The Impact of Nozzle Opening Thickness on Flow Characteristics and Primary Electron Beam Scattering in an Environmental Scanning Electron Microscope

Abstract

This paper describes the methodology of combining experimental measurements with mathematical–physics analyses in the investigation of flow in the aperture and nozzle. The aperture and nozzle separate the differentially pumped chamber from the specimen chamber in an environmental scanning electron microscope (ESEM). Experimental measurements are provided by temperature and pressure sensors that meet the demanding conditions of cryogenic temperature zones and low pressures. This aperture maintains the required pressure difference between the chambers. Since it separates the large pressure gradient, critical flow occurs on it and supersonic gas flow with the characteristic properties of critical flow in the state variables occurs behind it. As a primary electron beam passes through the differential pumped chamber and the given aperture, the aperture is equipped with a nozzle. The shape of the nozzle strongly influences the character of the supersonic flow. The course of state variables is also strongly influenced by this shape; thus, it affects the number of collisions the primary beam’s electrons have with gas molecules, and so the resulting image. This paper describes experimental measurements made using sensors under laboratory conditions in a specially created experimental chamber. Then, validation using mathematical–physical analysis in the Ansys Fluent system is described.

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

“…The nozzle angle of 18° was established as the most advantageous variant for the passage of the primary electron beam using the principles of one-dimensional isentropic flow theory [ 1 ]. This configuration ensures controlled gas expansion behind the nozzle [ 26 , 27 , 28 , 29 , 30 ].…”

“…The opening shapes of the nozzle lower part were compared with the variant that came out the most advantageous for electron scattering in the article [ 1 ], therefore, having a nozzle with an opening of 18° ( Figure 2 ).…”

“…As mentioned above, this variant came out of the previous analyses [ 1 ] as the most advantageous for the passage of the primary electron beam when the nozzle was opened at 18°. This variant is compared in this article with variants different from the Laval nozzle and has an open lower part of the nozzle ( Figure 2 ).…”

“…This paper deals with the issue of pumped vacuum chambers of environmental scanning electron microscopy (ESEM), and its content builds on and expands the area of research from the published paper [ 1 ]. In general, electron microscopy allows for a more detailed examination of samples than conventional optical microscopy [ 2 , 3 ].…”

“…The aperture is, therefore, equipped with a nozzle to model the supersonic gas flow, which adjusts the flow of the given supersonic gas flow. The influence of nozzle openings on the distribution of state variables in a given flow and their impact on the primary electron beam scattering was analyzed in the previous article [ 1 ]. In this paper, the character of the bottom part opening of the nozzle and its effect on electron beam scattering will be analyzed.…”