فجوة النطاق

هذا المقال هو عن solid state physics. إذا كنت تريد voltage control circuitry in electronics، انظر Bandgap voltage reference.

هذا المقال هو عن the electronic bandgap found in semiconductors. إذا كنت تريد the photonic band gap، انظر Photonic crystal.

Showing how electronic band structure comes about in the hypothetical example of a large number of carbon atoms being brought together to form a diamond crystal. The graph (right) shows the energy levels as a function of the spacing between atoms. When the atoms are far apart (right side of graph) each atom has valence atomic orbitals p and s which have the same energy. However when the atoms come closer together their orbitals begin to overlap. Due to Bloch's theorem which describes the hybridization of the orbitals of the N atoms in the crystal, the N atomic orbitals of equal energy split into N molecular orbitals each with a different energy. Since N is such a large number, adjacent orbitals are extremely close together in energy so the orbitals can be considered a continuous energy band. a is the atomic spacing in an actual crystal of diamond. At that spacing the orbitals form two bands, called the valence and conduction bands, with a 5.5 eV band gap between them. At room temperature, very few electrons have the thermal energy to surmount this wide energy gap and become conduction electrons, so diamond is an insulator. An analogous treatment of silicon with the same crystal structure yields a much smaller band gap of 1.1 eV making silicon a semiconductor.

فرجة الطاقة أو فجوة النطاق بالإنجليزية: Band gap أو فجوة الطاقة عبارة عن مجال طاقي في الجسم الصلب لا يمكن للإلكترونات فيه أن توجد. بالنظر إلى مخططات تركيب النطاق الإلكتروني للأجسام الصلبة نجد أن فجوة النطاق تمثل الفرق الطاقي، والذي غالباً ما يعبر عنه بالإلكترون فولت eV، بين أعلى نطاق التكافؤ وأسفل نطاق التوصيل. تبرز خاصة فجوة النطاق في العوازل وأشباه الموصلات حيث تحدد قيمة الفجوة الكثير من الخصائص البصرية والكهربائية للجسم الصلب، أما في الموصلات الكهربائية فإن نطاقي التكافؤ والتوصيل متداخلان، لذلك ليس لديها فجوة نطاق.

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 في فيزياء أشباه الموصلات

تمثيل لفجوة النطاق في مخطط تركيب النطاق لشبه موصل.

Every solid has its own characteristic energy-band structure. This variation in band structure is responsible for the wide range of electrical characteristics observed in various materials. Depending on the dimension, the band structure and spectroscopy can vary. The different types of dimensions are as listed: one dimension, two dimensions, and three dimensions.

In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden from other regions because there are no allowable electronic states for them to occupy. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band. Electrons are able to jump from one band to another. However, in order for a valence band electron to be promoted to the conduction band, it requires a specific minimum amount of energy for the transition. This required energy is an intrinsic characteristic of the solid material. Electrons can gain enough energy to jump to the conduction band by absorbing either a phonon (heat) or a photon (light).

A semiconductor is a material with an intermediate-sized, non-zero band gap that behaves as an insulator at T=0K, but allows thermal excitation of electrons into its conduction band at temperatures that are below its melting point. In contrast, a material with a large band gap is an insulator. In conductors, the valence and conduction bands may overlap, so there is no longer a bandgap with forbidden regions of electronic states.

The conductivity of intrinsic semiconductors is strongly dependent on the band gap. The only available charge carriers for conduction are the electrons that have enough thermal energy to be excited across the band gap and the electron holes that are left off when such an excitation occurs.

Band-gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor alloys, such as GaAlAs, InGaAs, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like molecular-beam epitaxy. These methods are exploited in the design of heterojunction bipolar transistors (HBTs), laser diodes and solar cells.

The distinction between semiconductors and insulators is a matter of convention. One approach is to think of semiconductors as a type of insulator with a narrow band gap. Insulators with a larger band gap, usually greater than 4 eV, are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions. Electron mobility also plays a role in determining a material's informal classification.

The band-gap energy of semiconductors tends to decrease with increasing temperature. When temperature increases, the amplitude of atomic vibrations increase, leading to larger interatomic spacing. The interaction between the lattice phonons and the free electrons and holes will also affect the band gap to a smaller extent.

 التفسير الرياضي

Classically, the ratio of probabilities that two states with an energy difference ΔE will be occupied by an electron is given by the Boltzmann factor:

$e^{\left({\frac {-\Delta E}{kT}}\right)}$

where:

• ΔE فرق الطاقة
• k is ثابت بولتسمان
• T is درجة الحرارة.

At the Fermi level (or chemical potential), the probability of a state being occupied is ½. If the Fermi level is in the middle of a band gap of 1 eV, this ratio is e⁻²⁰ or about 2.0⋅10⁻⁹ at the room-temperature thermal energy of 25.9 meV.

The relationship between band gap energy and temperature can be described by Varshni's empirical expression (named after Y. P. Varshni),

$E_{g}(T)=E_{g}(0)-{\frac {\alpha T^{2}}{T+\beta }}$, where E_g(0), α and β are material constants.

Furthermore, lattice vibrations increase with temperature, which increases the effect of electron scattering. Additionally, the number of charge carriers within a semiconductor will increase, as more carriers have the energy required to cross the band-gap threshold and so conductivity of semiconductors also increases with increasing temperature.

In a regular semiconductor crystal, the band gap is fixed owing to continuous energy states. In a quantum dot crystal, the band gap is size dependent and can be altered to produce a range of energies between the valence band and conduction band. It is also known as quantum confinement effect.

Band gaps also depend on pressure. Band gaps can be either direct or indirect, depending on the electronic band structure of the material.

It was mentioned earlier that the dimensions have different band structure and spectroscopy. For non-metallic solids, which are one dimensional, have optical properties that are dependent on the electronic transitions between valence and conduction bands. In addition, the spectroscopic transition probability is between the initial and final orbital and it depends on the integral. φ_i is the initial orbital, φ_f is the final orbital, ʃ φ_f^*ûεφ_i is the integral, ε is the electric vector, and u is the dipole moment.

Two-dimensional structures of solids behave because of the overlap of atomic orbitals. The simplest two-dimensional crystal contains identical atoms arranged on a square lattice. Energy splitting occurs at the Brillouin zone edge for one-dimensional situations because of a weak periodic potential, which produces a gap between bands. The behavior of the one-dimensional situations does not occur for two-dimensional cases because there are extra freedoms of motion. Furthermore, a bandgap can be produced with strong periodic potential for two-dimensional and three-dimensional cases.

 Direct and indirect band gap

المقالة الرئيسية: Direct and indirect bandgaps

Based on the their band structure, materials are characterised with a direct band gap or indirect band gap. In the free-electron model, k is the momentum of a free electron and assumes unique values within the Brillouin zone that outlines the periodicity of the crystal lattice. If the momentum of the lowest energy state in the conduction band and the highest energy state of the valence band of a material have the same value, then the material has a direct bandgap. If they are not the same, then the material has an indirect band gap and the electronic transition must undergo momentum transfer to satisfy conservation. Such indirect "forbidden" transitions still occur, however at very low probabilities and weaker energy. For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In contrast, for materials with an indirect band gap, a photon and phonon must both be involved in a transition from the valence band top to the conduction band bottom, involving a momentum change. Therefore, direct bandgap materials tend to have stronger light emission and absorption properties and tend to be better suited for photovoltaics (PVs), light-emitting diodes (LEDs), and laser diodes; however, indirect bandgap materials are frequently used in PVs and LEDs when the materials have other favorable properties.

 Light-emitting diodes and laser diodes

المقالة الرئيسية: Light-emitting diode

LEDs and laser diodes usually emit photons with energy close to and slightly larger than the band gap of the semiconductor material from which they are made. Therefore, as the band gap energy increases, the LED or laser color changes from infrared to red, through the rainbow to violet, then to UV.

 الخلايا الكهروضوئية

المقالة الرئيسية: Solar cell

The Shockley–Queisser limit gives the maximum possible efficiency of a single-junction solar cell under un-concentrated sunlight, as a function of the semiconductor band gap. If the band gap is too high, most daylight photons cannot be absorbed; if it is too low, then most photons have much more energy than necessary to excite electrons across the band gap, and the rest is wasted. The semiconductors commonly used in commercial solar cells have band gaps near the peak of this curve, for example silicon (1.1eV) or CdTe (1.5eV). The Shockley–Queisser limit has been exceeded experimentally by combining materials with different band gap energies to make tandem solar cells.

The optical band gap (see below) determines what portion of the solar spectrum a photovoltaic cell absorbs. A semiconductor will not absorb photons of energy less than the band gap; and the energy of the electron-hole pair produced by a photon is equal to the bandgap energy. A luminescent solar converter uses a luminescent medium to downconvert photons with energies above the band gap to photon energies closer to the band gap of the semiconductor comprising the solar cell.

 أمثلة لفجوات النطاق

المادة	الرمز	فجوة النطاق(eV) عند 302K	المرجع
سيليكون	Si	1.11
سلنيوم	Se	1.74
جرمانيوم	Ge	0.67
كربيد السيليكون	SiC	2.86
فوسفيد الألومنيوم	AlP	2.45
زرنيخيد الألومنيوم	AlAs	2.16
إثميد الألومنيوم	AlSb	1.6
نيتريد الألومنيوم	AlN	6.3
ألماس	C	5.5
فوسفيد الگاليوم الثلاثي	GaP	2.26
زرنيخيد الگاليوم الثلاثي	GaAs	1.43
نيتريد الگاليوم الثلاثي	GaN	3.4
كبريتيد الگاليوم الثنائي	GaS	2.5
إثميد الغاليوم	GaSb	0.7
نيتريد الإنديوم الثلاثي	InN	0.7
فوسفيد الإنديوم الثلاثي	InP	1.35
زرنيخيد الإنديوم الثلاثي	InAs	0.36
أكسيد الزنك	ZnO	3.37
كبريتيد الزنك	ZnS	3.6
سيلينيد الزنك	ZnSe	2.7
تيلوريد الزنك	ZnTe	2.25
كبريتيد الكادميوم	CdS	2.42
سلنيد الكادميوم	CdSe	1.73
تيلوريد الكادميوم	CdTe	1.49
كبريتيد الرصاص الثنائي	PbS	0.37
سيلينيد الرصاص الثنائي	PbSe	0.27
تيلوريد الرصاص الثنائي	PbTe	0.29
أكسيد النحاس الثنائي	CuO	1.2
أكسيد النحاس الأحادي	Cu2O	2.1

 فجوة النطاق البصرية مقابل الإلكترونية

In materials with a large exciton binding energy, it is possible for a photon to have just barely enough energy to create an exciton (bound electron–hole pair), but not enough energy to separate the electron and hole (which are electrically attracted to each other). In this situation, there is a distinction between "optical band gap" and "electronic band gap" (or "transport gap"). The optical bandgap is the threshold for photons to be absorbed, while the transport gap is the threshold for creating an electron–hole pair that is not bound together. The optical bandgap is at lower energy than the transport gap.

In almost all inorganic semiconductors, such as silicon, gallium arsenide, etc., there is very little interaction between electrons and holes (very small exciton binding energy), and therefore the optical and electronic bandgap are essentially identical, and the distinction between them is ignored. However, in some systems, including organic semiconductors and single-walled carbon nanotubes, the distinction may be significant.

 فجوات النطاق لأشباه الجسيمات الأخرى

In photonics, band gaps or stop bands are ranges of photon frequencies where, if tunneling effects are neglected, no photons can be transmitted through a material. A material exhibiting this behaviour is known as a photonic crystal. The concept of hyperuniformity has broadened the range of photonic band gap materials, beyond photonic crystals. By applying the technique in supersymmetric quantum mechanics, a new class of optical disordered materials has been suggested, which support band gaps perfectly equivalent to those of crystals or quasicrystals.

Similar physics applies to phonons in a phononic crystal.

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 المواد

• Aluminium gallium arsenide
• نيتريد البورون
• Indium gallium arsenide
• زرنيخيد الإنديوم
• زرنيخيد الگاليوم
• نيتريد الگاليوم
• جرمانيوم
• هيدروجين فلزي

 قائمة موضوعات الإلكترونيات

• إلكترونيات
• Bandgap voltage reference
• Condensed matter physics
• Direct and indirect bandgaps
• Electrical conduction
• Electron hole
• Field-effect transistor
• Photodiode
• Photoresistor
• Photovoltaics
• Solar cell
• Solid state physics
• Semiconductor
• Semiconductor devices
• Strongly correlated material
• Valence band

 انظر أيضاً

• Wide bandgap semiconductors
• Band bending
• Spectral density
• Pseudogap

 وصلات خارجية

• Direct Band Gap Energy Calculator
• Moriarty, Philip. "Energy Gap (and what makes glass transparent?)". Sixty Symbols. Brady Haran for the University of Nottingham.