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

O transporte de portadores em semicondutores gera corrente, por meio de mecanismos de deriva e difusão.
A corrente de deriva surge quando um campo elétrico externo faz com que partículas carregadas acelerem entre as colisões.
Considerando os elétrons, a velocidade adicional adicionada ao movimento térmico dos elétrons é chamada de velocidade de deriva. Pode ser obtido igualando o momento perdido durante as colisões e o momento ganho com o campo aplicado.
O fator de proporcionalidade - mobilidade - caracteriza o transporte de elétrons e buracos devido à deriva.
As densidades de corrente de deriva para ambas as portadoras podem ser expressas como o produto da densidade de carga, mobilidade e intensidade do campo elétrico. A soma desses dois fornece a densidade total da corrente de deriva. Aqui, o termo entre parênteses fornece condutividade.
A corrente de difusão resulta do movimento térmico aleatório de portadoras de regiões de alta a baixa densidade de portadoras.
A densidade da corrente de difusão é igual ao produto do fluxo portador e da constante de proporcionalidade, que inclui carga elementar e coeficiente de difusão. Sua relação com a mobilidade dá a relação de Einstein.
Se um campo elétrico e um gradiente de concentração estiverem presentes, tanto a corrente de deriva quanto a de difusão contribuem para a corrente total.

 noções básicas de semicondutores

A geração de corrente elétrica em semicondutores é fundamentalmente impulsionada por dois mecanismos: deriva e difusão. Esses processos são essenciais para a funcionalidade e desempenho de dispositivos baseados em semicondutores.
Corrente de deriva:
A deriva dos portadores de carga é iniciada por um campo elétrico externo (E). Partículas carregadas, como elétrons e buracos, experimentam uma aceleração entre colisões com átomos da rede. Para elétrons, isso resulta em uma velocidade de deriva (v_d) dada por:
<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="height: 16px;">
Onde μ_e é a mobilidade dos elétrons e E é a intensidade do campo elétrico.
A densidade de corrente (J) devido à deriva para elétrons (J_n) e buracos (J_p) pode ser expressa como:
<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="height: 20px;">
Onde q é a carga elementar, n e p são as concentrações de elétrons e buracos, respectivamente, e μ_n e μ_p são as mobilidades de elétrons e buracos. A densidade total de corrente de deriva (J_total) é a soma das densidades de corrente de elétrons e buracos:
<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="height: 20px;">
 A condutância (σ) é então a soma dos produtos da densidade de carga e mobilidade para cada tipo de portadora:
<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="height: 20px;">
Corrente de difusão:
 A difusão ocorre devido ao movimento térmico dos transportadores, passando de regiões de maior concentração para regiões de menor concentração. A densidade de corrente (J_difusão) é:
<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="height: 36px;">
D_n e D_p são os coeficientes de difusão para elétrons e lacunas, respectivamente, e dn/dx e dp/dx são os gradientes de concentração para elétrons e lacunas.
As relações de Einstein ligam a mobilidade e o coeficiente de difusão para elétrons e buracos:
<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="height: 36px;">
 Onde k é a constante de Boltzmann e T é a temperatura absoluta.
Quando um campo elétrico e um gradiente de concentração estão presentes, a densidade total de corrente é a soma dos componentes de deriva e difusão. Em aplicações do mundo real, esses fenômenos são analisados ​​utilizando as equações de semicondutores, um conjunto de equações diferenciais que descrevem o comportamento dos portadores de carga em um semicondutor.

 Noções básicas de semicondutores

O transporte de portadores em semicondutores gera corrente, por meio de mecanismos de deriva e difusão.
A corrente de deriva surge quando um campo elétrico externo causa ...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Basics of Semiconductors

Fundamentos de Semicondutores

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

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

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metal-semiconductor junctions

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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

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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