Depth Dose Functions Research Articles

Minority-carrier dynamics in β-gallium oxide probed by depth-resolved cathodoluminescence

The behavior of hole polarons in β-gallium oxide (Ga2O3) has attracted significant attention. Depth-resolved cathodoluminescence (CL) was used to investigate the minority carrier dynamics in β-Ga2O3. First, a model describing CL intensity was proposed by considering the depth-dose function and surface recombination. A universal depth-dose function for β-Ga2O3, which has the form of a third-degree polynomial, was presented based on Monte Carlo simulation by introducing a normalized depth, which is the depth normalized by the electron beam range. Second, two experimental approaches, plan-view and cross-sectional CL measurements, were applied to unintentionally doped β-Ga2O3 (−201) wafers, and the experimental results were compared with those of the proposed model. The hole diffusion length was estimated to be within the range of 200–400 nm through the plan-view measurement, whereas a hole diffusion length of 250 nm was obtained through the cross-sectional measurement. The values were consistent with each other, and the model reproduced the experimental results well. This indicates that the nonequilibrium minority hole in the unintentionally doped β-Ga2O3 is mobile and forms a ‘weak’ polaron. The reduced recombination velocity of the (−201) face was estimated to be approximately ten for the plan-view measurement, whereas that of ten or more was assumed for the cross-sectional measurement. No inconsistency was observed, but the low-energy plan-view measurement is considered more suitable for investigating the surface recombination velocity.

A simple calibration method for 106Ru– 106Rh eye applicators

Ru–Rh eye applicators are used for the radiotherapy of eye malignancies such as melanomas. We present a method of dosimetry of these beta particle emitting applicators. Method is based on a Plexiglas phantom (constructed for this purpose) containing spherical shells and very small, 1×1×1 mm 3 thermoluminescent dosimeters (TLD) as dosimeters. We determined 3-D depth doses and interpolated depth dose functions. Surface dose rate inhomogeneities and the consequences were considered and discussed. A possible influence of photon component of the emission on the results was analysed. The method has overall combined uncertainty ±6% which is comparable, and slightly better, than other recent dosimetric methods.

A method of normalizing cathodoluminescence images of electron transparent foils for thickness contrast applied to InGaN quantum wells.

The uniformity of panchromatic cathodoluminescence (CL) from In0.09Ga0.91N/GaN quantum wells at 100 K was investigated using a combined transmission electron microscope-cathodoluminescence instrument. A technique for correcting CL images of electron-transparent wedge specimens for thickness contrast artefacts is presented. The foil thickness was estimated using the dynamical formulation of the relationship between the thickness and the (experimentally observed) transmitted electron intensity. For a given thickness the CL intensity was calculated using the Everhart-Hoff depth-dose function and also taking into account surface recombination losses. Experimental CL images were normalized by dividing by the calculated CL value at each point. The procedure was successful in calculating the underlying materials contrast in CL images of thin specimens of InGaN single quantum wells. Non-uniformities in the CL emission on the scale of approximately 0.7 micro m were observed.

59. Verification of the 3-D dose calculation algorithm during total skin electron irradiation with the rotary-dual field technique

Total skin electron irradiation is the commonly used procedure in the treatment of mycosis fungoides. The aim of this paper was to verify the elaborated algorithm for dose calculation during total skin electron irradiation with rotary-dual fields technique (TSEI-RD). : Authors modified the 2-D algorithm published by Podgorsak taking account of dose distribution along the body midline and doses in the body on a larger depth than in the skin. Depth-dose function, beam profile were measured in TSEI-RD conditions (spoiler, source-skin distance SSD=350 cm, field size: 36 × 36 cm at 100 cm). Cylindrical vax phantom was used to calculate and then to measure the doses in a depth of 0.4 cm during exposure to the electron beam of 6 MeV (at the output of Clinac-2300CD accelerator). Phantom was rotating with the pre-calculated speed during constant exposure to two fields executed one by one in each fraction. Thermoluminescent detectors (TLD) were used for in-phantom dose measurements and Marcus ionization chamber was used for calibration of TLD. Dose homogeneity on the phantom surface was checked for three phantoms with different diameters of 20, 30 and 40 cm. Phantoms were irradiated at different rotating speeds. : Doses measured by TLD were on average by 4% lower than doses pre-calculated using the modified algorithm. Mean doses normalized to those pre-calculated and their standard deviations (both in per cents) were respectively: 96.1% and 0.4% for phantom with diameter of 20; 96.5% and 0.7% for diameter of 30 cm and 96.0% and 0.8% for diameter of 40 cm. : Measured doses proved correctness of elaborated algorithm. Very low standard deviations are resulting from regular cylindrical shape of the phantoms.

An iterative algorithm for determining depth profiles ofcollection probability by electron-beam-inducedcurrent

An iterative algorithm for the derivation of depth profiles ofthe minority carrier collection probability in a semiconductorwith or without a coating on the top is presented using energy-resolved electron-beam-induced current measurements inplanar geometry. The calculation is based on the depth-dosefunction of Everhart and Hoff (Everhart T Eand Hoff P H 1971 J. Appl. Phys. 42 5837) and on the penetration-rangefunction of Kanaya and Okayama (Kanaya K andOkayama S 1972 J. Phys. D: Appl. Phys. 5 43) or on that of Fitting (Fitting H-J1974 Phys. Status Solidi/ a 26 525). It canalso be performed with any other depth-dose functions. Using thisalgorithm does not require us to make any assumptions on the shapeof the collection profile within the depth of interest. Theinfluence of an absorbing top contact and/or a limitedthickness of the semiconductor layer appear in the result, butcan also be taken explicitly into account. Examples usingsilicon and CIS solar cells as well as a GaAs LED arepresented.

Polynomial expressions of electron depth dose as a function of energy in various materials: application to thermoluminescence (TL) dosimetry

The CEPXS/ONEDANT code package was used to produce a library of depth–dose profiles for monoenergetic electrons in various materials for energies ranging from 500 keV to 5 MeV in 10 keV increments. The various materials for which depth–dose functions were derived include: lithium fluoride (LiF), aluminum oxide (Al 2O 3), beryllium oxide (BeO), calcium sulfate (CaSO 4), calcium fluoride (CaF 2), lithium boron oxide (LiBO), soft tissue, lens of the eye, adiopose, muscle, skin, glass and water. All materials data sets were fit to five polynomials, each covering a different range of electron energies, using a least squares method. The resultant three dimensional, fifth-order polynomials give the dose as a function of depth and energy for the monoenergetic electrons in each material. The polynomials can be used to describe an energy spectrum by summing the doses at a given depth for each energy, weighted by the spectral intensity for that energy. An application of the polynomial is demonstrated by explaining the energy dependence of thermoluminescent detectors (TLDs) and illustrating the relationship between TLD signal and actual shallow dose due to beta particles.

Ionization chamber shift correction and surface dose measurements in electron beams

Cylindrical ionization chambers produce perturbations (gradient and fluence) in the medium, and hence the point of measurement is not accurately defined in electron beam dosimetry. The gradient perturbation is often corrected by a shift method depending on the type of ion chamber. The shift is in the range of 0.33-0.85 times the inner radius ( r) of the ion chamber, upstream from the centre of the chamber, depending upon the dosimetry protocol. This variation in shift causes the surface dose to be uncertain due to the high dose gradient. An investigation was conducted to estimate the effective point of measurement of cylindrical ion chambers in electron beams. Ionization measurements were taken with the ion chamber in air and in a phantom at source to chamber distances of <100 cm and >100 cm respectively. The data in air and in the phantom were fitted with the inverse square and electron depth dose functions, respectively. The intersection of the two functions provides an accurate estimate of the ion chamber shift and the surface dose. Our results show that the shift correction for an ion chamber is energy dependent. The measured shifts vary from 0.9 r to 0.5 r between 6 MeV and 20 MeV beams respectively. The surface dose measured with the ion chambers and mathematically determined values are in agreement to within 3%. The method presented in this report is unambiguous, fast and reliable for the estimation of surface dose and the shift needed in electron beam dosimetry.

Validation of reconstructed bremsstrahlung spectra between 6 MV and 25 MV from measured transmission data.

We have previously investigated a method of high-energy x-ray spectral reconstruction from transmission data by direct resolution of a matrix system. This technique uses the spectral vectorial algebra formalism. The resolution has previously been tested on a 12 MV photon beam. To extend and to test the validity of the results to the entire radiotherapy energy range, we have performed the method on photon beams with nominal energies of 6, 12, 15, and 25 MV. The influence on the 6 MV spectrum of a 60 degrees built-in wedge has also been investigated to test the sensitivity of the method and the results are reported. To validate our reconstructed spectra, dosimetric quantities such as tissue phantom ratios (TPR), water-to-air stopping power ratios (S/p) air water, and quality indexes TPR 10 (20) have been calculated. The results show good agreement between the measured and calculated data. Mean mass energy absorption coefficient ratios for different materials have also been computed and compared to data published recently and the results are very close (within +/- 0.5%). Primary depth dose functions in water have also been computed to deduce primary dose attenuation coefficients.

Dosimetry for linac with multileaf collimator

Our work shows measurments of depth dose function and beam profiles dependance on field's contour and size shaped by the multileaf collimator. All measurements were done for linear accelerator Clinac 2300 – Varian. Such obtained values were compared with analogical ones for square fields. Dose distributions across the beam for multileaf collimator and for individual blocks were analized. Work load needed for clinical dosimetry of multileaf collimator was estimated. Proposols for measurment protocol in clinical dosimetry is shown.

Equivalent squares of irregular photon fields.

The tables of equivalent fields published by the British Journal of Radiology (BJR) are intended for calculation of depth-dose functions in rectangular photon fields. We have investigated the validity of the equivalent-field concept for fields of arbitrary shape over a range of photon energies, field sizes and depths. We show that the empirical scatter-radius function (Day function) used to generate the equivalent-field tables is a good approximation to the average over energy of normalized scatter-air ratios extracted from BJR beam data for depths up to 10 cm. However, this function tends to diverge from the data as depth increases. Accuracy can be improved by making the Day function depend on depth. Equivalent squares, determined by sector integration of the original or modified Day functions, are suitable for megavoltage photon-beam dose calculations at central-axis and off-axis points in irregular as well as rectangular fields.

Monte Carlo calculation of penetration of electrons into poly(methylmethacrylate)

Monte-Carlo method is applied to the problem of penetration of 20 keV and 30 keV electrons to polymethylmethacrylate. In this paper the ranges and backscattering yields are calculated and a comparison with the results obtained by different methods is made. Depth-dose functions are depicted as well.

Kilovolt electron energy loss distribution in Si

Using the electron-beam-induced barrier currents and the Monte Carlo simulation methods it was possible to determine the depth-dose function as well as the distribution function of the generation source for electron-hole pairs perpendicular to the injection direction. The depth-dose function was compared with results obtained by Everhart and Hoff. By fitting the simulated barrier current profile to the measured one the authors could estimate the relatively small width of the space charge region of the p-n junction employed for the measurements. Furthermore, the spatial dose distribution of Si was described in an analytic approximation of the Monte Carlo simulation using two Gaussian functions concerned with the spreading of the penetrating electron beam and the diffusion of the primary electrons within the target, respectively. This approximation was based on treatments of the scattering process of the primary electrons given by Bethe and co-workers, Bothe and Archard.

Pulsed electron beam irradiation of nickel single crystals with silver overlayers

We report the effects of a single electron beam pulse (pulse width, 50 ns full width at half-maximum; electron energy, 25 keV; peak current density in the range 600–2500 A cm -2) on the Ni/Ag system, which was chosen because it shows nearly no mutual solubility in the equilibrium phase diagram. The samples were prepared by vacuum evaporating silver layers 70 and 185 nm thick onto nickel single crystals and were analysed by Rutherford backscattering spectrometry and scanning electron microscopy. Extended solid solubilities were attained. The maximum solubility was determined to be 16 at.% Ag in nickel. At the higher current densities mixing is accompanied by a strong loss of silver in the case of the 70 nm silver layer (up to 50% of the deposited layer). The experimental results are discussed on the basis of heat flow model calculations which use Monte Carlo data for the electron depth-dose function. We also propose a tentative explanation for the observed silver losses based on a boiling instability in very thin superheated films.

Thermal model of pulsed electron beam annealing in silicon

The thermal cycle induced in ion-implanted silicon by a polykinetic electron beam pulse (0–40 keV) has been determined starting from the experimental data of a pulsed electron beam processor. Within the pulse duration (50 ns) the silicon upper layer is brought to the melt temperature over a few tenths of a micron. However, due to the electron depth-dose function shape the melting layer generally includes a partially molten back end in which only a fraction of the latent heat has been absorbed. For a mean electron energy lower than 15 keV, a 0.2μm thick amorphous layer is nevertheless fully molten with a 0.8 J/cm 2 PEBA shot. The melt-solid interface velocity mostly depends on the thermal gradients in the solid beneath the melting layer. However, as the melting layer usually contains a partially molten back end, two solidification regimes generally occur because of the difference in the amount of latent heat to be evacuated in the bulk of the material. A thermal model is used to compute the melting and freezing kinetics. The PEBA induced thermal cycle in ion-implanted silicon is then mostly related to the electron energy deposition profile which determines both the physical state of the melting layer and the thermal gradient distribution in the underlying solid crystal. These thermal effects can be controlled by adjusting the electron beam parameters to the field emission diode geometry of the pulsed electron beam processor.

Determination of dopant-concentration diffusion length and lifetime variations in silicon by scanning electron microscopy

Compositional variations in Czochralski-grown silicon doped at levels above 1018/cm3 were observed with SEM in the EBIC mode employing large-area shallow p-n junctions. The EBIC contrast attributed to minority-carrier diffusion-length variations was related to dopant-concentration variations. Quantitative determination of dopant concentration, diffusion length, and lifetime variations on a microscale was obtained from the analysis of electron-beam-induced current measurements employing a model based on steady-state low-level excitation of minority carriers by the electron beam and on a phenomenological depth-dose function.

Concept of depth dose functions for radiotherapy beams: Definition and values for different energy beams

Depth dose functions are defined and based on empirically observed interrelation of percent depth doses for different energy beams. By using this function, if the depth dose for a given source-surface distance (SSD), field size and depth are known for a standard beam energy, the corresponding depth dose for another beam energy can be derived. The results obtained are accurate to within ±1% in a considerable range of SSD, field size and depths used in routine radiotherapy. The formulation can be extended to hold at depths between the surface and depth of maximum but is somewhat less accurate than ±1% for depths up to two times the depth of maximum. This method is of considerable usefulness in computer dosimetry algorithms to save memory space and/or to increase speed by avoiding multiple table look up procedures. It is the particular importance in irregular field dose calculations for high energy beams where specific measured data for separation of primary and scatter components of dose are not available.

Investigation of kilovolt electron energy dissipation in solids

A new technique to determine the depth distribution of energy loss, the so-called depth-dose function, is described for electrons whose energies ranged from 15 to 30 keV at normal and 45° incident angles. This method is based on a series of measurements of currents induced by the penetration of energetic electrons through a metal-oxide-semiconductor-structure (Al–SiO2–Si) specimen whose metal electrode is formed by an aluminum layer deposited in a stepwise manner. The experimental depth-dose function and range-energy relation are compared with other experimental and theoretical results. A particular interest was taken in the comparison of the experimental results with those predicted by our Monte Carlo calculations to confirm the good agreement between them. Furthermore, the ratio of the product of mobility and lifetime to the mean electron excitation energy in SiO2 was also determined to be μτ/EA = 0.10 × 10−11 cm/V2, which may be ranked between the values reported by Everhart and Hoff and by Goodman. The effects of space charge in SiO2 are also discussed.

Fundamental aspects of electron beam lithography. I. Depth-dose response of polymeric electron beam resists

The application of a phenomenological depth-dose theory to the exposure of negative electron resists is described in detail. The model predicts a cross-linking rate dnc/dt=(Gc/100) × (J0/e)(Va/RG)Λ(f) cm−3 sec−1, where Gc is the number of crosslinks produced per 100 eV lost in the polymer. Jo is the incident current density, Va the initial kinetic energy, RG the electron Grun range, and Λ(f) the depth-dose function in terms of the normalized penetration f=z/RG. Since the G value of a negative resist decreases with exposure, it is suggested that a more meaningful parameter characterizing a negative resist is the absorbed energy required to gel the polymer at the resist-substrate interface. This interface or threshold gel energy density, Eg(i), is independent of the beam parameters and varies from about 1022 eV cm−3 for polyvinyl ferrocene to 3.8×1018 eV cm−3 for epoxidized polybutadienes. The model predicts that the threshold sensitivity should vary as Va0.75 which agrees reasonably well with published experimental values. It also predicts that at a given accelerating voltage, there is a unique initial resist thickness at which the top surface and interface receive identical doses. This unique thickness turns out to be roughly the electron diffusion range RD. The transverse resolution or linewidth for negative resists has been investigated as a function of accelerating voltage and found to be given by twice the diffusion range. Since RD decreases with decreasing Va, the linewidth likewise decreases as the accelerating voltage is lowered. The optimum operating conditions for a 500-nm resist film for electron lithography are predicted to be Va≈5 kV exposed to yield about a 400-nm film after development. It should be noted that these conditions result in a maximum crosslink density per incident electron and a minimum linewidth. However, there may be specific applications where other sets of operating conditions are useful. A geometric model is suggested which appears to account for the observed behavior of sensitivity of negative resists.

Penetration and energy-loss theory of electrons in solid targets

Starting from a simple atomic model giving the potential between electrons and atoms as V(r) = Ze2as−1/srs with the empirical value s=fraction six-fifths, we combine the diffusion effect due to multiple collisions and the energy retardation in accordance with a modified Thomson-Whiddington law, with the scattering cross section in the Lenard absorption law. On this basis, consistent expressions are obtained for the fraction of transmitted electrons in amorphous solid targets, the backscattering fraction with depth, the fraction of electrons absorbed per unit mass-thickness and the depth-dose function, which are in good agreement with experiments over the energy range 10-1000 keV.A diffusion model represented by a sphere whose centre is located at the maximum energy dissipation depth, related to the diffusion depth and the range, is found to agree well with experiments.

Absorbed Dose Determination for X-rays in the Grenz-ray Region (5 to 20 keV Quantum Energy)

Determination of the absorbed dose for very low-energy X-rays is greatly simplified by the absence of scattered radiation. Absorber thickness can be scaled from one material to another by use of a relative effective density, which is the ratio of the mass energy absorption coefficients. Depth dose functions can be transferred from one material to another and from one FSD to another, and can be corrected for changes in air absorption. Exposure in roentgens can be measured directly with a suitable extrapolation chamber. The Fricke ferrous sulphate dosemeter is readily applicable, and a value of G = 14·8 was found for a 50 kvp unfiltered X-ray beam from a beryllium-window tube. It is concluded that the properties of very low-energy X-rays do not necessarily add to the uncertainties inherent in all X-ray absorbed-dose determinations.