List of Symbols

MOSFETmetal-oxide-semiconductor field-effect transistor
CMOS complementary MOSFET
SOI silicon on insulator
GMR giant magnetoresistance
TMR tunnel magnetoresistance
MRAM magnetoresistive random-access memory
SpinFET spin field-effect transistor
FinFET fin-shaped field-effect transistor
MTJ magnetic tunnel junction
STT spin transfer torque
UTB ultra-thin body
SOC spin-orbit coupling
SOF effective spin-orbit field
EY Elliot-Yafet mechanism
DP D’yakonov-Perel’ mechanism
DOS density of states
FMS ferromagnetic semiconductor
TCAD technology computer aided design
q fundamental charge
me electron rest mass
ϵ0 vacuum permittivity
ϵSi silicon permittivity
a silicon lattice constant
KB Boltzmann constant
reduced Planck constant
EF Fermi level
k wave vector
p momentum vector
k0 position of the valley minimum relative to the X-point in unstrained silicon
k position of the valley minimum relative to the Γ-point in unstrained silicon
mt transversal effective mass of silicon
ml longitudinal effective mass of silicon
Ũ(z) confinement potential
c speed of light
E electron energy
˜m electron effective mass
σx,y,zPauli matrices
T temperature
t film thickness
SO spin-orbit splitting
εxy shear strain component
NS electron concentration
L autocorrelation length
mean square value of the surface roughness fluctuations
D shear deformation potential
Ξ acoustic deformation potential
DOP optical deformation potential
νTA transversal acoustic phonon velocity
νLA longitudinal acoustic phonon velocity
ωop frequency of the optical phonons
τs spin lifetime
τm momentum relaxation time
Θ polar angle defining the spin injection orientation in (001) plane
Φ azimuthal angle defining the spin injection orientation in (001) plane
ΔΓ splitting at Γ-point in unstrained silicon
Jn electron current density vector
Jp hole current density vector
μn electron mobility
μp hole mobility
Dn electron diffusion coefficient
electric field vector
V electric potential
NDdonor doping concentration per unit volume
NC effective density of states in the conduction band
nabla operator
˜t time
VT thermal potential
n up-spin electron concentration per unit volume
n down-spin electron concentration per unit volume
s spin concentration per unit volume
Mup-spin chemical potential
Mdown-spin chemical potential
G spin chemical potential drop
P bulk spin polarization (ferromagnet)
Js spin current density vector
Li intrinsic spin diffusion length
λD Debye charge screening length
Lu up-stream spin diffusion length
Ld down-stream spin diffusion length
α polarization for spin current density
β polarization for spin density
α0 polarization for spin current density at the boundary
β0 polarization for spin density at the boundary
B(x)Bernoulli function