New Theoretical Treatment of Electroreflectance from Surfaces and Interfaces Having Large Built-in Fields

1992 ◽  
Vol 261 ◽  
Author(s):  
J. W. Garland ◽  
Z. Zhang ◽  
C. Kim ◽  
D. Yang ◽  
P. M. Raccah
Keyword(s):  
Numerical Calculation ◽  
Dielectric Function ◽  
Electric Fields ◽  
Accurate Determination ◽  
Bound State ◽  
Depletion Region ◽  
Quantum Mechanical ◽  
Theoretical Treatment ◽  
Surfaces And Interfaces

ABSTRACTWe have constructed a completely quantum-mechanical theoretical treatment of the modification of the local dielectric function by intense electric fields. It includes the numerical calculation of depletion-region bound-state energies and wavefunctions as well as band wavefunctions. We use this treatment to construct electroreflectance (ER) lineshapes. Our numerical results differ significantly from those of previously proposed ER lineshapes for GaAs with Nd >> 1016. They yield excellent fits to ER data and allow the accurate determination of doping levels and band bendings from ER data.

scholarly journals A new application of the quantum mechanical hypervirial theorems technique

2020 ◽  
Vol 9 ◽  
pp. 210
Author(s):  
M. E. Grypeos ◽  
Th. E. Liolios
Keyword(s):  
Wide Class ◽  
Ground State ◽  
State Energy ◽  
Bound State ◽  
Quantum Mechanical ◽  
Bound State Energy ◽  
New Approach ◽  
Analytic Determination ◽  
Gaussian Potential

A new approach is proposed on the basis of the quantum mechanical hypervirial theorems technique for the approximate analytic (or semi-analytic) determination of bound state energy eigenfunctions for quite a wide class of central potentials. The accuracy of the method is tested for the Gaussian potential and is best for the ground state.

scholarly journals A Theoretical Treatment of THz Resonances in Semiconductor GaAs p–n Junctions

Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2412 ◽  
Author(s):  
Mohsen Janipour ◽  
I. Burc Misirlioglu ◽  
Kursat Sendur
Keyword(s):  
Dielectric Function ◽  
Electric Fields ◽  
Semiconductor Heterostructures ◽  
Theoretical Treatment ◽  
Low Loss ◽  
Depletion Zone ◽  
Charge Densities ◽  
As Doping ◽  
Effective Masses ◽  
Spatially Varying

Semiconductor heterostructures are suitable for the design and fabrication of terahertz (THz) plasmonic devices, due to their matching carrier densities. The classical dispersion relations in the current literature are derived for metal plasmonic materials, such as gold and silver, for which a homogeneous dielectric function is valid. Penetration of the electric fields into semiconductors induces locally varying charge densities and a spatially varying dielectric function is expected. While such an occurrence renders tunable THz plasmonics a possibility, it is crucial to understand the conditions under which propagating resonant conditions for the carriers occur, upon incidence of an electromagnetic radiation. In this manuscript, we derive a dispersion relation for a p–n heterojunction and apply the methodology to a GaAs p–n junction, a material of interest for optoelectronic devices. Considering symmetrically doped p- and n-type regions with equal width, the effect of certain parameters (such as doping and voltage bias) on the dispersion curve of the p–n heterojunction were investigated. Keeping in sight the different effective masses and mobilities of the carriers, we were able to obtain the conditions that yield identical dielectric functions for the p- and n-regions. Our results indicated that the p–n GaAs system can sustain propagating resonances and can be used as a layered plasmonic waveguide. The conditions under which this is feasible fall in the frequency region between the transverse optical phonon resonance of GaAs and the traditional cut-off frequency of the diode waveguide. In addition, our results indicated when the excitation was slightly above the phonon resonance frequency, the plasmon propagation attained low-loss characteristics. We also showed that the existence or nonexistence of the depletion zone between the p- and n- interfaces allowed certain plasmon modes to propagate, while others decayed rapidly, pointing out the possibility for a design of selective filters.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Fast calibration of CBED patterns for quantitative analysis

1993 ◽  
Vol 51 ◽  
pp. 674-675
Author(s):  
M.A. Gribelyuk ◽  
M. Rühle
Keyword(s):  
Reciprocal Lattice ◽  
Accurate Determination ◽  
Incident Beam ◽  
Crystal Thickness ◽  
Structure Model ◽  
Beam Direction ◽  
Transmitted Beam ◽  
Reciprocal Vector ◽  
On Line

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

Computer-Assisted High-Re Solution TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 162-163
Author(s):  
F.A. Ponce ◽  
H. Hikashi
Keyword(s):  
Signal To Noise Ratio ◽  
Accurate Determination ◽  
Computer Software ◽  
Video Camera ◽  
Image Contrast ◽  
Objective Lens ◽  
Computer Assisted ◽  
Optical Parameters ◽  
Astigmatism Correction

The determination of the atomic positions from HRTEM micrographs is only possible if the optical parameters are known to a certain accuracy, and reliable through-focus series are available to match the experimental images with calculated images of possible atomic models. The main limitation in interpreting images at the atomic level is the knowledge of the optical parameters such as beam alignment, astigmatism correction and defocus value. Under ordinary conditions, the uncertainty in these values is sufficiently large to prevent the accurate determination of the atomic positions. Therefore, in order to achieve the resolution power of the microscope (under 0.2nm) it is necessary to take extraordinary measures. The use of on line computers has been proposed [e.g.: 2-5] and used with certain amount of success.We have built a system that can perform operations in the range of one frame stored and analyzed per second. A schematic diagram of the system is shown in figure 1. A JEOL 4000EX microscope equipped with an external computer interface is directly linked to a SUN-3 computer. All electrical parameters in the microscope can be changed via this interface by the use of a set of commands. The image is received from a video camera. A commercial image processor improves the signal-to-noise ratio by recursively averaging with a time constant, usually set at 0.25 sec. The computer software is based on a multi-window system and is entirely mouse-driven. All operations can be performed by clicking the mouse on the appropiate windows and buttons. This capability leads to extreme friendliness, ease of operation, and high operator speeds. Image analysis can be done in various ways. Here, we have measured the image contrast and used it to optimize certain parameters. The system is designed to have instant access to: (a) x- and y- alignment coils, (b) x- and y- astigmatism correction coils, and (c) objective lens current. The algorithm is shown in figure 2. Figure 3 shows an example taken from a thin CdTe crystal. The image contrast is displayed for changing objective lens current (defocus value). The display is calibrated in angstroms. Images are stored on the disk and are accessible by clicking the data points in the graph. Some of the frame-store images are displayed in Fig. 4.

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