BaTiO_3半导瓷阻温特性的数值模拟

Numerical simulation of the resistivity-temperature characteristic of semiconductive BaTiO_3 ceramics

在海望表面势垒模型的基础上,考虑到施主、受主、电子和空穴的迁移对晶界效应的影响,从理论上建立了一个关于电子能级的微分方程,按照四阶标准龙格-库塔公式求解该方程,从数值上得到了晶界势垒的能级图.进一步计算得到BaTiO3半导瓷在任意晶粒尺寸、任意施主、受主浓度掺杂下的定量的阻温关系.结果发现电阻率随施主浓度的增大形成U形曲线.掺入一定含量的受主将抵消一部分施主,使得取得最小室温电阻的施主浓度增大,同时室温电阻升高.材料的升阻比在指定的受主浓度掺杂和指定的晶粒尺寸下取得极大值.计算的结果与实验数据相符.

On the basis of Heywang model, a differential equation of electron level was set, after the migration of the donors, acceptor, electrons and holes has important influence on the grain boundary effect were considered. Energy band chart is obtained by solving the equation with Runge-Kutta method. The positive temperature coefficient effect of semiconductive BaTiO3 ceramics with different grain sizes and different donors and acceptors doping were computed quantitatively. It is found that the resistivity forms a U-shaped curve with the donor concentration increasing. The incorporation of aeceptor will offset a part of the donor, which leads to the rising of the room temperature resistivity and the increasing of the donor concentration at which the room-temperature resistivity obtains minimum; the resistance jumping shows a maximum at a certain acceptor doping concentration and grain size. The results are consistent with experimental data.