Name: drift and diffusion in semiconductors
Uploaded: 2024-07-08T13:20:08.000Z
Duration: 1 min 21 s
Channel: JoVE

半导体中的载流子输运通过漂移和扩散机制产生电流。
当外加电场导致带电粒子在碰撞之间加速时，会产生漂移电流。
从电子的角度来看，附加在电子热运动上的额外速度称为漂移速度。可通过将碰撞过程中损失的动量与外加电场获得的动量相等来求得。
比例系数——迁移率——表征由漂移引起的电子和空穴输运。
两种载流子的漂移电流密度均可表示为电荷密度、迁移率和电场强度的乘积。这两者的总和即为总漂移电流密度。其中，括号内的项表示电导率。
扩散电流源于载流子从高载流子密度区域向低载流子密度区域的随机热运动。
扩散电流密度等于载流子通量与比例常数的乘积，该比例常数包含基本电荷和扩散系数。其与迁移率的比值即为爱因斯坦关系。
如果同时存在电场和浓度梯度，则漂移电流和扩散电流均对总电流有贡献。

半导体基础知识

半导体中电流的产生主要是由两种机制进行驱动：漂移和扩散。这些过程对于半导体器件的功能和性能来说是至关重要的。
漂移电流：
电荷载体的漂移是由外部电场（E）进行启动的。电子和空穴等带电粒子在与晶格原子发生碰撞时会产生加速度。电子的漂移速度（v_d）可以由以下公式计算得出：
<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="text-align: center; height: 16px;">
其中 μ_e 是电子迁移率，E 是电场强度。
由电子（J_n）和空穴（J_p）的漂移所产生的电流密度（J）可以表示为：
<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="text-align: center; height: 20px;">
其中 q 是基本电荷，n 和 p 分别是电子和空穴的浓度，μ_n 和 μ_p 是电子和空穴的迁移率。 总漂移电流密度（J_total）是电子和空穴的电流密度之和：
<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="text-align: center; height: 20px;">
电导率（σ）是每种载流子的电荷密度和迁移率的乘积之和：
<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="text-align: center; height: 20px;">
扩散电流：
扩散是由于载流子从高浓度区域向低浓度区域发生移动时的热运动所产生的。其中的电流密度（J_diffusion）为：
<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="text-align: center; height: 36px;">
D_n 和 D_p 分别是电子和空穴的扩散系数，dn/dx 和 dp/dx 是电子和空穴的浓度梯度。
爱因斯坦关系能够将电子和空穴的迁移率与扩散系数联系起来：
<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="text-align: center; height: 36px;">
其中，k 为玻尔兹曼常数，T 为绝对温度。
当电场和浓度梯度同时存在时，总电流密度是漂移分量和扩散分量的总和。在实际应用中，这些现象可以使用半导体方程来对其进行分析，半导体方程是一组用来描述半导体中电荷载流子行为的微分方程。

半导体中的载流子输运通过漂移和扩散机制产生电流。  
当外加电场导致……时，便产生漂移电流。

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Basics of Semiconductors

KEY TERMS AND CONCEPTS

关键术语与概念

Carrier Transport

drift and diffusion in semiconductors

Drift and diffusion are the two main ways electric current forms in semiconductors. These charge-carrier motions help determine how semiconductor devices work and how well they perform. The carriers involved are electrons and holes.

Drift current begins when an external electric field acts on charge carriers. Electrons and holes move between collisions with lattice atoms, and this motion creates drift velocity. For electrons, drift velocity depends on electron mobility and the electric field strength.

The current density from drift can be written for electrons and for holes. It depends on the elementary charge, the concentrations of electrons and holes, and their mobilities. The total drift current density is the sum of the electron and hole parts. Conductance is then related to the charge density and mobility of each carrier.

Diffusion current comes from thermal motion. Carriers move from regions with higher concentration to regions with lower concentration. For electrons and holes, diffusion current density depends on the diffusion coefficients and the concentration gradients.

Mobility and diffusion are linked by the Einstein relations. These relations connect the electron and hole mobility terms with their diffusion coefficients, along with temperature, the Boltzmann constant, and absolute temperature. When both an electric field and a concentration gradient are present, the total current density is the sum of drift and diffusion. In real semiconductor analysis, these effects are described with semiconductor equations, which are differential equations for charge-carrier behavior.

Drift and Diffusion in Semiconductors

energy bands in solids

Valence and Conduction Bands in Silicon

Valence and conduction bands explain how electrons behave in solids. In isolated atoms, electrons occupy discrete energy levels that the Bohr model describes well. The hydrogen atom, for example, has specific electron energies labeled by the quantum number n, and higher n values give levels that are less negative and closer together. When atoms move close together in a solid, those discrete levels start to split. This happens because electron orbitals from neighboring atoms overlap. The Pauli...

semiconductors

Energy Bands in Metals and Insulators

Materials conduct electricity in different ways because their energy bands are arranged differently. Metals, semiconductors, and insulators can be compared with energy band diagrams. These diagrams show how easily electrons can move when an electric field is applied. Metals such as copper, zinc, and lead have low resistivity. Their conduction band is not fully occupied, or it overlaps with the valence band, so a band gap is essentially absent. Electrons in the highest valence energy levels can...

types of semiconductors

Intrinsic and Doped Semiconductors

Intrinsic semiconductors are very pure materials with no impurities. At absolute zero, they act as perfect insulators because the valence electrons are bound and the conduction band is empty. That means electrical conduction cannot occur under those conditions. The Fermi level helps describe the chance that an energy level is occupied by an electron at thermal equilibrium. In an intrinsic semiconductor, the Fermi level sits near the middle of the band gap at absolute zero. As temperature...

carrier generation and recombination

Semiconductor Charge Carriers: Creation and Loss

Carrier generation and recombination control how free charge carriers change inside a semiconductor. Carrier generation creates electron-hole pairs, or EHPs, when electrons move from the valence band into the conduction band and leave holes behind. Carrier recombination does the opposite and lowers the number of free carriers. In direct-bandgap semiconductors such as gallium arsenide, generation happens efficiently because energy absorption can move a valence electron straight to the...

carrier transport

Drift and diffusion are the two main ways electric current forms in semiconductors. These charge-carrier motions help determine how semiconductor devices work and how well they perform. The carriers involved are electrons and holes. Drift current begins when an external electric field acts on charge carriers. Electrons and holes move between collisions with lattice atoms, and this motion creates drift velocity. For electrons, drift velocity depends on electron mobility and the electric field...

p-n junction

P-N Junction Depletion Region

A p-n junction forms when p-type and n-type semiconductor materials are joined together. At the boundary, holes from the p-side and electrons from the n-side diffuse into the opposite side because of the concentration gradient. This movement leaves a region with no free charge carriers near the junction, called the depletion region. The charge density in the depletion region can be described on the n-side and p-side using the donor and acceptor doping concentrations, ND and NA. The fixed...

biasing of p-n junction

P-N Junction Diode Under Bias

P-N junction diodes change behavior under equilibrium, forward bias, and reverse bias. In equilibrium, no external voltage is applied across the junction. Carriers diffuse at the boundary and leave behind charged dopants. Acceptors remain on the p-side, and donors remain on the n-side. These fixed charges form a depletion region and an electric field that blocks further diffusion. The band diagram at equilibrium shows the Fermi levels on both sides aligned. That alignment means the junction is...

metal-semiconductor junctions

Schottky and Ohmic Metal Contacts

Metal contacts with semiconductors can form either Schottky or Ohmic junctions. The result depends on the work function of the metal, the work function of the semiconductor, and how electrons move when the two materials touch. At equilibrium, the Fermi levels align, so charge shifts until both sides match in energy. Schottky barriers form when a metal with work function Φm contacts a semiconductor with a different work function Φs. If Φm is greater than Φs, the semiconductor Fermi level starts...

biasing of metal-semiconductor junctions

How Bias Changes Metal-Semiconductor Current

Biasing metal-semiconductor junctions means applying a voltage across the junction. The metal connects to the voltage source, and the semiconductor is grounded. This setup helps control the direction and size of current in devices such as diodes, transistors, and photovoltaic cells. In a Schottky junction with an n-type semiconductor, a positive voltage on the metal lowers its Fermi level. A Fermi level is the energy level that helps describe how electrons are distributed. Lowering this level...

fermi level

Fermi Level in Semiconductors

The Fermi level is a key energy level in semiconductors. It sits between the lower-energy valence band and the higher-energy conduction band. The Fermi-Dirac function, which follows an S-shaped curve, shows the chance that an energy state is filled by an electron at a given temperature. At absolute zero, electrons occupy every energy state up to the Fermi level. States above it stay empty. As temperature rises, electrons gain energy and can move into vacant states above the Fermi level. In an...

fermi level dynamics

Vacuum Level and Schottky Barriers

Vacuum level and Schottky barriers help explain how electrons move between materials. The vacuum level is the energy needed for an electron to escape a material surface. In a semiconductor, it usually sits above the conduction band and serves as a reference for comparing electron energy. Electron affinity is the energy gap between the conduction band minimum and the vacuum level. It shows how easily a semiconductor can accept extra electrons. The work function is the least energy needed to...

key terms and concepts

Explore how electrons and holes create current in semiconductors through drift and diffusion, and see how mobility, concentration, and temperature shape carrier motion.

Drift and Diffusion in Semiconductors | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Drift and Diffusion in Semiconductors

Description

Transcript