Adjoint Optimization of Nanoscale Vacuum-Channel Transistor (NVCT) Geometry

A new, efficient method for optimizing NVCT geometry is presented. Previous work has shown how adjoint techniques can compute the shape gradient (i.e., gradient with respect to shape perturbations) of a prescribed-emission electron gun using only two particle-in-cell simulations [5]. This work provides an extension to the case of self-consistent emission in Hamiltonian systems by including external parameters as dynamical variables. The structure of the perturbed Hamilton's equations then yields a simple recipe for the evaluation of the adjoint problem. The adjoint problem can be evaluated as a perturbed and time-reversed version of the original simulation. From this, the full gradient can be extracted. This general approach is used to incorporate the modified emission current into the computed shape gradients, enabling full-device gradient-based optimization.