Superlattice 超晶格

A superlattice is a periodic structure of layers of two (or more) materials. Typically, the thickness of one layer is several nanometers. It can also refer to a lower-dimensional structure such as an array of quantum dots or quantum wells.
超晶格是由两种（或两种以上）材料层组成的周期性结构。通常，一层的厚度为几个纳米。它也可以指低维结构，如量子点阵列或量子阱。

Discovery 发现[edit]

Superlattices were discovered early in 1925 by Johansson and Linde^[1] after the studies on gold-copper and palladium-copper systems through their special X-ray diffraction patterns. Further experimental observations and theoretical modifications on the field were done by Bradley and Jay,^[2] Gorsky,^[3] Borelius,^[4] Dehlinger and Graf,^[5] Bragg and Williams^[6] and Bethe.^[7] Theories were based on the transition of arrangement of atoms in crystal lattices from disordered state to an ordered state.
早在 1925 年，Johansson 和 Linde 就通过特殊的 X 射线衍射图样对金-铜和钯-铜系统进行研究后发现了超晶格。Bradley 和 Jay、 ^[2] Gorsky、 ^[3] Borelius、 ^[4] Dehlinger 和 Graf、 ^[5] Bragg 和 Williams ^[6] 以及 Bethe 对该领域进行了进一步的实验观察和理论修正。 ^[7] 这些理论的基础是晶格中原子的排列从无序状态向有序状态的转变。

Mechanical properties 机械特性[edit]

J.S. Koehler theoretically predicted^[8] that by using alternate (nano-)layers of materials with high and low elastic constants, shearing resistance is improved by up to 100 times as the Frank–Read source of dislocations cannot operate in the nanolayers.
科勒（J.S. Koehler）从理论上预测 ^[8] ，通过使用高弹性常数和低弹性常数材料的交替（纳米）层，抗剪切能力可提高 100 倍，因为位错的 Frank-Read 源无法在纳米层中运作。

The increased mechanical hardness of such superlattice materials was confirmed firstly by Lehoczky in 1978 on Al-Cu and Al-Ag,^[9] and later on by several others, such as Barnett and Sproul^[10] on hard PVD coatings.
1978 年，Lehoczky 首先在 Al-Cu 和 Al-Ag ^[9] 上证实了这种超晶格材料机械硬度的提高，随后，Barnett 和 Sproul ^[10] 等人在硬 PVD 涂层上也证实了这一点。

Semiconductor properties 半导体特性[edit]

If the superlattice is made of two semiconductor materials with different band gaps, each quantum well sets up new selection rules that affect the conditions for charges to flow through the structure. The two different semiconductor materials are deposited alternately on each other to form a periodic structure in the growth direction. Since the 1970 proposal of synthetic superlattices by Esaki and Tsu,^[11] advances in the physics of such ultra-fine semiconductors, presently called quantum structures, have been made. The concept of quantum confinement has led to the observation of quantum size effects in isolated quantum well heterostructures and is closely related to superlattices through the tunneling phenomena. Therefore, these two ideas are often discussed on the same physical basis, but each has different physics useful for applications in electric and optical devices.
如果超晶格是由两种具有不同带隙的半导体材料构成，那么每个量子阱都会设定新的选择规则，从而影响电荷流经结构的条件。两种不同的半导体材料交替沉积在一起，在生长方向上形成周期性结构。自 1970 年埃萨基（Esaki）和津（Tsu）提出合成超晶格（synthetic superlattices）以来，这种超精细半导体（现称为量子结构）的物理学取得了长足的进步。量子约束的概念导致在孤立的量子阱异质结构中观察到量子尺寸效应，并通过隧道现象与超晶格密切相关。因此，这两个概念经常在相同的物理基础上进行讨论，但各自具有不同的物理特性，可用于电气和光学设备中。

Semiconductor superlattice types
半导体超晶格类型[edit]

Superlattice miniband structures depend on the heterostructure type, either type I, type II or type III. For type I the bottom of the conduction band and the top of the valence subband are formed in the same semiconductor layer. In type II the conduction and valence subbands are staggered in both real and reciprocal space, so that electrons and holes are confined in different layers. Type III superlattices involve semimetal material, such as HgTe/CdTe. Although the bottom of the conduction subband and the top of the valence subband are formed in the same semiconductor layer in Type III superlattice, which is similar with Type I superlattice, the band gap of Type III superlattices can be continuously adjusted from semiconductor to zero band gap material and to semimetal with negative band gap.
超晶格迷你带结构取决于异质结构类型，即 I 型、II 型或 III 型。对于 I 型，导带的底部和价带的顶部在同一半导体层中形成。在 II 型超晶格中，导带和价带在实空间和倒易空间交错排列，因此电子和空穴被限制在不同的层中。III 型超晶格涉及半金属材料，如碲化镉汞。虽然在 III 型超晶格中，传导子带的底部和价子带的顶部形成在同一半导体层中，这与 I 型超晶格相似，但 III 型超晶格的带隙可以从半导体不断调整为零带隙材料和负带隙半金属。

Another class of quasiperiodic superlattices is named after Fibonacci. A Fibonacci superlattice can be viewed as a one-dimensional quasicrystal, where either electron hopping transfer or on-site energy takes two values arranged in a Fibonacci sequence.
另一类准周期超晶格是以斐波那契命名的。Fibonacci 超晶格可被视为一维准晶体，其中电子跳跃转移或现场能量取两个按 Fibonacci 序列排列的值。

Semiconductor materials 半导体材料[edit]

Semiconductor materials, which are used to fabricate the superlattice structures, may be divided by the element groups, IV, III-V and II-VI. While group III-V semiconductors (especially GaAs/Al_xGa_1−xAs) have been extensively studied, group IV heterostructures such as the Si_xGe_1−x system are much more difficult to realize because of the large lattice mismatch. Nevertheless, the strain modification of the subband structures is interesting in these quantum structures and has attracted much attention.
用于制造超晶格结构的半导体材料可按元素组别分为 IV、III-V 和 II-VI。III-V 族半导体（尤其是 GaAs/Al _x Ga _1−x As）已被广泛研究，而 IV 族异质结构（如 Si _x Ge _1−x 体系）由于存在较大的晶格失配而更难实现。然而，在这些量子结构中，子带结构的应变修饰非常有趣，并引起了广泛关注。

In the GaAs/AlAs system both the difference in lattice constant between GaAs and AlAs and the difference of their thermal expansion coefficient are small. Thus, the remaining strain at room temperature can be minimized after cooling from epitaxial growth temperatures. The first compositional superlattice was realized using the GaAs/Al_xGa_1−xAs material system.
在砷化镓/砷化铝体系中，砷化镓和砷化铝的晶格常数差异和热膨胀系数差异都很小。因此，从外延生长温度冷却后，室温下的剩余应变可降至最低。利用 GaAs/Al _x Ga _1−x As 材料体系实现了第一个成分超晶格。

A graphene/boron nitride system forms a semiconductor superlattice once the two crystals are aligned. Its charge carriers move perpendicular to the electric field, with little energy dissipation. h-BN has a hexagonal structure similar to graphene's. The superlattice has broken inversion symmetry. Locally, topological currents are comparable in strength to the applied current, indicating large valley-Hall angles.^[12]
石墨烯/氮化硼体系在两种晶体对齐后形成半导体超晶格。h-BN 具有与石墨烯类似的六边形结构。超晶格具有破碎的反转对称性。在局部，拓扑电流的强度与外加电流相当，这表明谷-霍尔角很大。 ^[12]

Production 生产[edit]

Superlattices can be produced using various techniques, but the most common are molecular-beam epitaxy (MBE) and sputtering. With these methods, layers can be produced with thicknesses of only a few atomic spacings. An example of specifying a superlattice is [Fe
₂₀V
₃₀]₂₀. It describes a bi-layer of 20Å of Iron (Fe) and 30Å of Vanadium (V) repeated 20 times, thus yielding a total thickness of 1000Å or 100 nm. The MBE technology as a means of fabricating semiconductor superlattices is of primary importance. In addition to the MBE technology, metal-organic chemical vapor deposition (MO-CVD) has contributed to the development of superconductor superlattices, which are composed of quaternary III-V compound semiconductors like InGaAsP alloys. Newer techniques include a combination of gas source handling with ultrahigh vacuum (UHV) technologies such as metal-organic molecules as source materials and gas-source MBE using hybrid gases such as arsine (AsH
₃) and phosphine (PH
₃) have been developed.
超晶格可通过各种技术生产，但最常见的是分子束外延（MBE）和溅射。通过这些方法，可以生产出厚度仅为几个原子间距的层。指定超晶格的一个例子是 [ Fe
₂₀V
₃₀ ] ₂₀ 。 它描述了一个由 20 埃的铁 (Fe) 和 30 埃的钒 (V) 组成的双层，重复 20 次，因此总厚度为 1000 埃或 100 纳米。作为制造半导体超晶格的一种手段，MBE 技术具有极其重要的意义。除 MBE 技术外，金属有机化学气相沉积（MO-CVD）也为超导体超晶格的发展做出了贡献，超晶格由四元 III-V 化合物半导体（如 InGaAsP 合金）组成。较新的技术包括将气源处理与超高真空（UHV）技术相结合，如将金属有机分子作为源材料和使用混合气体（如砷化氢（ AsH
₃ ）和磷化氢（ PH
₃ ））的气源 MBE。

Generally speaking MBE is a method of using three temperatures in binary systems, e.g., the substrate temperature, the source material temperature of the group III and the group V elements in the case of III-V compounds.
一般来说，MBE 是一种在二元体系中使用三种温度的方法，例如，在 III-V 族化合物的情况下，基底温度、III 族和 V 族元素的源材料温度。

The structural quality of the produced superlattices can be verified by means of X-ray diffraction or neutron diffraction spectra which contain characteristic satellite peaks. Other effects associated with the alternating layering are: giant magnetoresistance, tunable reflectivity for X-ray and neutron mirrors, neutron spin polarization, and changes in elastic and acoustic properties. Depending on the nature of its components, a superlattice may be called magnetic, optical or semiconducting.
生产出的超晶格的结构质量可通过 X 射线衍射或中子衍射光谱进行验证，其中包含特征性卫星峰。与交替分层有关的其他效应包括：巨磁阻、X 射线和中子反射镜的可调反射率、中子自旋极化以及弹性和声学特性的变化。根据其成分的性质，超晶格可称为磁性、光学或半导体。

Miniband structure 迷你带结构[edit]

The schematic structure of a periodic superlattice is shown below, where A and B are two semiconductor materials of respective layer thickness a and b (period: ${\displaystyle d=a+b}$). When a and b are not too small compared with the interatomic spacing, an adequate approximation is obtained by replacing these fast varying potentials by an effective potential derived from the band structure of the original bulk semiconductors. It is straightforward to solve 1D Schrödinger equations in each of the individual layers, whose solutions ${\displaystyle \psi }$ are linear combinations of real or imaginary exponentials.
周期性超晶格的结构示意图如下，其中 A 和 B 是两种半导体材料，层厚分别为 a 和 b（周期： ${\displaystyle d=a+b}$ ）。当 a 和 b 与原子间距相比不是太小时，用从原始块体半导体带状结构中导出的有效电势来代替这些快速变化的电势，就可以得到适当的近似值。可以直接求解各层的一维薛定谔方程，其解法 ${\displaystyle \psi }$ 是实指数或虚指数的线性组合。

For a large barrier thickness, tunneling is a weak perturbation with regard to the uncoupled dispersionless states, which are fully confined as well. In this case the dispersion relation ${\displaystyle E_{z}(k_{z})}$, periodic over ${\displaystyle 2\pi /d}$ with over ${\displaystyle d=a+b}$ by virtue of the Bloch theorem, is fully sinusoidal:
对于较大的势垒厚度，隧道效应是对非耦合无色散态的微弱扰动，而非耦合无色散态也是完全受限的。在这种情况下，根据布洛赫定理，在 ${\displaystyle 2\pi /d}$ 和 ${\displaystyle d=a+b}$ 上的周期性色散关系 ${\displaystyle E_{z}(k_{z})}$ 是完全正弦的：

${\displaystyle \ E_{z}(k_{z})={\frac {\Delta }{2}}(1-\cos(k_{z}d))}$

and the effective mass changes sign for ${\displaystyle 2\pi /d}$:
而有效质量在 ${\displaystyle 2\pi /d}$ 时会改变符号：

${\displaystyle \ {m^{*}={\frac {\hbar ^{2}}{\partial ^{2}E/\partial k^{2}}}}|_{k=0}}$

In the case of minibands, this sinusoidal character is no longer preserved. Only high up in the miniband (for wavevectors well beyond ${\displaystyle 2\pi /d}$) is the top actually 'sensed' and does the effective mass change sign. The shape of the miniband dispersion influences miniband transport profoundly and accurate dispersion relation calculations are required given wide minibands. The condition for observing single miniband transport is the absence of interminiband transfer by any process. The thermal quantum k_BT should be much smaller than the energy difference ${\displaystyle E_{2}-E_{1}}$ between the first and second miniband, even in the presence of the applied electric field.
在小带的情况下，这种正弦特性不再保留。只有在小频带的高处（波矢量远远超过 ${\displaystyle 2\pi /d}$ 时）才真正 "感应 "到顶部，有效质量才会改变符号。小波段色散的形状对小波段传输影响很大，因此需要对宽小波段进行精确的色散关系计算。观察单个 miniband 传输的条件是没有任何过程进行 miniband 间传输。即使在外加电场的作用下，热量子 k _B T 也应远远小于第一和第二迷你带之间的能量差 ${\displaystyle E_{2}-E_{1}}$ 。

Bloch states 布洛赫态[edit]

For an ideal superlattice a complete set of eigenstates states can be constructed by products of plane waves ${\displaystyle e^{i\mathbf {k} \cdot \mathbf {r} }/2\pi }$ and a z-dependent function ${\displaystyle f_{k}(z)}$ which satisfies the eigenvalue equation
对于一个理想超晶格，可以通过平面波 ${\displaystyle e^{i\mathbf {k} \cdot \mathbf {r} }/2\pi }$ 和一个满足特征值方程的与 z 有关的函数 ${\displaystyle f_{k}(z)}$ 的乘积来构建一套完整的特征状态。

${\displaystyle \left(E_{c}(z)-{\frac {\partial }{\partial z}}{\frac {\hbar ^{2}}{2m_{c}(z)}}{\frac {\partial }{\partial z}}+{\frac {\hbar ^{2}\mathbf {k} ^{2}}{2m_{c}(z)}}\right)f_{k}(z)=Ef_{k}(z)}$.

As ${\displaystyle E_{c}(z)}$ and ${\displaystyle m_{c}(z)}$ are periodic functions with the superlattice period d, the eigenstates are Bloch state ${\displaystyle f_{k}(z)=\phi _{q,\mathbf {k} }(z)}$ with energy ${\displaystyle E^{\nu }(q,\mathbf {k} )}$. Within first-order perturbation theory in k², one obtains the energy
由于 ${\displaystyle E_{c}(z)}$ 和 ${\displaystyle m_{c}(z)}$ 是超晶格周期为 d 的周期函数，因此特征状态是能量为 ${\displaystyle E^{\nu }(q,\mathbf {k} )}$ 的布洛赫态 ${\displaystyle f_{k}(z)=\phi _{q,\mathbf {k} }(z)}$ 。在 k ² 的一阶微扰论中，可以得到能量

${\displaystyle E^{\nu }(q,\mathbf {k} )\approx E^{\nu }(q,\mathbf {0} )+\langle \phi _{q,\mathbf {k} }\mid {\frac {\hbar ^{2}\mathbf {k} ^{2}}{2m_{c}(z)}}\mid \phi _{q,\mathbf {k} }\rangle }$.

Now, ${\displaystyle \phi _{q,\mathbf {0} }(z)}$ will exhibit a larger probability in the well, so that it seems reasonable to replace the second term by
现在， ${\displaystyle \phi _{q,\mathbf {0} }(z)}$ 在井中将表现出更大的概率，因此用以下项代替第二项似乎是合理的

${\displaystyle E_{k}={\frac {\hbar ^{2}\mathbf {k} ^{2}}{2m_{w}}}}$

where ${\displaystyle m_{w}}$ is the effective mass of the quantum well.
其中 ${\displaystyle m_{w}}$ 是量子井的有效质量。

Wannier functions 万尼尔函数[edit]

By definition the Bloch functions are delocalized over the whole superlattice. This may provide difficulties if electric fields are applied or effects due to the superlattice's finite length are considered. Therefore, it is often helpful to use different sets of basis states that are better localized. A tempting choice would be the use of eigenstates of single quantum wells. Nevertheless, such a choice has a severe shortcoming: the corresponding states are solutions of two different Hamiltonians, each neglecting the presence of the other well. Thus these states are not orthogonal, creating complications. Typically, the coupling is estimated by the transfer Hamiltonian within this approach. For these reasons, it is more convenient to use the set of Wannier functions.
顾名思义，布洛赫函数在整个超晶格上是去局域化的。如果施加电场或考虑超晶格有限长度造成的影响，这可能会带来困难。因此，使用不同的基态集往往有助于更好地局部化。一个诱人的选择是使用单量子阱的特征态。然而，这种选择有一个严重的缺陷：相应的状态是两个不同哈密顿的解，每个都忽略了另一个量子井的存在。因此，这些状态并不是正交的，从而造成了复杂性。通常，在这种方法中，耦合是通过转移哈密顿来估算的。由于这些原因，使用万尼尔函数集更为方便。

Wannier–Stark ladder 万尼尔-斯塔克梯子[edit]

Applying an electric field F to the superlattice structure causes the Hamiltonian to exhibit an additional scalar potential eφ(z) = −eFz that destroys the translational invariance. In this case, given an eigenstate with wavefunction ${\displaystyle \Phi _{0}(z)}$ and energy ${\displaystyle E_{0}}$, then the set of states corresponding to wavefunctions ${\displaystyle \Phi _{j}(z)=\Phi _{0}(z-jd)}$ are eigenstates of the Hamiltonian with energies E_j = E₀ − jeFd. These states are equally spaced both in energy and real space and form the so-called Wannier–Stark ladder. The potential ${\displaystyle \Phi _{0}(z)}$ is not bounded for the infinite crystal, which implies a continuous energy spectrum. Nevertheless, the characteristic energy spectrum of these Wannier–Stark ladders could be resolved experimentally.
对超晶格结构施加电场 F 会使哈密顿方程产生额外的标量势 eφ(z) = -eFz，从而破坏平移不变性。在这种情况下，给定一个具有波函数 ${\displaystyle \Phi _{0}(z)}$ 和能量 ${\displaystyle E_{0}}$ 的特征态，那么与波函数 ${\displaystyle \Phi _{j}(z)=\Phi _{0}(z-jd)}$ 相对应的状态集合就是哈密顿的特征态，其能量为 E = E ₀ - jeFd。这些状态在能量空间和实空间的间隔相等，构成了所谓的万尼尔-斯塔克梯形。对于无限晶体来说，势 ${\displaystyle \Phi _{0}(z)}$ 是无界的，这意味着能谱是连续的。然而，这些万尼尔-斯塔克梯子的特征能谱可以通过实验解析出来。

Transport 运输[edit]

The motion of charge carriers in a superlattice is different from that in the individual layers: mobility of charge carriers can be enhanced, which is beneficial for high-frequency devices, and specific optical properties are used in semiconductor lasers.
电荷载流子在超晶格中的运动与在单层中的运动不同：电荷载流子的迁移率可以得到增强，这对高频设备是有益的，而特定的光学特性则可用于半导体激光器。

If an external bias is applied to a conductor, such as a metal or a semiconductor, typically an electric current is generated. The magnitude of this current is determined by the band structure of the material, scattering processes, the applied field strength and the equilibrium carrier distribution of the conductor.
如果在导体（如金属或半导体）上施加外部偏压，通常会产生电流。电流的大小由材料的带状结构、散射过程、外加场强和导体的平衡载流子分布决定。

A particular case of superlattices called superstripes are made of superconducting units separated by spacers. In each miniband the superconducting order parameter, called the superconducting gap, takes different values, producing a multi-gap, or two-gap or multiband superconductivity.
超晶格的一种特殊情况称为超条带，是由被间隔物分隔的超导单元组成的。在每个小带中，超导阶参数（称为超导间隙）取值不同，从而产生多间隙、双间隙或多带超导。

Recently, Felix and Pereira investigated the thermal transport by phonons in periodic^[13] and quasiperiodic^[14][15][16] superlattices of graphene-hBN according to the Fibonacci sequence. They reported that the contribution of coherent thermal transport (phonons like-wave) was suppressed as quasiperiodicity increased.
最近，Felix 和 Pereira 根据斐波那契数列研究了石墨烯-卤化硼周期性 ^[13] 和准周期性 ^{[14] [15] [16]} 超晶格中声子的热传输。他们报告说，随着准周期性的增加，相干热传输（声子类波）的贡献被抑制。

Other dimensionalities 其他维度[edit]

Soon after two-dimensional electron gases (2DEG) had become commonly available for experiments, research groups attempted to create structures^[17] that could be called 2D artificial crystals. The idea is to subject the electrons confined to an interface between two semiconductors (i.e. along z-direction) to an additional modulation potential V(x,y). Contrary to the classical superlattices (1D/3D, that is 1D modulation of electrons in 3D bulk) described above, this is typically achieved by treating the heterostructure surface: depositing a suitably patterned metallic gate or etching. If the amplitude of V(x,y) is large (take ${\displaystyle V(x,y)=-V_{0}(\cos 2\pi x/a+\cos 2\pi y/a),V_{0}>0}$ as an example) compared to the Fermi level, ${\displaystyle |V_{0}|\gg E_{f}}$, the electrons in the superlattice should behave similarly to electrons in an atomic crystal with square lattice (in the example, these "atoms" would be located at positions (na,ma) where n,m are integers).
在二维电子气（2DEG）普遍用于实验后不久，研究小组试图创造可称为二维人工晶体的结构 ^[17] 。其原理是将局限在两个半导体界面（即沿 Z 轴方向）的电子置于额外的调制电势 V(x,y) 中。与上述经典超晶格（1D/3D，即三维体中电子的 1D 调制）相反，这通常是通过处理异质结构表面来实现的：沉积适当图案的金属栅极或蚀刻。如果 V(x,y)的振幅与费米级 ${\displaystyle |V_{0}|\gg E_{f}}$ 相比较大（以 ${\displaystyle V(x,y)=-V_{0}(\cos 2\pi x/a+\cos 2\pi y/a),V_{0}>0}$ 为例），超晶格中电子的行为应类似于方形晶格原子晶体中的电子（在本例中，这些 "原子 "将位于 n、m 为整数的 (na,ma) 位置）。

The difference is in the length and energy scales. Lattice constants of atomic crystals are of the order of 1Å while those of superlattices (a) are several hundreds or thousands larger as dictated by technological limits (e.g. electron-beam lithography used for the patterning of the heterostructure surface). Energies are correspondingly smaller in superlattices. Using the simple quantum-mechanically confined-particle model suggests ${\displaystyle E\propto 1/a^{2}}$. This relation is only a rough guide and actual calculations with currently topical graphene (a natural atomic crystal) and artificial graphene^[18] (superlattice) show that characteristic band widths are of the order of 1 eV and 10 meV, respectively. In the regime of weak modulation (${\displaystyle |V_{0}|\ll E_{f}}$), phenomena like commensurability oscillations or fractal energy spectra (Hofstadter butterfly) occur.
不同之处在于长度和能量尺度。原子晶体的晶格常数约为 1 埃，而超晶格 (a) 的晶格常数则因技术限制（例如用于异质结构表面图案化的电子束光刻技术）而大几百或几千埃。超晶格的能量也相应较小。使用简单的量子力学约束粒子模型可以得出 ${\displaystyle E\propto 1/a^{2}}$ 。这种关系只是一种粗略的指导，对目前流行的石墨烯（天然原子晶体）和人造石墨烯 ^[18] （超晶格）的实际计算表明，特征带宽分别为 1 eV 和 10 meV。在弱调制条件下（ ${\displaystyle |V_{0}|\ll E_{f}}$ ），会出现类似可比性振荡或分形能谱（霍夫斯塔特蝴蝶）的现象。

Artificial two-dimensional crystals can be viewed as a 2D/2D case (2D modulation of a 2D system) and other combinations are experimentally available: an array of quantum wires (1D/2D) or 3D/3D photonic crystals.
人造二维晶体可被视为二维/二维情况（二维系统的二维调制），实验中还存在其他组合：量子线阵列（一维/二维）或三维/三维光子晶体。

Applications 应用[edit]

The superlattice of palladium-copper system is used in high performance alloys to enable a higher electrical conductivity, which is favored by the ordered structure. Further alloying elements like silver, rhenium, rhodium and ruthenium are added for better mechanical strength and high temperature stability. This alloy is used for probe needles in probe cards.^[19]
钯铜系统的超晶格被用于高性能合金中，以实现更高的导电性，有序结构有利于导电性的提高。此外，还添加了银、铼、铑和钌等合金元素，以获得更好的机械强度和高温稳定性。这种合金可用于探针卡中的探针。 ^[19]

See also 另请参见[edit]

• Cu-Pt type ordering in III-V semiconductor
  III-V 族半导体中的铜铂型有序化
• Tube-based nanostructures
  管基纳米结构
• Wannier function 万尼尔函数

References 参考资料[edit]

• H.T. Grahn, "Semiconductor Superlattices", World Scientific (1995). ISBN 978-981-02-2061-7
  H.T. Grahn，"Semiconductor Superlattices"，World Scientific (1995)。国际标准书号 978-981-02-2061-7
• Schuller, I. (1980). "New Class of Layered Materials". Physical Review Letters. 44 (24): 1597–1600. Bibcode:1980PhRvL..44.1597S. doi:10.1103/PhysRevLett.44.1597.
  Schuller, I. (1980)."新型层状材料》。物理评论快报》。44 (24):1597-1600.Bibcode：1980PhRvL..44.1597S. doi: 10.1103/PhysRevLett.44.1597.
• Morten Jagd Christensen, "Epitaxy, Thin Films and Superlattices", Risø National Laboratory, (1997). ISBN 8755022987 Superlattice at Google Books [1]
  Morten Jagd Christensen，"外延、薄膜和超晶格"，里瑟国家实验室，（1997 年）。ISBN 8755022987 Superlattice at Google Books [1] （超晶格在谷歌图书）[1]。
• C. Hamaguchi, "Basic Semiconductor Physics", Springer (2001). Superlattice at Google Books ISBN 3540416390
  C.Hamaguchi, "Basic Semiconductor Physics", Springer (2001).超晶格，谷歌图书 ISBN 3540416390
• Wacker, A. (2002). "Semiconductor superlattices: A model system for nonlinear transport". Physics Reports. 357 (1): 1–7. arXiv:cond-mat/0107207. Bibcode:2002PhR...357....1W. CiteSeerX 10.1.1.305.3634. doi:10.1016/S0370-1573(01)00029-1. S2CID 118885849.
  Wacker, A. (2002)."半导体超晶格：非线性传输模型系统"。物理报告》。357 (1):1-7. ArXiv: cond-mat/0107207.Bibcode：2002PhR...357....1W.CiteSeerX 10.1.1.305.3634. doi: 10.1016/S0370-1573(01)00029-1.S2CID 118885849.
• Haugan, H. J.; Szmulowicz, F.; Mahalingam, K.; Brown, G. J.; Munshi, S. R.; Ullrich, B. (2005). "Short-period InAs/GaSb type-II superlattices for mid-infrared detectors". Applied Physics Letters. 87 (26): 261106. Bibcode:2005ApPhL..87z1106H. doi:10.1063/1.2150269. [2]^{[dead link]}
  Haugan, H. J.; Szmulowicz, F.; Mahalingam, K.; Brown, G. J.; Munshi, S. R.; Ullrich, B. (2005)."用于中红外探测器的短周期 InAs/GaSb II 型超晶格"。应用物理快报》。87 (26):261106.Bibcode：2005ApPhL..87z1106H. doi: 10.1063/1.2150269.[2] ^{[dead link]}

Further reading 更多阅读[edit]

• Mendez, E. E.; Bastard, G. R. (1993). "Wannier-Stark Ladders and Bloch Oscillations in Superlattices". Physics Today. 46 (6): 34–42. Bibcode:1993PhT....46f..34M. doi:10.1063/1.881353.
  Mendez, E. E.; Bastard, G. R. (1993)."Wannier-Stark Ladders and Bloch Oscillations in Superlattices".今日物理学》。46 (6):34-42.Bibcode：1993PhT....46f..34M. doi: 10.1063/1.881353.