# Mathematical-Physics Analyses of the Nozzle Shaping at the Aperture Gas Outlet into Free Space under ESEM Pressure Conditions

## TL;DR

This paper studies how nozzle shape affects gas flow and electron beam dispersion in an ESEM under low-pressure conditions.

## Contribution

The novelty lies in combining experimental and mathematical-physics approaches to analyze nozzle shaping effects on electron beam dispersion in ESEM.

## Key findings

- Nozzle shape significantly influences supersonic flow and shock wave formation beyond the aperture.
- Shock waves impact electron scattering, thereby affecting image quality in ESEM.
- Low-pressure conditions are critical in determining the behavior of the electron beam dispersion.

## Abstract

The paper presents a methodology that combines experimental measurements and mathematical-physics analyses to investigate the flow behavior in a nozzle-equipped aperture associated with the solution of its impact on electron beam dispersion in an environmental scanning electron microscope (ESEM). The shape of the nozzle significantly influences the character of the supersonic flow beyond the aperture, especially the shape and type of shock waves, which are highly dense compared to the surrounding gas. These significantly affect the electron scattering, which influences the resulting image. This paper analyzes the effect of aperture and nozzle shaping under specific low-pressure conditions and its impact on the electron dispersion of the primary electron beam.