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

Le transport de porteurs dans les semi-conducteurs génère du courant, par des mécanismes de dérive et de diffusion.
Le courant de dérive se produit lorsqu’un champ électrique externe provoque l’accélération des particules chargées entre les collisions.
En ce qui concerne les électrons, la vitesse supplémentaire ajoutée au mouvement thermique des électrons est appelée vitesse de dérive. On peut l’obtenir en égalisant la quantité de mouvement perdue lors des collisions et la quantité de mouvement obtenue à partir du champ appliqué.
Le facteur de proportionnalité - mobilité - caractérise le transport d’électrons et de trous dû à la dérive.
Les densités de courant de dérive pour les deux porteurs peuvent être exprimées comme le produit de la densité de charge, de la mobilité et de l’intensité du champ électrique. La somme de ces deux donne la densité totale du courant de dérive. Ici, le terme entre parenthèses donne la conductivité.
Le courant de diffusion résulte du mouvement thermique aléatoire des porteurs des régions à forte et à faible densité de porteuses.
La densité du courant de diffusion est égale au produit du flux porteur et de la constante de proportionnalité, qui comprend la charge élémentaire et le coefficient de diffusion. Son rapport avec la mobilité donne la relation d’Einstein.
Si un champ électrique et un gradient de concentration sont présents, le courant de dérive et le courant de diffusion contribuent tous deux au courant total.

bases des semi-conducteurs

La génération de courant électrique dans les semi-conducteurs est fondamentalement régie par deux mécanismes : la dérive et la diffusion. Ces processus sont essentiels à la fonctionnalité et aux performances des dispositifs à semi-conducteurs.
Courant de dérive:
La dérive des porteurs de charge est déclenchée par un champ électrique externe (E). Les particules chargées, telles que les électrons et les trous, subissent une accélération entre les collisions avec les atomes du réseau. Pour les électrons, cela se traduit par une vitesse de dérive (v_d) donnée par:
<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="height: 16px;">
Où μ_e est la mobilité électronique et E est l’intensité du champ électrique.
La densité de courant (J) due à la dérive des électrons (J_n) et des trous (J_p) peut être exprimée comme suit:
<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="height: 20px;">
Où q est la charge élémentaire, n et p, sont respectivement les concentrations d'électrons et de trous, et μ_n et μ_p sont les mobilités des électrons et des trous. La densité totale de courant de dérive (J_total) est la somme des densités de courant d'électrons et de trous :
<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="height: 20px;">
La conductance (σ) est alors la somme des produits de la densité de charge par la mobilité pour chaque type de porteur:
<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="height: 20px;">
Courant de diffusion:
La diffusion se produit en raison du mouvement thermique des porteurs, se déplaçant des régions de concentration plus élevée vers les régions de concentration plus faible. La densité de courant (J_diffusion) est:
<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="height: 36px;">
D_n et D_p sont respectivement les coefficients de diffusion pour les électrons et les trous, et dn/dx et dp/dx sont les gradients de concentration pour les électrons et les trous.
Les relations d'Einstein lient la mobilité et le coefficient de diffusion pour les électrons et les trous:
<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="height: 36px;">
Où k est la constante de Boltzmann et T est la température absolue.
Lorsqu'un champ électrique et un gradient de concentration sont présents, la densité de courant totale est la somme des composantes de dérive et de diffusion. Dans les applications réelles, ces phénomènes sont analysés à l'aide des équations des semi-conducteurs, un ensemble d'équations différentielles qui décrivent le comportement des porteurs de charge dans un semi-conducteur.

Bases des semi-conducteurs

Le transport de porteurs dans les semi-conducteurs génère du courant, par des mécanismes de dérive et de diffusion.
Le courant de dérive se produit lorsqu’un champ électrique externe provoque ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Basics of Semiconductors

Les bases des semi-conducteurs

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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