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## 物理代写|半导体物理代写Semiconductor Physics代考|Thermal Properties

When a temperature gradient exists in a semiconductor in addition to an applied electric field, the total current density (in one dimension) is ${ }^5$
$$J=\sigma\left(\frac{1}{q} \frac{d E_F}{d x}-\mathscr{P} \frac{d T}{d x}\right)$$
where $\mathscr{P}$ is the thermoelectric power, so named to indicate that for an open-circuit condition the net current is zero and an electric field is generated by the temperature gradient. For a nondegenerate semiconductor with a mean free time between collisions $\tau_m \propto E^{-s}$ as discussed previously, the thermoelectric power is given by
$$\mathscr{P}=-\frac{k}{q}\left{\frac{\left[\frac{5}{2}-s+\ln \left(N_C / n\right)\right] n \mu_n-\left[\frac{5}{2}-s-\ln \left(N_\nu / p\right)\right] p \mu_p}{n \mu_n+p \mu_p}\right}$$
( $k$ is Boltzmann constant). This equation indicates that the thermoelectric power is negative for $n$-type semiconductors and positive for $p$-type semiconductors, a fact often used to determine the conduction type of a semiconductor. The thermoelectric power can also be used to determine the resistivity and the position of the Fermi level relative to the band edges. At room temperature the thermoelectric power $\mathscr{P}$ of $p$-type silicon increases with resistivity: $1 \mathrm{mV} / \mathrm{K}$ for a $0.1 \Omega$-cm sample and $1.7 \mathrm{mV} / \mathrm{K}$ for a $100 \Omega$-cm sample. Similar results (except a change of the sign for $\mathscr{P}$ ) can be obtained for $n$-type silicon samples.

Another important thermal effect is thermal conduction. It is a diffusion type of process where the heat flow $Q$ is driven by the temperature gradient
$$Q=-\kappa \frac{d T}{d x} .$$
The thermal conductivity $\kappa$ has the major components of phonon (lattice) conduction $\kappa_L$ and mixed free-carrier conduction $\kappa_M$ of electrons and holes,
$$\kappa=\kappa_L+\kappa_M \text {. }$$

## 物理代写|半导体物理代写Semiconductor Physics代考|HETEROJUNCTIONS AND NANOSTRUCTURES

A heterojunction is a junction formed between two dissimilar semiconductors. For semiconductor-device applications, the difference in energy gap provides another degree of freedom that produces many interesting phenomena. The successful applications of heterojunctions in various devices is due to the capability of epitaxy technology to grow lattice-matched semiconductor materials on top of one another with virtually no interface traps. Heterojunctions have been widely used in various device applications. The underlying physics of epitaxial heterojunction is matching of the lattice constants. This is a physical requirement in atom placement. Severe lattice mismatch will cause dislocations at the interface and results in electrical defects such as interface traps. The lattice constants of some common semiconductors are shown in Fig. 32, together with their energy gaps. A good combination for heterojunction devices is two materials of similar lattice constants but different $E_g$. As can be seen, $\mathrm{GaAs} / \mathrm{AlGaAs}$ (or /AlAs) is a good example.

It turns out that if the lattice constants are not severely mismatched, good-quality heteroepitaxy can still be grown, provided that the epitaxial-layer thickness is small enough. The amount of lattice mismatch and the maximum allowed epitaxial layer are directly related. This can be explained with the help of Fig. 33. For a relaxed, thick heteroepitaxial layer, dislocations at the interface are inevitable due to the phys-ical mismatch of terminating bonds at the interface. However, if the heteroepitaxial layer is thin enough, the layer can be physically strained to the degree that its lattice constant becomes the same as the substrate (Fig. 33c). When that happens, dislocations can be eliminated.

## 物理代写|半导体物理代写Semiconductor Physics代考|Thermal Properties

.热性能

$$J=\sigma\left(\frac{1}{q} \frac{d E_F}{d x}-\mathscr{P} \frac{d T}{d x}\right)$$
，其中$\mathscr{P}$为热电功率，这样命名是为了表明在开路条件下，净电流为零，温度梯度产生电场。对于具有碰撞间平均自由时间$\tau_m \propto E^{-s}$的非简并半导体，热电功率由
$$\mathscr{P}=-\frac{k}{q}\left{\frac{\left[\frac{5}{2}-s+\ln \left(N_C / n\right)\right] n \mu_n-\left[\frac{5}{2}-s-\ln \left(N_\nu / p\right)\right] p \mu_p}{n \mu_n+p \mu_p}\right}$$

$$Q=-\kappa \frac{d T}{d x} .$$

$$\kappa=\kappa_L+\kappa_M \text {. }$$

.

## 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。

Posted on Categories:Semiconductor Physics, 半导体物理, 物理代写

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## 物理代写|半导体物理代写Semiconductor Physics代考|Diffusion

In the preceding section the excess carriers are uniform in space. In this section, we discuss the situations where excess carriers are introduced locally, causing a condition of nonuniform carriers. Examples are local injection of carriers from a junction, and nonuniform illumination. Whenever there exists a gradient of carrier concentration, a process of diffusion occurs by which the carriers migrate from the region of high concentration toward the region of low concentration, to drive the system toward a state of uniformity. This flow or flux of carriers, taking electrons as an example, is governed by the Fick’s law,
$$\left.\frac{d \Delta n}{d t}\right|x=-D_n \frac{d \Delta n}{d x},$$ and is proportional to the concentration gradient. The proportionality constant is called the diffusion coefficient or diffusivity $D_n$. This flux of carriers constitutes a diffusion current, given by $$J_n=q D_n \frac{d \Delta n}{d x},$$ and $$J_p=-q D_p \frac{d \Delta p}{d x} .$$ Physically, diffusion is due to random thermal motion of carriers as well as scattering. Because of this, we have $$D=v{t h} \tau_m .$$

## 物理代写|半导体物理代写Semiconductor Physics代考|Thermionic Emission

Another current conduction mechanism is thermionic emission. It is a majoritycarrier current and is always associated with a potential barrier. Note that the critical parameter is the barrier height, not the shape of the barrier. The most-common device is the Schottky-barrier diode or metal-semiconductor junction (see Chapter 3). Referring to Fig. 26, for the thermionic emission to be the controlling mechanism, the criterion is that collision or the drift-diffusion process within the barrier layer to be negligible. Equivalently, the barrier width has to be narrower than the mean free path, or in the case of a triangular barrier, the slope of the barrier be reasonably steep such that a drop in $k T$ in energy is within the mean free path. In addition, after the carriers are injected over the barrier, the diffusion current in that region must not be the lim- iting factor. Therefore, the region behind the barrier must be another $n$-type semiconductor or a metal layer.

Due to Fermi-Dirac statistics, the density of electrons (for $n$-type substrate) decreases exponentially as a function of their energy above the conduction band edge. At any finite (nonzero) temperature, the carrier density at any finite energy is not zero. Of special interest here is the integrated number of carriers above the barrier height. This portion of the thermally generated carriers are no longer confined by the barrier so they contribute to the thermionic-emission current. The total electron current over the barrier is given by (see Chapter 3 )
$$J=A^* T^2 \exp \left(-\frac{q \phi_B}{k T}\right) .$$
where $\phi_B$ is the barrier height, and
$$A^* \equiv \frac{4 \pi q m^* k^2}{h^3}$$
is called the effective Richardson constant and is a function of the effective mass. The $A^*$ can be further modified by quantum-mechanical tunneling and reflection.

## 物理代写|半导体物理代写Semiconductor Physics代考|Diffusion

$$\left.\frac{d \Delta n}{d t}\right|x=-D_n \frac{d \Delta n}{d x},$$，并与浓度梯度成正比。比例常数称为扩散系数或扩散率$D_n$。载流子的这种通量构成了扩散电流，由$$J_n=q D_n \frac{d \Delta n}{d x},$$和$$J_p=-q D_p \frac{d \Delta p}{d x} .$$给出，在物理上，扩散是由于载流子的随机热运动和散射。因此，我们有$$D=v{t h} \tau_m .$$

## 物理代写|半导体物理代写半导体物理学代考|热离子发射

.

$$J=A^* T^2 \exp \left(-\frac{q \phi_B}{k T}\right) .$$

$$A^* \equiv \frac{4 \pi q m^* k^2}{h^3}$$

## 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。

Posted on Categories:Semiconductor Physics, 半导体物理, 物理代写

## avatest™帮您通过考试

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## 物理代写|半导体物理代写Semiconductor Physics代考|Donors and Acceptors

When a semiconductor is doped with donor or acceptor impurities, impurity energy levels are introduced that usually lie within the energy gap. A donor impurity has a donor level which is defined as being neutral if filled by an electron, and positive if empty. Conversely, an acceptor level is neutral if empty and negative if filled by an electron. These energy levels are important in calculating the fraction of dopants being ionized, or electrically active, as discussed in Section 1.4.3.

To get a feeling of the magnitude of the impurity ionization energy, we use the simplest calculation based on the hydrogen-atom model. The ionization energy for the hydrogen atom in vacuum is
$$E_H=\frac{m_0 q^4}{32 \pi^2 \varepsilon_0^2 \hbar^2}=13.6 \mathrm{eV} .$$
The ionization energy for a donor $\left(E_C-E_D\right)$ in a lattice can be obtained by replacing $m_0$ by the conductivity effective mass of electrons ${ }^5$
$$m_{c e}=3\left(\frac{1}{m_1^}+\frac{1}{m_2^}+\frac{1}{m_3^*}\right)^{-1}$$
and by replacing $\varepsilon_0$ by the permittivity of the semiconductor $\varepsilon_s$ in Eq. 31:
$$E_C-E_D=\left(\frac{\varepsilon_0}{\varepsilon_s}\right)^2\left(\frac{m_{c e}}{m_0}\right) E_H .$$

## 物理代写|半导体物理代写Semiconductor Physics代考|Calculation of Fermi Level

The Fermi level for the intrinsic semiconductor (Eq. 27) lies very close to the middle of the bandgap. Figure 11a depicts this situation, showing schematically from left to right the simplified band diagram, the density of states $N(E)$, the Fermi-Dirac distribution function $F(E)$, and the carrier concentrations. The shaded areas in the conduction band and the valence band represent electrons and holes, and their numbers are the same; i.e., $n=p=n_i$ for the intrinsic case.

When impurities are introduced to the semiconductor crystals, depending on the impurity energy level and the lattice temperature, not all dopants are necessarily ionized. The ionized concentration for donors is given by ${ }^{36}$
$$N_D^{+}=\frac{N_D}{1+g_D \exp \left[\left(E_F-E_D\right) / k T\right]}$$
where $g_D$ is the ground-state degeneracy of the donor impurity level and equal to 2 because a donor level can accept one electron with either spin (or can have no electron). When acceptor impurities of concentration $N_A$ are added to a semiconductor crystal, a similar expression can be written for the ionized acceptors
$$N_A^{-}=\frac{N_A}{1+g_A \exp \left[\left(E_A-E_F\right) / k T\right]}$$
where the ground-state degeneracy factor $g_A$ is 4 for acceptor levels. The value is 4 because in most semiconductors each acceptor impurity level can accept one hole of either spin and the impurity level is doubly degenerate as a result of the two degenerate valence bands at $\boldsymbol{k}=0$.

## 物理代写|半导体物理代写Semiconductor Physics代考|捐助者和接受者

$$E_H=\frac{m_0 q^4}{32 \pi^2 \varepsilon_0^2 \hbar^2}=13.6 \mathrm{eV} .$$

$$m_{c e}=3\left(\frac{1}{m_1^}+\frac{1}{m_2^}+\frac{1}{m_3^*}\right)^{-1}$$

$$E_C-E_D=\left(\frac{\varepsilon_0}{\varepsilon_s}\right)^2\left(\frac{m_{c e}}{m_0}\right) E_H .$$

## 物理代写|半导体物理代写半导体物理学代考|计算费米能级

.计算费米能级

$$N_D^{+}=\frac{N_D}{1+g_D \exp \left[\left(E_F-E_D\right) / k T\right]}$$

$$N_A^{-}=\frac{N_A}{1+g_A \exp \left[\left(E_A-E_F\right) / k T\right]}$$

## 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。