Space-charge-limited current and capacitance in double-junction diodes

Abstract

An analytical theory is given for the space-charge-limited current in n-i-n or p-i-p diodes. The exact I-V characteristic is obtained in a parametric form. In the limit of high currents or for a large width of the intrinsic (i) base region the characteristics reduce to a Mott–Gurney form. In the low-current limit a linear I-V characteristic is obtained. The space-charge barrier presents a conceptually different case from a conventional barrier current in that the position of the barrier moves depending on the biasing condition. It is this motion which is responsible for the linear regime—which extends over a substantial range (∼10kT/e) of the applied voltage. The distribution of the electrostatic potential and of the quasi-Fermi level in the base, as well as the position of the potential maximum (the virtual cathode), are shown for different current levels. The differential capacitance of the double-junction diode is calculated and shown to be strongly dependent on the applied bias.