ELE533 Bipolar Devices

Final Exam
August 9, 2002

  1. For a forward biased P+N junction, show that the voltage across the n-neutral region becomes significant when the hole injection equals the donor doping.
    Assume Jn = 0

    0 = q n un (-dV/dx) + q Dn (dn/dx)

    Dn = Vt un

    un n dV = un Vt dn

    dV/Vt = dn/n


    [V(wn) - V(0)]/Vt = ln [n(wn)/n(0)]

    Van = V(0) - V(wn) = Vt ln [ ND + Pn(0)/ND]

    True, since the electron concentration at the contact, n(wn), is ND and,
    at the edge of the depletion region, n(0) = ND + pn(0)

    n(0) = ND + pn(0) is a statment of charge neutrality. Negative charge, n(0), equals the positive charge, ND + pn(0).

    If pn(0) equals ND, Van is significant since, Van = Vt ln(2) = 18mV. 18mV of the applied voltage appears across the neutral region rather than across the junction. The resulting current is 1/2 what it would be if this fraction of the applied voltage had appeared across the junction.