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

La funzione di Fermi-Dirac, rappresentata da una curva sigmoidea, indica la probabilità che uno stato energetico sia occupato da un elettrone ad una data temperatura.
Il livello di Fermi rappresenta lo stato energetico con una probabilità di occupazione del 50% e si trova tra le bande di valenza e conduzione.
Allo zero assoluto, gli stati energetici fino al livello di Fermi sono riempiti, mentre quelli superiori sono vuoti. A temperature più elevate, gli stati al di sopra del livello di Fermi possono essere riempiti.
Nei semiconduttori intrinseci, concentrazioni uguali di lacune ed elettroni implicano che il livello di Fermi si trovi al centro della banda proibita.
Nei semiconduttori di tipo n, una maggiore concentrazione di elettroni sposta il livello di Fermi vicino alla banda di conduzione.
Nei semiconduttori di tipo p, il livello di Fermi si trova vicino alla banda di valenza, a causa di una maggiore concentrazione di lacune.
All'aumentare della temperatura, più elettroni passano dalla banda di valenza a quella di conduzione, spostando il livello di Fermi più vicino alla banda di conduzione.
Quando materiali con diversi livelli di Fermi si connettono, gli elettroni fluiscono dal livello di Fermi più alto a quello più basso per allineare i livelli di Fermi alla giunzione per stabilire l'equilibrio.

livello fermi

La funzione di Fermi-Dirac è rappresentata da una curva a forma di S che indica la probabilità che uno stato energetico sia occupato da un elettrone ad una data temperatura. Il livello di Fermi è il livello energetico al quale c'è una probabilità del 50% di trovare un elettrone, ed è posizionato tra la banda di valenza a energia più bassa e la banda di conduzione ad energia più alta.


Alla temperatura dello zero assoluto, gli elettroni riempiono tutti gli stati energetici fino al livello di Fermi, lasciando vuoti gli stati superiori. All’aumentare della temperatura, l’energia degli elettroni aumenta ed essi diventano capaci di occupare gli stati vacanti al di sopra del livello di Fermi.


Nei semiconduttori intrinseci, dove la concentrazione di elettroni e lacune è uguale, il livello di Fermi è situato al centro della banda. Ciò viene modificato quando vengono aggiunte impurità per creare semiconduttori di tipo n o di tipo p. Nei semiconduttori di tipo n, i quali presentano un eccesso di elettroni, il livello di Fermi si avvicina alla banda di conduzione. Al contrario, nei semiconduttori di tipo p, dove c’è una maggiore concentrazione di lacune, il livello di Fermi si avvicina alla banda di valenza.


L’aumento della temperatura porta un numero maggiore di elettroni a compiere il salto dalla banda di valenza a quella di conduzione, spingendo nel processo il livello di Fermi verso la banda di conduzione. Questo spostamento influisce sulla conduttività del semiconduttore.


Quando materiali con diversi livelli di Fermi entrano in contatto, gli elettroni fluiscono dalla regione con livelli di Fermi più alti a quella inferiore. Il movimento degli elettroni allinea i livelli di Fermi alla giunzione, stabilendo un equilibrio. Questo concetto gioca un ruolo cruciale nel funzionamento di numerosi componenti elettronici, consentendo la regolazione della conduttività elettrica e delle prestazioni dei dispositivi elettronici.

Livello Fermi

La funzione di Fermi-Dirac, rappresentata da una curva sigmoidea, indica la probabilità che uno stato energetico sia occupato da un elettrone in un dato ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Basics of Semiconductors

Fondamenti dei semiconduttori

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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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

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types of semiconductors

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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...

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carrier transport

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p-n junction

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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.

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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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