Mathieu's Functions and Electrons in a Periodic Lattice

1971 ◽  
Vol 39 (10) ◽  
pp. 1225-1230 ◽  
Author(s):  
Thomas R. Carver
Keyword(s):  
Periodic Lattice

Effects of dopant concentration on the microstructure of tin- doped indium oxide thin films

1990 ◽  
Vol 48 (4) ◽  
pp. 716-717
Author(s):  
I. A. Rauf
Keyword(s):  
Thin Films ◽  
Indium Oxide ◽  
Ionic Radius ◽  
Free Carrier ◽  
Electron Gun ◽  
Periodic Lattice ◽  
Oxide Thin Films ◽  
Transmission Electron ◽  
The Difference ◽  
Dopant Atoms

To understand the electronic conduction mechanism in Sn-doped indium oxide thin films, it is important to study the effect of dopant atoms on the neighbouring indium oxide lattice. Ideally Sn is a substitutional dopant at random indium sites. The difference in valence (Sn4+ replaces In3+) requires that an extra electron is donated to the lattice and thus contributes to the free carrier density. But since Sn is an adjacent member of the same row in the periodic table, the difference in the ionic radius (In3+: 0.218 nm; Sn4+: 0.205 nm) will introduce a strain in the indium oxide lattice. Free carrier electron waves will no longer see a perfect periodic lattice and will be scattered, resulting in the reduction of free carrier mobility, which will lower the electrical conductivity (an undesirable effect in most applications).One of the main objectives of the present investigation is to understand the effects of the strain (produced by difference in the ionic radius) on the microstructure of the indium oxide lattice when the doping level is increased to give high carrier densities. Sn-doped indium oxide thin films were prepared with four different concentrations: 9, 10, 11 and 12 mol. % of SnO2 in the starting material. All the samples were prepared at an oxygen partial pressure of 0.067 Pa and a substrate temperature of 250°C using an Edwards 306 coating unit with an electron gun attachment for heating the crucible. These deposition conditions have been found to give optimum electrical properties in Sn-doped indium oxide films. A JEOL 2000EX transmission electron microscope was used to investigate the specimen microstructure.

scholarly journals Integrated Double-Sided Random Microlens Array Used for Laser Beam Homogenization

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 673
Author(s):  
Wei Yuan ◽  
Cheng Xu ◽  
Li Xue ◽  
Hui Pang ◽  
Axiu Cao ◽  
...  
Keyword(s):  
Laser Beam ◽  
Microlens Array ◽  
Energy Utilization ◽  
Utilization Rate ◽  
Periodic Lattice ◽  
Lattice Distribution ◽  
Speckle Field ◽  
High Laser ◽  
Alignment Problem ◽  
In Series

Double microlens arrays (MLAs) in series can be used to divide and superpose laser beam so as to achieve a homogenized spot. However, for laser beam homogenization with high coherence, the periodic lattice distribution in the homogenized spot will be generated due to the periodicity of the traditional MLA, which greatly reduces the uniformity of the homogenized spot. To solve this problem, a monolithic and highly integrated double-sided random microlens array (D-rMLA) is proposed for the purpose of achieving laser beam homogenization. The periodicity of the MLA is disturbed by the closely arranged microlens structures with random apertures. And the random speckle field is achieved to improve the uniformity of the homogenized spot by the superposition of the divided sub-beams. In addition, the double-sided exposure technique is proposed to prepare the rMLA on both sides of the same substrate with high precision alignment to form an integrated D-rMLA structure, which avoids the strict alignment problem in the installation process of traditional discrete MLAs. Then the laser beam homogenization experiments have been carried out by using the prepared D-rMLA structure. The laser beam homogenized spots of different wavelengths have been tested, including the wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B). The experimental results show that the uniformity of the RGB homogenized spots is about 91%, 89%, and 90%. And the energy utilization rate is about 89%, 87%, 86%, respectively. Hence, the prepared structure has high laser beam homogenization ability and energy utilization rate, which is suitable for wide wavelength regime.

scholarly journals Modeling shocks in periodic lattice materials

2017 ◽  
Author(s):  
Mark C. Messner ◽  
Mathew I. Barham ◽  
Mukul Kumar ◽  
Nathan R. Barton
Keyword(s):  
Periodic Lattice ◽  
Lattice Materials

SELF-AVOIDING WALKS ON QUASILATTICES

1993 ◽  
Vol 07 (06n07) ◽  
pp. 1569-1575 ◽  
Author(s):  
KEITH BRIGGS
Keyword(s):  
Critical Points ◽  
Asymptotic Properties ◽  
Universality Class ◽  
Periodic Lattice ◽  
Self Avoiding Walks

I consider the asymptotic properties of self-avoiding walks on a variety of quasilattices. The critical points and exponents are estimated. Walks on several of the patterns appear to belong to the same universality class as walks on the hexagonal periodic lattice.

scholarly journals Observation of topological phase with critical localization in a quasi-periodic lattice

2021 ◽  
Author(s):  
Teng Xiao ◽  
Dizhou Xie ◽  
Zhaoli Dong ◽  
Tao Chen ◽  
Wei Yi ◽  
...  
Keyword(s):  
Periodic Lattice ◽  
Topological Phase
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