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

Der Ladungsträgertransport in Halbleitern erzeugt Strom durch Drift- und Diffusionsmechanismen.
Driftstrom entsteht, wenn ein externes elektrisches Feld geladene Teilchen zwischen Kollisionen beschleunigt.
Unter Berücksichtigung der Elektronen wird die zusätzliche Geschwindigkeit, die der thermischen Bewegung der Elektronen hinzugefügt wird, als Driftgeschwindigkeit bezeichnet. Sie kann erhalten werden, indem der bei Kollisionen verlorene Impuls mit dem aus dem angelegten Feld gewonnenen Impuls gleichgesetzt wird.
Der Proportionalitätsfaktor - Mobilität- charakterisiert den Elektronen- und Lochtransport aufgrund von Drift.
Die Driftstromdichten für beide Träger können als Produkt aus Ladungsdichte, Mobilität und elektrischer Feldstärke ausgedrückt werden. Die Summe dieser beiden ergibt die Gesamtdriftstromdichte. Hier gibt der Begriff in Klammern die Leitfähigkeit an.
Der Diffusionsstrom resultiert aus der zufälligen thermischen Bewegung von Ladungsträgern aus Bereichen mit hoher zu niedriger Ladungsträgerdichte.
Die Diffusionsstromdichte entspricht dem Produkt aus Ladungsträgerfluss und Proportionalitätskonstante, die Elementarladung und Diffusionskoeffizient umfasst. Sein Verhältnis zur Beweglichkeit ergibt die Einstein-Beziehung.
Liegen sowohl ein elektrisches Feld als auch ein Konzentrationsgradient vor, tragen sowohl der Drift- als auch der Diffusionsstrom zum Gesamtstrom bei.

grundlagen der halbleiter

Die Erzeugung von elektrischem Strom in Halbleitern wird grundsätzlich durch zwei Mechanismen angetrieben: Drift und Diffusion. Diese Prozesse sind für die Funktionalität und Leistung von Halbleiterbauelementen von wesentlicher Bedeutung.

Driftstrom:

Die Drift von Ladungsträgern wird durch ein externes elektrisches Feld (E) ausgelöst. Geladene Teilchen wie Elektronen und Löcher erfahren eine Beschleunigung zwischen Kollisionen mit Gitteratomen. Für Elektronen ergibt sich daraus eine Driftgeschwindigkeit (v_d), die gegeben ist durch:

<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="height: 16px;">

Wobei μ_e die Elektronenbeweglichkeit und E die elektrische Feldstärke ist.

Die Stromdichte (J) aufgrund der Drift von Elektronen (J_n) und Löchern (J_p) kann wie folgt ausgedrückt werden:

<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="height: 20px;">

Wobei q die Elementarladung ist, n und p die Konzentrationen von Elektronen bzw. Löchern und μ_n und μ_p die Beweglichkeiten von Elektronen und Löchern. Die gesamte Driftstromdichte (J_total) ist die Summe der Elektronen- und Lochstromdichten:

<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="height: 20px;">

Die Leitfähigkeit (σ) ist dann die Summe der Produkte aus Ladungsdichte und Beweglichkeit für jeden Trägertyp:

<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="height: 20px;">

Diffusionsstrom:

Diffusion tritt aufgrund der thermischen Bewegung von Trägern auf, die sich von Bereichen höherer Konzentration zu Bereichen niedrigerer Konzentration bewegen. Die Stromdichte (J_diffusion) beträgt:

<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="height: 36px;">

D_n und D_p sind die Diffusionskoeffizienten für Elektronen bzw. Löcher und dn/dx und dp/dx sind die Konzentrationsgradienten für Elektronen und Löcher.

Die Einstein-Beziehungen verknüpfen Mobilität und Diffusionskoeffizient sowohl für Elektronen als auch für Löcher:

<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="height: 36px;">

Wobei k die Boltzmann-Konstante und T die absolute Temperatur ist.

Wenn sowohl ein elektrisches Feld als auch ein Konzentrationsgradient vorhanden sind, ist die gesamte Stromdichte die Summe der Drift- und Diffusionskomponenten. In realen Anwendungen werden diese Phänomene mithilfe der Halbleitergleichungen analysiert, einer Reihe von Differentialgleichungen, die das Verhalten von Ladungsträgern in einem Halbleiter beschreiben.

Grundlagen der Halbleiter

Der Ladungsträgertransport in Halbleitern erzeugt Strom durch Drift- und Diffusionsmechanismen.
Driftstrom entsteht, wenn ein externes elektrisches Feld ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

Basics of Semiconductors

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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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