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Firisy committed Jul 4, 2024
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## 1.0 Preview

In this chapter, we will:
Describe three classifications of solids—amorphous 非晶体, polycrystalline 多晶体, and single crystal.
Discuss the concept of a unit cell.
Describe three simple crystal structures and determine the volume and surfacedensity of atoms in each structure.
Describe the diamond crystal structure.
Briefly discuss several methods of forming single-crystal semiconductor materials.
* Describe three classifications of solids—amorphous 非晶体, polycrystalline 多晶体, and single crystal.
* Discuss the concept of a unit cell.
* Describe three simple crystal structures and determine the volume and surfacedensity of atoms in each structure.
* Describe the diamond crystal structure.
* Briefly discuss several methods of forming single-crystal semiconductor materials.

## 1.3 Space Lattices

Expand All @@ -22,6 +22,7 @@ In this chapter, we will:
#### Volume Density of Atoms

1.5 (b)

$$
\frac1{8}\times8+1=2\\
Volume\space Density=\frac{\#atoms\space per\space unit\space cell}{volume\space of \space unit\space cell}={2\over a^3}
Expand Down Expand Up @@ -91,8 +92,6 @@ NaCl

#### covalent bonding 共价键

H~2~

the outer silicon atoms always have valence electrons available for additional covalent bonding - infinite structure

#### metallic bonding 金属键
Expand All @@ -119,7 +118,7 @@ thermal energy(function of temperature) - atom randomly fluctuate

lack of an atom - **vacancy**

<img src="./assets/image-20240410102423914.png" alt="image-20240410102423914" style="zoom:33%;" />
<img src="../assets/image-20240410102423914.png" alt="image-20240410102423914" style="zoom:33%;" />

多了一个 **interstitial**

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## 3.1 Allowed and Forbidden Energy Bands

<img src="./assets/image-20240704140255482.png" alt="image-20240704140255482" style="zoom:53%;" /><img src="./assets/image-20240704140432020.png" alt="image-20240704140432020" style="zoom:33%;" />
<img src="../assets/image-20240704140255482.png" alt="image-20240704140255482" style="zoom:53%;" /><img src="../assets/image-20240704140432020.png" alt="image-20240704140432020" style="zoom:33%;" />



<img src="./assets/image-20240704140502040.png" alt="image-20240704140502040" style="zoom:50%;" />
<img src="../assets/image-20240704140502040.png" alt="image-20240704140502040" style="zoom:50%;" />



<img src="./assets/image-20240704144925972.png" alt="image-20240704144925972" style="zoom:53%;" />
<img src="../assets/image-20240704144925972.png" alt="image-20240704144925972" style="zoom:53%;" />

### 3.1.3 The $k$-Space Diagram

Expand All @@ -30,7 +30,7 @@ $\alpha$ is given by$\sqrt{\frac{2mE}{\hbar^2}}=\frac{p}{\hbar}=k$, so we obtain
$$
E=\frac{k^2\hbar^2}{2m}
$$
<img src="./assets/image-20240704144228103.png" alt="image-20240704144228103" style="zoom:25%;" />
<img src="../assets/image-20240704144228103.png" alt="image-20240704144228103" style="zoom:25%;" />

Now, we consider the relation between $E$ and $k$ form Equation for the particle in the single-crystal lattice.

Expand All @@ -44,21 +44,21 @@ f(\alpha a)=\cos ka
$$
![image-20240704145326035](./assets/image-20240704145326035.png)

<img src="./assets/image-20240704145501812.png" alt="image-20240704145501812" style="zoom:25%;" />
<img src="../assets/image-20240704145501812.png" alt="image-20240704145501812" style="zoom:25%;" />

the right side can also be written as $\cos ka=\cos(ka+2n\pi)=\cos(ka-2n\pi)$

then we gain

<img src="./assets/image-20240704150237183.png" alt="image-20240704150237183" style="zoom:25%;" />
<img src="../assets/image-20240704150237183.png" alt="image-20240704150237183" style="zoom:25%;" />

## 3.2 Electrical Conduction In Solids

### 3.2.1 The Energy Band and the Bond Model

<img src="./assets/image-20240704140810574.png" alt="image-20240704140810574" style="zoom:50%;" />
<img src="../assets/image-20240704140810574.png" alt="image-20240704140810574" style="zoom:50%;" />

<img src="./assets/image-20240704141325933.png" alt="image-20240704141325933" style="zoom:50%;" />
<img src="../assets/image-20240704141325933.png" alt="image-20240704141325933" style="zoom:50%;" />



Expand All @@ -73,7 +73,7 @@ if a force is applied to a particle and the particle moves.
$$
dE=Fdx=Fv\cdot dt
$$
<img src="./assets/image-20240704141339201.png" alt="image-20240704141339201" style="zoom:33%;" />
<img src="../assets/image-20240704141339201.png" alt="image-20240704141339201" style="zoom:33%;" />

### 3.2.3 Electron Effective Mass

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