Name: valence and conduction bands in silicon
Uploaded: 2024-07-08T13:20:08.000Z
Duration: 1 min 1 s
Channel: JoVE

固体は、異なる電子配置とエネルギー準位を持つ原子で構成されています。
2つの同一の孤立した原子が互いに接近すると、それらの相互作用により、各エネルギーレベルが2つの異なるレベルに分割されます。
この分裂は、原子内の2つの電子が同時に同じエネルギー状態を占めることはできないというパウリの排他原理の結果です。
いくつかの原子が集まって固体を形成すると、エネルギー準位が分裂して連続したバンドが形成されます。平衡原子間間隔では、バンドは価電子バンドと伝導バンドに分かれます。
絶対零度の温度では、価電子バンドは電子で満たされたエネルギー準位で構成されます。
価電子帯の上には伝導帯があり、これには空いているエネルギー準位が含まれています。
これら2つのバンド間のエネルギーギャップは、バンドギャップと呼ばれます。これは、価電子帯の上部と伝導帯の下部との間のエネルギー差を表します。

半導体の基礎

Energy Bands in Solids

孤立した原子は、ボーアの原子模型でよく説明される離散的なエネルギーレベルを持っています。また、ボーアの原子模型は水素原子の電子のエネルギーを E_n として定量化します。量子数「n」が高いほど、負の値が小さくなり、電子エネルギーレベルが近くなります。

バンド形成:
固体のように原子が接近すると、隣接する原子の電子軌道が重なり合うため、これらの離散的なエネルギーレベルが分裂し始めます。この分裂は、2 つの電子が同時に同じ量子状態を占めることはできないというパウリの排他原理によって発生します。結合する原子が増えるにつれて、離散的なエネルギーレベルの数が増え、分裂が非常に細かくなり、連続したエネルギーバンドが形成されます。平衡原子間距離と呼ばれる特定のポイントで、これらのバンドは、電子で満たされた価電子帯と、絶対零度で空になる伝導帯になります。
半導体のエネルギーバンド:
シリコンのような半導体では、エネルギーバンド構造はより複雑で、14 個の電子があります。内側の 10 個の電子は深いエネルギーレベルを占め、結合には寄与しません。残りの 4 個の価電子は 3s および 3p サブシェルにあり、材料の化学的および電気的特性を決定します。シリコン原子が結晶格子を形成すると、3s および 3p サブシェルが重なり合ってバンドを形成します。結晶内の平衡距離では、これらのバンドには価電子帯の 4N 状態と伝導帯の 4N 状態が含まれます (N はシリコン原子の数)。
バンドギャップの大きさは、電子が伝導帯に励起される容易さを決定するため、非常に重要です。このバンドギャップは半導体にとって十分に小さいため、熱エネルギーまたは光によってギャップを横切って電子が励起され、電気伝導が起こります。

固体は、異なる電子配置とエネルギー準位を持つ原子で構成されています。
2つの同一の孤立した原子が互いに接近すると、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Basics of Semiconductors

KEY TERMS AND CONCEPTS

主要用語と概念

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 exclusion principle also applies, since no two electrons can share the same quantum state. As more atoms are added, the splitting becomes so small that it appears as a continuous energy band.

At the equilibrium interatomic distance, these bands form the valence band and the conduction band. The valence band is filled with electrons at this point. The conduction band is empty at absolute zero temperature. This separation helps explain why some solids conduct electricity and others do not.

Silicon shows how band formation works in a semiconductor. A silicon atom has 14 electrons, but the inner 10 electrons stay in deep energy levels and do not take part in bonding. The remaining four valence electrons, which occupy the 3s and 3p subshells, control the material’s chemical and electrical behavior. As silicon atoms arrange into a crystal lattice, the 3s and 3p subshells overlap and form bands.

In the crystal, the valence band and conduction band each contain 4N states, where N is the number of silicon atoms. The bandgap, or energy gap between the bands, is important because it controls how easily electrons can move into the conduction band. In semiconductors, this gap is small enough that thermal energy or light can excite electrons across it, which allows electrical conduction.

Valence and Conduction Bands in Silicon

energy bands in solids

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

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

Learn how atomic energy levels split into valence and conduction bands, and why silicon’s small bandgap lets heat or light drive conduction.

Valence and Conduction Bands in Silicon | 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

Valence and Conduction Bands in Silicon

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