Surface Technology - riassunti brevi

Surface technology

Mean free path

Mean free path λ = ^kT/_Qp air at room T: λ = 6.7×10^-3 m

Gas flux

Gas flux: Φ = ^p/_RT, μ = 1/2₀

Flow through the opening

Flow (through the opening) = _Q1Q = √^RT/_mM, v = ¹/_√2πNP_net (through the opening) = Φ₁ - Φ₂! = (1-m12)!₂ Q^(P₁-P₂)/_√2RT

Net rate

Net rate = ⁿ = ^{A(P₁ - P₂)}/_R area ^Δ

Pump speed

Pump speed: S_p = Q/P₀ => inlet pressure

Over the duct length

Over the duct length: P₀-P₀ = QC inlet to the duct

Ultimate pressure

Ultimate pressure: P₀ = Q_L/S_O

Leakage

P: leakage = S₀ = intrinsic speed leakage

Change in pressure

Change in pressure: PS = √^d/_Qe + Q_e

Rate of surface vaporization

Rate of surface vaporization: Φ_e = α(^Pv-P)√^2πMRT0 d: vapor PP: pressure above

Maximum Φ_e = ^J/πv

Expanded mass per area

Expanded mass per area (generic): dM_S = M E(n+l) cosφ _cosθ dA_S 2πr²nl_d - melt depth below crucible

w - melt surface width

Film thickness

Film thickness: d = ^d/^p _dAS

Thickness distribution

Thickness distribution: d = d₀ ¹/_{1+(e/^θ)² q}

q = 3/2 point source

q = 2 surface source

Atomic fraction of impurity

Atomic fraction of impurity (residual gases): x_i = A. ^P/_√Mν

A: coefficient p_diff/_ptr P: partial pressure of the impurity

Effective current density

Effective current density: J = qniυ_i

Sputtering

Sputtering: ( ^X_A/_{XO substrate} ) ^X_A

Effective current density: J = qniυ_i

Equality of the moments (shear measure)

Equality of the moments (shear measure): d⁴d^SF^T = M_⁴ + M_^S

Surface Technology Mean free path \(\lambda = \frac{kT}{Qp}\) air at room T: \(\lambda = 6.7 \cdot 10^{-8}\,m\)

Gas flux

Gas flux: \(\Phi = \frac{mol}{m^2T} = \frac{\bar{Q}}{V}\)

\(\bar{Q} = \frac{RT}{\sqrt{2\pi\,MMN}}\) M = mass

Flow through the opening

\(\dot{Q}_{net} \space\) (through the opening) \( = \Phi_1 - \Phi_2\)

Net rate

Net rate: \(\dot{n} = \frac{A(P_2 - P_2)}{4RT}\)

Pump speed

Pump speed: \(Sp = Q/P_{inlet\space pressure}\)

Over the duct length

Over the duct length: \(\frac{P_1 - P_2}{P_1} = \frac{QC}{\dot{Q}/C}\: \text{inlet\space to\space the\space duct}\)

Ultimate pressure

Ultimate pressure: \(Po = Q/So\)

Leakage

P = leakage So = intrinsic speed leakage

Change in pressure

Change in pressure: \(PS = - \frac{\sqrt{d}}{dt} + Qe\)

Rate of surface vaporization

Rate of surface vaporization: \(\varphi_e = \frac{\dot{A}(P_V - P)}{\sqrt{2\pi NMG}}\)0 Maximum \(\Phi_e = \frac{\bar{Q}P_V}{4RT}\) \((\alpha = 1,\space P=0)\)

Evaporated mass per area from a point source

\(\frac{dM_S}{dAS} = \frac{M_E\cos\theta}{4\pi R^2}\)

Evaporated mass per area from a surface source

\(\frac{dM_S}{dAS} = \frac{M_E\cos\theta}{\pi R^2}\)

Film thickness

Film thickness: \(d = \frac{\dot{d}}{\rho \frac{dAS}{dt}}\)

Atomic fraction of impurity

Atomic fraction of impurity (residual gases): \(X_i = A_{\frac{P}{\sqrt{mgT}}}\cdot\frac{MMv}{\sqrt{\rho air}}\)

A = coefficient P = partial pressure of the impurity

Effective current density

Effective current density: \(J=q\cdot ini/vi\)

Sputtering

Sputtering: \(\left(\frac{XA}{XB}\right)_{\text{substrate}} \left(\frac{XA}{X^0B}\right)_{\text{bulk}} \left(\frac{SA}{SA}\right)\)

S = sputter yield \(\propto E^{1/2}\space \text{energy of incident particles}\)

Equality of the moments (shear measures)

Equality of the moments (shear measures): \(\frac{d^2 + ds^2F_f}{2} = M_f + M_s\)

Thickness distribution

Thickness distribution: \(d = d_0 = \left[1 + (\frac{E}{B})^2\right]^{\frac{q}{2}}\)

q = 3/2 point source

q = 2 surface source

MMi = \(\mu = \text{molar mass of impurity}\)

\(\rho = \text{film density}\)

\(\frac{dr}{dt} \text{ deposition rate} = \frac{di}{dG}\) (thickness/time)

V_b = \(\frac{A}{V_T}^9\) t = target g = ground v = voltage A = area

n\cdot c \overline{w} = d melt depth below crucible w = melt surface width

M_f = \(\frac{Ed^3}{12R(1 - u^2)}\) W

M_s = \(\frac{Esd^3}{12R(1 - u_s)}\) R = radius of curvature

Stoney: σ_f = Esd_fGR(1-ν_s)d_f

Diffusion

Diffusion: D = D₀ exp(-Q/RT) a - b ≠ interatomic distance ≈ grain size

Fraction of time spent diffusing in GBS for A regime: f = 3δ₀⁵ S

Diffusion along dislocation: D_e = D_l