Nanoparticle size distribution measurement scheme using mass-to-charge ratio measurements with Vacuum Ultraviolet irradiation in medium vacuum

With increasing demand for Virtual Metrology (VM) and Advanced Process Control (APC) in semiconductor manufacturing, the importance of in-situ quantitative monitoring of process results has grown beyond in-situ qualitative monitoring. Particle Size Distribution (PSD) analysis of nanoparticles ranging from several to hundreds of nanometers (nm) in diameter offers a possible method for the quantitative monitoring of plasma processes. However, conventional Particle Beam Mass Spectrometer (PBMS) systems designed for PSD analysis require pressures greater than hundreds of millitorrs for operation, which limits their applicability to modern semiconductor processes that require a medium vacuum. We propose a new PSD measurement scheme to perform PSD analysis for medium-vacuum processes. The hardware configuration includes a Vacuum Ultraviolet (VUV) irradiation chamber and a mass-to-charge ratio ($m/q$) measurement device consisting of a stacked-quadrupole-based charged particle funnel and Quadrupole Mass Analyzer (QMA). With this configuration, a PSD measurement algorithm is developed using a direct photoionization model-based Non-negative Least Squares (NNLSQ) method with gradient descent optimization. The PSD is estimated from multiple $m/q$ distributions measured under various VUV irradiation levels. The simulation results demonstrate that the proposed $m/q$ measurement scheme achieves an $m/q$ selection efficiency of 21% and a resolution of ± 3% for singly charged spherical Sodium Chloride (NaCl) nanoparticles at the sizes of 5–50 nm, which follow Maxwellian velocity distributions at 20 °C in the free molecular regime. Furthermore, under ideal photoionization-dominant conditions for NaCl nanoparticles with randomly assigned initial charges, peak-normalized target monodispersed PSDs with distribution change slopes ranging from $-$0.4 to 0.5 ${\text{nm}}^{-1}$ can be estimated in the size range of 5–50 nm, with mode errors within 5.6% and Geometric Standard Deviation (GSD) errors within 2.0%.