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Interfacial Disorder in InAs/GaSb Heterostructures Grown by Molecular Beam Epitaxy
Published in M. O. Manasreh, Antimonide-Related Strained-Layer Heterostructures, 2019
M. E. Twigg, B. R. Bennett, P. M. Thibado, B. V. Shanabrook, L. J. Whitman
One of the best-known consequences of the translational symmetry of a crystal lattice is Bloch’s Theorem, which states, in part, that the electron density in such a solid must have the same periodicity as the lattice [40]. As is obvious to anyone acquainted with the physics of semiconductor devices, Bloch’s Theorem is useful in understanding electron transport in crystalline solids. Bloch’s Theorem is also important in understanding the transport of high energy electrons (accelerated by several hundred thousand volts) that pass through a thin (5–1000 nm) film sample imaged in a transmission electron microscope (TEM) [41]. The TEM imaging technique projects a highly-magnified image of the high-energy electron wave function (which consists of a series of Bloch waves) onto a phosphor screen or recording medium, and in so doing reveals the structure (including lattice periodicity) of the crystal under study.
Semiconductor Light Sources and Detectors
Published in Shyamal Bhadra, Ajoy Ghatak, Guided Wave Optics and Photonic Devices, 2017
where uk(r) is known as the Bloch cell function, having the same period as the potential variation. Thus, Bloch’s theorem states that the eigenfunctions of the wave equation for a periodic potential can be represented as the product of the plane wave eik→⋅r→ and a periodic function with the same period as the lattice constant of the crystal. Here k→ represents the propagation vector of the travelling wave whose magnitude is given by k = 2π/λ, where λ is the de Broglie wavelength associated with the electron. The momentum of the electron is related to k→ through the relation:
Basic Electronic Structures and Charge Carrier Generation in Organic Optoelectronic Materials
Published in Sam-Shajing Sun, Larry R. Dalton, Introduction to Organic Electronic and Optoelectronic Materials and Devices, 2016
Because bands are solutions of the Bloch equation, in order for the materials to form or exhibit electronic bands, it is crucial that the materials possess a periodic potential structure to satisfy the Bloch’s theorem requirements. In most typical amorphous molecular or polymeric solids where the closely packed periodic potential structures are absent or very poor, it is not surprising that the bands are difficult to form or ever exist. However, in certain polycrystalline materials where both amorphous and crystalline domains coexist, bands may exist in the crystalline domains. Therefore, the band size (BS) may be defined as the average size of the actual periodic domain or path (or an effective conjugation size corresponding to the size of a particle box) where Bloch function is applicable and where electron transport is of coherent or tunneling type. In a classic single crystal semiconductor, since the Bloch function can be applicable to the whole crystal (except the boundary or edge regions of the crystal), the band size is therefore roughly the same as the single crystal size. On the contrary, in the amorphous domains where the bands are poor or do not exist, charge transport follows incoherent or hopping mechanisms, as will be discussed in detail in Chapter 4 of this book. The mean free path (MFP, l), or mean free distance (MFD), is defined in semiconductor physics as an average nonscattering (ballistic) electron transport length between two consecutive scattering centers as expressed by () l=vτ
Science of 2.5 dimensional materials: paradigm shift of materials science toward future social innovation
Published in Science and Technology of Advanced Materials, 2022
Hiroki Ago, Susumu Okada, Yasumitsu Miyata, Kazunari Matsuda, Mikito Koshino, Kosei Ueno, Kosuke Nagashio
In these non-periodic situations, theoretical description of physical properties is limited by the inapplicability of the Bloch theorem. There have been several theoretical attempts to describe the electronic structure of quasiperiodic 2D superlattices. For the 30-degree TBG mentioned above, the 12-fold rotational symmetric electronic structure can be successfully described by quasi-bands defined in quasi momentum space [128]. Quite recently, it was shown that energy gaps in 2D quasiperiodic systems can generally be characterized by a set of topological numbers called the second Chern numbers, which can be interpreted as quantized integers in the high-dimensional quantum Hall effect [137]. These concepts serve as a fundamental framework to describe the physical properties in quasiperiodic twisted 2D systems, where the Bloch theory is not applicable. The above-mentioned, highly controlled nanoscale architectures consisting of 2D materials, such as graphene, hBN, and TMDC, that exhibit extraordinarily properties can also be categorized as 2.5D materials.
Innovative structural design of chiral lattices with low frequency wide multiple band gaps and vibration suppression
Published in Mechanics of Advanced Materials and Structures, 2023
Hong-yun Yang, Shu-liang Cheng, Xiao-feng Li, Qun Yan, Bin Wang, Ya-jun Xin, Yong-tao Sun, Qian Ding, Hao Yan, Ya-jie Li, Qing-xin Zhao
Bloch’s theorem can be used to analyze the propagation of waves in periodic materials. The basic lattice vector ei(i = 1, 2) in the orthogonal Cartesian coordinate system (i, j) can be expressed as: