Peculiarities of deformation of round thin-film membranes and experimental determination of their effective characteristics

Abstract

The features of thin-film membranes, which are formed above round holes in silicon substrates using the Bosch-process are considered. The membrane has a complex shape due to the presence of the stress state of the initial films. The analysis of the dependence of the membrane deflection w on the supplied overpressure P is used to calculate the mechanical characteristics of the membranes. In this case, it is necessary to determine directly on the membrane its diameter, the thickness of the constituent layers, the change in the topography of the membrane surface over its entire area as the overpressure increases. Determination of the membrane diameter and the thicknesses of the constituent layers is shown by the example of p-Si*/SiNx/SiO2 and SiNx/SiO2/SiNx/SiO2 membranes. We used spectral ellipsometry, energy-dispersive X-ray spectroscopy, optical profilometry, optical microscopy. The influence of the peculiarities of the fixing conditions on the stress-strain state of membranes is shown, and the assessment is carried out by means of numerical modeling. A technique has been developed for measuring and calculating the mechanical characteristics of membranes that have an initial deflection. The calculation result is shown on the example of a membrane with an initial deflection of 2 μm --- SiNx/SiO2/SiNx/SiO2 and a membrane with an initial deflection of 30 μm --- Al/SiO2/Al. Keywords: stress, bulging method, films, thin-layer coating, film thickness, membrane, pressure blister test, residual stress, microelectromechanical systems, MEMS, silicon substrate, large deformations, strain, deflections, circular membrane, bulge testing.

Technique for investigation of the shape changes of wafers and thin-film membranes by using geomorphometric approaches

“…To demonstrate the analysis of MEMS structures, thinfilm membranes formed by the Bosch process [32][33][34] were studied (Figs. 3−6).…”

“…The method consists in fixing the edges of the membrane along the perimeter, applying (one-sided) overpressure to it from one side, analyzing the dependence of the deflection of the membrane on the value of the applied overpressure, calculating the elastic modulus or other values [35][36][37][38][39]. Since the membranes formed by the Bosch process differ in the presence of an initial deflection and a complex shape even before the overpressure is applied, the study of their stress-strain state requires detailed consideration [32,33].…”

“…However, when working with the DEM of thin-film membranes, including membranes with an initial deflection, and membranes in the process of bulge testing, there is an important feature: the fact that there are areas without data in the analyzed DEM (Figs. 4−6) caused by too large an angle of inclination of these areas [32,34].…”

Investigation of the real shape changes of round thin-film membranes during the bulge testing

“…Currently the special attention is given to the issues of analysis of a stress-strain state, appearing in microelectromechanical systems (MEMS). Circular membranes fixed on the contour in terms of the membrane formed from thin films created on a silicon substrate after deep through etching of silicon from the back of the wafer (Bosch process) were studied [1][2][3][4]. Such membranes are used in Xray optics [2], as sensitive elements of sensors of various physical quantities [5,6] and others.…”

“…To determine the mechanical characteristics of membranes (their constituent films), the bulge testing is widely used, and to analyze the experimental data obtainedrelations of the theory of thin wafers and shells, with various modifications [1,2,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The method consists in applying unilateral overpressure to the membrane from its reverse side, analyzing the dependence of the deflection of the membrane on the value of the applied pressure, calculating mechanical characteristics from this dependence (Young's modulus or etc.…”