ELE533 Bipolar Devices

Mid Term Exam
October 25, 2005


  1. Consider a silicon pn junction. The p side is uniformly doped with 5x1018 acceptors/cm3. The n side is doped with 2x1016 donors/cm3.
    The contact on the p-side is 2 microns from the junction. The contact on the n-side is 10 microns from the junction. The junction area is 10 microns by 10 microns.

    1. What is the built in potential?
      Vbi = VT ln[NAND / ni2] = 0.877V

    2. What is the position of the Fermi level relative to the intrinsic level on the n side of the junction?

      Ef - Ei = VT ln[ND /ni] = 0.365V

    3. What is the value of the saturation current, Is, in the equation,
      I = Is*eV/Vt

      Is = A q ni2 Dp / ND Wn = 1.8 x 10-17 A

      where, Dp = VT up = 0.0259*440

    4. Draw the equilibrium energy band diagram for this junction, including numerical values for the Fermi level position relative to the intrinsic level on each side. Show the built-in potential on the diagram.

      Vn = 0.365 eV,   Vp = 0.51 eV,   Vbi = 0.87 eV