Controlled Fluxes of Silicon Nanoparticles to a Substrate in Pulsed Radio-Frequency Argon–Silane Plasmas

It has been hypothesized that high-energy impact of very small silicon nanoparticles on a substrate may lead to epitaxial growth of silicon films at low substrate temperature. A possible means for producing such energetic nanoparticle fluxes involves pulsing an RF silane-containing plasma, and applying a positive DC bias to the substrate during the afterglow phase of each pulse so as to collect the negatively charged particles generated during the RF power on phase. We here report numerical modeling to provide a preliminary assessment of the feasibility of this scheme. The system modeled is a parallel-plate capacitively-coupled RF argon–silane plasma at pressures around 100 mTorr. Simulation results indicate that it is possible to achieve a periodic steady state in which each pulse delivers a controlled flux of nanoparticles to the biased substrate, that average particle sizes can be kept below 2–3 nm, that impact energies of the negatively-charged nanoparticles that are attracted by the applied bias can be maintained in the ~1 eV/atom range thought to be conducive to epitaxial growth without causing film damage, and that the volume fraction of neutral nanoparticles that deposit by low-velocity diffusion can be kept well below 1 %. The effects of several operating parameters are explored, including RF voltage, pressure, the value of the applied DC bias, and RF power on and off time during each pulse

A contribution to the amaranthine quarrel between true and average electrical mobility in the free molecular regime

Landau and Lipschitz's approach—termed here H&B due to the use of Happel and Brenner's slow rotation approximation—for calculating the average electrical mobility over all orientations of an ion in the free molecular regime is shown in this manuscript to be an invalid assumption for non-globular ions when a fixed electrical field is present. The reason behind the invalidity seems to be the confusion between average “settling” velocity (the calculation intended by H&B) and the average mobility (drag) in the direction of the field. When a missing orientation is taken into account by rotating the drag tensor, the average mobility obtained through Landau's approach coincides with well-known orientationally averaged Kinetic Theory Methods such as those of Mason and McDaniel (M&M). H&B's averaging approach, however, can be related to the true mobility displacement of the ion or, in other words, the displacement occurring in the direction of the velocity. This true mobility displacement only agrees with the average mobility displacement if ion velocity and electrical field have always the same direction, which only happens under special cases. Analytical and numerical calculations of collision cross-sections of linear and planar structures using a momentum transfer kinetic theory approach are chosen here as a means to prove that a single rotation of the drag tensor is sufficient to show agreement between both methods. A projected area approach is also used to prove the inadequacy of the H&B method

The size-mobility relationship of ions, aerosols, and other charged particle matter

Electrical Mobility is arguably the property upon which some of the most successful classification criteria are based for aerosol particles and ions in the gas phase. Once the value of mobility is empirically obtained, it can be related to a geometrical descriptor of the charged entity through a size-mobility relationship. Given the multiscale range of sizes in the aerosol field, approaches that can provide accurate transformations from mobility to size are not straightforward, and many times rely on experimentally derived parameters. The most well-known size-mobility analytical expression covering the whole Knudsen range for spherical particles is the semi-empirical Stokes-Millikan correlation. This expression matches Stokes' drag friction coefficient in the continuum regime and the friction factor for a predominantly diffuse reemission of the gas molecule in the free molecular regime, as theorized by Epstein, with empirical slip coefficients chosen to agree with Millikan's oil drop experiments. Despite its success, the Stokes-Millikan correlation has its shortcomings. For example, it needs to be modified to predict the mobility of non-spherical entities and needs correction terms when potential interactions or reduced mass effects are non-negligible. The Stokes-Millikan asymptotic behavior also fails to predict the gradual transition from diffuse to specular reemission behavior that is observed for increasingly smaller ions within the free molecular regime. Here we make an attempt at providing a comprehensive account of the existing mass-mobility relations in the continuum, transition and free molecular regimes for both spherical and non-spherical particles. Epstein's diffuse interaction is critically explored experimentally and numerically for different gases in the free molecular regime with the observation that, as the size of the particle increases, a progression from specular to diffuse reemission occurs for all gases studied. The rate at which this variation happens seems to differ from gas to gas and to be related to the conditions for which diffuse reemission effects stem from a combination of scattering and potential interactions

Modeling of an Inverted Drift Tube for Improved Mobility Analysis of Aerosol Particles

A new mobility particle analyzer, which has been termed Inverted Drift Tube, has been modeled analytically as well as numerically and proven to be a very capable instrument. The basis for the new design have been the shortcomings of the previous ion mobility spectrometers, in particular (a) diffusional broadening which leads to degradation of instrument resolution and (b) inadequate low and fixed resolution (not mobility dependent) for large sizes. To overcome the diffusional broadening and have a mobility based resolution, the IDT uses two varying controllable opposite forces, a flow of gas with velocity v gas , and a linearly increasing electric field that opposes the movement. A new parameter, the separation ratio Λ = v drift /v gas , is employed to determine the best possible separation for a given set of nanoparticles. Due to the system’s need to operate at room pressure, two methods of capturing the ions at the end of the drift tube have been developed, Intermittent Push Flow for a large range of mobilities, and Nearly-Stopping Potential Separation, with very high separation but limited only to a narrow mobility range. A chromatography existing concept of resolving power is used to differentiate between peak resolution in the IDT and acceptable separation between similar mobility sizes

Analysis of Ion Motion and Diffusion Confinement in Inverted Drift Tubes and Trapped Ion Mobility Spectrometry Devices

Ion motion in trapped ion mobility spectrometers (TIMS) and inverted drift tubes (IDT) has been investigated. The two-dimensional (2D) axisymmetric analytical solution to the Nernst–Planck equation for constant gas flows and opposed linearly increasing fields is presented for the first time and is used to study the dynamics of ion distributions in the ramp region. It is shown that axial diffusion confinement is possible and that broad packets of ions injected initially into the system can be contracted. This comes at the expense of the generation of a residual radial field that pushes the ions outward. This residual electric field is of significant importance as it hampers sensitivity and resolution when parabolic velocity profiles form. When radio frequency (RF) is employed at low pressures, this radial field affects the stability of ions inside the mobility cell. Trajectories and frequencies for stable motion are determined through the study of Mathieu’s equation. Finally, effective resolutions for the ramp and plateau regions of the TIMS instrument are provided. While resolution depends on the inverse of the square root of mobility, when proper parameters are used, resolutions in the thousands can be achieved theoretically for modest distances and large mobilities

Optimization of long range potential interaction parameters in ion mobility spectrometry

The problem of optimizing Lennard-Jones (L-J) potential parameters to perform collision cross section (CCS) calculations in ion mobility spectrometry has been undertaken. The experimental CCS of 16 small organic molecules containing carbon, hydrogen, oxygen, nitrogen, and fluoride in N2 was compared to numerical calculations using Density Functional Theory (DFT). CCS calculations were performed using the momentum transfer algorithm IMoS and a 4-6-12 potential without incorporating the ion-quadrupole potential. A ceteris paribus optimization method was used to optimize the intercept σ and potential well-depth ϵ for the given atoms. This method yields important information that otherwise would remain concealed. Results show that the optimized L-J parameters are not necessarily unique with intercept and well-depth following an exponential relation at an existing line of minimums. Similarly, the method shows that some molecules containing atoms of interest may be ill-conditioned candidates to perform optimizations of the L-J parameters. The final calculated CCSs for the chosen parameters differ 1% on average from their experimental counterparts. This result conveys the notion that DFT calculations can indeed be used as potential candidates for CCS calculations and that effects, such as the ion-quadrupole potential or diffuse scattering, can be embedded into the L-J parameters without loss of accuracy but with a large increase in computational efficiency

A parallelized tool to calculate the electrical mobility of charged aerosol nanoparticles and ions in the gas phase

Electrical Mobility is a transport property that describes a particle behavior in the gas phase. When dealing with the free molecular regime, ascertaining the shape of a nanoparticle or an ion directly from measurements of mobility becomes quite difficult as the particle no longer can be assumed to have spherical shape. Here we propose an efficient parallelized tool, IMoS, that makes use of all-atom models to calculate the mobility of nanoparticles in a variety of gases. The program allows for different types of calculations that range from the efficient Projection Approximation (PA) algorithm to the 4-6-12 Lennard-Jones potential Trajectory Method. It also includes a diffuse inelastic simulation that achieves Millikan's predicted 1.36 value over PA. When compared to experimental results, the error of the most efficient calculations is shown to be approximately 2–4% on average

Ion Mobility Mass Spectrometry Uncovers Guest‐Induced Distortions in a Supramolecular Organometallic Metallosquare

The encapsulation of the tetracationic palladium metallosquare with four pyrene-bis-imidazolylidene ligands [1]4+ with a series of organic molecules was studied by Electrospray ionization Travelling Wave Ion-Mobility Mass Spectrometry (ESI TWIM-MS). The method allowed to determine the Collision Cross Sections (CCSs), which were used to assess the size changes experienced by the host upon encapsulation of the guest molecules. When fullerenes were used as guests, the host is expanded ΔCCS 13 Å2 and 23 Å2 , for C60 or C70 , respectively. The metallorectangle [1]4+ was also used for the encapsulation of a series of polycyclic aromatic hydrocarbons (PAHs) and naphthalenetetracarboxylic diimide (NTCDI), to form complexes of formula [(NTCDI)2 (PAH)@1]4+ . For these host:guest adducts, the ESI IM-MS studies revealed that [1]4+ is expanded by 47-49 Å2 .. The energy-minimized structures of [1]4+ , [C60 @1]4+ , [C70 @1]4+ , [(NTCDI)2 (corannulene)@1]4+ in the gas phase were obtained by DFT calculations

Measurement and Theory of Gas-Phase Ion Mobility Shifts Resulting from Isotopomer Mass Distribution Changes

The unanticipated discovery of recent ultra-high-resolution ion mobility spectrometry (IMS) measurements revealing that isotopomers—compounds that differ only in the isotopic substitution sites—can be separated has raised questions as to the physical basis for their separation. A study comparing IMS separations for two isotopomer sets in conjunction with theory and simulations accounting for ion rotational effects provides the first-ever prediction of rotation-mediated shifts. The simulations produce observable mobility shifts due to differences in gas−ion collision frequency and translational-to-rotational energy transfer. These differences can be attributed to distinct changes in the moment of inertia and center of mass between isotopomers. The simulations are in broad agreement with the observed experiments and consistent with relative mobility differences between isotopomers. These results provide a basis for refining IMS theory and a new foundation to obtain additional structural insights through IMS

Fundamentals of ion mobility in the free molecular regime. Interlacing the past, present and future of ion mobility calculations

While existing ion mobility calculators are capable of feats as impressive as calculating collision cross sections (CCS) within a few per cent and within a very reasonable time, the simplifications assumed in their estimations precludes them from being more precise, potentially overreaching with respect to the interpretation of existing calculations. With ion mobility instrumentation progressively reaching resolutions of several hundreds to thousands (accuracy in the range of ∼0.1%), a more accurate theoretical description of gas-phase ion mobility becomes necessary to correctly interpret experimental state-of-the-art separations. This manuscript entails an effort to consolidate the most relevant theoretical work pertaining to ion mobility within the ‘free molecular’ regime, describing in detail the rationale for approximations up to the two-temperature theory, using both a momentum transfer approach as well as the solution to the moments of the Boltzmann equation for the ion. With knowledge of the existing deficiencies in the numerical methods, the manuscript provides a series of necessary additions in order to better simulate some of the separations observed experimentally due to second-order effects, namely, high field effects, dipole alignment, angular velocities and moments of inertia, potential interactions and inelastic collisions among others