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

Die Fermi-Dirac-Funktion, dargestellt durch eine Sigmoidkurve, gibt die Wahrscheinlichkeit an, dass ein Energiezustand bei einer bestimmten Temperatur von einem Elektron besetzt wird.
Das Fermi-Niveau stellt den Energiezustand mit einer Belegungswahrscheinlichkeit von 50 Prozent dar und liegt zwischen dem Valenz- und dem Leitungsband.
Am absoluten Nullpunkt sind die Energiezustände bis zum Fermi-Niveau gefüllt, während die darüber liegenden leer sind. Bei höheren Temperaturen können Zustände oberhalb des Fermi-Niveaus gefüllt werden.
In intrinsischen Halbleitern bedeuten gleiche Konzentrationen von Löchern und Elektronen, dass das Fermi-Niveau in der Mitte der Bandlücke liegt.
In n-Typ-Halbleitern verschiebt eine höhere Elektronenkonzentration das Fermi-Niveau in die Nähe des Leitungsbandes.
In p-Typ-Halbleitern liegt das Fermi-Niveau aufgrund einer höheren Lochkonzentration in der Nähe des Valenzbandes.
Mit steigender Temperatur gehen mehr Elektronen vom Valenz- in das Leitungsband über, wodurch das Fermi-Niveau näher an das Leitungsband heranrückt.
Wenn sich Materialien mit unterschiedlichen Fermi-Niveaus verbinden, fließen Elektronen vom höheren Fermi-Niveau zum niedrigeren, um die Fermi-Niveaus an der Verbindungsstelle auszurichten und ein Gleichgewicht herzustellen.

fermi-niveau

Die Fermi-Dirac-Funktion wird durch eine S-förmige Kurve dargestellt, die die Wahrscheinlichkeit angibt, dass ein Energiezustand bei einer bestimmten Temperatur von einem Elektron besetzt wird. Das Fermi-Niveau ist das Energieniveau, bei dem eine 50-prozentige Chance besteht, ein Elektron zu finden, und es liegt zwischen dem Valenzband mit niedrigerer Energie und dem Leitungsband mit höherer Energie.

Bei der absoluten Nulltemperatur füllen Elektronen alle Energiezustände bis zum Fermi-Niveau und lassen die oberen Zustände leer. Mit steigender Temperatur nimmt die Energie der Elektronen zu und sie können die freien Zustände über dem Fermi-Niveau besetzen.

In intrinsischen Halbleitern, bei denen die Konzentration von Elektronen und Löchern gleich ist, befindet sich das Fermi-Niveau in der Mitte der Bandlücke. Dies ändert sich, wenn Verunreinigungen hinzugefügt werden, um entweder n-Typ- oder p-Typ-Halbleiter zu erzeugen. In n-Typ-Halbleitern mit einem Überschuss an Elektronen verschiebt sich das Fermi-Niveau näher an das Leitungsband. Umgekehrt bewegt sich das Fermi-Niveau in p-Typ-Halbleitern, in denen eine höhere Konzentration von Löchern vorliegt, näher an das Valenzband.

Der Temperaturanstieg führt dazu, dass mehr Elektronen den Sprung vom Valenzband zum Leitungsband schaffen und dabei das Fermi-Niveau in Richtung des Leitungsbands verschieben. Diese Verschiebung beeinflusst die Leitfähigkeit des Halbleiters.

Wenn Materialien mit unterschiedlichen Fermi-Niveaus in Kontakt kommen, fließen Elektronen aus dem Bereich der höheren Fermi-Niveaus in den Bereich der niedrigeren. Die Bewegung der Elektronen richtet die Fermi-Niveaus an der Verbindungsstelle aus und stellt ein Gleichgewicht her. Dieses Konzept spielt eine entscheidende Rolle beim Betrieb zahlreicher elektronischer Komponenten und ermöglicht die Regulierung und Anpassung der elektrischen Leitfähigkeit und der Leistung elektronischer Geräte.

Fermi-Niveau

Die Fermi-Dirac-Funktion, dargestellt durch eine Sigmoidkurve, gibt die Wahrscheinlichkeit an, dass ein Energiezustand von einem Elektron bei einem gegebenen ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

Basics of Semiconductors

Grundlagen der Halbleiter

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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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semiconductors

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types of semiconductors

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p-n junction

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biasing of p-n junction

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metal-semiconductor junctions

Schottky and Ohmic Metal Contacts

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biasing of metal-semiconductor junctions

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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

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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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