Semiconductor Process & Litho

Deal-Grove Thermal Oxidation

x²+Ax = B(t+τ). Enter the rate constants for your temperature/ambient.

Parabolic B (µm²/hr)

Linear B/A (µm/hr)

Time t (hr)

Initial oxide (µm)

Photolithography Resolution

Rayleigh: CD = k₁·λ/NA, DOF = k₂·λ/NA². Pick a source or set λ.

Exposure source

λ (nm)

k₁

k₂ (DOF factor)

Etch — Rate, Time & Selectivity

depth = rate·time; selectivity S = R_film/R_mask; anisotropy A = 1−R_lat/R_vert.

Etch rate (nm/min)

Target depth (nm)

Selectivity to mask

Lateral:vertical ratio

KOH / TMAH V-Groove

(100) Si self-terminates on (111) planes at 54.74°. Self-limiting depth = W/√2.

Mask opening W (µm)

Etch depth so far (µm)

Thin-Film Deposition (CVD / ALD)

CVD: time = thickness/rate. ALD: cycles = thickness/GPC.

CVD rate (nm/min)

Target thickness (nm)

ALD GPC (nm/cycle)

Step coverage (%)

Sheet Resistance & Resistivity

R_s = ρ/t; R = R_s·(L/W). 4-point probe: R_s = 4.532·V/I (thin film).

Resistivity ρ (Ω·cm)

Film thickness t (µm)

Length L (squares)

Width W (squares)

4-pt probe V (mV)

4-pt probe I (mA)

Formula reference

Deal-Grove: x_ox²+A·x_ox=B(t+τ), A=B/(B/A), τ=(x_i²+A·x_i)/B. Solve x_ox=(A/2)[√(1+(t+τ)/(A²/4B))−1]. Silicon consumed ≈ 0.46·x_ox. Linear limit x≈(B/A)t, parabolic limit x≈√(Bt).

Lithography (Rayleigh): CD=k₁λ/NA; DOF=k₂λ/NA². Immersion raises NA above 1.

Etch: depth=rate·time; mask loss=depth/S; anisotropy A=1−R_lat/R_vert; undercut=depth·(R_lat/R_vert).

KOH (100) Si: sidewall 54.74°; self-limiting depth d_max=W/√2≈0.707·W; opening narrows as depth grows.

Deposition: CVD time=t/rate; ALD cycles=t/GPC; bottom thickness=top·step-coverage.

Sheet R: R_s=ρ/t (Ω/sq); R=R_s·L/W; four-point probe R_s=(π/ln2)(V/I)=4.532·V/I.