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Title:  A microscopic theory of tunneling 
Author(s):  Kleiman, George Gershon 
Director of Research:  Duke, C.B. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  impurityassisted tunneling
Matsubara perturbation theory Semiconductor tunneling 
Abstract:  A microscopic theory of impurityassisted tunneling is constructed in which the currentcarrying (extended) eigenstates of the average one electron potential in a tunnel junction are utilized as the basis functions which are mixed by the Hamiltonian associated with the presence of a static or dynamic impurity anywhere in the system. In such a system, the oneelectron propagator and its concomitant current across the junction easily can be calculated at zero bias by standard techniques for manipulating temperature Green's functions, The presence of a finite bias across the junction is incorporated into the theory via the principle of rigidoccupancy; i.e, the equilibrium occupation of the (currentcarrying) manybody eigenstates of the system is taken to be unaffected by the presence of the bias. Therefore the rigid occupancy hypothesis relates the nonequilibrium current flow to the equilibrium (zerobias) properties of the junction system so that we obtain a theory of nonequilibrium current flow which is not based on linearresponse theory, The hypothesis is incorporated into the Matsubara perturbation theory by treating the chemical potentials of the left and righthand electrodes as separate Lagrangian multipliers determined after the completion of all Matsubara sums to be related by ~=~LeV. Therefore, for purposes of constructing and solving Dyson's equations for the renormalized oneelectron propagators, the theory reduces to the conventional equilibrium theory defined using distortedwave (i,e. nonplanewave) states. The usual transfer Hamiltonian results are recovered by expanding the transmission probability. Using this theory, we have constructed and solved the Dysonis equations associated with bare vertex functions for both a static deltafunction impurity and dynamic deltafunction impurity vibrating at a (Einstein) local mode frequency, All electronimpurity (l~calmodephonon) interactions appear in this formalism as selfenergy corrections to the extendedbasis electronic wave functions, The position of the impurity relative to the junctionregion determines both the sign and magnitude of these corrections, Therefore, the asymmetries in the tunnel characteristics which can be traced to the position of the impurities enter the theory via the asymmetry in the impurityinduced selfenergy of the two (i,e, left ~right and right ~ left) linearlyindependent currentcarrying basis states. Resonant elastic tunneling through impurity states of energy Er near the zerobias Fermi energy, ,~ causes conductance minima(maxima) for E > r ,(E <'). Zerobias anomalies in photosensitive GaAs:Au pn tunnel diodes have been identified with this mechanism. The major new prediction is that resonant elastic impurityassisted tunneling strongly affects inelastic impurityassisted tunneling: e,g., if an "impurity" state is localized near the oxide in a MOS junction then large cusplike phonon structure in the conductance appears only for majority carrier tunneling from the semiconductor into the metal, This prediction, and its correlation with a zerobias anomaly is borne out in IIIV tunnel diodes and metalSi:B3P junctions. 
Issue Date:  1971 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/30462 
Rights Information:  © 1971 George Gershon Kleiman 
Date Available in IDEALS:  20120328 
Identifier in Online Catalog:  6025323 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois