Hole tunneling through the emitter-base junction of a heterojunction bipolar transistor

Starting with the 4X4 Luttinger-Kohn Hamiltonian, we develop a scattering-matrix approach to study coherent hole transport through the valence-band energy profile across the emitter-base junction of typical abrupt and graded Pnp heterojunction bipolar transistors. The tunneling and reflection coefficients of heavy and light holes are calculated for the upper and lower 2X2 Hamiltonians obtained through a unitary transform of the 4X4 Luttinger-Kohn Hamiltonian. The probability for a transition from heavy (light) to light (heavy) hole while tunneling across the emitter-base junction is calculated as a function of the value of the wave vector parallel to the emitter-base heterointerface for both abrupt and graded heterojunctions. For holes injected from the emitter into the base, the probability of heavy-to light-hole conversion is shown to be quite different when calculated with the upper and lower Hamiltonians. On the other hand, the probability of light-to heavy-hole conversion is nearly the same for the upper and lower Hamiltonians. The energy dependence of the heavy-and Light-hole tunneling coefficients is shown to be quite different from those calculated using a parabolic-band model, in which the effects of mixing and anisotropy in the valence band are neglected.