The Effects of Piezoelectricity Matrix Constants on the Charge of a Thin Membrane

Abstract

This article is devoted to the comparison of the influence of the piezoelectric matrix properties on the magnitude of the resulting charge when a thin piezoelectric membrane of circular cross section, made from aluminium gallium nitride (Al-GaN), is loaded. The size of change of the electric charge was determined by the numerical analysis and the by the change of the properties of the piezoelectric matrix. The matrix constants were obtained from various sources introduced in world databases.KEYWORDS: piezoelectric, gallium nitride, constitutive equations, average, variance, deviation IntroductionThin Al-GaN membranes have different configurations for their application. In the case of a membrane of a circular cross section (as shown in Fig 1, in the analysed device), it is most common for the measurement of pressure. To apply pressure onto the membrane, it must be fixed around its circumference. The internal structure of piezoelectric materials is highly dependent on their manufacturing process, which then is reflected on their properties. Even a small change in the properties of the piezoelectric material can lead to more pronounced changes in the electrical charge obtained in the so called direct piezoelectric effect, or the change in the properties can lead to significantly different deformations in an inverse piezoelectric effect. Using a numerical methods, we can predict the behaviour of the pressure sensors. It is possible to simulate the different properties of the Al-GaN material and to obtain the assumed values of the electrical charge, respectively the deformation of the material. The first part of the article is devoted to the comparison of the results of 10 sets with different material constants for the aluminium gallium nitride material. Applied material constants were taken from research reports and contributions introduced in world databases [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In the second part of the article, we compare the obtained results with the results measured during the experiment [17]. The investigated modelThe numerical model is based on a thin membrane used in experimental measurements. The configuration and geometrical properties of the membrane are shown in Fig. 1. It is made of a piezoelectric Al-GaN layer over GaN. The ratio of each corresponding layer is 99.9524% GaN overlaid with 0.0476 % Al-GaN. The membrane is circular with a diameter of 750 µm. The membrane is placed over a ceramic substrate measuring 350 x 350 µm. The thickness of each layer is 4.22 µm and 0.02 µm for GaN and Al-GaN respectively. Once a charge is created, a thin 2D layer of electron gas is produced between the layers and it acts as a transmitter for the Unauthenticated Download Date | 5/12/18 6:08 AM

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