PhD Thesis Colloquium

Date: 15 July 2015

Quantum-Continuum Based Model of Semiconductor Nanostructures

Bhamy Maithry Shenoy

Supervisor: D. Roy Mahapatra

Abstract

Semiconductor nano-structures grown in various configurations such as thin films, nanowires, quantum dots and heterostructures are important elements of micro and nano-electronics. During device operation, they may produce various effects due to nonlinearity, coupling between various physical processes and residual stress. Reliable prediction of all these effects require theoretical models which is consistent across scales and physical phenomena for better understanding of interfacial defects, fracture and adverse effects in terms of electrical resistance, energy band structure and device gains. Models based on either first principle or continuum theory alone cannot predict the behaviour of the nanostructures. Restriction on the number of atoms and restriction on applying dynamic conditions in relation to the exchange interaction energies in the functional ultimately limits the former approach. Whereas the latter approach cannot capture fundamental properties and it needs large number of parameters from several experiments. In the present thesis, a quantum-continuum approach is developed to describe the interactions among various physical fields namely thermal field (molecular vibration), electrical field (charge transport), mechanical stress field and the quantum-mechanical field. The coupled model accommodates the atomic scale information by estimating physical properties such as thermal conductivity, residual strain, etc. via the first principle methods. A variational calculus based framework is proposed to solve the resulting coupled problem using finite element computation. In order to validate the proposed multi-scale coupled-field modelling approach, an example computational problem is reduced to a quasi one-dimensional representation of a thin film heterostructure in thickness dimension while assuming periodic structure in the planner dimensions. The effect of various boundary conditions on the electronic properties of the thin films with examples of group III-V and group II-VI semiconductors is analysed. Influence of coupled interactions altering the electrostatic potential, electron and hole energies are demonstrated. The developed computational scheme is applied to analyse the interface structure and residual strain field in quantum dot nano-structures embedded in a matrix, with an example of Si quantum dot in amorphous SiO2 matrix. Length-scale correlation among various fundamental properties such as interface width, sub-stoichiometric ratio, defect statistics and strain with the diameter of embedded quantum dot are established. Since the quantum dot diameter can be determined experimentally, such length-scale correlations are useful in estimating the interface and strain related properties such as energy band gap for device design. The residual strain and interface-induced changes in the optoelectronic properties are estimated and results are verified with published experimental data. The computational scheme is further applied to understand problems involving ionic transport and semiconductor-fluid interfaces with application in nano-fluidic field effect transistors in micro-fluidic flow environment. Nanowire arrays of Si, Si/SiO2 and ZnO nanostructures in microfluidic channel are considered as examples. These nanowires can function as electrodes, sense, trap and lyse biological cells for diagnostic purpose, assist micro-organism movement and enable molecular binding. The influence of nanowire diameter on the sensitivity to various different biological samples is analysed. To summarize, the thesis proposes a generalized framework with demonstrated computational examples having potential applications in nanostructure based devices. The contribution made in this thesis would be useful in advancing the current understanding of nano-scale phenomena involving electro-thermal-mechanical interactions, quantum effect, nanostructure heterojunctions, semiconductor-fluid interfaces and several others, and toward developing better tools in designing new nanoelectronic devices from concepts to operation.