List of Symbols

Roman Symbols

An Area of a given diffusion path n
B Bulk modulus
C Capacitance
Ca Atomic concentration
Ciklm Components of the elastic stiffness tensor
Cl Lattice site concentration
cp Specific heat capacity
Cv Vacancy concentration
Cv,eq Equilibrium vacancy concentration
Cvt Trapped vacancy concentration
d Diameter
Da Atomic diffusion coefficient
Dv Vacancy diffusion coefficient
Dv,0 Pre-exponential factor for vacancy diffusion
E Young's modulus
E Electric field
e Electron charge
Ea Activation energy for diffusion
F Force
f Relaxation factor
G Vacancy source/sink term
j Electric current density
Ja Atomic flux
Jv Vacancy flux
kb Boltzmann constant
kt Thermal conductivity
kt,0 Thermal conductivity at the reference temperature T0
l Length
n Current density exponent
na Number of atoms
nv Number of vacancies
p Hydrostatic pressure
Q* Transport heat
R Electric resistance
Rp Radius of a circular patch
Siklm Components of the elastic compliance tensor
T Temperature
t Thickness
T0 Reference temperature
u Displacement
ui Components of the displacement vector
V Volume
v Velocity
Ve Electric potential
w Width
Z* Effective valence

Greek Symbols

α Linear temperature coefficient
αth Coefficient of thermal expansion
μ Electrochemical potential
β Quadratic temperature coefficient
Δ Change of any changeable quantity
δ Grain boundary/interface thickness
δik Kronecker delta function
εdi Diffuse interface thickness parameter
εik Components of the total strain tensor
Γ Interface
γm Interfacial free energy of the metal
γik Components of the engineering shear strain tensor
γs Surface energy
κ Relative permittivity or dielectric constant of a material
μ Chemical potential
Vector differential operator
ν Poisson ratio
Ω Domain
Ωa Atomic volume
ωr Release rate
ωt Trapping rate
Ωv Vacancy volume
φ Order parameter
ρ Electrical resistivity
ρm Mass density
σ Trace of the hydrostatic mechanical stress tensor
σe Electrical conductivity
σe,0 Electrical conductivity at the reference temperature
σik Components of the elastic stress tensor
σthr Threshold stress for void nucleation
τik Components of the shear stress tensor
τv Vacancy relaxation time
θc Equilibrium contact angle




M. Rovitto: Electromigration Reliability Issue in Interconnects for Three-Dimensional Integration Technologies