Drift Velocity Data Research Articles

Full-band Monte Carlo model of electron and hole transport in strained Si including inelastic acoustic phonon scattering

Full-band Monte Carlo simulations of electron and hole transport in strained Si on Si0.7Ge0.3 have been performed with a transport model which includes a wave-vector-dependent inelastic acoustic phonon scattering rate. Only two unambiguously determined deformation potentials are needed to achieve excellent agreement with experimental drift velocity versus electric field data for unstrained Si over the very wide temperature range from 20 to 430 K. For strained Si, this model yields in-plane lattice mobilities of 3490 cm2/(V s) for electrons and 1760 cm2/(V s) for holes at 300 K. Drift velocity and energy versus electric field characteristics are given as reference for conventional device simulations. In contrast to simpler transport models, we do not find a pronounced Gunn effect at 77 K.

Electromigration transport mechanisms in Al thin-film conductors

Electromigration occurs along grain boundaries in polycrystalline thin-film conductors when the grain size is significantly larger than the conductor width. As circuit feature sizes have been reduced, microstructures have become near bamboo and alternate diffusion mechanisms must operate within the bamboo grains. In this article we examine drift velocity data to determine electromigration mechanisms in bamboo grains. We present measurements of the temperature and width dependence of the drift velocity of thin-film conductors with bamboo microstructures. The activation energy for drift is consistent with lattice diffusion in Al. There is no width dependence of the drift velocity in the range 0.6–2.7 μm, indicating a negligible flux of atoms along the conductor edges. We compare these measurements with data available for a variety of conductor microstructures, and with drift data for bulk Al. The drift velocities of conductors with bamboo microstructures obtained from a variety of sources show very good agreement, and are similar to drift velocities observed in bulk Al. We conclude that the dominant mode of electromigration in thin-film conductors with bamboo microstructures and bulk Al is the same, and occurs by lattice vacancy diffusion.

A study of the morphology of a discontinuous section of a first year arctic pressure ridge

The upper and lower surfaces of a 300 m long section of a first year pressure ridge containing both linear and corner regions have been surveyed. The upper surface survey employed conventional ground based techniques combined with aerial stereo-photography, whilst the lower surface was surveyed with a narrow beam echo sounder mounted on a tethered submersible. The ridge was sited on the southern edge of a re-frozen lead, and estimates based on the block thicknesses and on ice drift velocity data records, place the time of formation between January 25 and 30, 1991, about 3 months prior to the survey. The southern edge of the keel consisted of large blocks and rafted sections of the original sheet, whilst the northern edge was composed of smaller scale consolidated rubble from the re-frozen ice of the lead. The section of ridge surveyed contained about 3 times as much ice volume as would be estimated by applying the triangular geometry of the classical 2-dimensional ridge, most of the excess volume being associated with the corner regions. Profiles of the draft across the structure had a fractal dimension of 1.5, similar to values reported by other authors for unweathered ice structures. Considerations of the equilibrium of the complete structure suggest that when formed it was capable of sustaining significant bending moments on scales of 20m and that up to 3 thicknesses of rafted ice of the original sheet must have been present.

Determination of cross-section for Ar +He elastic collisions from drift velocity data: Monte Carlo simulation

The Monte Carlo simulation of the motion of Ar + ions in He buffer gas in a uniform electric field has been carried out. The total cross-section for elastic collisions between the Ar + ion and the He atom was considered in the form σ T( v) = C/ v where v is the relative velocity of the Ar + ion and the He atom. The constant C was adjusted in such a way that the calculated values of the drift velocity of the Ar + ion agree with the corresponding experimentally measured values. The cross-section was also calculated from the potential between the Ar + ion and the He atom by the Jeffreys—Wentzel—Kramers—Brillouin (JWKB) approximation in order to check the results from the Monte Carlo simulation.

A Comparison of Electromigration in Bulk and Thin - Film Aluminum

AbstractThe dominant mode of electromigration in polycrystalline Al thin - film conductors is along grain boundaries when the conductor width is significantly larger than the grain size. Integrated circuit feature sizes, however, have now decreased to the point where microstructures are no longer polycrystalline, but are near - bamboo. Electromigration must operate along pathways other than grain boundaries in the bamboo segments. Here drift velocity data is presented for bamboo microstructures with widths down to 0.6 μm and compared with drift data available in the literature for thin films with a variety of microstructures and bulk Al. Bamboo films show lower drift velocities and higher activation energies for drift than polycrystalline films. The data for bamboo microstructures is consistent with drift measurements performed on bulk Al indicating that the transport mechanism in bamboo films is identical to that in bulk Al.

Electron collision cross sections of boron trichloride

Three vibrational and two dissociation cross sections of BCl3 in the range 0–30 eV have been unfolded from recent electron drift velocity data in BCl3/Ar and BCl3/He mixtures.

Drift mobility of excess electrons in liquid ethane, subjected to high electric fields

Drift velocity data of excess electrons in liquid ethane reveal the presence of two regions of linear dependence of the velocities vs. electric field intensity. From the slopes of these plots, two different mobilities are calculated in the temperature range 111 to 216K. It is postulated that the electron may exist, in liquid ethane, depending on the electrical field, in two states, a solvated electron, es, and a nonlocalized or semifree electron, symbolized by e, the latter being formed by extracting the electron from its solvation shell under the influence of high electrical fields. The two mobilities μes and μes are then assigned to the respective species, es and e. In accord to the above hypothesis, an Arrhenius plot of 1nμes vs. (1/T) shows a rough linearity, (although some curvature of the plot exists). Also, in accord to the postulated two states of the electron in liquid ethane (at low and high electrical fields, respectively), the mobility μe results proportional to T−frsol3/2, as predicted approximately by the Cohen-Lekner theory of nonlocalized scattering electrons.

Low energy electron collision cross sections for silane

Electron collision cross sections for silane in the energy range 0–5 eV are presented. We show that the conventional two-term solution of the Boltzmann equation is not correct for unfolding the cross sections from swarm data in pure silane, silane-Ar, and silane-Kr mixtures. A Monte Carlo method is used to derive the cross sections for the these systems and the two-term solution is used in silane-He mixtures. It is shown that experimental drift velocity data for the silane-He system is a valuable adjunct for unfolding the silane cross sections from existing swarm data.

Momentum Transfer Cross Section for e??Kr Scattering

The momentum transfer cross section for electrons in krypton has been derived over the energy range Q-4 eV from an analysis of drift velocity and DT/I-' data for hydrogen-krypton mixtures. At energies in the vicinity of the Ramsauer-Townsend minimum, the present work differs significantly from derivations based on analyses of drift velocity data alone. The overall uncertainty in the derived cross section reflects the experimental errors in the transport coefficients, the uncertainty in the cross sections used to represent the hydrogen component in the mixtures, and the uncertainty associated with the X2 minimisation. The present cross section is compared with recent theoretical calculations and other experimental derivations.

Warm and hot hole drift velocity in GaAs studied by Monte Carlo simulation

We have studied hole mobilities and drift velocities in undoped GaAs at 77 and 300 K using the Monte Carlo method. Two different sets of valence band parameters were used (V1: A=7.98, B=5.16, C=6.56; V2: A=7.65, B=4.82, C=7.7). The results show that the low-field mobility is sensitively dependent on the particular choice of valence band parameters. The low-field mobilities obtained were 440 cm2/V s(V1) and 330 cm2/V s(V2) at 300 K, and 17 150 cm2/V s(V1) and 11 400 cm2/V s(V2) at 77 K. The warm hole transport coefficients β0 and γ0 were extracted from the drift velocity data. At 77 K, β0=−7×10−9 m2/V2 and γ0 was estimated to be 2×10−10 m2/V2(V1). At 300 K the corresponding estimated values were −2×10−13 m2/V2 and 5×10−14 m2/V2, respectively. The warm hole region is limited to E<0.04 kV/cm at 77 K and to E<10 kV/cm at 300 K. Anisotropy in the drift velocity is negligible in the warm hole region and relatively small at higher electric fields. Complete velocity saturation was not observed for the electric fields considered here (E<60 kV/cm).

Momentum transfer cross section of xenon deducted from electron drift velocity data

Momentum transfer cross section of xenon is deduced from experimental electron drift velocity data over the energy range from 0.02 to 10 eV by using an algorithm based on a Boltzmann equation method. The result shows that the Ramsauer-Townsend minimum is located at an electron energy of 0.7 eV with a magnitude of 9*10-17 cm2. It is found that the present momentum transfer cross section is in excellent agreement with the experimental data points of Register et al. (1986) and that the calculated diffusion coefficient (parallel direction to the electric field) from the deduced cross section agrees very well with the measurements of Hashimoto and Nakamura (1990) for E/N above 0.07 Td. The fractional difference between the calculated electron drift velocity and the experimental one is suppressed within 1.2% at E/N below 0.1 Td and within 3% at E/N above 0.1 Td. Above an electron energy of 8.32 eV, inelastic collision cross sections are necessary for the deduction of the momentum transfer cross section. Therefore, the total excitation cross section of Hayashi (1983) and the ionization cross section of Krishnakumar and Srivastava (1988) are used to deduce the momentum transfer cross section over a range of high electron energies. As a result, the peak of the deduced momentum transfer cross section is located at an electron energy of 5 eV with a magnitude of 3*10-15 cm2.

Some Recent Studies of Electron Swarms in Gases

Some recent studies of electron swarms in gases under the action of an electric field are introduced. The studies include a new type of continuity equation for electrons having a form in which the partial derivative of the electron density with respect to position and to time are interchanged, a method to deduce the time-of-flight and arrival-time-spectrum swarm parameters based on a Fourier-transformed Boltzmann equation, an examination of the correspondence between experimental and theoretical electron drift velocities, and an automatic technique to deduce the electron-gas molecule collision cross section from electron drift velocity data. We also briefly introduce a method for the deduction of electron collision cross sections with gas molecules having vibrational excitation cross sections greater than the elastic momentum transfer cross section by using a gas mixture technique, an integral type of method for solution of the Boltzmann equation with salient numerical stability, a quantitative analysis of the effect of Penning ionisation, and the behaviour of electron swarms under radio frequency electric fields.

Momentum Transfer Cross Section for Electrons in Mercury Vapour Derived from Drift Velocity Measurements in Mercury Vapour?Gas Mixtures

The Bradbury-Nielsen time-of-flight method has been used to measure electron drift velocities at 573 K in pure mercury vapour, a mixture of 46�80% helium-53� 20% mercury vapour and a mixture of 9�37% nitrogen-90� 63% mercury vapour. The E/N and pressure ranges used were O� 2 to 1� 5 Td and 5�4 to 15�2 kPa for pure mercury vapour, 0 �08 to 3�0 Td and 5 �40 to 26�88kPa for the mixture containing helium and 0�06 to 5�0Td and 3�33 to 16�67kPa for the mixture containing nitrogen. It is shown that the use of mixtures significantly reduces the dependence of the measured drift velocity on the pressure, due to the effect of mercury dimers, from that measured in pure mercury vapour. An iterative procedure to derive the momentum transfer cross section for electrons in mercury vapour over the range 0�04 to 4 eV with an uncertainty between �5 and 10% is described. It is concluded that previously published momentum transfer cross sections for mercury vapour derived from drift velocity data are significantly in error, due to diffusion effects and the procedure used to correct for the influence of dimers. The present cross section is in good agreement with the semi-empirical calculations of Walker (personal communication).

Momentum transfer cross section of argon deduced from electron drift velocity data

The momentum transfer cross section of argon is deduced from experimental electron drift velocity data over the energy range from 0.02 to 100 eV. A method proposed earlier by Suzuki et al. (1989) which is improved by adding a minimising procedure of the fractional difference between calculated and experimental electron drift velocities, is used. In an E/N range below 0.1 Td, the electron drift velocity data of Robertson (1977) at a gas temperature of 89.6 K are analysed and the cross section for the low-energy region is deduced. The result shows that the Ramsauer-Townsend minimum is located at an electron energy of 0.23 eV with a magnitude of 9.35*10-18 cm2. It is found that the present result is in excellent agreement with the theoretically determined values of Dasgupta and Bhatia (1985) and that the characteristic energy calculated from the present cross section agrees very well with the measurements of Milloy and Crompton (1982). In an E/N range above 0.1 Td, the experimental electron drift velocity data of Nakamura and Kurachi (1988) and Kucukarpaci and Lucas (1981) are analysed to deduce the cross section for the high-energy region. In order to obtain consistency among the present momentum transfer cross sections, ionisation cross sections by Krishnakumar and Srivastava (1988) and excitation cross sections by de Heer et al. (1979), reference is made to the ionisation coefficient data by Kruithof (1940), Abdulla et al. (1981) and Ishizuka et al. (1987). It is found that the peak of the momentum transfer cross section is located at an electron energy of 10 eV with a magnitude of 1.5*10-15 cm2.

The Momentum Transfer Cross Section for Krypton

A form of modified effective range theory (MERT) has been used to analyse drift velocity data for both pure krypton and molecular hydrogen-krypton mixtures. The present momentum transfer cross section reproduces the data to within 4% for pure krypton and to within 1 �0% for the H2-Kr mixtures.

Momentum transfer cross section of krypton deduced from electron drift velocity data

The momentum transfer cross section of krypton is deduced from experimental electron drift velocity data over the energy range from 0.01 to 100 eV by using an algorithm based on a Boltzmann equation method. This energy range covers the Ramsauer-Townsend minimum and the peak of the momentum transfer cross section. The results show that the Ramsauer-Townsend minimum is located at an electron energy of 0.6 eV and the magnitude of the cross section there is 2.3*10-17 cm2, while the peak is located at an electron energy of 8.0 eV with a magnitude of 2.0*10-15 cm2. For electron energies above 9.91 eV, the threshold of inelastic collisions, a set of cross sections for these collisions is necessary. Since the total excitation cross section used seemed less accurate than the ionisation cross section, the momentum transfer cross section was determined by consulting the experimental ionisation coefficient data as well as electron drift velocity data and by modifying the excitation cross section. It is found that the momentum transfer cross section is not affected by choice of excitation cross section for electron energies below 30 eV. The diffusion coefficient and the characteristic energy are also calculated by using the momentum transfer cross section determined here to find good agreement with experiment. The energy distributions are calculated and compared with the energy distributions proposed by Morse et al. (1935). The agreement of these two energy distributions is very good at E/N=0.1 Td.

Momentum Transfer Cross Section for Electrons in Krypton Derived from Measurements of the Drift Velocity in H2?Kr Mixtures

Measurements of electron drift velocities have been made in 0�4673% and 1�686% hydrogenkrypton mixtures at 293 K and values of E/ N from 0�08 to 2�5 Td with an estimated uncertainty of <�0�7%. The data have been used in conjunction with the H2 cross sections of England et aL (1988) to derive the momentum transfer cross section for krypton over the energy range 0�05 to 6�0 eV. The drift velocity data have also been used to test the Kr momentum transfer cross sections of Koizumi et aL (1986) and Hunter (personal communication 1988). The cross section of Koizumi et aL is clearly incompatible with the present measurements while the cross section of Hunter has been used to predict these measurements to within 1% to 3%.

A Study of the Vibrational Excitation of H2 by Measurements of the Drift Velocity of Electrons in H2−Ne Mixtures

Measurements of electron drift velocities have been made in 1�160% and 2�892% hydrogen-neon mixtures at 294 K and values of EI N from 0�12 to 1�7 Td. The measurements are highly sensitive to the region of the threshold of the v = 0 → 1 vibrational excitation cross section for hydrogen and have enabled more definitive tests of proposed cross sections to be made than was possible using drift velocity data for H2−He and H2−Ar mixtures. The theoretical v = 0 → 1 vibrational excitation cross section of Morrison et al. (1987) is shown to be incompatible with the present measurements. A new set of hydrogen cross sections has been derived from the available electron swarm measurements in pure hydrogen and hydrogen mixtures.

Momentum transfer cross sections for low-energy electrons in krypton and xenon from characteristic energies

Characteristic energies of low-energy electrons in krypton and xenon gases have been measured at room temperature by the Townsend method as a function of reduced electric field. For both gases, observed characteristic energies were twice or even three times as large as the early estimates by Frost and Phelps (1964) based on the momentum transfer cross sections for electrons in these gases derived from drift velocity data. The cross sections were determined from the present experimental data over an energy range from 0.01 to 6.0 eV for krypton and from 0.01 to 5.0 eV for xenon. The minimum values and positions of Ramsauer minima in the derived cross sections were 1.0*10-17 cm2 at 0.5 eV for krypton and 4.0*10-17 cm2 at 0.6 eV for xenon. These minimum values are both definitely smaller than the previous experimental results of Frost and Phelps, while being rather close to, but still somewhat smaller than, those of Hoffmann and Skarsgard (1969). Theoretical cross sections calculated for krypton and xenon by Sin Fai Lam (1982) and by McEachran and Stauffer (1984) and those for krypton by Fon et al. (1984) all agree with the present experimental ones within +or-30% for energies below about 5 eV in both gases.

Cross Sections for Electron?Carbon Monoxide Collisions in the Range 1?4 eV

The scattering of electrons from CO molecules has been studied over the energy range from 1 to 4 eV by analysing drift velocity data for pure CO and CO-inert gas mixtures at 294 K. The validity of using the so-called 'two term approximation' for the velocity distribution function in the solution of the Boltzmann equation to analyse drift velocity data for the pure gas (and thus also for the gas mixtures) has been established. The momentum transfer cross section for CO has been determined in the energy range 1-4 eV, and the measurements of the vibrational cross sections by Ehrhardt et al. (1968) have been renormalized. By using a solution of the Boltzmann equation which avoids the two term approximation, these cross sections have been shown to be consistent with previous measurement.s of the transport parameter D 1.1 fl in pure CO.