)
    (5.25*10^7-9.75*10^7)/2 + sqrt((5.25*10^7-9.75*10^7/2)^2+1.8*10^10^2) =
    1.29*10^8 electron concentration
    Hole concentration
    p0=(Na-Nd)/2 + sqrt((Na-Nd/2)^2+ni^2)
    (-5.25*10^7+9.75*10^7)/2 + sqrt(((-5.25*10^7+9.75*10^7)/2)^2+1.5*10^8^2))=
    1.74*10^8 hole concentration

    Ef-Efi
    n0=niexp[(Ef-Efi)/kT]

    1.29*10^8=(1.5*10^8)exp([Ef-Efi]/(300*8.61*10^-6))

    Ef-Efi=(-0.00389)
     
  8. Oct 13, 2015 #7

    mfb

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    Those numbers look more reasonable.
     
  9. Oct 13, 2015 #8
    Okay thank you
     
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