ELE533 Bipolar Devices

Mid Term Exam
July 19, 2002

  1. A silicon wafer is doped with 3E17 boron and 2E17 phosphorus atoms.
    Calculate the electron and hole concentrations, E f , and the resistivity at room temperature.

    NA = 3x1017cm-3
    ND = 2x1017cm-3

    NA + ND = 5x1017cm-3

    The hope concentration, p = NA - ND = 1017cm-3.

    The electron concentration, n = ni2/p = 2x1020/1017 = 2x103 cm-3.

    Ef - Ei = -Vt ln [(NA - ND)/ni] = -0.0259 ln [1017/1.5x1010] = -0.407V

    Resistivity

    Mobility depends on the total doping, NA + ND = 5x1017cm-3. From the table hole mobility is about 300 cm2/V-s.

    rho = 1/[qup(NA - ND)] = 1/[1.6x10-19 x 300x1017] = 0.2 ohm-cm

    Doping
    cm-3
    Electron
    Mobility
    (cm2 V-sec)
    Hole
    Mobility
    (cm2 V-sec)
    1014
    1500
    450
    1015
    1500
    450
    1016
    1400
    440
    1017
    1200
    410
    1018
    800
    200
    1019
    200
    150
    1020
    90
    50