Arte SheetsLearn. Try. Understand.

Semiconductor PVD & Thin-Film Vacuum Coating, Magnetron Sputtering Rate & Cosine Throw

Magnetron Sputtering PVD Deposition Rate & Throw Formula

Calculate Total Sputtered Atom Emission Rate (10¹⁹ atoms/s), Knudsen Cosine Wafer-Center Flux (10¹⁶ atoms/cm²·s), Film Deposition Rate (nm/min), and 500 nm Seed Coat Time (min).

Raise a magnetron wafer chuck from 8.5 to 14.0 cm to improve uniformity and inverse-square cosine throw slashes PVD deposition rate by 63%!

DC and RF **Planar Magnetron Sputtering (`PVD`)** traps electrons in a race-track `E x B` plasma to bombard a high-purity metal target with `Ar⁺` ions at Target Current `I` (`A`, Ion Arrival Rate `I / e` where `e = 1.60217663 * 10^{-19}` C). Each `400–600` eV `Ar⁺` impact ejects **Sputter Yield `Y` target atoms/ion** (`Y ≈ 1.8–2.3` for Cu/Ag, `~0.5–0.8` for Ti/W!), emitting **`dot_N = (I / e) * Y`** (`atoms/s`) in a **Knudsen Cosine Angular Distribution** (`J ~ cos(theta)`). In ballistic high vacuum (`P ~ 2–5` mTorr, negligible gas scattering), **Wafer-Centerline Atomic Flux** at Throw Distance `h` (`cm`) equals **`J_s = dot_N / (PI() * h^2)`** (`atoms/(cm²·s)`), growing a solid film of Molar Mass `M` (`g/mol`) and Bulk Density `rho` (`g/cm³`) at **`R_{dep} = J_s * (M / (rho * N_A)) * 10^7 * 60`** (`nm/min`, `N_A = 6.02214076 * 10^{23}` mol⁻¹)!

Verify on a Copper Seed-Layer DC Magnetron Cathode—Target_Discharge_Current `I` = 0.85 A (B2), `Ar⁺->Cu` Sputter_Yield `Y` = 1.85 atoms/ion (B3 -> Total Ejected Flux = `0.981 * 10^{19}` atoms/s in E2), Target-to-Substrate_Throw `h` = 8.50 cm (B4), Copper_Atomic_Weight `M` = 63.546 g/mol (B5), and Copper_Density `rho` = 8.96 g/cm³ (B6): Wafer-Center Flux hits `4.32 * 10^{16}` atoms/(cm²·s) (E3), Film Growth Rate reaches `305.5` nm/min (E4), depositing a `500` nm electroplating seed layer in `1.64` min (E5)!

DC Magnetron Copper PVD KPI (I=0.85 A, Y=1.85, Cu M=63.546, h=8.5 vs 14.0 cm)FormulaVerified Output
Ejected Atom Rate (x10¹⁹ atoms/s)((Current_A / 1.60217663e-19) * Yield) / 1e190.981 x 10¹⁹ atoms/s
Wafer-Center Flux (x10¹⁶ /cm²·s)(Ejected_Atoms_s / (PI() * h_cm^2)) / 1e164.32 (1.59 @ long-throw h=14.0 cm!)
Film Deposition Rate (nm/min)Js * (M / (rho * 6.02214076e23)) * 6e8305.5 nm/min (112.6 nm/min @ 14.0 cm)
Time for 500 nm Seed Layer (min)500 / Deposition_Rate_nm_min1.64 min (4.44 min cycle @ 14.0 cm)

Sputter Yield, Knudsen Cosine Throw Flux & Thin-Film Growth Rate Formula

Validate `Target_Current I > 0.02` A, `Sputter_Yield Y` in `(0.05, 8.0]`, `Throw_Distance h` in `[2.0, 50.0]` cm, `Atomic_Weight M` in `[6, 250]` g/mol, and `Film_Density rho` in `[1.5, 23.0]` g/cm³!

=LET(ic_a, B2, sy_a, B3, ht_c, B4, mw_g, B5, rf_g, B6, nd_s, (ic_a / 0.000000000000000000160217663) * sy_a, js_c, nd_s / (PI() * (ht_c ^ 2)), rd_n, js_c * (mw_g / (rf_g * 602214076000000000000000)) * 600000000, IF(OR(ic_a <= 0.02, sy_a <= 0.05, sy_a > 8, ht_c < 2, ht_c > 50, mw_g < 6, mw_g > 250, rf_g < 1.5, rf_g > 23), "Invalid PVD Input", ROUND(500 / rd_n, 2)))

Long-Throw 14.0 cm High-Aspect Trench Collimation Rate Penalty Check (Set Throw Distance B4 = 14.0 cm)

Retract the substrate pedestal to Long-Throw `h` B4 = 14.0 cm to collimate bottom coverage inside TSV vias: `(8.5 / 14.0)^2 = 0.369` cuts Wafer Flux E3 to `1.59 * 10^{16}` atoms/(cm²·s) and Deposition Rate E4 to `112.6` nm/min—stretching `500` nm seed coat time E5 to `4.44` min!

=IF(ISTEXT(E5), E5, LET(nd_s, (B2 / 0.000000000000000000160217663) * B3, js_c, nd_s / (PI() * (B4 ^ 2)), ROUND(js_c * (B5 / (B6 * 602214076000000000000000)) * 600000000, 1)))

Try the example

Use the original values or change them to test your understanding.

Further reading