M. Cruz-Irisson

Theory of Raman Scattering by Phonons in Germanium Nanostructures

Within the linear response theory, a local bond-polarization model based on the displacement–displacement Green’s function and the Born potential including central and non-central interatomic forces is used to investigate the Raman response and the phonon band structure of Ge nanostructures. In particular, a supercell model is employed, in which along the [001] direction empty-column pores and nanowires are constructed preserving the crystalline Ge atomic structure. An advantage of this model is the interconnection between Ge nanocrystals in porous Ge and then, all the phonon states are delocalized. The results of both porous Ge and nanowires show a shift of the highest-energy Raman peak toward lower frequencies with respect to the Raman response of bulk crystalline Ge. This fact could be related to the confinement of phonons and is in good agreement with the experimental data. Finally, a detailed discussion of the dynamical matrix is given in the appendix section.

Chaotic noise MOS generator based on logistic map

The Birkhoffs ergodic theorem (BET), bifurcation diagram (BD) and Lyapunovs exponent (LE) are used in order to design a chaotic noise generator that is governed by the logistic map (LM). For this, a MOS analog circuit that operates in the current-mode, which is based on translinear principle (TLP), is used. To iterate the transference function of this circuit and also to maintain the parameter control of the LM, a current amplifier has been used. The specifications of the design are obtained from the analysis of the model. The results demonstrate the correct operation of the circuit, even when a mismatching of 2% is considered between the devices that control the operation region. The statistical distribution of the output signal on the circuit is similar to uniform distribution and it is related with the parameter value that rules the transfer function of the circuit.

Ab-initio study of anisotropic and chemical surface modifications of β-SiC nanowires

The electronic band structure and electronic density of states of cubic SiC nanowires (SiCNWs) in the directions [001], [111], and [112] were studied by means of Density Functional Theory (DFT) based on the generalized gradient approximation and the supercell technique. The surface dangling bonds were passivated using hydrogen (H) atoms and OH radicals in order to study the effects of this passivation on the electronic states of the SiCNWs. The calculations show a clear dependence of the electronic properties of the SiCNWs on the quantum confinement, orientation, and chemical passivation of the surface. In general, surface passivation with either H or OH radicals removes the dangling bond states from the band gap, and OH saturation appears to produce a smaller band gap than H passivation. An analysis of the atom-resolved density of states showed that there is substantial charge transfer between the Si and O atoms in the OH-terminated case, which reduces the band gap compared to the H-terminated case, in which charge transfer mainly occurs between the Si and C atoms.

Computational simulation of the effects of oxygen on the electronic states of hydrogenated 3C-porous SiC

A computational study of the dependence of the electronic band structure and density of states on the chemical surface passivation of cubic porous silicon carbide (pSiC) was performed using ab initio density functional theory and the supercell method. The effects of the porosity and the surface chemistry composition on the energetic stability of pSiC were also investigated. The porous structures were modeled by removing atoms in the [001] direction to produce two different surface chemistries: one fully composed of silicon atoms and one composed of only carbon atoms. The changes in the electronic states of the porous structures as a function of the oxygen (O) content at the surface were studied. Specifically, the oxygen content was increased by replacing pairs of hydrogen (H) atoms on the pore surface with O atoms attached to the surface via either a double bond (X = O) or a bridge bond (X-O-X, X = Si or C). The calculations show that for the fully H-passivated surfaces, the forbidden energy band is larger for the C-rich phase than for the Si-rich phase. For the partially oxygenated Si-rich surfaces, the band gap behavior depends on the O bond type. The energy gap increases as the number of O atoms increases in the supercell if the O atoms are bridge-bonded, whereas the band gap energy does not exhibit a clear trend if O is double-bonded to the surface. In all cases, the gradual oxygenation decreases the band gap of the C-rich surface due to the presence of trap-like states.

Numerical calculation of the lyapunov exponent for the logistic MAP

Chaotic maps can be used to describe the behavior of dynamical systems and they are characterized by a parameter. The logistic map (LM) is a chaotic map very used in different areas. In the analysis of the dynamical system an important feature is the system stability, which can be determined using the Lyapunov Exponent (LE). In this paper two ways to compute numerically the LE for the LM are shown. In the first alternative, the Birkhoffpsilas Ergodic Theorem (BET) and the orbit produced by the LM are used. In the second alternative, the stationary distribution rhoest of the LM is estimated using the first derived of the logistic function and the central values of each interval in the partition used in the estimation.

Computational Modeling of the Size Effects on the Optical Vibrational Modes of H-Terminated Ge Nanostructures

The vibrational dispersion relations of porous germanium (pGe) and germanium nanowires (GeNWs) were calculated using the ab initio density functional perturbation theory with a generalized gradient approximation with norm-conserving pseudopotentials. Both pores and nanowires were modeled using the supercell technique. All of the surface dangling bonds were saturated with hydrogen atoms. To address the difference in the confinement between the pores and the nanowires, we calculated the vibrational density of states of the two materials. The results indicate that there is a slight shift in the highest optical mode of the Ge-Ge vibration interval in all of the nanostructures due to the phonon confinement effects. The GeNWs exhibit a reduced phonon confinement compared with the porous Ge due to the mixed Ge-dihydride vibrational modes around the maximum bulk Ge optical mode of approximately 300 cm−1; however, the general effects of such confinements could still be noticed, such as the shift to lower frequencies of the highest optical mode belonging to the Ge vibrations.

Modeling the effects of Si-X (X = F, Cl) bonds on the chemical and electronic properties of Si-surface terminated porous 3C-SiC

Abstract Porous silicon carbide offers a great potential as a sensor material for applications in medicine and energetics; however, the theoretical chemical characterization of its surface is almost nonexistent, and a correct understanding of its chemical properties could lead to the development of better applications of this nanostructure. Hence, a study of the effects of different passivation agents on the structure and electronic properties of porous silicon carbide by means of density functional theory and the supercell technique was developed. The porous structures were modeled by removing columns of atoms of an otherwise perfect SiC crystal in the [001] direction, so that the porous structure exhibits a surface exclusively composed of Si atoms (Si-rich) using different surface passivation agents, such as hydrogen (H), fluoride (F) and chloride (Cl). The results demonstrate that all of the passivation schemes exhibit an irregular band gap energy evolution due to a hybridization change of the surface. The structural analysis shows a great dependence of the bond characteristics on the electronegativity of the bonded atoms, and all of the structural and electronic changes could be explained due to steric effects. These results could be important in the characterization of pSiC because they provide insight into the most stable surface configurations and their electronic structures.

DFT study of the electronic structure of Cubic-SiC nanopores with a c-terminated surface

A study of the dependence of the electronic structure and energetic stability on the chemical surface passivation of cubic porous silicon carbide (pSiC) was performed using density functional theory (DFT) and the supercell technique. The pores were modeled by removing atoms in the [001] direction to produce a surface chemistry composed of only carbon atoms (C-phase). Changes in the electronic states of the porous structures were studied by using different passivation schemes: one with hydrogen (H) atoms and the others gradually replacing pairs of H atoms with oxygen (O) atoms, fluorine (F) atoms, and hydroxide (OH) radicals. The results indicate that the band gap behavior of the C-phase pSiC depends on the number of passivation agents (other than H) per supercell. The band gap decreased with an increasing number of F, O, or OH radical groups. Furthermore, the influence of the passivation of the pSiC on its surface relaxation and the differences in such parameters as bond lengths, bond angles, and cell volume are compared between all surfaces. The results indicate the possibility of nanostructure band gap engineering based on SiC via surface passivation agents.

Cryptosystem with one dimensional chaotic maps

This paper presents a 64-bits chaotic block cryptosystem, which uses as noise generator one-dimensional chaotic maps with 8 bits sub-blocks data. These chaotic maps use a control parameter that allows them to operate in the chaotic region, which guarantees that each sub-block of data is mixed with unpredictable random noise. Statistical mechanic tools such as: bifurcation diagram, Lyapunov exponent, and invariant distribution have been used to analyze and evaluate the behavior of the noise generator. The cryptosystem has been evaluated using concepts of information theory, such as: entropy, as a diffusion measure in the encryption process, and mutual information as a measure of relationship between plaintext and its respective cryptogram. The noise generator has been used on the non-balanced and dynamic network proposed by L. Kocarev. The randomness of the cryptograms has been evaluated using the NIST random tests. The proposed cryptosystem can be a component in software applications that provides security to stored or communicated information. The proposed cryptosystem has a similar behavior to the one of currently used cryptosystems and it has been designed with chaotic sequence generators, which are aperiodic by definition.

Band-gap engineering of halogenated silicon nanowires through molecular doping

AbstractIn this work, we address the effects of molecular doping on the electronic properties of fluorinated and chlorinated silicon nanowires (SiNWs), in comparison with those corresponding to hydrogen-passivated SiNWs. Adsorption of n-type dopant molecules on hydrogenated and halogenated SiNWs and their chemisorption energies, formation energies, and electronic band gap are studied by using density functional theory calculations. The results show that there are considerable charge transfers and strong covalent interactions between the dopant molecules and the SiNWs. Moreover, the results show that the energy band gap of SiNWs changes due to chemical surface doping and it can be further tuned by surface passivation. We conclude that a molecular based ex-situ doping, where molecules are adsorbed on the surface of the SiNW, can be an alternative path to conventional doping. Graphical abstractMolecular doping of halogenated silicon nanowires