Magnetic Filter-Enhanced Plasma Etching: Scaling Laws and Yield Optimisation for Semiconductor Structures

This paper investigates the use of transverse magnetic filters to enhance plasma etching performance in semiconductor manufacturing, motivated by experimental advances in caesium-free negative-ion sources. By selectively cooling low-energy electrons in reactive plasmas (e.g., H2/Ar mixtures) to approximately 0.3 eV while leaving noble-gas populations largely unaffected, the magnetic filter enables improved species selectivity, higher etch yield, and enhanced process stability. A physics-based scaling relationship is derived linking etch yield enhancement to electron-density modulation and electron-temperature separation, with model parameters calibrated using Langmuir probe measurements. The resulting framework predicts improved etch-yields of approximately 20% at 95% confidence for industrial wafer-processing tools, accompanied by reductions in defect density and RF power consumption. In addition, a resolution limit for virtual plasma masking is introduced, demonstrating that reconfigurable sub-micron patterning can be achieved without physical masks through controlled magnetic-field topology. Numerical simulations validate the experimental trends, showing improved etch anisotropy, throughput, and uniformity under magnetically filtered conditions. Open-source simulation tools are provided for yield estimation and uncertainty propagation to support reproducibility. The results highlight the potential of magnetic-filter-assisted plasmas as scalable, energy-efficient process enablers for advanced semiconductor manufacturing and multi-physics plasma systems.