A NOVEL FORMULATION OF THE ADJOINT METHOD IN THE OPTIMAL DESIGN OF QUANTUM ELECTRONIC DEVICES

The adjoint method is used to efficiently and accurately compute gradients with respect to the design parameters in the identification of optimal designs of electronic devices whose physical behavior is determined by solutions of the Schrodinger equation. In this study, the optimal design problem is formulated as the minimization of a least-squares performance metric. Key to our approach is the use of finite dimensional approximation based on the propagation matrix method and the reformulation of the underlying boundary value problem for an approximating time-independent Schrodinger equation as a terminal value problem. In this way the efficient computation of highly accurate gradients (i.e., with zero truncation error) required for optimization becomes amenable to the use of the adjoint method as it is typically applied in the context of evolution equations. The numerical stability of the method and the convergence of the approximating solutions to the state equations and their gradients with respect to the design parameters as well as the convergence of the solutions to the optimal design problems themselves are all rigorously established.