Abstract
The controlled introduction of elastic strains is an appealing strategy for modulating the physical properties of semiconductor materials. With the recent discovery of large elastic deformation in nanoscale specimens as diverse as silicon and diamond, employing this strategy to improve device performance necessitates first-principles computations of the fundamental electronic band structure and target figures-of-merit, through the design of an optimal straining pathway. Such simulations, however, call for approaches that combine deep learning algorithms and physics of deformation with band structure calculations to custom-design electronic and optical properties. Motivated by this challenge, we present here details of a machine learning framework involving convolutional neural networks to represent the topology and curvature of band structures in k-space. These calculations enable us to identify ways in which the physical properties can be altered through “deep” elastic strain engineering up to a large fraction of the ideal strain. Algorithms capable of active learning and informed by the underlying physics were presented here for predicting the bandgap and the band structure. By training a surrogate model with ab initio computational data, our method can identify the most efficient strain energy pathway to realize physical property changes. The power of this method is further demonstrated with results from the prediction of strain states that influence the effective electron mass. We illustrate the applications of the method with specific results for diamonds, although the general deep learning technique presented here is potentially useful for optimizing the physical properties of a wide variety of semiconductor materials.
Highlights
Elastic strain engineering (ESE) has emerged as a promising tool to enhance the performance of functional materials, whereby characteristics of semiconductor materials, such as carrier mobility, can be modulated solely through the introduction of strain[1]
We present here a physics- Model description informed, convolutional neural network (CNN) technique that is more versatile, accurate, and efficient in its capability to facilitate autonomous deep learning of the electronic band structure of crystalline solids than the neural network architecture hitherto employed to address this class of problems
Band structure and physics-informed machine learning (ML) Our method seeks to develop accurate predictions of the band energy dispersion for the top valence band (VB, n = nVB), the lowest conduction band (CB, n = nCB), and their adjacent two bands (n = nVB − 1 and n = nCB + 1) could all be represented via 4 vectors each of which has a length of m3
Summary
Elastic strain engineering (ESE) has emerged as a promising tool to enhance the performance of functional materials, whereby characteristics of semiconductor materials, such as carrier mobility, can be modulated solely through the introduction of strain[1]. While our earlier deep ESE calculations are adequate for rapid data collection in a highly specialized model[13,15], they do not offer sufficient flexibility and accuracy for optimizing a broader consideration of physical characteristics such as the effective mass of electrons and holes, which is a second-derivative of En(k; ε) with respect to k and a strong sensitivity to noise. It is solution for a series of Bloch waves, each of which has a predicted dispersive form.
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