Holes In Si Research Articles

Impact ionization coefficient and energy distribution function at high fields in semiconductors

Impact ionization coefficients in semiconductors are numerically calculated following Keldysh’s method [Sov. Phys. JETP 21, 1135 (1965)]. This requires deriving expressions for an energy-dependent mean free path l(ε) and an energy-dependent impact ionization scattering rate rii(ε). In the derivation of rii(ε), a nonparabolic ε-k relation as well as a smooth transition from the phonon-assisted impact ionization to the phononless impact ionization are considered. Numerically calculated impact ionization coefficients for electrons and holes in Ge, Si, and GaAs agree very well with experimental data. The calculated Keldysh energy distribution function is also compared with the standard Maxwellian distribution. The average mean free path l̄, which is a function of the electric field, has values within the range often quoted in the literature.

Monte Carlo algorithm for generation-recombination noise in semiconductors

We present an original Monte Carlo procedure to account for generation-recombination noise through impurity centers in semiconductors. Numerical calculations are specialized to the case of holes in Si at 77 K. Results are found to compare favorably with available experiments.

Scanning tunneling microscopy on Si(112)

Using scanning tunneling microscopy (STM) we have measured a macroscopic Si(112) surface. A large part of the surface consisted of narrow (111) terraces with a step height corresponding to a Si double layer. Projected into the [112] direction the surface showed rows of atomic features, which are orientated along the [110] direction. We identified neighboring atoms at a distance in agreement with the ideal Si lattice, adatoms and holes with twice this distance corresponding to a local reconstruction along the rows and triangular arrangements of atoms. The separation between the rows only in some cases agreed with that of a microscopic Si(112) surface. This fact and the frequent observation of 7×7 reconstructed Si(111) facets do not indicate a large stability of Si(112).

Heteroepitaxy of semiconductor-on-insulator structures: Si and Ge on CaF2/Si(111)

Si and Ge layers have been grown on CaF2/Si(111) by molecular-beam epitaxy. Both Ge and Si grow as islands, and both the island size and the spacing between nucleation sites are considerably larger for Ge (∼300 nm) than for Si (∼100 nm). In addition, Ge and Si layers are found to be a mixture of type-A (aligned with the underlying CaF2) and type-B (rotated 180° about the surface normal with respect to the underlying CaF2) regions. The crystalline quality and surface morphology of the Ge layers are much better than those of the Si layers. This is thought to be due to the larger island size of the Ge deposits and to a greater ease of movement of the boundaries between type-A and type-B regions in Ge. Hall measurements show electron mobilities of up to 664 cm2/V s in Si layers and hole mobilities of 234 cm2/V s for Ge layers. Finally, the use of a GexSi1−x-Si superlattice, when grown on a GexSi1−x buffer layer which is lattice matched to the CaF2 at the growth temperature, is shown to improve Si heteroepitaxy.

Measurement of hole mobility in heavily doped n-type silicon

Accurate measurements of the mobility (and diffusion coefficient) of minority-carrier holes in Si:P with doping in the 1019cm-3range have been done. The technique employed the measurement of diffusion length by means of lateral bipolar transistors of varied base widths, and the measurement of minority-carrier lifetime on the same wafers from the time decay of luminescence radiation after excitation with a short laser pulse. Minority-carrier hole mobility is found to be about a factor of two higher than the mobility of holes as majority carriers in p-type Si of identical doping levels.

Diffusion coefficient of holes in silicon by Monte Carlo simulation

A theoretical investigation of the diffusivity of holes in Si as a function of temperature, field strength, and field direction is reported. Calculations have been performed with the Monte Carlo procedure. The theoretical analysis explains the main features exhibited by the experimental data available from the literature. Minor discrepancies between theory and experiment are discussed in terms of microscopic mechanisms and/or reliability of the different experimental techniques used.

Raman scattering studies in phosphorus implanted and laser annealed boron doped Si

Implantation of P in B bulk doped Si (hole concentration = 2.1×10 20 cm −3) followed by multiple pulse laser annealing with a XeCl laser has produced the incorporation of P in substitutional sites of the matrix and also charge carrier compensation. We report in this paper light scattering studies of these samples, in which a decrease of the hole-induced softening of the Si-Raman line is observed. This softening depends on the type and concentration of free carriers and thus, in our case, on the degree of compensation. This softening is discussed in terms of the interaction of the continuum of free carrier excitations with the Raman phonon. We also report the observation of the vibrations of 11B- 31 P pairs.

On the weak-field magnetoresistance of holes in Ge and Si

The weak-field magnetoresistance in p-type Ge and Si is studied theoretically in the range from 77 to 300 K. The energy band model is based on the k⋅p perturbation calculations of Kane and includes both the nonparabolicity and the warped nature of the valence band. Light and heavy holes are included. Acoustic phonon, nonpolar optical phonon, and impurity scattering are considered. No adjustable parameters are introduced into the calculations and the material parameters are those applied successfully before to the low field mobility and Hall factor. Satisfactory agreement between theory and available experimental data is obtained. For Ge the agreement is quantitative throughout the temperature and impurity concentration ranges. For Si the agreement is good at 300 K. At 77 K the agreement in Si is satisfactory.

Ambipolar diffusion of high-density electrons and holes in Ge, Si, and GaAs: Many-body effects

Many-body effects are incorporated into a theory for the density dependence of the electron-hole ambipolar diffusion coefficient in semiconductors. Self-energy shifts of the free-carrier band edges lead to a band-gap gradient in the presence of a carrier-density gradient and therefore a diffusion coefficient which is less than that obtained from the independent-particle Boltzmann transport theory. The diffusion coefficient decreases with increasing carrier density until carrier degeneracy becomes important, after which the coefficient increases with density as in the independent-particle theory. The difference between the two theories is most apparent for high-effective-mass semiconductors and low carrier temperatures. Results are calculated for Ge, Si, and GaAs for common lattice and carrier temperatures of 100 and 300 K, with silicon showing the largest influence from many-body effects.

Effective Masses of Heavy and Light Holes in Ge and Si

Effective Masses of Heavy and Light Holes in Ge and Si

Drift and diffusion of hot holes in silicon

The mobility and the diffusion coefficient versus electric field strength were calculated from current and noise data on Si hole injection diodes. The results were interpreted in terms of the structure of the valence band.

On the diffusivity of holes in silicon

The longitudinal diffusion coefficient of holes in Si has been measured with time-of-flight and noise techniques at 300 K for field strengths ranging from about 0.5 up to 40 kV/cm. As the electric field increases, the diffusion coefficient decreases to about 0.3 of its Ohmic value much more sharply than results previously reported in literature. The experimental results are interpreted by a Monte Carlo simulation which includes warping and nonparabolicity effects of the heavy-hole band.

Noise and diffusion of hot holes in Si

A recent attempt to interpret white-noise data of hot holes in Si suggests the conflicting results of having an equilibrium carrier energy in the region of field where non-ohmic behaviour is clearly evident. This contradiction arises when different theoretical approaches are tested on the experimental data. Since, as is shown on basic principles, white noise and diffusion describe the same physical phenomenon, a microscopic interpretation of the above experiments has been carried out by means of a Monte Carlo determination of the longitudinal diffusion coefficient. Agreement between theory and experiments resolves the previous contradiction and shows that the Monte Carlo technique can be an effective instrument in studying noise phenomena.

Time-resolved hole transport ina−SiO2

The transport of excess holes in amorphous Si${\mathrm{O}}_{2}$ is reported as a function of field and temperature, with an emphasis on the behavior at short times ($t\ensuremath{\ge}10$ nsec) after the hole is introduced into the glass. The unusual features of the transport for $t\ensuremath{\gtrsim}{10}^{\ensuremath{-}5}$ seconds can be rationalized on the basis of the continuous-time random-walk model (CTRW) of Scher and Montroll. It is hypothesized that at short times the hole hops, perhaps as a small polaron, from one oxygen nonbonding orbital to one of the nearest-neighbor oxygen orbitals. The hole is eventually trapped at a structural defect and the transport continues as a tunneling from one defect to another, causing the unusual transport phenomena associated with the CTRW. The temperature dependence of the hole transport is markedly non-Arrhenius below 200\ifmmode^\circ\else\textdegree\fi{}K, which is consistent with the small-polaron model.

On the electric field dependence of the conductivity of holes in Si at low temperatures. II. The influence of the variation of steady‐state hole density with electric field on the conductivity

AbstractMeasurements of the electric field dependence of the hole conductivity of Si with various doping levels and orientations are performed at 20.3 and 27.1 K. A description of the essential characteristics of the experimental results is achieved within the frame of a theoretical model. In this model, the field dependence of the hole mobility (taking into account non‐parabolicity of the valence band and non‐equipartition of acoustic phonon energy in the distribution function as well as in the momentum relaxation time) and the field dependence of the hole concentration (based on Lax′ cascade theory) are combined. Comparison of experimental and numerical results gives the relation between the participation of optical phonons in the hole capture process on shallow acceptors and the transition from super‐ to sublinear current‐voltage characteristics in high‐purity p‐Si at low temperatures and at electric field strengths below the breakdown range.

The effect of the material velocity—Field characteristic on the small-signal microwave impedance of punchthrough devices

The theoretical dependence of the small-signal impedance of microwave punchthrough diodes (BARITT) on the shape of the velocity-field characteristic is studied with the aid of a small-signal computer simulation and a simple analytical model, in an attempt to assess what semiconductor material might give the smallest negative Q factor. Four different types of velocity-field characteristics are considered showing, respectively, soft saturation (e.g., holes in Si), negative mobility (e.g., electrons in GaAs), constant mobility (e.g., electrons in GaP), and hard saturation (e.g., electrons in GaAs <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> ). A clear picture emerges of the effect of the velocity-field characteristics on the microwave negative resistance with Si appearing to be the near optimum material; GaAs provides little if any negative resistance due to poor phasing of the injected ac space charge and the other two materials are intermediate.

On the Electric Field Dependence of the Conductivity of Holes in Si at Low Temperatures 1. The Drift Velocity under Consideration of the Non‐Equipartition of Acoustic Phonon Energy

AbstractThe field dependence of the drift pelocity of holes in Si is discussed within a non‐parabolic valence band model. Taking into consideration the non‐equipartition of acoustic phonon energy both in a field‐dependent distribution function and in the relaxation time of holes, a satisfactory description of the experimental drift velocity can be given at low temperatures in a wide field range.

ChemInform Abstract: THE STANDARD THERMODYNAMIC FUNCTIONS FOR THE FORMATION OF ELECTRONS AND HOLES IN GE, SI, GAAS, AND GAP

Chemischer InformationsdienstVolume 6, Issue 42 Physical Inorganic Chemistry ChemInform Abstract: THE STANDARD THERMODYNAMIC FUNCTIONS FOR THE FORMATION OF ELECTRONS AND HOLES IN GE, SI, GAAS, AND GAP C. D. THURMOND, C. D. THURMONDSearch for more papers by this author C. D. THURMOND, C. D. THURMONDSearch for more papers by this author First published: October 21, 1975 https://doi.org/10.1002/chin.197542019Citations: 2AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume6, Issue42October 21, 1975 RelatedInformation

Hole drift velocity in silicon

Drift velocities for holes in high-purity Si were measured for fields between about 3 and 5\ifmmode\times\else\texttimes\fi{}${10}^{4}$ V/cm and temperatures between 6 and 300\ifmmode^\circ\else\textdegree\fi{}K for the crystallogrphic directions $〈100〉$, $〈110〉$, and $〈111〉$. The Ohmic mobility is theoretically interpreted on the basis of a two-band model consisting of a spherical parabolic and a spherical nonparabolic band, and the relaxation-time approximation. The low-temperature Ohmic mobility is strongly influenced by the nonparabolicity of the heavy-hole band. The high-field region ($E\ensuremath{\ge}{10}^{3}$ V/cm) was analyzed using a single warped heavy-hole band model and a Monte Carlo technique. Anisotropy of hot-hole drift velocity is associated with warping of the valence band. Optical- and acoustic-scattering mechanisms are found to be of comparable strength.

The Standard Thermodynamic Functions for the Formation of Electrons and Holes in Ge, Si, GaAs , and GaP

The forbidden energy gaps of Ge, Si, , and have been used to obtain the standard Gibbs energy, enthalpy and entropy of formation of electrons and holes for each semiconductor up to the melting points. The forbidden energy gap is the standard Gibbs energy of formation of electrons and holes and the enthalpy and entropy have been obtained from the energy gap as a function of temperature and familiar thermodynamic relationships. Energy gaps as a function of temperature, available in the literature, have been fit to the semiempirical equation of Varshni and used to extrapolate the energy gaps and thereby the three thermodynamic functions to the melting points. It is well known that the energy gaps, i.e., the Gibbs energies, decrease with increasing temperature but it is not well known that the enthalpy of formation increases with temperature and that it is proportional to the slope of the familiar logarithmic plot of the intrinsic carrier concentration over vs.. Examples of the utility of the enthalpy function are given. It is the entropy that leads to the decrease in energy gap with increasing temperature and its magnitude is large near the respective melting points (10–13 cals/deg, i.e.,) arising from the interactions of electrons and holes with the lattice. The intrinsic carrier concentrations were calculated from the forbidden energy gaps and the average effective masses which were estimated for the higher temperatures.