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物理代写|微电子芯片原理代写Microelectronics代考|ELECENG4109 pn JUNCTION

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物理代写|微电子芯片原理代写Microelectronics代考|pn JUNCTION

We begin our study of semiconductor devices with the $p n$ junction for three reasons. (1) The device finds application in many electronic systems, e.g., in adaptors that charge the batteries of cellphones. (2) The $p n$ junction is among the simplest semiconductor devices, thus providing a good entry point into the study of the operation of such complex structures as transistors.

(3) The pn junction also serves as part of transistors. We also use the term “diode” to refer to $p n$ junctions.

We have thus far seen that doping produces free electrons or holes in a semiconductor, and an electric field or a concentration gradient leads to the movement of these charge carriers. An interesting situation arises if we introduce $n$-type and $p$-type dopants into two adjacent sections of a piece of semiconductor. Depicted in Fig. $2.16$ and called a “pn junction,” this structure plays a fundamental role in many semiconductor devices. The $p$ and $n$ sides are called the “anode” and the “cathode,” respectively.

物理代写|微电子芯片原理代写Microelectronics代考|pn Junction in Equilibrium

Let us first study the $p n$ junction with no external connections, i.e., the terminals are open and no voltage is applied across the device. We say the junction is in “equilibrium.” While seemingly of no practical value, this condition provides insights that prove useful in understanding the operation under nonequilibrium as well.

We begin by examining the interface between the $n$ and $p$ sections, recognizing that one side contains a large excess of holes and the other, a large excess of electrons. The sharp concentration gradient for both electrons and holes across the junction leads to two large diffusion currents: electrons flow from the $n$ side to the $p$ side, and holes flow in the opposite direction. Since we must deal with both electron and hole concentrations on each side of the junction, we introduce the notations shown in Fig. 2.18.

The diffusion currents transport a great deal of charge from each side to the other, but they must eventually decay to zero. This is because if the terminals are left open (equilibrium condition), the device cannot carry a net current indefinitely.

We must now answer an important question: what stops the diffusion currents? We may postulate that the currents stop after enough free carriers have moved across the junction so as to equalize the concentrations on the two sides. However, another effect dominates the situation and stops the diffusion currents well before this point is reached.

To understand this effect, we recognize that for every electron that departs from the $n$ side, a positive ion is left behind, i.e., the junction evolves with time as conceptually shown in Fig. 2.19. In this illustration, the junction is suddenly formed at $t=0$, and the diffusion currents continue to expose more ions as time progresses. Consequently, the immediate vicinity of the junction is depleted of free carriers and hence called the “depletion region.”

物理代写|微电子芯片原理代写Microelectronics代考|pn JUNCTION

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pn结也是晶体管的一部分。我们也使用术语“二极管”来指代$p n$结

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MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。