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Steady state temperature of wafers?

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data

    A 50mm wafer, 2mm thick is implanted with Boron at 100keV and 1mA. Considering only conductive cooling, given that thermal resistance is 10K/W, to room temperature of 25oC, determine the steady state wafer temperature and also the time constant for heating

    2. Relevant equations

    I know that Net Q = CdT/dt = Qin - ( T - To) / thermal resistance.

    3. The attempt at a solution

    I can determine Qin by using 1ev = 1.602 X 10^-19 J. But I am stuck on how to proceed. Could someone please help?
  2. jcsd
  3. Feb 23, 2009 #2


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    Okay, how many Boron atoms are impinging on the wafer every second? How much energy do they (collectively) carry?
  4. Feb 23, 2009 #3
    The boron atoms would collectively carry 100 X 1.602 X 10 ^ -19 J since 1 keV carries 1.602 X 10 ^ -19 J

    How many atoms impinging per second is not given, is this something I can calculate from the information that has been provided in the question? If yes, what equation is required?

  5. Feb 23, 2009 #4


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    No, each boron atom carries 100 x 1.602E-19 J. As to the number, here's a hint: why do they tell you the implant current?
  6. Feb 23, 2009 #5
    I think I am stalled, really stalled on this one! The only other piece of information that describes / models this physical situation would be:

    T = To + (Tf - To) e ^(-t/tau).

    I know that I am supposed to obtain Tf as the steady state wafer temperature and tau as the time heating constant. I am blocked, please help!
  7. Feb 23, 2009 #6


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