Carnio, Edoardo (2018) The metal-insulator transition in doped semiconductors : an ab initio approach. PhD thesis, University of Warwick.

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Abstract

In this thesis we study the Anderson metal-insulator transition starting from an atomistically correct ab initio description of a doped semiconductor. In particular, we use density functional theory to simulate model systems of sulphur-doped silicon (Si:S) with few impurities in a large cell. From the resulting Kohn-Sham Hamiltonian, we build an effective tight-binding Hamiltonian for larger systems with an arbitrary number of dopants. Our effective model assumes the same potential around single and paired impurities, for up to ten nearest neighbours and disregarding configurations of three and more close impurities. We generate up to a thousand disorder realisations for systems of 16 3 to 22 3 atoms and a large range of impurity concentrations. From the diagonalisation of these realisations we study the formation of an impurity band in the band gap of the host semiconductor. With increasing impurity concentration, this band undergoes an Anderson metal-insulator transition, namely (i) it approaches and merges with the conduction band and (ii) its states delocalise starting from the band centre. From the multifractal fluctuations of the wave functions near criticality, we characterise the Anderson transition in terms of its critical concentration nc and exponent. We identify two regimes: for energies in a “hybridization region”, where the conduction band seems to influence the impurity band, we observe an increase from v ≈ 0:5 to v ≈ 1, compatibly with the experimental values; deeper in the band, instead, the estimates of v fluctuate between 1 and 1:5, compatibly with v ≈ 1:59 (v ≈1:3) found in the Anderson model without (with) electron-electron interactions. Our results suggest a possible resolution of the long-standing exponent puzzle due to the interplay between conduction and impurity states.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Doped semiconductors, Density functionals, Hamiltonian systems -- Industrial applications, Silicon -- Industrial applications
Official Date:	2018
Dates:	Date Event 2018 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Department of Physics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Römer, Rudolf
Extent:	xiii, 132 leaves : charts
Language:	eng

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