Band Structure Of Silicon Research Articles

Hydrogenated Si clusters: Band formation with increasing size.

The electronic structures of various Si clusters of different sizes (with hydrogenated surfaces) are evaluated using a nearest-neighbor empirical tight-binding Hamiltonian which describes well the band structure and fundamental band gap of crystalline silicon. The largest cluster contains 3109 Si atoms and 852 H atoms, has a diameter of 49 \AA{}, and has both a normalized Si density of states and a band gap very close to those of crystalline Si.

Impact-ionization theory consistent with a realistic band structure of silicon

We investigate impact-ionization processes in Si with use of a realistic band structure. The band structure and the corresponding wave functions, obtained with an empirical pseudopotential method, are used to evaluate the matrix elements for the ionization transitions. The matrix element includes the direct and the exchange terms with the umklapp terms associated with the periodic part of the Bloch function. It is shown that these ionization processes are IinherentlyP anisotropic and that it is crucial to take account of this anisotropy in analyzing the ionization processes. The anisotropy (wave-vector dependence) of the ionization probability is manifested through the strong restrictions imposed by energy and the momentum conservation during the transition under a realistic band structure.

A novel approach for including band-structure effects in a Monte Carlo simulation of electron transport in silicon

We present a novel approach for including the effects of realistic silicon band structure in the simulation of electron transport with a Monte Carlo method. This will be achieved by an electron effective-mass and energy–over–wave-vector relation, which are derived directly from the density of states. Consistent with this model, the scattering rates as well as the equations of motion are determined by the density of states. With our approach the computation tables in three-dimensional momentum space can be replaced by one-dimensional tables in energy space. The necessary amount of memory size and table lookup time is therefore significantly reduced. The number of free parameters in our model is not higher than in the full band-structure model. We show by comparison with full band-structure Monte Carlo and experimental results that there is no loss in physical meaning by the use of the new method.

Calculation of the band structure and superconductivity in the hexagonal close-packed phase of silicon

We report a calculation of the band structure and superconductivity of silicon in the hexagonal close-packed phase under pressure. The effect of pressure on the band structure is obtained by means of the linear muffin-tin orbital method. The superconducting transition temperatureTc is calculated using the formulas of Allen and Dynes1 as well as those of McMillan2. It is found that the value ofTc increases with pressure up to 74.3 GPa. The increase inTc is attributed to the continuous s → d electron transfer under pressure. The calculated values ofTc are compared with the available experimental data. Further, Heine's fifth power law3 has been tested from thed-band widths obtained from the band-structure results.

The spin-orbit splitting in the Si bandstructure measured by means of spin-resolved photoemission

Abstract Spin-, angle- and energy-resolved photoemission with circularly polarized synchrotron radiation from BESSY has been applied to deduce information about the electronic structure of silicon in the Λ-direction. We used the highly symmetrical experimental set-up of normal radiation incidence and normal electron emission. This method, which has in the past several times been applied to metals and rare gas crystals with medium and high atomic numbers, has thus been applied now to a semiconductor with a low atomic number ( Z = 14). For photon energies between 5.5 and 10 eV we find a peak V in the photoemission spectra which corresponds to a transition from the valence bands in the bulk band structure of silicon in the Λ-direction. The electrons which contribute to the peak are spin polarized due to a spin-orbit splitting Δ E so smaller than 50 meV. Adsorption of 0.5 ML Ag or Au induces band bendings and work function changes and yields a sharper peak and less secondary electron background than the clean Si(1 1 1)-surface. For both the clean and adsorbate covered surface and k ⊥ away from Γ we determine Δ E so from a spin analysis of peak V and find values between 20 and 35 meV with typical errors of 10 meV. These values in Λ-direction are smaller than the Δ E so -value of 44 meV at the Γ-point [1, 2].

A Model Calculation of the Dielectric Band Structure of Diamond and Silicon

AbstractA model microscopic dielectric response previously proposed is used to calculate the dielectric band structure of diamond and silicon along several symmetry directions in the Brillouin zone. The most screened dielectric eigenpotentials at the Γ point are also obtained. Comparison of the present results with previous model calculations provides an indication that the model dielectric response used is satisfactorily accurate and realistically incorporates local‐field effects.

A lucky drift model, including a soft threshold energy, for the relation between gate and substrate currents in MOSFETs

Substrate and gate currents in MOSFETs are formulated by interpreting the lucky drift model with a soft threshold energy from the distribution function point of view. A modified Keldysh formula is introduced to the ionization relaxation time. Unknown parameters in the formulation are determined by fitting the calculation to the measured relations between gate and substrate currents in MOSFETs. Impact ionization coefficient reported by Lee et al. [16], is also subsidiarily used for determining the parameters. The model can eliminate the nonphysical fitting parameter on the Schottky barrier lowering effect, which was necessary in past models. Fitting parameters concerning the ionization relaxation time, thus obtained, are compared with various theoretical calculations. It is recognized that the relation between gate and substrate currents in MOSFETs reflects the energy dependent ionization rate which originates from electron-electron interaction in the complicated energy band structure of silicon.

Effect of electron band structure on energy distribution of secondaries in silicon

A study is made of the cascade process which describes the energy loss and multiplication of secondary electrons and holes in crystalline silicon irradiated by low energy electrons. The pair creation scattering rates are evaluated in framework of statistical model which takes into account the electron band structure of silicon. Kinetic equations for the excited electron and hole energy distributions are solved numerically in the isotropic scattering approximation for some primary energies E p — E F ⩽ ħω pl . The derived energy distribution function permits a smooth interpolation ƒ( E) ∼ ⦶ E - E F ⦶ - s . The calculations result in a weak energy dependence of the mean pair creation energy.

Electronic properties of micro-n-i-p-istructures in silicon

The electronic properties of ultrathin, heavily doped n-i-p-i structures in silicon have been studied with use of the ab initio pseudopotential method. Three doping configurations are used to model n-i-p-i structures by replacing silicon atoms with aluminum and arsenic atoms. The doped silicon samples are found to retain an indirect energy band gap. The heavy doping levels result in the formation of impurity bands. The top of the valence band and the bottom of the conduction band are impurity-related bands. The electron-hole charge separation even occurs when the n- and p-type impurities are nearest neighbors. The heavy doping significantly increases the electron-hole recombination matrix elements as compared to the light-doping case in which the bulk silicon band structure can be used to determine the matrix elements. However, the matrix elements for the three n-i-p-i structures in Si which were investigated are still 5 orders of magnitude smaller than those for the direct-band-gap transition in GaAs.

Band structure of silicon from the semiempirical modified neglect of diatomic differential overlap method.

We present results of band-structure calculations for silicon produced using self-consistent matrix elements in a tight-binding framework. The matrix elements are extracted from the Fock matrix of a converged modified neglect of diatomic differential overlap (MNDO) calculation on a molecular cluster of silicon atoms. Our initial results indicate no band gap and the valence p subbands above the conduction s subband. By adjusting two of the MNDO parameters, we obtain a band structure that is considerably improved, but which still suffers from some of the usual deficiencies of the tight-binding method. We compare our results with other recently published semiempirical studies.

Monte-Carlo simulation of submicrometer Si n-MOSFETs at 77 and 300 K

Monte Carlo simulation results for small silicon n-MOSFETs at 77 and 300 K are presented. A complete description of the silicon band structure including consistent scattering rates, electron-electron scattering, and plasma effects is included in the calculation for the first time. The dependence of transconductance on channel length is in excellent agreement with the experiments of G.A. Sai-Halasz et al. (see ibid., vol.EDL-8, p.463-6, Oct. 1987 and ibid., vol.EDL-9, p.464-6, Sep. 1988) and serves to support the expectation of significant velocity overshoot in these devices. For extremely short channels ( >

Piezo-Hall coefficients of n-type silicon

The effect of uniaxial mechanical stress on the Hall coefficient of n-type silicon has been measured for various crystallographic orientations, and piezo-Hall coefficients P12 and P11-P44 have been derived for electron concentrations n between 1014 and 1016 cm−3 and temperatures ranging from −80 to +100 °C. In this range the piezo-Hall effect is found to be as important as the piezoresistance effect which is understood in terms of the many-valley band structure of silicon with anisotropic energy minima. For Hall plates in the (100) and the (110) plane of silicon the resulting longitudinal and transverse piezo-Hall coefficients at room temperature are plotted as a function of their orientation in the plane. It turns out that the piezo-Hall as well as the piezoresistance effects are minimized for a Hall plate in the (110) plane with the current flow roughly parallel to 〈11̄1〉.

Minimal tight-binding Hamiltonian for semiconductors.

We present a minimal tight-binding Hamiltonian which describes properly both valence and conduction bands of tetrahedrally coordinated semiconductors. We find that, for a correct description of the electronic structure, it is necessary to include a realistic wave-function basis and at least the interaction matrix element between ${\mathrm{sp}}^{3}$ orbitals in second-neighbor atoms pointing towards the common neighbor. Using Slater orbitals as basis functions and a six-parameter Hamiltonian, the band structure of silicon is reproduced with a root-mean-square deviation with respect to the experimental one of 0.3 eV.

Transition Probability of Impact Ionization by Holes in Silicon

AbstractAn analytical expression is developed for the transition probability per unit time for impact ionization by holes. The approach is based upon time dependent perturbation calculations and the Bloch functions for the states of electrons and holes. The threshold energy of ionization by holes is calculated for the valley L1 for the electron band structure of silicon. The results obtained for the probability are in good agreement with experimental results for threshold energy and theoretical results for the ionization probability.

The band structure of silicon based on X-ray diffraction data

The band structure of silicon based on X-ray diffraction data

Band structure of silicon by the self-consistent variational cellular method

The self-consistent formulation of the variational cellular method has been developed in order to calculate the electronic structure of crystals with an arbitrary number of atoms per unit cell. Applications for silicon have been carried out. Silicon, chosen here as a test case, is treated as a face-centered cubic lattice with four “atoms” per unit cell by adding empty cells. The electronic charge density was taken muffin-tin, assuming a constant value in the interstitial region between the inscribed sphere and the Wigner–Seitz polyhedrum. The spherical symmetric electronic charge density in the inscribed sphere was obtained by adding a limited number of contributions of Brillouin zone states using the “mean value point theory” developed by Baldereschi and Chadi-Cohen. Our results are in good agreement with those obtained by other methods.

On the Shaw Potential and Its Application to Self‐Consistent Band Structure and Total Energy Calculations for Silicon

On the Shaw Potential and Its Application to Self‐Consistent Band Structure and Total Energy Calculations for Silicon

Transferable nonorthogonal tight-binding parameters for silicon.

Nonorthogonal Slater-Koster (``tight-binding'') parameters have been fitted to linear muffin-tin orbital band structures of silicon in the hypothetical sc, fcc, and bcc structures at the density of ordinary diamond-cubic silicon. First- and second-neighbor parameters are used for all three structures. When the eight parameters (${H}_{\mathrm{ss}\ensuremath{\sigma}}$,...,${S}_{\mathrm{pp}\ensuremath{\pi}}$) are plotted as a function of neighbor distance, they describe approximate smooth curves which align well with the values found by Mattheiss and Patel for diamond-cubic Si, even though local coordination is entirely different. This suggests an approximate transferability of tight-binding parameters, at least if the volume is constant and coordination number is four or higher.

The use of Wannier function in the calculations of band structure of covalent crystals

A variational precedure has been used to build up Wannier functions to study the energy bands of diamond, silicon and α-tin. For the case of silicon the Wannier function, density of charge and band structure are calculated self-consistently and a simple method in a non-self-consistent way has been used to compute the band structure of diamond, silicon and α-tin. The method seems to be effective to describe the electronic properties of covalent crystals.

Effect of the electron-electron interaction on the band structure of semiconductors

Many-body effects in a semiconductor are taken into account by means of an approximation to the self-energy of the system. The analysis of the Coulomb—hole contribution suggests a description of this term by means of a local density dependent potential. Non-locality, frequency and a small local density dependences are included in the screened exchange part of the self-energy. The method gives satisfactory results for the band structure of silicon.