复合圆柱壳的温控压电电子学效应分析

论文总字数：29878字

摘 要

本文研究了由压电材料和半导体材料制作的复合圆柱壳在恒定温度改变的情况下，发生径向膨胀后的内部相关效应。文中建立了该问题的一维简化模型，列出了对应于该模型的相关方程及边界条件，解方程后得出了压电材料及半导体材料内部电势、径向位移、载流子浓度等的解析表达式，代入边界条件，利用MATLAB求解待定系数。在求出待定系数后，作出在不同温度增量下以及不同初始载流子浓度下的各变量分布曲线进行对比分析。文中进行了两种情况下的圆柱壳压电电子学效应的分析，一种为圆柱壳内径处不受约束，温度改变时自由膨胀，一种是圆柱壳内径处受机械约束，温度改变时内径处无位移，我们分析了这两种情况下的压电电子学效应并进行了对比分析。本文最后得出了温度改变时，圆柱壳内各量对温度比较敏感，温度对于圆柱壳内半导体层内的载流子分布确实有调控作用，这是压电层内热弹性、热释电效应和压电效应耦合作用产生的电场对其作用的结果，同时，半导体内电势、电场、电位移、载流子浓度增量分布受初始载流子浓度影响较大。当圆柱壳内径处固定时，其压电电子学效应较内径自由时弱的结论。

关键词：热效应；压电效应；半导体；复合材料；压电电子学效应

Abstract

In this paper, the internal effects of radial expansion of composite cylindrical shells which made of piezoelectric dielectrics and nonpiezoelectric semiconductors under constant temperature change are studied.A simplified one-dimensional model of the problem is established, and the relevant equations and boundary conditions corresponding to the model are listed. After solving the equation, the analytical expressions of internal potential, radial displacement and carrier concentration in piezoelectric and semiconductor layers are obtained. The boundary conditions are substituted and the undetermined coefficients are solved by using MATLAB. After calculating the undetermined coefficients, the distribution curves of variables under different temperature increments and different initial carrier concentrations were compared and analyzed. We analyze cylindrical shells under two different conditions. One is that the inner diameter of cylindrical shells is not constrained, and the other is that the inner diameter of cylindrical shells is constrained by mechanical forces, so that it won’t displaced when the temperature changes. The piezoelectric effects of these two cases are analyzed and compared. In the end, it is concluded that when the temperature changes, each quantity in the cylindrical shell is sensitive to the temperature. Temperature does regulate the carrier distribution in the semiconductor layer of the cylindrical shell.This is the result of the electric field produced through thermoelastic, pyroelectric and piezoelectric effects. At the same time, the potential, electric field, and the incremental carrier concentration distribution in the semiconductor are greatly affected by the initial carrier concentration. When the inner diameter of the cylindrical shell is fixed, the piezoelectric effect is weaker than that of the free inner diameter.

KEY WORDS: Thermal, piezoelectric, semiconductor, composite, piezotronic

目 录

摘要 ……………………………………………………………………………………………Ⅰ

Abstract …………………………………………………………………………………… Ⅱ

第一章 绪论 1

1.1引言 1

1.2压电半导体材料理论研究历史及现状 2

1.3压电材料与半导体材料简介 3

1.3.1半导体材料 3

1.3.2压电材料及压电效应 4

1.3.3 压电半导体材料 4

1.4压电电子学效应 6

1.5热释电效应 6

1.6 本文主要研究内容 7

第二章 复合圆柱壳的一维简化模型及其分析 8

2.1 引言 8

2.2 压电半导体基本方程 8

2.3 一维简化模型建立及其分析 9

2.4本章小结 14

第三章 数值算例 15

3.1圆柱壳内径处自由 16

3.2圆柱壳内径处固定 23

3.3本章小结 32

第四章 结论与展望 33

4.1 结论 33

4.2展望 33

参考文献 ……………………………………………………………………………………35

致谢 …………………………………………………………………………………………38

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