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## Index

abbreviations
Definition of Terms and
accelerating the simulator
4.2.4 Accelerating the Simulator
access time
applications of single-electronics
5 Applications
approximate of the matrix exponential operator
3.3.1 Krylov Subspace Approximate
Arnoldi algorithm
H Arnoldi Algorithm
asymmetry in tunnel junctions
2.7 The Double Tunnel
background charge
2.7 The Double Tunnel | 2.7 The Double Tunnel | 2.8 Single Electron Transistor | 2.8 Single Electron Transistor | 5.2.3 Random Background Charge
independence
5.2.10 Multi Island Memory
independent memory
5.2.9 Qo Independent Memory
barrier
2.4.2 Tunnel Rate
bibliography
Bibliography
birth-death process
3.2 Tunneling: a Stochastic
bit error
Bit Errors
Bloch oscillations
1 Introduction: What is
Boltzmann approximation
B Fermi Energy Dependence
branch
3.1.1 Notation
capacitance
calculation
A Capacitance Calculations
effective
3.1.5 Method of Critical
of arbitrary arrangement of spheres
A.4 Capacitance of an
of sphere
A.1 Self Capacitance of
of sphere with dielectric shell
A.2 Self Capacitance of
of spheres in a line
A.4 Capacitance of an
of two spheres
A.3 Capacitance of Two
stray
2.6 Influence of the | 2.7 The Double Tunnel
capacitance matrix
2.1.1 Electron Electron Interaction | 3.1.2 Electrostatic Energy
elements of
2.1.1 Electron Electron Interaction
inverse of
2.1.1 Electron Electron Interaction
carrier concentration
Material Properties | 2.1.1 Electron Electron Interaction
characteristic energies
2.1 Characteristic Energies
charge
background
2.7 The Double Tunnel | 2.7 The Double Tunnel | 2.8 Single Electron Transistor | 2.8 Single Electron Transistor | 5.2.3 Random Background Charge
polarization
2.2 Work Done by | 2.7 The Double Tunnel
relaxation
2.2 Work Done by
charge, electric
1 Introduction: What is
charge-node
3.1.1 Notation
circuit editor
4.2.1 Graphical User Interface
circuit, single-electron
3.1.1 Notation
circuits
manufacturability
5.2.5 Manufacturability
co-tunneling
2.9 Co Tunneling | 5.2.2 Error Rate/Probability
elastic
2.9 Co Tunneling
inelastic
2.9 Co Tunneling | 2.9 Co Tunneling
second order at zero temperature
F Second Order Co
code structure of SIMON
4.2 Code structure
combination of Monte Carlo method with direct calculation
3.6 Combination of Monte
comparison between master equation and Monte Carlo method
3.5 Comparison between Master
complexity of memories
5.2.11 Discussion of Simulation
conduction band edge
2.4.2 Tunnel Rate
conservation of particles
E Fermi's Golden Rule
Cooper pair
1 Introduction: What is
1 Introduction: What is | 2.5 Minimum Tunnel Resistance | 2.7 The Double Tunnel
Coulomb energy
5.2.1 Operation Temperature
Coulomb gap
2.7 The Double Tunnel
Coulomb oscillations
1 Introduction: What is | 2.8 Single Electron Transistor | 5.2.1 Operation Temperature
critical charge
3.1.5 Method of Critical
critical voltage, method of
3.1.5 Method of Critical
current oscillations
2.6 Influence of the
current source
Current Sources
curriculum vitae
Curriculum Vitae
decay process
5.2.2 Error Rate/Probability
degeneracy carrier concentration
Material Properties
density of states
2.4.2 Tunnel Rate | 2.9 Co Tunneling
discussion of simulation results
5.2.11 Discussion of Simulation
divergence of tunnel rate
2.9 Co Tunneling
double tunnel junction
2.7 The Double Tunnel
IV-characteristic
2.7 The Double Tunnel
free energy of
2.7 The Double Tunnel
dripping tap
1 Introduction: What is
duration to next tunnel event
4.2.2 Flow Chart
dynamic memory
5.2.7 Multi Tunnel Junction
effective capacitance
3.1.5 Method of Critical
effective mass
Material Properties | 2.1.2 Quantum Confinement Energies
elastic co-tunneling
2.9 Co Tunneling
electric charge
1 Introduction: What is
electromagnetic environment
influence of
2.6 Influence of the
electron box
1 Introduction: What is
electron cloud
1 Introduction: What is
electron-electron interaction
2.1.1 Electron Electron Interaction
electrostatic charging energy
2.1.1 Electron Electron Interaction
electrostatic energy
3.1.2 Electrostatic Energy
of double tunnel junction
2.7 The Double Tunnel
energy
2.1 Characteristic Energies
electrostatic
2.1.1 Electron Electron Interaction | 3.1.2 Electrostatic Energy
Fermi
2.1.1 Electron Electron Interaction
free
3.1.4 Free Energy
Helmholtz's free
2.3 Helmholtz's Free Energy
level
2.4.2 Tunnel Rate
levels
2.1.2 Quantum Confinement Energies
quantum confinement
2.1.2 Quantum Confinement Energies
spectrum
2.4 Tunneling
energy gap
Material Properties
error
bit
Bit Errors
error probability
5.2.2 Error Rate/Probability
error rate
5.2.1 Operation Temperature | 5.2.2 Error Rate/Probability
event tree
3.6 Combination of Monte
exponential of a matrix
3.3.1 Krylov Subspace Approximate
fabrication techniques
5.1 Fabrication Techniques
Fermi energy
Material Properties | 2.1.1 Electron Electron Interaction
change in
2.1.1 Electron Electron Interaction
dependence on free charge carrier concentration
B Fermi Energy Dependence
Fermi function
2.4.2 Tunnel Rate
integration of
D Integration of Fermi
Fermi's golden rule
2.4.2 Tunnel Rate | 2.9 Co Tunneling | E Fermi's Golden Rule
Fermi-Dirac distribution
2.4.2 Tunnel Rate
2.9 Co Tunneling
finite potential well
C.2 The Finite Potential
flip-flop
5.2.6 Single Electron Flip
floating-node
3.1.1 Notation
flow chart
4.2.2 Flow Chart
free energy
2.3 Helmholtz's Free Energy | 3.1.4 Free Energy
change in
2.4.2 Tunnel Rate
of arbitrary circuit
3.1 Free Energy of
of double tunnel junction
2.7 The Double Tunnel
single-electron transistor
2.8 Single Electron Transistor
frequency of Coulomb oscillations
1 Introduction: What is
frequent state space
3.6 Combination of Monte
global rule
2.6 Influence of the
gold clusters
5.1.5 Gold Clusters
golden rule
2.4.2 Tunnel Rate | 2.9 Co Tunneling | E Fermi's Golden Rule
graphical circuit editor
4.2.1 Graphical User Interface
graphical user interface
4.2 Code structure
Helmholtz's free energy
2.3 Helmholtz's Free Energy
high impedance environment
2.6 Influence of the
image charge method
A.3 Capacitance of Two
implementation issues
4 Implementation Issues
impurity
2.7 The Double Tunnel
independence tobackground charge
5.2.10 Multi Island Memory
inelastic co-tunneling
2.9 Co Tunneling | 2.9 Co Tunneling
infinite potential well
2.1.2 Quantum Confinement Energies | C.1 The Infinite Potential
influence of electromagnetic environment
2.6 Influence of the
instable regions of operation
3.1.5 Method of Critical
integration of Fermi functions
D Integration of Fermi
intermediate virtual state
2.9 Co Tunneling
intrinsic carrier concentration
Material Properties
inversive congruential method
4.2.3 Random Number Generator
IV-characteristic
of double tunnel junction
2.7 The Double Tunnel
of tunnel junction
2.4.2 Tunnel Rate
Jordan canonical form
3.3.1 Krylov Subspace Approximate
Krylov subspace approximate
3.3.1 Krylov Subspace Approximate
lattice constant
Material Properties
lattice structure
4.2.3 Random Number Generator
linear congruential method
4.2.3 Random Number Generator
shuffled
4.2.3 Random Number Generator
local rule
2.6 Influence of the
low impedance environment
2.6 Influence of the
macro-node
3.1.1 Notation
macroscopic quantum tunneling of charge
2.9 Co Tunneling
manufacturability of single-electron circuits
5.2.5 Manufacturability
many body problem
3.2 Tunneling: a Stochastic
Markov process
3.2 Tunneling: a Stochastic
master equation
3.2 Tunneling: a Stochastic
comparison with Monte Carlo method
3.5 Comparison between Master
simulation method
3.3 Master Equation Method
material properties, table of
Material Properties
matrix
exponential
3.3.1 Krylov Subspace Approximate
memory
Q0-independent
5.2.9 Qo Independent Memory
background charge independent
5.2.9 Qo Independent Memory
complexity
5.2.11 Discussion of Simulation
dynamic
5.2.7 Multi Tunnel Junction
multi-island
5.2.10 Multi Island Memory
multi-tunnel-junction
5.2.7 Multi Tunnel Junction
ring
5.2.8 Ring Memory
static
5.2.6 Single Electron Flip
metal
2.1.1 Electron Electron Interaction
metal tunnel junction
D Integration of Fermi
method of critical voltage
3.1.5 Method of Critical
minimum tunnel resistance
2.5 Minimum Tunnel Resistance
Monte Carlo
simulation method
3.4 Monte Carlo Method
combination with direct calculation
3.6 Combination of Monte
comparison with master equation method
3.5 Comparison between Master
Monte Carlo method
resolution limit
Step Size
multi-island memory
5.2.10 Multi Island Memory
multi-tunnel-junction memory
5.2.7 Multi Tunnel Junction
node
3.1.1 Notation
charge-
3.1.1 Notation
floating-
3.1.1 Notation
macro-
3.1.1 Notation
potential-
3.1.1 Notation
nonlinear congruential method
4.2.3 Random Number Generator
notation
3.1.1 Notation
occupation probability
2.4.2 Tunnel Rate
occupation probability of state
3.2 Tunneling: a Stochastic
opaqueness
2.4.1 Transmission Probability
open system
2.2 Work Done by
operation temperature
5.2.1 Operation Temperature
orthodox theory
2.4 Tunneling | 2.4.2 Tunnel Rate
orthonormal basis in Krylov subspace
3.3.1 Krylov Subspace Approximate
outlook
6 Outlook
3.3 Master Equation Method | G Rational Padé Approximations
particle
1 Introduction: What is
planar quantum dots
5.1.3 Planar Quantum Dots
point process
3.2 Tunneling: a Stochastic
Poisson distribution
3.2 Tunneling: a Stochastic
Poisson process
3.2 Tunneling: a Stochastic
polarization charge
2.2 Work Done by | 2.7 The Double Tunnel
poly-silicon structures
5.1.4 Poly Silicon Structures
potential barrier
2.4.2 Tunnel Rate
rectangular
C.3 The Rectangular Potential
potential well
finite
C.2 The Finite Potential
infinite
2.1.2 Quantum Confinement Energies | C.1 The Infinite Potential
potential-node
3.1.1 Notation
power consumption
5.2.4 Power Consumption
pseudo random numbers
4.2.3 Random Number Generator | 4.2.3 Random Number Generator
Q0-independent memory
5.2.9 Qo Independent Memory
quantum confinement energy
2.1.2 Quantum Confinement Energies
quantum dot
C.1 The Infinite Potential
quantum fluctuations
1 Introduction: What is
random background charge
5.2.3 Random Background Charge
random number generator
4.2.3 Random Number Generator
inversive congruential method
4.2.3 Random Number Generator
linear congruential
4.2.3 Random Number Generator
nonlinear congruential method
4.2.3 Random Number Generator
shift-register method
4.2.3 Random Number Generator
shuffled linear congruential method
4.2.3 Random Number Generator
step size
Step Size
rare state space
3.6 Combination of Monte
rectangular potential barrier
C.3 The Rectangular Potential
relative permittivity
Material Properties
resolution limit of Monte Carlo method
Step Size
ring memory
5.2.8 Ring Memory
Schrödinger equation
C Solutions to Schrödinger's
self-capacitance
2.1.1 Electron Electron Interaction
semiconductor
2.1.1 Electron Electron Interaction
shift-register method
4.2.3 Random Number Generator
short circuit
3.1.2 Electrostatic Energy
shuffled linear congruential method
4.2.3 Random Number Generator
SIMON
4 Implementation Issues
acceleration
4.2.4 Accelerating the Simulator
block diagram
4.2 Code structure
flow chart
4.2.2 Flow Chart
screen shot
4.2.1 Graphical User Interface | 4.2.1 Graphical User Interface
simulation of single-electron devices
3 Simulation of Single
single electronics
1 Introduction: What is
single-electron memories
5.2 Single Electron Memories
single-electron transistor
2.8 Single Electron Transistor
single-electronics
applications of
5 Applications
space correlated tunneling
2.8 Single Electron Transistor
space-correlated tunneling
2.7 The Double Tunnel
stable regions of operation
3.1.5 Method of Critical
staircase characteristic
2.7 The Double Tunnel
state transition diagram
3.2 Tunneling: a Stochastic
static memory
5.2.6 Single Electron Flip
step edge cut-off fabrication method
5.1.2 Step Edge Cut
step size
Step Size
stray capacitance
2.7 The Double Tunnel
strength parameter
2.4.1 Transmission Probability
summary of the equations describing single-electron tunnel devices
4.1 Summary of the
superconductors
1 Introduction: What is
symbols, list of
List of Symbols
terms, definition of
Definition of Terms and
Thévenin equivalent circuit
3.1.5 Method of Critical
theory of single electron tunneling
2 Theory of Single
thermal energy
1 Introduction: What is
thermal fluctuations
1 Introduction: What is
total capacitance
2.1.1 Electron Electron Interaction
transient simulation
4.2.2 Flow Chart
transistor, singel-electron
2.8 Single Electron Transistor
transmission probability
2.4.1 Transmission Probability
transmission rate
E Fermi's Golden Rule
tunnel
resistance
2.4.2 Tunnel Rate
time
2.4 Tunneling
tunnel junction
1 Introduction: What is
IV-characteristic
2.4.2 Tunnel Rate
current biased
1 Introduction: What is
double
2.7 The Double Tunnel
metal
2.4.2 Tunnel Rate | D Integration of Fermi
tunnel rate
E Fermi's Golden Rule
Nth-order co-
2.9 Co Tunneling
divergence of
2.9 Co Tunneling
second order co-
2.9 Co Tunneling
tunnel resistance
1 Introduction: What is
condition for
2.5 Minimum Tunnel Resistance
minimum
2.5 Minimum Tunnel Resistance
tunneling
2.4 Tunneling
a stochastic process
3.2 Tunneling: a Stochastic
macroscopic
2.9 Co Tunneling
space correlated
2.8 Single Electron Transistor
space-correlated
2.7 The Double Tunnel
theory of single electron
2 Theory of Single
uniformly distributed PRN
4.2.3 Random Number Generator
user interface
4.2 Code structure
voltage-controlled voltage source
Voltage-Controlled Voltage Sources
work done by voltage source
3.1.3 Work of Voltage
work done by voltage sources
2.2 Work Done by
work function
Material Properties
write error

Christoph Wasshuber