Computation of potential profile for complex heterostructures with quantum wells for semiconductor nanodevices

In this paper a mathematical tool allows computing the potential profile of a single heterojunction analytically. When multilayer structure is analysed, usually numerical methods are used for self-consistent solution of transport equations, Poisson´s and Schrodinger equations. For the computation of the potential relief we use the Anderson model for a heterojunction. Dopants are fully ionized and are distributed evenly over the doping region. Interface states on the metallurgical interface are absent. Influence of the image forces on the potential in the contact regions and contribution from the free carriers to the field of the space charges are negligibly small. All these conditions allow us to find analytical expressions for the spatial dependence of the potential. We consider each region of a semiconductor structure as a subcircuit having proper voltage-current characteristic (VCC). The space charge regions are approximated by nonlinear resistance.