Quantum MonteCarlo Simulation of Single Electron Tunneling Transistors'

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Quantum Monte-Carlo Simulation of Single
Electron Tunneling Transistors.

• B.Gelmont
• University of Virginia

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Single Electron Tunneling Transistor (SET)

• Basic principles of operation.
• Small size ( 10 nm-100 nm).
• Tunneling contacts.
• Coulomb blockade.
• Threshold voltage.
• Coulomb Staircase.
• Unique transport properties of the SET.
• Kondo effect.

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Possible Applications.

• Current control sources.
• Supersensitive electrometry, dc current and
  resistance standards, temperature standard
• Terahertz radiation detection.
• Logic device with the presence or absence of a
  single electron .
• The pump and turnstile devices as frequency
  controlled current sources.
• Basic building blocks of quantum-dot cellular
  automata (QCA) or as memory elements.

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Present understanding.

• The perturbation theory in the limit of the small
  quantum resistance in comparison with the
  tunneling resistance.
• The Renormalization Group analysis and instanton
  techniques in the limit of high tunneling
  conductance.
• No general consensus about the dependence of the
  charging energy on the ratio of the quantum and
  tunneling resistances.

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Quantum Monte-Carlo (QMC).

• QMC requires mapping of quantum ensemble on
  classical system of higher dimension
  (Trotter-like formula of exponential operators).
• The problem is how to develop QMC technique for
  fermions.
• Two different ways to transform the path integral
  into a form suitable for the QMC simulation.

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Objectives

• To develop a QMC algorithm for tight binding
  model of electrons in semiconductor quantum dots.
• To simulate SETs and study I-V characteristics,
  Coulomb blockade, and Kondo effects.
• To develop QMC algorithm for free electrons in
  the metallic dots and to simulate SETs at
  different ratios of the quantum and the tunneling
  resistances.
• To perform simulation of a line of QCA cells, to
  demonstrate the transmission of information from
  cell to cell.
• QMC algorithm for random distances between sites.

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Computer problem

• QMC simulations generally demand large amounts of
  computational resources.
• To realize the full potential of computer
  simulation, the computational bottlenecks must be
  overcome by employing parallel computing
  techniques.
• We propose to develop a QMC simulator based on
  Message Passing Interface (MPI) parallel
  computing technique.

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Time-table

• Year 1 Year 2 Year 3

Develop QMC algorithm for tight binding
model Simulation of SETs Develop QMC algorithm
for the metallic dot