半导体材料

半导体

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在纯硅中掺入少许的硼（最外层有三个电子），就反而少了一个电子，而形成一个电洞（hole），这样就形成P型半导体少了一个带负电荷的电子，可视为多了一个正电荷）。

目录

[隐藏]

?1概观

?2半导体的能带结构

o 2.1能量-动量色散

?3载子的产生与复合

?4半导体的掺杂

o 4.1掺杂物

o 4.2载子浓度

o 4.3掺杂对半导体能带结构的影响

?5半导体材料的制造

?6应用

?7延伸阅读

o7.1材料

o7.2物理学

o7.3工业

?8参考资料

?9相关条目

?10外部链接

o10.1半导体行业网站

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Diamantstruktur Diamantstruktur Zinkblendestruktur (Elementarzelle)

（Pauli exclusion principle），同一个量子态内不能有两个电子，已经被填满的能带无法导电，因为该能带内的所有量子态都已经被电子占据，所以半导体材料的传导带不会被电子占满，让电子可以在其中的量子态间移动。

费米-狄拉克分布。

在价带内的电子获得能量后便可跃升到传导带，而这便会在价带内留下一个空缺，也就是所谓的“电洞”（electron holes）。传导带中的电子和价带中的电洞都对电流传递有贡献，电洞本身不会移动，但是其它电子可以移动到这个电洞上面，等效于电洞本身往反方向移动。相对于带负电的电子，电洞的电性为正电。

由化学键结的观点来看，获得足够能量、进入传导带的电子也等于有足够能量可以打破电子与固体原子间的共价键（covalent bonds），而变成自由电子，进而对电流传导做出贡献。

半导体和导体之间有个显著的不同是半导体的电流传导同时来自电流与电洞的贡献，而导体的费米能阶（Fermi level）则已经在传导带内，因此电子不需要很大的能量即可找到空缺的量子态供其跳跃、造成电流传导。

固体材料内的电子能量分布遵循费米-狄拉克分布（Fermi-Dirac Distribution）。在绝对零度时，材料内电子的最高能量即为费米能阶，当温度高于绝对零度时，费米能阶为所有能阶中，被电子占据机率等于0.5的能阶。半导体材料内电子能量分布为温度的函数也使其导电特性受到温度很大的影响，当温度很低时，可以跳到传导带的电子较少，因此导电性也会变得较差。

[编辑]能量-动量色散

上述关于能带结构的内容为了简化，因此跳过了一个重要的现象，称为“能量的色散”（dispersion of energy）。同一个能带内之所以会有不同能量的量子态，原因是能带的电

子具有不同波向量（wave vector），或是k-向量。在量子力学中，k-向量即为粒子的动量，不同的材料会有不同的能量-动量关系（E-k relationship）。

硅的能带结构。对于间接能隙半导体而言，电子从传导带落至价带时，能量的释放牵涉到动量守衡，故大部分以声子的形式释放能量，发光效率不高。

能量-动量色散关系式能决定电子或电洞的“等效质量”（effective mass），以m*代表，公式如下：

等效质量可视为联系量子力学与古典力学的一个参数。这个参数对于半导体材料而言十分重要，例如它和电子或电洞的“迁移率”（electrons or holes mobility）有高度关联。电子或电洞的迁移率对于半导体元件的载子传输是相当基本的参数。

电子和电洞的等效质量不相等，这也造成了两者的迁移率不同，进而让N-通道和P-通道的MOSFET导电性不同。

砷化镓的能带结构。对于直接能隙半导体而言，电子从传导带落至价带时，能量的释放不必牵涉到动量守衡，故全部以光子的形式释放能量。

当离子化的辐射能量落在半导体时，可能会让价带中的电子吸收到足够能量而跃迁至传导带，并在价带中产生一个电洞，这种过程叫做“电子-电洞对的产生”（generation of electron-hole pair）。而其他够大的能量，如热能，也可以同样产生出电子-电洞对。

电子-电洞对则会经由复合（recombination）的过程而被消灭。根据能量守恒的观念，在传导带中的电子必须回到价带，将所得到的能量释放出来。能量释放的形式包括热能或辐射能，而这两种能量量子化后的表征分别是声子（phonon）以及光子（photon）。

对于处在稳态（steady state）的半导体而言，电子-电洞对的产生与复合速率是相等的。而在一个已给定的温度下，电子-电洞对的数量可由量子统计求得。量子力学处理此类问题时必须同时遵守能量以及动量守恒。

[编辑]半导体的掺杂

更多资料：掺杂（半导体）

半导体之所以能广泛应用在今日的数位世界中，凭借的就是其能借由在其晶格中植入杂质改变其电性，这个过程称之为掺杂（doping）。掺杂进入本质半导体（intrinsic semiconductor）的杂质浓度与极性皆会对半导体的导电特性产生很大的影响。而掺杂过的半导体则称为外质半导体（extrinsic semiconductor）。

[编辑]掺杂物

哪种材料适合作为某种半导体材料的掺杂物（dopant）需视两者的原子特性而定。一般而言，掺杂物依照其带给被掺杂材料的电荷正负被区分为施体（donor）与受体（acceptor）。施体原子带来的价电子（valence electrons）大多会与被掺杂的材料原子产生共价键，进而被束缚。而没有和被掺杂材料原子产生共价键的电子则会被施体原子微弱地束缚住，这个电子又称为施体电子。和本质半导体的价电子比起来，施体电子跃迁至传导带所需的能量较低，比较容易在半导体材料的晶格中移动，产生电流。虽然施体电子获得能量会跃迁至传导带，但并不会和本质半导体一样留下一个电洞，施体原子在失去了电子后只会固定在半导体材料的晶格中。因此这种因为掺杂而获得多余电子提供传导的半导体称为n型半导体（n-type semiconductor），n代表带负电荷的电子。

和施体相对的，受体原子进入半导体晶格后，因为其价电子数目比半导体原子的价电子数量少，等效上会带来一个的空位，这个多出的空位即可视为电洞。受体掺杂后的半导体称为p 型半导体（p-type semiconductor），p代表带正电荷的电洞。

以一个硅的本质半导体来说明掺杂的影响。硅有四个价电子，常用于硅的掺杂物有三价与五价的元素。当只有三个价电子的三价元素如硼（boron）掺杂至硅半导体中时，硼扮演的即是受体的角色，掺杂了硼的硅半导体就是p型半导体。反过来说，如果五价元素如磷（phosphorus）掺杂至硅半导体时，磷扮演施体的角色，掺杂磷的硅半导体成为n型半导体。

一个半导体材料有可能先后掺杂施体与受体，而如何决定此外质半导体为n型或p型必须视掺杂后的半导体中，受体带来的电洞浓度较高或是施体带来的电子浓度较高，亦即何者为此外质半导体的“多数载子”（majority carrier）。和多数载子相对的是少数载子（minority carrier）。对于半导体元件的操作原理分析而言，少数载子在半导体中的行为有着非常重要的地位。

[编辑]载子浓度

掺杂物浓度对于半导体最直接的影响在于其载子浓度。在热平衡的状态下，一个未经掺杂的本质半导体，电子与电洞的浓度相等，如下列公式所示：

n = p = n i

掺杂物对于能带结构的另一个重大影响是改变了费米能阶的位置。在热平衡的状态下费米能阶依然会保持定值，这个特性会引出很多其他有用的电特性。举例来说，一个p-n接面（p-n junction）的能带会弯折，起因是原本p型半导体和n型半导体的费米能阶位置各不相同，但是形成p-n接面后其费米能阶必须保持在同样的高度，造成无论是p型或是n型半导体的传导带或价带都会被弯曲以配合接面处的能带差异。

上述的效应可以用能带图（band diagram）来解释，如右图。在能带图里横轴代表位置，纵轴则是能量。图中也有费米能阶，半导体的本质费米能阶（intrinsic Fermi level）通常以E i来表示。在解释半导体元件的行为时，能带图是非常有用的工具。

[编辑]半导体材料的制造

为了满足量产上的需求，半导体的电性必须是可预测并且稳定的，因此包括掺杂物的纯度以及半导体晶格结构的品质都必须严格要求。常见的品质问题包括晶格的错位（dislocation）、双晶面（twins），或是堆栈错误（stacking fault）都会影响半导体材料的特性。对于一个半导体元件而言，材料晶格的缺陷通常是影响元件性能的主因。

目前用来成长高纯度单晶半导体材料最常见的方法称为裘可拉斯基制程（Czochralski process）。这种制程将一个单晶的晶种（seed）放入溶解的同材质液体中，再以旋转的方式缓缓向上拉起。在晶种被拉起时，溶质将会沿着固体和液体的接口固化，而旋转则可让溶质的温度均匀。

[编辑]应用

半导体器件可以通过结构和材料上的设计达到控制电流传输的目的，并以此为基础构建各种处理不同信号的电路。这是半导体在当前电子技术中广泛应用的原因

Contents

[hide ]

? 1 Explaining semiconductor energy bands ? 2 Energy bands and electrical conduction ? 3 Holes: electron absence as a charge carrier ?

4 Energy –momentum dispersion ?

5 Carrier generation and recombination ?

6 Semi-insulators ?

7 Doping o 7.1 Dopants o 7.2 Carrier concentration o 7.3 Effect on band structure ?

8 Preparation of semiconductor materials ?

9 See also ? 10 References ? 11 External links

[edit ] Explaining semiconductor energy bands

There are three popular ways to classify the electronic structure of a

crystal. ? Band structure

atoms - crystal - vacuum

In a single H-atom an electron resides in well known Putting two atoms together leads to delocalized orbits across two atoms, yielding a

This can be continued with more atoms. Note: This picture shows a metal, not an actual

Continuing to

add creates a crystal, which

may then be cut into a tape and fused together at the ends to allow circular For this

regular solid the band structure can be calculated

orbits. Note

that the

orbits are

called s,p,d

in order of

increasing

circular

current. covalent bond . Due to the Pauli exclusion principle , every state can contain only one

electron. semiconductor . currents. or measured.

Integrating over the k axis gives the bands of a semiconductor showing a full valence band and an empty conduction band. Generally stopping at the vacuum level is undesirable, because some people want to

calculate: photoemission

, inverse

photoemission

After the band structure is determined states can be combined to generate wave packets . As this is analogous to wave packages in free space, the results are similar.

An alternative

description , which does not really appreciate the strong Coulomb interaction, shoots free electrons into the crystal and looks at the scattering.

A third

alternative

description

uses strongly localized

unpaired

electrons in

chemical

bonds, which

looks almost

like a Mott

insulator .

[edit ] Energy bands and el ectrical conduction

Like in other solids, the electrons in semiconductors can have energies only within certain bands (ie. ranges of levels of energy) between the energy of the ground state, corresponding to electrons tightly bound to

the atomic nuclei of the material, and the free electron energy, which is the energy required for an electron to escape entirely from the material. The energy bands each correspond to a large number of discrete quantum states of the electrons, and most of the states with low energy (closer to the nucleus) are full, up to a particular band called the valence band. Semiconductors and insulators are distinguished from metals because the valence band in the semiconductor materials is nearly filled under usual operating conditions, thus causing more electrons to be available in the "conduction band," which is the band immediately above the valence band.

The ease with which electrons in a semiconductor can be excited from the valence band to the conduction band depends on the band gap between the bands, and it is the size of this energy bandgap that serves as an arbitrary dividing line (roughly 4 eV) between semiconductors and insulators.

In the picture of covalent bonds, an electron moves by hopping to a neighboring bond. Because of the Pauli exclusion principle it has to be lifted into the higher anti-bonding state of that bond. In the picture of delocalized states, for example in one dimension - that is in a nanowire, for every energy there is a state with electrons flowing in one direction and one state for the electrons flowing in the other. For a net current to flow some more states for one direction than for the other direction have to be occupied and for this energy is needed. For a metal this can be a very small energy while in the semiconductor the next higher states lie above the band gap. Often this is stated as: full bands do not contribute to the electrical conductivity. However, as the temperature of a semiconductor rises above absolute zero, there is more energy in the semiconductor to spend on lattice vibration and — more importantly for us — on lifting some electrons into an energy states of the conduction band. The current-carrying electrons in the conduction band are known as "free electrons", although they are often simply called "electrons" if context allows this usage to be clear.

Electrons excited to the conduction band also leave behind electron holes, or unoccupied states in the valence band. Both the conduction band electrons and the valence band holes contribute to electrical conductivity. The holes themselves don't actually move, but a neighboring electron can move to fill the hole, leaving a hole at the place it has just come from, and in this way the holes appear to move, and the holes behave as if they were actual positively charged particles.

One covalent bond between neighboring atoms in the solid is ten times stronger than the binding of the single electron to the atom, so freeing the electron does not imply destruction of the crystal structure.

[edit] Holes: electron absence as a charge carrier

The motion of holes, which was introduced for semiconductors, can also be applied to metals, where the Fermi level lies within the conduction band. With most metals the Hall effect reveals electrons to be the charge carriers, but some metals have a mostly filled conduction band, and the Hall effect reveals positive charge carriers, which are not the ion-cores, but holes. Contrast this to some conductors like solutions of salts, or plasma. In the case of a metal, only a small amount of energy is needed for the electrons to find other unoccupied states to move into, and hence for current to flow. Sometimes even in this case it may be said that a hole was left behind, to explain why the electron does not fall back to lower energies: It cannot find a hole. In the end in both materials electron-phonon scattering and defects are the dominant causes for resistance.

Fermi-Dirac distribution. States with energy ε below the Fermi energy, here μ, have higher probability n to be occupied, and those above are less likely to be occupied. Smearing of the distribution increases with temperature.

The energy distribution of the electrons determines which of the states are filled and which are empty. This distribution is described by Fermi-Dirac statistics. The distribution is characterized by the temperature of the electrons, and the Fermi energy or Fermi level. Under absolute zero conditions the Fermi energy can be thought of as the energy

up to which available electron states are occupied. At higher temperatures, the Fermi energy is the energy at which the probability of a state being occupied has fallen to 0.5.

The dependence of the electron energy distribution on temperature also explains why the conductivity of a semiconductor has a strong temperature dependency, as a semiconductor operating at lower temperatures will have fewer available free electrons and holes able to do the work.

[edit] Energy–momentum dispersion

In the preceding description an important fact is ignored for the sake of simplicity: the dispersion of the energy. The reason that the energies of the states are broadened into a band is that the energy depends on the value of the wave vector, or k-vector, of the electron. The k-vector, in quantum mechanics, is the representation of the momentum of a particle.

The dispersion relationship determines the effective mass, m*, of electrons or holes in the semiconductor, according to the formula:

[edit] Carrier generation and recombination

For more details on this topic, see Carrier generation and recombination.

When ionizing radiation strikes a semiconductor, it may excite an electron out of its energy level and consequently leave a hole. This process is known as electron–hole pair generation. Electron-hole pairs are constantly generated from thermal energy as well, in the absence of any external energy source.

Electron-hole pairs are also apt to recombine. Conservation of energy demands that these recombination events, in which an electron loses an amount of energy larger than the band gap, be accompanied by the emission of thermal energy (in the form of phonons) or radiation (in the form of photons).

In some states, the generation and recombination of electron–hole pairs are in equipoise. The number of electron-hole pairs in the steady state at a given temperature is determined by quantum statistical mechanics. The precise quantum mechanical mechanisms of generation and recombination are governed by conservation of energy and conservation of momentum.

As the probability that electrons and holes meet together is proportional to the product of their amounts, the product is in steady state nearly constant at a given temperature, providing that there is no significant electric field (which might "flush" carriers of both types, or move them from neighbour regions containing more of them to meet together) or externally driven pair generation. The product is a function of the temperature, as the probability of getting enough thermal energy to produce a pair increases with temperature, being approximately exp(?E

G / kT), where k is Boltzmann's constant, T is absolute temperature and E

G is band gap.

The probability of meeting is increased by carrier traps – impurities or dislocations which can trap an electron or hole and hold it until a pair is completed. Such carrier traps are sometimes purposely added to reduce the time needed to reach the steady state.

[edit] Semi-insulators

Some materials are classified as semi-insulators. These have electrical conductivity nearer to that of electrical insulators. Semi-insulators

find niche applications in micro-electronics, such as substrates for HEMT. An example of a common semi-insulator is gallium arsenide.[3]

[edit] Doping

For more details on this topic, see Doping (semiconductor).

The property of semiconductors that makes them most useful for constructing electronic devices is that their conductivity may easily be modified by introducing impurities into their crystal lattice. The process of adding controlled impurities to a semiconductor is known as doping. The amount of impurity, or dopant, added to an intrinsic (pure) semiconductor varies its level of conductivity. Doped semiconductors are often referred to as extrinsic. By adding impurity to pure semiconductors, the electrical conductivity may be varied not only by the number of impurity atoms but also, by the type of impurity atom and the changes may be thousand folds and million folds. For example, 1 cm3 of a metal or semiconductor specimen has a number of atoms on the order of 1022. Since every atom in metal donates at least one free electron for conduction in metal, 1 cm3of metal contains free electrons on the order of 1022. At the temperature close to 20 °C , 1 cm3 of pure germanium contains about 4.2×1022atoms and 2.5×1013free electrons and 2.5×1013 holes (empty spaces in crystal lattice having positive charge) The addition of 0.001% of arsenic (an impurity) donates an extra 1017free electrons in the same volume and the electrical conductivity increases about 10,000 times."

[edit] Dopants

The materials chosen as suitable dopants depend on the atomic properties of both the dopant and the material to be doped. In general, dopants that produce the desired controlled changes are classified as either electron acceptors or donors. A donor atom that activates (that is, becomes incorporated into the crystal lattice) donates weakly-bound valence electrons to the material, creating excess negative charge carriers. These weakly-bound electrons can move about in the crystal lattice relatively freely and can facilitate conduction in the presence of an electric field. (The donor atoms introduce some states under, but very close to the conduction band edge. Electrons at these states can be easily excited to the conduction band, becoming free electrons, at room temperature.) Conversely, an activated acceptor produces a hole. Semiconductors doped with donor impurities are called n-type, while those doped with acceptor impurities are known as p-type. The n and p type designations indicate which charge carrier acts as the material's

majority carrier. The opposite carrier is called the minority carrier, which exists due to thermal excitation at a much lower concentration compared to the majority carrier.

For example, the pure semiconductor silicon has four valence electrons. In silicon, the most common dopants are IUPAC group 13 (commonly known as group III) and group 15 (commonly known as group V) elements. Group 13 elements all contain three valence electrons, causing them to function as acceptors when used to dope silicon. Group 15 elements have five valence electrons, which allows them to act as a donor. Therefore, a silicon crystal doped with boron creates a p-type semiconductor whereas one doped with phosphorus results in an n-type material.

[edit] Carrier concentration

The concentration of dopant introduced to an intrinsic semiconductor determines its concentration and indirectly affects many of its electrical properties. The most important factor that doping directly affects is the material's carrier concentration. In an intrinsic semiconductor under thermal equilibrium, the concentration of electrons and holes is equivalent. That is,

n = p = n i

If we have a non-intrinsic semiconductor in thermal equilibrium the relation becomes:

n0·p0 = (n i)2

Where n0is the concentration of conducting electrons, p0is the electron hole concentration, and n i is the material's intrinsic carrier concentration. Intrinsic carrier concentration varies between materials and is dependent on temperature. Silicon's n i, for example, is roughly 1.0×1010 cm?3 at 300 kelvin (room temperature).

In general, an increase in doping concentration affords an increase in conductivity due to the higher concentration of carriers available for conduction. Degenerately (very highly) doped semiconductors have conductivity levels comparable to metals and are often used in modern integrated circuits as a replacement for metal. Often superscript plus and minus symbols are used to denote relative doping concentration in semiconductors. For example, n+ denotes an n-type semiconductor with a high, often degenerate, doping concentration. Similarly, p- would indicate a very lightly doped p-type material. It is useful to note that

even degenerate levels of doping imply low concentrations of impurities with respect to the base semiconductor. In crystalline intrinsic silicon, there are approximately 5×1022atoms/cm3. Doping concentration for silicon semiconductors may range anywhere from 1013cm?3to 1018cm?3. Doping concentration above about 1018 cm?3 is considered degenerate at room temperature. Degenerately doped silicon contains a proportion of impurity to silicon in the order of parts per thousand. This proportion may be reduced to parts per billion in very lightly doped silicon. Typical concentration values fall somewhere in this range and are tailored to produce the desired properties in the device that the semiconductor is intended for.

[edit] Effect on band structure

Band diagram of a p+n junction. The band bending is a result of the positioning of the Fermi levels in the p+ and n sides.

Doping a semiconductor crystal introduces allowed energy states within the band gap but very close to the energy band that corresponds to the dopant type. In other words, donor impurities create states near the conduction band while acceptors create states near the valence band. The gap between these energy states and the nearest energy band is usually referred to as dopant-site bonding energy or E B and is relatively small. For example, the E B for boron in silicon bulk is 0.045 eV, compared with silicon's band gap of about 1.12 eV. Because E B is so small, it takes little energy to ionize the dopant atoms and create free carriers in the conduction or valence bands. Usually the thermal energy available at room temperature is sufficient to ionize most of the dopant.

Dopants also have the important effect of shifting the material's Fermi level towards the energy band that corresponds with the dopant with the greatest concentration. Since the Fermi level must remain constant in a system in thermodynamic equilibrium, stacking layers of materials with different properties leads to many useful electrical properties. For example, the p-n junction's properties are due to the energy band bending that happens as a result of lining up the Fermi levels in contacting regions of p-type and n-type material.

This effect is shown in a band diagram. The band diagram typically indicates the variation in the valence band and conduction band edges versus some spatial dimension, often denoted x. The Fermi energy is also usually indicated in the diagram. Sometimes the intrinsic Fermi energy, E

, which is the Fermi level in the absence of doping, is shown. These i

diagrams are useful in explaining the operation of many kinds of semiconductor devices.

[edit] Preparation of semiconductor materials

Semiconductors with predictable, reliable electronic properties are necessary for mass production. The level of chemical purity needed is extremely high because the presence of impurities even in very small proportions can have large effects on the properties of the material. A high degree of crystalline perfection is also required, since faults in crystal structure (such as dislocations, twins, and stacking faults) interfere with the semiconducting properties of the material. Crystalline faults are a major cause of defective semiconductor devices. The larger the crystal, the more difficult it is to achieve the necessary perfection. Current mass production processes use crystal ingots between 100 mm and 300 mm (4-12 inches) in diameter which are grown as cylinders and sliced into wafers.

Because of the required level of chemical purity and the perfection of the crystal structure which are needed to make semiconductor devices, special methods have been developed to produce the initial semiconductor material. A technique for achieving high purity includes growing the crystal using the Czochralski process. An additional step that can be used to further increase purity is known as zone refining. In zone refining, part of a solid crystal is melted. The impurities tend to concentrate in the melted region, while the desired material recrystalizes leaving the solid material more pure and with fewer crystalline faults.

In manufacturing semiconductor devices involving heterojunctions between different semiconductor materials, the lattice constant, which is the length of the repeating element of the crystal structure, is important for determining the compatibility of materials.

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