Quantum mechanical tunneling in an ohmic contact

The tunneling probability for majority carriers in an ohmic contact to n-type GaAs has been calculated by directly solving the Schrödinger equation for the wave functions in the semiconductor depletion region. The direct solution is straightforward and relies on fewer assumptions than previous calculations based on the WKB approximation. It also provides a useful application of undergraduate quantum mechanics to an important area of VLSI semiconductor technology. The direct solution can be performed on an 80286 machine in less than a minute and yields tunneling probabilities roughly twice as large as the WKB approximation at most electron energies. The tunneling probability is then used to calculate the contact resistance as a function of doping for the contact. The contact resistances are approximately one-half the resistances calculated using the WKB method.