ELE533 Bipolar Devices

Mid Term Exam
October 25, 2005

Name_____________________________________

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?

      V_bi = V_T ln[N_AN_D / n_i²] = 0.877V

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

      E_f - E_i = V_T ln[N_D /n_i] = 0.365V

   3. What is the value of the saturation current, Is, in the equation,

      I = Is*e^V/Vt

      Is = A q n_i² D_p / N_D W_n = 1.8 x 10^-17 A

      where, D_p = V_T u_p = 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.

      
      

      V_n = 0.365 eV,   V_p = 0.51 eV,   V_bi = 0.87 eV