Thermionic injection and space-charge-limited current in reach-through p+np+ structures

Abstract

The current transport mechanisms of reach-through p+np+ and its related structures have been studied. It has been established that when the applied voltage is slightly greater than the reach-through voltage, at which the n layer is completely depleted, the current increases exponentially with voltage by thermionic injection or diffusion over the potential barrier. The current-voltage relationship is given by J ≅ A*T2 exp[−q(VFB − V)2/4kTVFB], where A* is the effective Richardson constant, T the temperature, V the applied voltage, and VFB the flat-band voltage defined as qNDL2/2εs, where ND and L are the ionized impurity density and the length of the n layer, respectively. When the injected carrier density rises to a value comparable to the impurity density, the space-charge-limited (SCL) effect causes the current to vary less rapidly with the applied voltage. The SCL effect is derived based on an accurate expression of the velocity-field relation, i.e., vs/(1 + Es/E), where vs is the scattering-limited velocity and Es is the critical field given by the ratio of vs to the low-field mobility. In the high-current limit, we obtain the linear current-voltage expression J ≃ qNDvs(V/VFB). Experimental structures are made from epitaxial n on p+ silicon substrate with an epitaxial layer thickness of 8.5 μm and doping concentration of 5 × 1014 cm−3. The second p+ layer of about 1 μm is formed by diffusion. Good agreement has been obtained between the experimental results and theoretical predictions.