Name: fermi level in semiconductors
Uploaded: 2024-07-08T13:20:09.000Z
Duration: 1 min 18 s
Channel: JoVE

Функция Ферми-Дирака, представленная сигмовидной кривой, указывает на вероятность того, что энергетическое состояние будет занято электроном при данной температуре.
Уровень Ферми представляет собой энергетическое состояние с вероятностью 50 процентов и лежит между валентной и проводимой зонами.
При абсолютном нуле энергетические состояния до уровня Ферми заполнены, в то время как те, что выше – пусты. При более высоких температурах состояния выше уровня Ферми могут быть заполнены.
В собственных полупроводниках равные концентрации дырок и электронов означают, что уровень Ферми лежит в середине запрещенной зоны.
В полупроводниках n-типа более высокая концентрация электронов смещает уровень Ферми близко к зоне проводимости.
В полупроводниках p-типа уровень Ферми находится вблизи валентной зоны из-за более высокой концентрации дырок.
По мере повышения температуры все больше электронов переходит из валентной зоны в зону проводимости, приближая уровень Ферми к зоне проводимости.
Когда материалы с разными уровнями Ферми соединяются, электроны перетекают с более высокого уровня Ферми на низкий, чтобы выровнять уровни Ферми на стыке и установить равновесие.

Уровень Ферми

Функция Ферми-Дирака представлена ​​S-образной кривой, показывающей вероятность занятия энергетического состояния электроном при данной температуре. Уровень Ферми — это энергетический уровень, на котором существует пятидесятипроцентная вероятность найти электрон, и он расположен между валентной зоной с более низкой энергией и зоной проводимости с более высокой энергией.
При абсолютной нулевой температуре электроны заполняют все энергетические состояния вплоть до уровня Ферми, оставляя верхние состояния пустыми. С повышением температуры энергия электронов увеличивается, и они становятся способными занимать вакантные состояния выше уровня Ферми.
В собственных полупроводниках, где концентрации электронов и дырок равны, уровень Ферми расположен в середине запрещенной зоны. Ситуация меняется, когда добавляются примеси для создания полупроводников n- или p-типа. В полупроводниках n-типа при избытке электронов уровень Ферми смещается ближе к зоне проводимости. И наоборот, в полупроводниках p-типа, где концентрация дырок выше, уровень Ферми перемещается ближе к валентной зоне.
Повышение температуры приводит к тому, что большее количество электронов совершает прыжок из валентной зоны в зону проводимости, подталкивая при этом уровень Ферми к зоне проводимости. Этот сдвиг влияет на проводимость полупроводника.
При контакте материалов с разными уровнями Ферми электроны перетекают из области более высоких уровней Ферми в область с более низкими уровнями. Движение электронов выравнивает уровни Ферми на стыке, устанавливая равновесие. Эта концепция играет решающую роль в работе многочисленных электронных компонентов, позволяя регулировать и подправлять электропроводность и производительность электронных устройств.

Функция Ферми-Дирака, представленная сигмовидной кривой, указывает на вероятность того, что энергетическое состояние будет занято электроном при заданном ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Basics of Semiconductors

Основы полупроводников

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 intrinsic semiconductor, the number of electrons equals the number of holes. A hole is the missing electron state left in the valence band. In this case, the Fermi level lies near the middle of the band gap. Adding impurities changes this balance and creates n-type or p-type semiconductors.

In an n-type semiconductor, extra electrons shift the Fermi level closer to the conduction band. In a p-type semiconductor, a higher number of holes moves the Fermi level closer to the valence band. Higher temperature also lets more electrons jump from the valence band to the conduction band, which nudges the Fermi level toward the conduction band and changes conductivity.

When materials with different Fermi levels touch, electrons flow from the region with the higher Fermi level to the region with the lower one. This movement continues until the Fermi levels align at the junction. The resulting equilibrium is important for many electronic components because it helps control electrical conductivity and device performance.

Fermi Level 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 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...

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

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

Learn how the Fermi level changes with temperature, doping, and semiconductor type, and how it affects electron flow, equilibrium, and conductivity.

Fermi Level 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

Fermi Level in Semiconductors

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