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物理代写|半导体物理代写Semiconductor Physics代考|EE539/482 ENERGY BANDS AND ENERGY GAP

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物理代写|半导体物理代写Semiconductor Physics代考|ENERGY BANDS AND ENERGY GAP

The energy-momentum $(E-k)$ relationship for carriers in a lattice is important, for example, in the interactions with photons and phonons where energy and momentum have to be conserved, and with each other (electrons and holes) which leads to the concept of energy gap. This relationship also characterizes the effective mass and the group velocity, as will be discussed later.

The band structure of a crystalline solid, that is, the energy-momentum $(E-k)$ relationship, is usually obtained by solving the Schrödinger equation of an approximate one-electron problem. The Bloch theorem, one of the most-important theorems basic to band structure, states that if a potential energy $V(r)$ is periodic in the direct lattice space, then the solutions for the wavefunction $\psi(r, k)$ of the Schrödinger equation ${ }^{14,16}$
$$\left[-\frac{\hbar^2}{2 m^*} \nabla^2+V(\boldsymbol{r})\right] \psi(\boldsymbol{r}, \boldsymbol{k})=E(\boldsymbol{k}) \psi(\boldsymbol{r}, \boldsymbol{k})$$
are of the form of a Bloch function
$$\psi(\boldsymbol{r}, \boldsymbol{k})=\exp (j \boldsymbol{k} \cdot \boldsymbol{r}) U_b(\boldsymbol{r}, \boldsymbol{k}) .$$
Here $b$ is the band index, $\psi(r, k)$ and $U_b(\boldsymbol{r}, \boldsymbol{k})$ are periodic in $\boldsymbol{R}$ of the direct lattice. Since
\begin{aligned} \psi(\boldsymbol{r}+\boldsymbol{R}, \boldsymbol{k}) &=\exp [j \boldsymbol{k} \cdot(\boldsymbol{r}+\boldsymbol{R})] U_b(\boldsymbol{r}+\boldsymbol{R}, \boldsymbol{k}) \ &=\exp (j \boldsymbol{k} \cdot \boldsymbol{r}) \exp (j \boldsymbol{k} \cdot \boldsymbol{R}) U_b(\boldsymbol{r}, \boldsymbol{k}) \end{aligned}
and is equal to $\psi(r, k)$, it is necessary that $\boldsymbol{k} \cdot \boldsymbol{R}$ is a multiple of $2 \pi$. It is the property of Eq. 4 that the reciprocal lattice can be used when $\boldsymbol{G}$ is replaced with $\boldsymbol{k}$ for visualizing the $E-k$ relationship.

物理代写|半导体物理代写Semiconductor Physics代考|CARRIER CONCENTRATION AT THERMAL EQUILIBRIUM

One of the most-important properties of a semiconductor is that it can be doped with different types and concentrations of impurities to vary its resistivity. Also, when these impurities are ionized and the carriers are depleted, they leave behind a charge density that results in an electric field and sometimes a potential barrier inside the semiconductor. Such properties are absent in a metal or an insulator.

Figure 7 shows three basic bond representations of a semiconductor. Figure 7 a shows intrinsic silicon, which is very pure and contains a negligibly small amount of impurities. Each silicon atom shares its four valence electrons with the four neigh-boring atoms, forming four covalent bonds (also see Fig. 1). Figure $7 \mathrm{~b}$ shows an $n$-type silicon, where a substitutional phosphorous atom with five valence electrons has replaced a silicon atom, and a negative-charged electron is donated to the lattice in the conduction band. The phosphorous atom is called a donor. Figure $7 \mathrm{c}$ similarly shows that when a boron atom with three valence electrons substitutes for a silicon atom, a positive-charged hole is created in the valence band, and an additional electron will be accepted to form four covalent bonds around the boron. This is $p$-type, and the boron is an acceptor.

These names of $n$ – and $p$-type had been coined when it was observed that if a metal whisker was pressed against a $p$-type material, forming a Schottky barrier diode (see Chapter 3 ), a positive bias was required on the semiconductor to produce a noticeable current. ${ }^{25,26}$ Also, when exposed to light, a positive potential was generated with respect to the metal whisker. Conversely, a negative bias was required on an $n$-type material to produce a large current.

物理代写|半导体物理代写Semiconductor Physics代考|ENERGY BANDS AND ENERGY GAP

$$\left[-\frac{\hbar^2}{2 m^*} \nabla^2+V(\boldsymbol{r})\right] \psi(\boldsymbol{r}, \boldsymbol{k})=E(\boldsymbol{k}) \psi(\boldsymbol{r}, \boldsymbol{k})$$

\begin{aligned} \psi(\boldsymbol{r}+\boldsymbol{R}, \boldsymbol{k}) &=\exp [j \boldsymbol{k} \cdot(\boldsymbol{r}+\boldsymbol{R})] U_b(\boldsymbol{r}+\boldsymbol{R}, \boldsymbol{k}) \ &=\exp (j \boldsymbol{k} \cdot \boldsymbol{r}) \exp (j \boldsymbol{k} \cdot \boldsymbol{R}) U_b(\boldsymbol{r}, \boldsymbol{k}) \end{aligned}

物理代写|半导体物理代写半导体物理学代考|载流子浓度AT热平衡

$n$ -和$p$ -型的名称是在观察到如果将金属晶须压在$p$型材料上，形成肖特基势垒二极管(见第三章)时产生的，需要在半导体上有正偏置才能产生明显的电流。${ }^{25,26}$同样，当暴露在光下时，金属须会产生一个正电位。相反，在$n$类型的材料上需要负偏置才能产生大电流

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。