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

Транспорт носителей в полупроводниках генерирует ток с помощью механизмов дрейфа и диффузии.
Дрейфующий ток возникает, когда внешнее электрическое поле заставляет заряженные частицы ускоряться между столкновениями.
Рассматривая электроны, дополнительная скорость, добавляемая к тепловому движению электронов, называется скоростью дрейфа. Его можно получить, приравняв импульс, потерянный при столкновениях, и импульс, полученный от приложенного поля.
Коэффициент пропорциональности - подвижность - характеризует перенос электронов и дырок из-за дрейфа.
Плотности дрейфующего тока для обеих несущих могут быть выражены как произведение плотности заряда, подвижности и напряженности электрического поля. Сумма этих двух значений дает общую плотность дрейфового тока. Здесь член в скобках обозначает проводимость.
Диффузионный ток возникает в результате случайного теплового движения носителей из областей с высокой и низкой плотностью носителей.
Плотность диффузионного тока равна произведению несущего потока на константу пропорциональности, которая включает элементарный заряд и коэффициент диффузии. Его отношение к подвижности дает отношение Эйнштейна.
Если присутствуют как электрическое поле, так и градиент концентрации, то и дрейф, и диффузионный ток вносят свой вклад в общий ток.

Основы теории полупроводников

Генерация электрического тока в полупроводниках в основном обусловлена ​​двумя механизмами: дрейфом и диффузией. Эти процессы необходимы для функциональности и производительности полупроводниковых устройств.
Дрейфовый ток:
Дрейф носителей заряда начинается под действием внешнего электрического поля (Е). Заряженные частицы, такие как электроны и дырки, испытывают ускорение при столкновениях с атомами решетки. Для электронов это приводит к скорости дрейфа (v_d), определяемой следующим образом:
<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="height: 16px;">
Где μ_e — подвижность электронов, а E — напряженность электрического поля.
Плотность тока (J), обусловленная дрейфом электронов (J_n) и дырок (J_p), можно выразить как:
<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="height: 20px;">
Где q — элементарный заряд, n и p — концентрации электронов и дырок соответственно, а µ_n и µ_p — подвижности электронов и дырок. Полная плотность дрейфового тока (J_total) представляет собой сумму плотностей электронного и дырочного тока:
<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="height: 20px;">
Тогда проводимость (σ) представляет собой сумму произведений плотности заряда и подвижности для каждого типа носителей:
<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="height: 20px;">
Диффузионный ток:
 Диффузия происходит за счет теплового движения носителей, перемещающихся из областей с большей концентрацией в области с меньшей концентрацией. Плотность тока (J_диффузия) равна:
<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="height: 36px;">
Здесь D_n и D_p — коэффициенты диффузии электронов и дырок соответственно, а dn/dx и dp/dx — градиенты концентрации электронов и дырок.
Соотношения Эйнштейна связывают подвижность и коэффициент диффузии как для электронов, так и для дырок:
<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="height: 36px;">
 Где k — постоянная Больцмана, а T — абсолютная температура.
Когда присутствуют и электрическое поле, и градиент концентрации, полная плотность тока представляет собой сумму дрейфовой и диффузионной составляющих. В реальных приложениях эти явления анализируются с помощью уравнений полупроводника — набора дифференциальных уравнений, описывающих поведение носителей заряда в полупроводнике.

Транспорт носителей в полупроводниках генерирует ток с помощью механизмов дрейфа и диффузии.
Дрейфовый ток возникает, когда внешнее электрическое поле вызывает...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Basics of Semiconductors

Основы полупроводников

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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