A microscopic theory of tunneling

Kleiman, George Gershon

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https://hdl.handle.net/2142/30462 Copy

Description

Title

A microscopic theory of tunneling

Author(s)

Kleiman, George Gershon

Issue Date

1971

Director of Research (if dissertation) or Advisor (if thesis)

Duke, C.B.

Department of Study

Physics

Discipline

Physics

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• impurity-assisted tunneling
• Matsubara perturbation theory
• Semiconductor tunneling

Language

en

Abstract

"A microscopic theory of impurity-assisted tunneling is constructed in which the current-carrying (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 one-electron 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 rigid-occupancy; i.e, the equilibrium occupation of the (current-carrying) many-body eigenstates of the system is taken to be unaffected by the presence of the bias. Therefore the rigid occupancy hypothesis relates the non-equilibrium current flow to the equilibrium (zero-bias) properties of the junction system so that we obtain a theory of nonequilibrium current flow which is not based on linear-response theory, The hypothesis is incorporated into the Matsubara perturbation theory by treating the chemical potentials of the left and right-hand electrodes as separate Lagrangian multipliers determined after the completion of all Matsubara sums to be related by ~=~L-eV. Therefore, for purposes of constructing and solving Dyson's equations for the renormalized one-electron propagators, the theory reduces to the conventional equilibrium theory defined using distorted-wave (i,e. non-plane-wave) 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 delta-function impurity and dynamic delta-function impurity vibrating at a (Einstein) local mode frequency, All electron-impurity (l~cal-mode-phonon) interactions appear in this formalism as self-energy corrections to the extended-basis electronic wave functions, The position of the impurity relative to the junction-region 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 impurity-induced self-energy of the two (i,e, left ~right and right ~ left) linearly-independent current-carrying basis states. Resonant elastic tunneling through impurity states of energy Er near the zero-bias Fermi energy, ,~ causes conductance minima(maxima) for E > r ,(E <'). Zero-bias anomalies in photosensitive GaAs:Au p-n tunnel diodes have been identified with this mechanism. The major new prediction is that resonant elastic impurity-assisted tunneling strongly affects inelastic impurity-assisted tunneling: e,g., if an ""impurity"" state is localized near the oxide in a M-O-S junction then large cusp-like phonon structure in the conductance appears only for majority carrier tunneling from the semiconductor into the metal, This prediction, and its correlation with a zero-bias anomaly is borne out in III-V tunnel diodes and metal-Si:B3P junctions."

Type of Resource

text

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http://hdl.handle.net/2142/30462

Copyright and License Information

© 1971 George Gershon Kleiman

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