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. There are two distinguishing features of our approach. First, the transmission coefficient is determined using a semiclassical approximation, so we can explicitly compute the gradient of the objective function. Second, in contrast with earlier treatments, manufacturing uncertainties are incorporated in the model through random variables; the optimal design problem is formulated in a probabilistic setting and then solved using a stochastic collocation method. 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 technique, which shows an improvement in accuracy over 69% with respect to brute-force, Monte-Carlo-based methods.