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

Transport nośników w półprzewodnikach generuje prąd poprzez mechanizmy dryfu i dyfuzji.
Prąd dryfu powstaje, gdy zewnętrzne pole elektryczne powoduje przyspieszenie naładowanych cząstek między zderzeniami.
Biorąc pod uwagę elektrony, dodatkowa prędkość dodana do ruchu termicznego elektronów nazywana jest prędkością dryfu. Można go uzyskać, zrównując pęd utracony podczas zderzeń z pędem uzyskanym z przyłożonego pola.
Współczynnik proporcjonalności - ruchliwość - charakteryzuje transport elektronów i w wyniku dryfu.
Gęstości prądu dryftu dla obu nośników można wyrazić jako iloczyn gęstości ładunku, ruchliwości i natężenia pola elektrycznego. Suma tych dwóch daje całkowitą gęstość prądu dryftu. Tutaj termin w nawiasach podaje przewodność.
Prąd dyfuzyjny wynika z losowego ruchu termicznego nośników z obszarów o wysokiej i niskiej gęstości nośników.
Gęstość prądu dyfuzyjnego jest równa iloczynowi strumienia nośnego i stałej proporcjonalności, która obejmuje ładunek elementarny i współczynnik dyfuzji. Jego stosunek do ruchliwości daje relację Einsteina.
Jeśli występuje zarówno pole elektryczne, jak i gradient stężenia, zarówno dryft, jak i prąd dyfuzyjny przyczyniają się do całkowitego prądu.

podstawy półprzewodników

Generowanie prądu elektrycznego w półprzewodnikach jest zasadniczo napędzane przez dwa mechanizmy: dryf i dyfuzję. Procesy te są niezbędne dla funkcjonalności i wydajności urządzeń półprzewodnikowych.

Prąd dryfu:

Dryf nośników ładunku inicjowany jest przez zewnętrzne pole elektryczne (E). Naładowane cząstki, takie jak elektrony i dziury, doświadczają przyspieszenia pomiędzy zderzeniami z atomami sieci. W przypadku elektronów skutkuje to prędkością dryfu (v_d) określoną wzorem:

<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="height: 16px;">

Gdzie μ_e to ruchliwość elektronów, a E to natężenie pola elektrycznego.

Gęstość prądu (J) wynikającą z dryfu elektronów (J_n) i dziur (J_p) można wyrazić jako:

<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="height: 20px;">

Gdzie q to ładunek elementarny, n i p to odpowiednio koncentracja elektronów i dziur, a μ_n i μ_p to ruchliwość elektronów i dziur. Całkowita gęstość prądu dryfu (J_total) jest sumą gęstości prądu elektronów i dziur:

<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="height: 20px;">

Przewodność (σ) jest wówczas sumą iloczynów gęstości ładunku i ruchliwości dla każdego typu nośnika:

<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="height: 20px;">

Prąd dyfuzyjny:

 Dyfuzja zachodzi w wyniku ruchu termicznego nośników przemieszczających się z obszarów o wyższym stężeniu do obszarów o niższym stężeniu. Gęstość prądu (J_diffusion) wynosi:

<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="height: 36px;">

D_n i D_p to współczynniki dyfuzji, odpowiednio, elektronów i dziur, a dn/dx i dp/dx to gradienty stężeń elektronów i dziur.

Relacje Einsteina łączą ruchliwość i współczynnik dyfuzji zarówno dla elektronów, jak i dziur:

<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="height: 36px;">

Gdzie k jest stałą Boltzmanna, a T jest temperaturą bezwzględną.

Gdy występuje zarówno pole elektryczne, jak i gradient stężeń, całkowita gęstość prądu jest sumą składników dryfu i dyfuzji. W zastosowaniach rzeczywistych zjawiska te analizuje się za pomocą równań półprzewodnika – zestawu równań różniczkowych opisujących zachowanie nośników ładunku w półprzewodniku.

Podstawy półprzewodników

Transport nośników w półprzewodnikach generuje prąd poprzez mechanizmy dryfu i dyfuzji.
Prąd dryfu powstaje, gdy zewnętrzne pole elektryczne powoduje ...

Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

Basics of Semiconductors

KEY TERMS AND CONCEPTS

KLUCZOWE TERMINY I POJĘCIA

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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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

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biasing of p-n junction

P-N Junction Diode Under Bias

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biasing of metal-semiconductor junctions

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fermi level

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Vacuum Level and Schottky Barriers

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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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