Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2017 / Paper 1 / Section A(ii) / 4

Assume that each target's incorporated flux is proportional to its applied power over this operating range, and that the same composition convention is used throughout. The calibration gives $F_A/F_B=0.35/0.65$ at equal powers. Holding the A target unchanged while making the two incorporated fluxes equal therefore requiresThe B power decreases because B originally supplies more material. This linear magnetron sputtering approximation neglects power-dependent yield, target condition, resputtering and changes in sticking probability. A second composition measurement is the experimental check.

In the intended additive-deposition model, A originally contributes $0.35\times 2.2=0.77\mathrm{nm}{\mathrm{s}}^{-1}$. At equal incorporated contributions, B also supplies $0.77\mathrm{nm}{\mathrm{s}}^{-1}$, giving $1.54\mathrm{nm}{\mathrm{s}}^{-1}$. Equivalently, the new total incorporated flux is $0.35+0.35=0.70$ times the calibrated total.

There is a composition-convention qualification. If the percentages represent mass flux and the mass density stays fixed, the preceding thickness calculation follows directly. If they instead represent atomic fractions, a constant atomic number density would justify the same result, whereas constant mass density alone does not. With atomic masses $M_A,M_B$ and constant mass density, the ratio would beThe PDF does not specify atomic versus mass percentages or the two elements. Thus 1.54 nm/s is the intended common flux-to-thickness approximation, and the formula above states the additional dependence if atomic fraction and constant mass density are meant literally.

Approximate each source as localized, keep the angular factors unchanged and use inverse-square flux dilution. The increased distance givesThis carries the composition/thickness convention of the previous answer. A greater source distance reduces fractional distance and angle variation across a given substrate, improving composition uniformity at the cost of rate. A real magnetron sputtering target is extended, with an angular emission distribution, and gas scattering can change the distance law; this is an estimate rather than a calibrated prediction.