Boltzmann Transport Equation Solver Research Articles

SU-E-T-720: Dosimetric Verification of Deterministic Acuros XB Radiation Transport Algorithm for IMRT and VMAT Plans with the RPC H&N Phantom

Purpose: Acuros XB (AXB), a novel deterministic dose calculation algorithm based on grid‐based Boltzmann transport equation solver (GBBS), was recently implemented in Eclipse treatment planning system (TPS). The purposes of this study were to verify the dosimetric performance of AXB by (1) comparing measured and calculated data and (2) comparing AXB with the existing Eclipse anisotropic analytical algorithm (AAA). Methods: Clinically equivalent intensity modulated radiation therapy(IMRT) and volumetric modulated arc therapy (VMAT) plans were created in Eclipse for the Radiological Physics Center (RPC) head and neck IMRT phantom using the RPC phantom dose prescription specifications. Each plan was calculated with two different algorithms, AXB 11.0.91 and AAA 10.0.24. Each treatment plan was delivered to the RPC phantom three times for reproducibility using a Varian Clinac21iX. Dose distributions were measured with thermoluminescent dosimeters(TLDs) and radiochromic film (GafChromic® EBT2). Gamma analysis (7%/4mmDTA) was used to quantify the agreement between AXB and AAA calculated dose distributions and those measured using films. The computation times for AAA and AXB were also evaluated. Results: In this study, good agreement was observed between measured and calculated doses both from AAA and AXB (dose‐to‐medium in medium). Comparing the calculations with TLD measurements, agreement for both AAA and AXB were < 5% (ranges from 0.2% to 4.6% for AAA, 0.1% to 3.6% for AXB) for IMRT and VMAT plans. The gamma analysis results for both AAA and AXB met the RPC 7%/4 mm criteria (over 90% passed). The AAA and AXB computation times were comparable for IMRT but AXB was ∼3 times faster than AAA for VMAT. Conclusions: The AXB was determined to be accurate using the RPC IMRT H&N phantom measurements and in good agreement with the AAA while having shorter calculation times for VMAT as compared to the AAA.

SU-E-T-734: Evaluation of a New, Grid-Based Linear Boltzmann Transport Equation Solver for Dose Calculation in the Presence of High-Density Materials

Purpose: To evaluate the accuracy of a new, deterministic linear Boltzmann transport equation solver, AcurosXB, for radiotherapydose calculations in the presence of high‐density materials by comparison with Monte Carlo.Methods: AcurosXB, EGSnrc‐based Monte Carlo and Analytic Anisotropic Algorithm (AAA) were used to model 6MV and 18MV photon beams incident on phantom and patient geometries containing stainless steel and titanium high‐density objects. Monte Carlo was used as the evaluation benchmark while AAA was included as a representative of the convolution‐based clinical modeling algorithms currently used for radiotherapy treatment planning. Calculation geometries include a virtual cubic phantom created in MatLab, a cubic water phantom containing stainless steel rods and prosthetic hips and patient CT images with associated clinical treatment plans. Dose distributions were processed and analyzed in MatLab.Results: Agreement between AcurosXB and Monte Carlo is within 5% and 2mm. There is a backscatter peak position offset of up to one pixel (2mm) between AcurosXB and Monte Carlo which can be accounted for by differences in voxel coordinate definition, contour definition and interpolation effects. Additional differences between AcurosXB and Monte Carlo fall within statistical variance associated with Monte Carlo. Disagreement between AAA and Monte Carlo was far more dramatic; AAA was unable to model the sharp backscatter peak associated with photon transport across low‐ to high‐density boundaries resulting in inaccurate dose distribution through and past high density regions Conclusions: AcurosXB has shown to be an improvement on existing algorithms for calculating dose distribution in the presence of high‐density regions, nearly matching the current gold standard Monte Carlo method. Discrepancies between AcurosXB and Monte Carlo do not translate into clinically significant dose differences, while AAA has shown to under‐ or over‐estimate dose by as much as 20%. Varian Medical Systems has provided AcurosXB hardware and software for research activities.

Dosimetric impact of an brachytherapy source cable length modeled using a grid‐based Boltzmann transport equation solver

To evaluate the dose distributions of an 192Ir source (model VS2000) in homogeneous water geometry calculated using a deterministic grid-based Boltzmann transport equation solver (GBBS) in the commercial treatment planning system (TPS) (BRACHYVISION-ACUROS V8.8). Using percent dose differences (%deltaD), the GBBS (BV-ACUROS) was compared to the (1) published TG-43 data, (2) MCNPX Monte Carlo (MC) simulations of the 192Ir source centered in a 15 cm radius water sphere, and (3) TG-43 output from the TPS using vendor supplied (BV-TG43-vendor) and user extended (BV-TG43-extended) 2D anisotropy functions F(r, theta). BV-ACUROS assumes 1 mm of NiTi cable, while the TPS TG-43 algorithm uses data based on a 15 cm cable. MC models of various cable lengths were simulated. The MC simulations resulted in > 20% dose deviations along the cable for 1, 2, and 3 mm cable lengths relative to 15 cm. BV-ACUROS comparisons with BV-TG43-vendor and BV-TG43-extended yielded magnitude of differences, consistent with those seen in MC simulations. However, differences > 20% extended further (theta < or = 10 degrees) when using the vendor supplied anisotropy function F(ven0(r, theta). These differences were also seen in comparisons of F(r, theta) derived from the TPS output. The results suggest that %deltaD near the cable region is larger than previously estimated. The spatial distribution of the dose deviation is highly dependent on the reference TG-43 data used to compare to GBBS. The differences observed, while important to realize, should not have an impact on clinical dosimetry in homogeneous water.

Thermal conductivity modeling of compacted type nanocomposites

Due to different interface densities and arrangements, the compacted type nanocomposites may yield even lower thermal conductivity than embedded type nanocomposites. In this paper, the phonon transport and thermal conductivity in compacted type nanocomposites (nanowires and nanoparticles) are investigated using a deterministic phonon Boltzmann transport equation solver. The effects of interface density and characteristic size on the phonon energy transport in nanocomposites are studied. It is found that the silicon-germanium compacted nanoparticle composites can have lower value of thermal conductivity than that of compacted nanowire composites under the same characteristic size (21.6% lower when the characteristic size is 3 nm).

Quasi-Ballistic Transport in Nanowire Field-Effect Transistors

In this paper, we investigate quasi-ballistic transport in nanowire field-effect transistors (NW-FETs). In order to do so, we address the 1-D Boltzmann transport equation (BTE) and find its exact analytical solution for any potential profile with the constraint of dominant elastic scattering. A simulation code implementing a self-consistent Schrodinger-Poisson solver in the transverse direction and the present BTE solution in the longitudinal direction is worked out, providing the I-V characteristics of the NW-FET. Such characteristics are compared with those computed using a numerical BTE solver accounting for both inelastic and elastic collisions, and the two of them turn out to agree very nicely. From this comparison, it may be concluded that inelastic scattering plays a minor role for small-diameter FETs with device lengths in the decananometer range. Next, a methodology for the calculation of the transmission and backscattering coefficients is worked out for the first time starting from the scattering probabilities. The aforementioned coefficients turn out to be functions of the ratio between the carrier transit time and a suitably averaged momentum-relaxation time. Therefore, one of the main conclusions of this paper is that, so long as inelastic collisions are negligible, the so-called kT layer plays no role in 1-D quasi-ballistic carrier transport.

Investigation on tritium breeding capability of solid-liquid breeders in a (DT) fusion driven hybrid reactor

In design of deuterium-tritium (DT) fusion driven hybrid reactors, maintaining tritium self-sufficiency is very important to decrease operational costs. A (DT) fusion driven hybrid reactor must produce its own tritium to annihilate external investment on tritium production. Tritium Breeding Ratio (TBR) should be greater than 1.05 to maintain tritium self-sufficiency of the (DT) fusion plasma. Tritium is an artificial isotope that can be bred by using the breeding reactions of 6Li and 7Li isotopes. Therefore use and selection of lithium bearing coolants and blanket materials are very important with respect to tritium self-sufficiency of the (DT) fusion plasma. In this study, tritium breeding potential of various solid breeders Li2TiO3, Li8ZrO6, Li4SiO4, Li2ZrO3 or Li2O with different coolants Li2BeF4 (Flibe), NaF.LiF.BeF2 (Flinabe) or natural lithium in the hybrid blanket using different nuclear carbide fuels was investigated. Computations were carried out by using Scale4.3 solving Boltzmann transport equation. According to numerical results, among the solid breeders Li2O and Li8ZrO6 and among the liquid breeders, natural lithium had the highest contribution to TBR. Furthermore addition of uranium to thorium fuel improved tritium production.

Simulation of hole phonon-velocity in strained Si/SiGe metal-oxide-semiconductor transistor

Hole phonon velocity in a strained Si inversion layer grown on a relaxed SiGe substrate has been theoretically investigated. We used: (i) a 20 band k.p Hamiltonian method for the valence-band structure calculation, (ii) a self-consistent Schrödinger and Poisson equations solver for the confined hole subband determination, (iii) a direct matrix Boltzmann transport equation solver including hole-phonon interactions for the carrier velocity estimation in the subband structure. The present work particularly focuses on the influence of SiGe alloy composition and strained Si layer thickness on the hole dynamic in the inversion layer. Our results highlight the linear slope of the hole velocity enhancement factor with strain in the Si layer. But at the same time, large strain facilitates transfer in the parasitic channel at the Si/SiGe interface for which the carrier mobility is highly degraded. Consequently, in order to optimize a p-channel transistor with Si layer strain on SiGe virtual substrate, a compromise must be found between mobility in Si layer and parasitic transfer phenomenon in this interface. Our results suggest that a 10 nm Si layer thickness strain on a relaxed Si0.7Ge0.3 allows one to take advantage of the strain-induced enhancements of carrier transport characteristics. At the same time this compromise is realistic from a technological point of view.

Short-range electron-electron scattering in silicon with a non-parabolic band structure

In this paper we propose a new methodology to treat the short-range electron-electron interaction within both deterministic and stochastic Boltzmann Transport Equation (BTE) solvers, while accounting for a spherical and non-parabolic band structure. Our approach is based on a suitable transformation of the integration variable within the scattering integrals, which allows us to perform analytically the integration in the angular part of crystal momenta. This methodology is applied to a deterministic BTE solver based on the expansion of the distribution function in spherical harmonics: we start from a double vector-integral, and we are left with a standard double integral to be numerically computed. Quantitatively large corrections to the high-energy tail of the distribution are found.

Representation of ion implantation projected range profiles by Pearson distribution curves for silicon technology

Several authors have reported difficulties in fitting Pearson curves to implants into amorphous targets. However, we show that accurate Pearson curve fitting to simulations of projected range profiles in amorphous targets is possible when implant profiles are available for which optimised moments can be generated. In previous literature few comparisons can be found between Pearson curve fits and the original implant profiles whereas, in the current paper, comparisons are made with high-resolution simulated profiles for B, P and As implanted into amorphous Si. These profiles were derived using Monte-Carlo simulations each of 1,000,000 ion trajectories. Fit coefficients that allow the regeneration of Pearson curves, optimised to fit Monte-Carlo implant profiles, are provided for the ions, B, P, As and Sb implanted, with energies in the range 25–300 keV, into targets of amorphous Si, silicon dioxide and silicon nitride. Comparisons of infinite and optimised moments, for B and P implants, show that the best fit moments (and corresponding Pearson type) can only be determined as part of an optimisation process, and not from infinite moments directly (such as moments from a backward Boltzmann transport equation solver).