This paper describes a method for calculating under low-level injection conditions the minority carrier current in a heavily-doped diffused region, examples of which are the emitter region of a double-diffused transistor and the diffused regions of a p-L-n rectifier or a thyristor. Based on the assumption that the minority-carrier quasi-Fermi potential is constant, the method is simpler and has wider applicability than that given by Klein. For the three standard types of impurity profiles — the exponential, the Gaussian, and the erfc, it yields a common expression for the minority carrier current Jp at the junction edge, namely Jp = qp[τp0(qEkT)], where p and E are, respectively, the minority carrier concentration and field at the junction edge, τp0 the minority carrier lifetime, and (kTq) the thermal voltage. The basis of the constant quasi-Fermi potential assumption is examined, and conditions for its validity are derived.The validity of the treatment presented is verified by exact numerical solutions for a n+−p−p+ diffused junction rectifier whose n+-region has a doping profile of the erfc type.
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