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

Il trasporto del vettore nei semiconduttori genera corrente, attraverso meccanismi di deriva e diffusione.
La corrente di deriva si verifica quando un campo elettrico esterno provoca l'accelerazione delle particelle cariche tra le collisioni.
Considerando gli elettroni, la velocità aggiuntiva aggiunta al movimento termico degli elettroni è chiamata velocità di deriva. Può essere ottenuto equiparando la quantità di moto persa durante le collisioni e la quantità di moto ottenuta dal campo applicato.
Il fattore di proporzionalità - mobilità - caratterizza il trasporto di elettroni e lacune dovuto alla deriva.
Le densità di corrente di deriva per entrambe le portanti possono essere espresse come il prodotto della densità di carica, della mobilità e dell'intensità del campo elettrico. La somma di questi due fornisce la densità totale della corrente di deriva. Qui, il termine tra parentesi dà conduttività.
La corrente di diffusione deriva dal movimento termico casuale dei portatori dalle regioni ad alta e bassa densità di portanti.
La densità della corrente di diffusione è uguale al prodotto del flusso portante e della costante di proporzionalità, che include la carica elementare e il coefficiente di diffusione. Il suo rapporto con la mobilità dà la relazione di Einstein.
Se sono presenti sia un campo elettrico che un gradiente di concentrazione, sia la corrente di deriva che quella di diffusione contribuiscono alla corrente totale.

nozioni di base sui semiconduttori

La generazione di corrente elettrica nei semiconduttori è fondamentalmente guidata da due meccanismi: deriva e diffusione. Questi processi sono essenziali per la funzionalità e le prestazioni dei dispositivi basati su semiconduttori.

Corrente di deriva:

La deriva dei portatori di carica viene avviata da un campo elettrico esterno (E). Le particelle cariche, come elettroni e lacune, subiscono un'accelerazione tra le collisioni con gli atomi del reticolo. Per gli elettroni, ciò si traduce in una velocità di deriva (vd) data da:

<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="height: 16px;">

Dove μe è la mobilità degli elettroni ed E è l'intensità del campo elettrico.

La densità di corrente (J) dovuta alla deriva degli elettroni (Jn) e delle lacune (Jp) può essere espressa come:

<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="height: 20px;">

Dove q è la carica elementare, n e p sono rispettivamente le concentrazioni di elettroni e lacune, e μn e μp sono le mobilità di elettroni e lacune. La densità di corrente di deriva totale (Jtotal) è la somma delle densità di corrente di elettroni e lacune:

<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="height: 20px;">

La conduttanza (σ) è quindi la somma dei prodotti di densità di carica, mobilità per ciascun tipo di portatore:

<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="height: 20px;">

Corrente di diffusione:

La diffusione avviene a causa del movimento termico dei portatori, che si spostano da regioni a concentrazione maggiore a regioni a concentrazione minore. La densità di corrente (Jdiffusion) è:

<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="height: 36px;">

Dn e Dp sono i coefficienti di diffusione rispettivamente per elettroni e lacune, e dn/dx e dp/dx sono i gradienti di concentrazione per elettroni e lacune.

Le relazioni di Einstein collegano la mobilità e il coefficiente di diffusione, sia degli elettroni che delle lacune:

<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="height: 36px;">

Dove k è la costante di Boltzmann e T è la temperatura assoluta.

Quando sono presenti sia un campo elettrico che un gradiente di concentrazione, la densità di corrente totale è la somma delle componenti di deriva e diffusione. Nelle applicazioni del mondo reale, questi fenomeni vengono analizzati utilizzando le equazioni dei semiconduttori, un insieme di equazioni differenziali che descrivono il comportamento dei portatori di carica in un semiconduttore.

Nozioni di Base sui Semiconduttori

Il trasporto del vettore nei semiconduttori genera corrente, attraverso meccanismi di deriva e diffusione.
La corrente di deriva si verifica quando un campo elettrico esterno provoca ...

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

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

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semiconductors

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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

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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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