  We consider the optimal design of a sequence of quantum barriers in order to
manufacture an electronic device at the nanoscale such that the dependence of
its transmission coefficient on the bias voltage is linear. The technique
presented here is easily adaptable to other response characteristics. The
transmission coefficient is computed using the Wentzel-Kramers-Brillouin (WKB)
method, so we can explicitly compute the gradient of the objective function. In
contrast with earlier treatments, manufacturing uncertainties are incorporated
in the model through random variables and the optimal design problem is
formulated in a probabilistic setting. As a measure of robustness, a weighted
sum of the expectation and the variance of a least-squares performance metric
is considered. Several simulations illustrate the proposed approach.
