Name: fermi level in semiconductors
Uploaded: 2024-07-08T13:20:09.000Z
Duration: 1 min 18 s
Channel: JoVE

シグモイド曲線で表されるフェルミ・ディラック関数は、特定の温度でエネルギー状態が電子によって占められる確率を示します。
フェルミ準位は、50%の占有確率でエネルギー状態を表し、価電子帯と伝導帯の間にあります。
絶対零度では、フェルミ準位までのエネルギー状態は満たされ、それ以上のエネルギー状態は空です。より高い温度では、フェルミ準位より上の状態が満たされる可能性があります。
固有半導体では、正孔と電子の濃度が等しいということは、フェルミ準位がバンドギャップの中央にあることを意味します。
n型半導体では、電子濃度が高いほど、フェルミ準位が伝導帯の近くにシフトします。
p型半導体では、正孔濃度が高いため、フェルミ準位は価電子帯の近くにあります。
温度が上昇すると、より多くの電子が価電子から伝導帯に遷移し、フェルミ準位が伝導帯に近づきます。
フェルミ準位の異なる材料が結合すると、電子は高いフェルミ準位から低いフェルミ準位に流れ、接合部でフェルミ準位を整列させて平衡を確立します。

フェルミ準位

フェルミ・ディラック分布関数は、特定の温度で電子が占めるエネルギー状態の確率を示す S 字型の曲線で表されます。フェルミ準位は、電子が見つかる確率が 50% のエネルギー準位で、低エネルギー価電子帯と高エネルギー伝導帯の間にあります。

絶対零度では、電子はフェルミ準位までのすべてのエネルギー状態を満たし、上位の状態は空のままです。温度が上昇すると、電子のエネルギーが増加し、フェルミ準位より上の空の状態を占有できるようになります。

電子と正孔の濃度が等しい真性半導体では、フェルミ準位はバンドギャップの中央にあります。不純物を追加して n 型または p 型の半導体を作成すると、この状態は変化します。電子が過剰である n 型半導体では、フェルミ準位は伝導帯に近づきます。逆に、正孔の濃度が高い p 型半導体では、フェルミ準位は価電子帯に近づきます。

温度が上昇すると、価電子帯から伝導帯に移動する電子の数が増え、その過程でフェルミ準位が伝導帯に近づきます。この変化は半導体の伝導性に影響します。

フェルミ準位に異なる材料が接触すると、電子はフェルミ準位の高い領域から低い領域に流れます。電子の動きによって接合部のフェルミ準位が整列し、平衡が確立されます。この概念は、多数の電子部品の動作において重要な役割を果たし、電気伝導性と電子機器の性能の調整を可能にします。

シグモイド曲線で表されるフェルミ・ディラック関数は、特定の...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Basics of Semiconductors

半導体の基礎

KEY TERMS AND CONCEPTS

主要用語と概念

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 intrinsic semiconductor, the number of electrons equals the number of holes. A hole is the missing electron state left in the valence band. In this case, the Fermi level lies near the middle of the band gap. Adding impurities changes this balance and creates n-type or p-type semiconductors.

In an n-type semiconductor, extra electrons shift the Fermi level closer to the conduction band. In a p-type semiconductor, a higher number of holes moves the Fermi level closer to the valence band. Higher temperature also lets more electrons jump from the valence band to the conduction band, which nudges the Fermi level toward the conduction band and changes conductivity.

When materials with different Fermi levels touch, electrons flow from the region with the higher Fermi level to the region with the lower one. This movement continues until the Fermi levels align at the junction. The resulting equilibrium is important for many electronic components because it helps control electrical conductivity and device performance.

Fermi Level 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 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...

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

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

Learn how the Fermi level changes with temperature, doping, and semiconductor type, and how it affects electron flow, equilibrium, and conductivity.

Fermi Level in Semiconductors | JoVE K12

JoVE Core 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Fermi Level in Semiconductors

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