Semiconductor Exam Formulas

J_N = dN/Adt = P/sqrt(2*pi*m*k_B*T)

J_N = flux of atoms hitting a surface of a vacuum system (atoms/m²s) and the loss rate of atoms from an evaporative source

N = number of impurity atoms

A = surface area of wafer

t = time

P = pressure (Pa)

m = mass of atom/molecule

k_B = boltzman constant (1.38E-38)

T = temperature (K)

R_d = deposition rate (m/s)

m = mass of an atom (kg)

k_B = boltzman constant (1.38E-23 J/K)

ρ = mass density of the deposited film (kg/m³)

T = temperature (K)

P_e = equilibrium pressure (Pa)

A = surface area of evaporation (m²)

r = source to substrate distance (m)

R_d = depostion rate (m/s)

J_ion = ion flux on target cathode ($\text{ions}\cdot\text{m}^{-2}\cdot\text{s}^{-1}$)

S = sputter yield

E_T = transport efficiency

ρ = density of deposited film material (kg/m³)

m = mass of single sputtered atom (kg)

J_ion = ion flux on target cathode (ions m^-2 s^-1)

V = plate voltage (V)

d = dark space thickness (m)

m_ion = ion mass (kg)

Equation through diffusion through the boundary layer

R_d = deposition rate

F = flux

N = atomic density

k_s = surface rate coefficent

h_g = mass transfer coefficent (cm/s)

C_G = concentration of species in the gas

C_s = concentration of species on surface

C_T = total concentration

Y = mole fraction

k_s = reaction rate coefficent

k_o = initial reaction rate coefficent?

Ea = activation energy

kb = boltzman

T = temp

Qp = precursor molar rate flow

Pp = precursor partial pressure

P_T = total pressure

Qc = carrier gas molar flow rate