场引晶体管理论:XI.双极电化电流（薄及厚、纯及不纯基体,单及双MOS栅极）

场引晶体管本质双极，包括电子和空穴表面和体积沟道和电流，一或多个外加横向控制电场．自1952年Shockley发明，55年来它被认为单极场引晶体管，因电子电流理论用多余内部和边界条件，不可避免忽略空穴电流．多余条件，诸如电中性和常空穴电化电势，导致仅用电子电流算内部和终端电学特性的错误解．当忽略的空穴电流与电子电流可比，可在亚阈值区和强反型区，错误解有巨大误差．本文描述普适理论，含有电子和空穴沟道和电流．用z轴宽度方向均匀的直角平行六面体（x，y，z）晶体管，薄或厚、纯或杂基体，一或二块MOS栅极，描述两维效应及电势、电子空穴电化电势的正确内部和边界条件．没用多余条件，导出四种常用MOS晶体管，直流电流电压特性完备解析方程：半无限厚不纯基上一块栅极（传统的Bulk MOSFET），与体硅以氧化物绝缘的不纯硅薄层上一块栅极（SOI），在沉积到绝缘玻璃的不纯硅薄层上一块栅极（SOI TFT），和薄纯基上两块栅极（FinFETs）．

The Theory of Field-Effect Transistors: XI.The Bipolar Electrochemical Currents (1-2-MOS-Gates on Thin-Thick Pure-Impure Base)

The field-effect transistor is inherently bipolar, having simultaneously electron and hole surface and volume channels and currents. The channels and currents are controlled by one or more externally applied transverse electric fields. It has been known as the unipolar field-effect transistor for 55-years since Shockley's 1952 invention, because the electron-current theory inevitably neglected the hole current from over-specified internal and boundary conditions,such as the electrical neutrality and the constant hole-electrochemical-potential, resulting in erroneous solutions of the internal and terminal electrical characteristics from the electron channel current alone, which are in gross error when the neglected hole current becomes comparable to the electron current, both in subthreshold and strong inversion. This report presents the general theory, that includes both electron and hole channels and currents. The rectangular (x, y, z) parallelepiped transistors,uniform in the width direction (z-axis), with one or two MOS gates on thin and thick, and pure and impure base, are used to illustrate the two-dimensional effects and the correct internal and boundary conditions for the electric and the electron and hole electrochemical potentials. Complete analytical equations of the DC current-voltage characteristics of four common MOS transistor structures are derived without over-specification the 1-gate on semi-infinite-thick impure-base (the traditional bulk transistor), the 1-gate on thin impure-silicon layer over oxide-insulated silicon bulk(SOI) ,the 1-gate on thin impure-silicon layer deposited on insulating glass (SOI TFT),and the 2-gates on thin pure-base(FinFETs).