Learning compact physics‐aware delayed photocurrent models using dynamic mode decomposition

Abstract

Radiation-induced photocurrent in semiconductor devices can be simulated using complex physics-based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high-level circuit simulations where it is computationally infeasible to evaluate detailed models for multiple individual circuit elements. In this work we demonstrate a procedure for learning compact delayed photocurrent models that are efficient enough to implement in large-scale circuit simulations, but remain faithful to the underlying physics. Our approach utilizes dynamic mode decomposition (DMD), a system identification technique for learning reduced-order discrete-time dynamical systems from time series data based on singular value decomposition. To obtain physics-aware device models, we simulate the excess carrier density induced by radiation pulses by solving numerically the ambipolar diffusion equation, then use the simulated internal state as training data for the DMD algorithm. Our results show that the significantly reduced-order delayed photocurrent models obtained via this method accurately approximate the dynamics of the internal excess carrier density-which can be used to calculate the induced current at the device boundaries-while remaining compact enough to incorporate into larger circuit simulations.

Development of data‐driven exponential integrators with application to modeling of delay photocurrents

“…The main purpose of this section is to evaluate the effectiveness of the empirical training rule for low‐resolution models, established in Section 4.2.3. Such models are of particular interest for circuit simulations because of their low computational costs.Remark We note that projection‐based order reduction similar to the approach in Hanson et al [18] can be applied to any high‐resolution model to obtain a more efficient one. Such reduced order ETI models are, however, beyond the scope of this paper.…”

“…Remark It is easy to see that the scheme (15) has the generic form (3) with respectively. Clearly, one can attempt to approximate and directly from solution snapshots along the same lines as in Hanson et al [18], without assuming any additional information for these maps. However, such an approach treats and as “black‐box” matrices and does take advantage of their structure (18), which remains “hidden” from the training process.…”

“…DMD is an "equation-free" technique that can learn (3) purely from data without assuming any knowledge of an underlying mathematical model. We used DMD in the development of a compact model in Hanson et al [18] that targeted primarily simulation of constant-in-space radiation pulses. In that case we were able to obtain an accurate model using training data generated solely from constant-in-space source terms.…”

“…Clearly, one can attempt to approximate A and B directly from solution snapshots along the same lines as in Hanson et al [18], without assuming any additional information for these maps. However, such an approach treats A and B as "black-box" matrices and does take advantage of their structure (18), which remains "hidden" from the training process. For example, the dynamic operator Φ is common to both A and B but if they are treated as "black-boxes" this fact will not be leveraged during the training, possibly increasing the amount of the necessary training data.…”

“…This paper continues our efforts to develop compact numerical delay photocurrent models commenced in References [18, 19]. The model in the first paper is a discrete time dynamical system obtained by using dynamic mode decomposition (DMD) [9] to perform system identification, followed by a projection‐based order reduction step.…”