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

يولد نقل الموجة الحاملة في أشباه الموصلات تيارا من خلال آليات الانجراف والانتشار.
ينشأ تيار الانجراف عندما يتسبب مجال كهربائي خارجي في تسارع الجسيمات المشحونة بين الاصطدامات.
بالنظر إلى الإلكترونات ، فإن السرعة الإضافية المضافة إلى الحركة الحرارية للإلكترونات تسمى سرعة الانجراف. يمكن الحصول عليها عن طريق مساواة الزخم المفقود أثناء الاصطدامات والزخم المكتسب من المجال المطبق.
يميز عامل التناسب - التنقل - نقل الإلكترون والثقب بسبب الانجراف.
يمكن التعبير عن كثافة تيار الانجراف لكلا الموجات الحاملة على أنها نتاج كثافة الشحنة والتنقل وشدة المجال الكهربائي. مجموع هذين الاثنين يعطي كثافة تيار الانجراف الإجمالية. هنا ، يعطي المصطلح الموجود بين قوسين الموصلية.
ينتج تيار الانتشار عن الحركة الحرارية العشوائية للناقلات من مناطق الكثافة الحاملة العالية إلى المنخفضة.
تساوي كثافة تيار الانتشار ناتج تدفق الموجة الحاملة وثابت التناسب ، والذي يتضمن الشحنة الأولية ومعامل الانتشار. نسبته مع التنقل يعطي علاقة أينشتاين.
إذا كان كل من المجال الكهربائي وتدرج التركيز موجودا ، فإن كل من تيار الانجراف والانتشار يساهمان في التيار الكلي.

أساسيات أشباه الموصلات

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يتم توليد التيار الكهربائي في أشباه الموصلات بشكل أساسي بواسطة آليتين: الانجراف والانتشار. تعتبر هذه العمليات ضرورية لوظيفة وأداء الأجهزة القائمة على أشباه الموصلات.


الانجراف الحالي:


يبدأ انجراف حاملات الشحنة بواسطة مجال كهربائي خارجي (E). تتعرض الجسيمات المشحونة، مثل الإلكترونات والثقوب، لتسارع بين الاصطدامات مع ذرات الشبكة. بالنسبة للإلكترونات، يؤدي ذلك إلى سرعة الانجراف (v_d) التي تعطى بواسطة:


<img alt="Equation 1" src="/files/ftp_upload/15155/15155_Equation_1.svg" style="height: 16px;">

حيث μ_e هي حركة الإلكترون و E هي شدة المجال الكهربائي.


يمكن التعبير عن كثافة التيار (J) الناتجة عن انجراف الإلكترونات (J_n) والثقوب (J_p) على النحو التالي:


<img alt="Equation 2" src="/files/ftp_upload/15155/15155_Equation_2.svg" style="height: 20px;">

حيث q هي الشحنة الأولية، وn وp هما تركيزات الإلكترونات والثقوب، على التوالي، وμn وμp هما حركية الإلكترونات والثقوب. إجمالي كثافة تيار الانجراف (J_total) هو مجموع كثافات الإلكترون وتيار الثقب:


<img alt="Equation 3" src="/files/ftp_upload/15155/15155_Equation_3.svg" style="height: 20px;">

 إن التوصيل (σ) هو إذن مجموع منتجات كثافة الشحنة والتنقل لكل نوع من أنواع الموجات الحاملة:


<img alt="Equation 4" src="/files/ftp_upload/15155/15155_Equation_4.svg" style="height: 20px;">

الانتشار الحالي:


 يحدث الانتشار نتيجة للحركة الحرارية للحاملات، التي تنتقل من مناطق ذات تركيز أعلى إلى مناطق ذات تركيز أقل. الكثافة الحالية (J_diffusion) هي:


<img alt="Equation 5" src="/files/ftp_upload/15155/15155_Equation_5.svg" style="height: 36px;">

D_n وD_p هما معاملا الانتشار للإلكترونات والثقوب، على التوالي، وdn/dx وdp/dx هما تدرج التركيز للإلكترونات والثقوب.


تربط علاقات أينشتاين بين معامل الحركة والانتشار لكل من الإلكترونات والثقوب:


<img alt="Equation 6" src="/files/ftp_upload/15155/15155_Equation_6.svg" style="height: 36px;">

 حيث k هو ثابت بولتزمان، وT هي درجة الحرارة المطلقة.


عند وجود كل من المجال الكهربائي وتدرج التركيز، تكون كثافة التيار الإجمالية هي مجموع مكونات الانجراف والانتشار. في تطبيقات العالم الحقيقي، يتم تحليل هذه الظواهر باستخدام معادلات أشباه الموصلات، وهي مجموعة من المعادلات التفاضلية التي تصف سلوك حاملات الشحنة في أشباه الموصلات.


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يولد نقل الموجة الحاملة في أشباه الموصلات تيارا من خلال آليات الانجراف والانتشار.
ينشأ تيار الانجراف عندما يتسبب مجال كهربائي خارجي في ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Basics of Semiconductors

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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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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

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Semiconductor Charge Carriers: Creation and Loss

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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

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

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electrical engineering

Drift and Diffusion in Semiconductors

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