Ion-implantation-caused special damage profiles determined by spectroscopic ellipsometry in crystalline and in relaxed (annealed) amorphous silicon

We previously developed a fitting method of several parameters to evaluate ion-implantation-caused damage profiles from spectroscopic ellipsometry (SE) (M. Fried et al., J. Appl. Phys., 71 (1992) 2835). Our optical model consists of a stack of layers with fixed and equal thicknesses and damage levels described by a depth profile function (coupled half Gaussians). The complex refractive index of each layer is calculated from the actual damage level by Bruggeman effective medium approximation (EMA) using crystalline (c-Si) and amorphous (a-Si) silicon as end-points. Two examples are presented of the use of this method with modified optical models. First, we investigated the surface damage formed by room temperature B+ and N+ implantation into silicon. For the analysis of the SE data we added a near surface amorphous layer to the model with variable thickness. Second, we determined 20 keV B+ implantation-caused damage profiles in relaxed (annealed) amorphous silicon. In this special case, the complex refractive index of each layer was calculated from the actual damage level by the EMA using relaxed a-Si and implanted a-Si as end-points. The calculated profiles are compared with Monte Carlo simulations (TRIM code); good agreement is obtained

Determination of complex dielectric functions of ion implanted and implanted‐annealed amorphous silicon by spectroscopic ellipsometry

Measuring with a spectroscopic ellipsometer (SE) in the 1.8–4.5 eV photon energy region we determined the complex dielectric function (ϵ = ϵ1 + iϵ2) of different kinds of amorphous silicon prepared by self‐implantation and thermal relaxation (500 °C, 3 h). These measurements show that the complex dielectric function (and thus the complex refractive index) of implanted a‐Si (i‐a‐Si) differs from that of relaxed (annealed) a‐Si (r‐a‐Si). Moreover, its ϵ differs from the ϵ of evaporated a‐Si (e‐a‐Si) found in the handbooks as ϵ for a‐Si. If we use this ϵ to evaluate SE measurements of ion implanted silicon then the fit is very poor. We deduced the optical band gap of these materials using the Davis–Mott plot based on the relation: (ϵ2E2)1/3 ∼ (E− Eg). The results are: 0.85 eV (i‐a‐Si), 1.12 eV (e‐a‐Si), 1.30 eV (r‐a‐Si). We attribute the optical change to annihilation of point defects

Ion-implantation induced anomalous surface amorphization in silicon

Spectroscopic ellipsometry (SE), high-depth-resolution Rutherford backscattering (RBS) and channeling have been used to examine the surface damage formed by room temperature N and B implantation into silicon. For the analysis of the SE data we used the conventional method of assuming appropriate optical models and fitting the model parameters (layer thicknesses and volume fraction of the amorphous silicon component in the layers) by linear regression. The dependence of the thickness of the surface-damaged silicon layer (beneath the native oxide layer) on the implantation parameters was determined: the higher the dose, the thicker the disordered layer at the surface. The mechanism of the surface amorphization process is explained in relation to the ion beam induced layer-by-layer amorphization. The results demonstrate the applicability of Spectroscopic ellipsometry with a proper optical model. RBS, as an independent cross-checking method supported the constructed optical model

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

In this paper we present a full-fledged scheme for the second order accurate, divergence-free evolution of vector fields on an adaptive mesh refinement (AMR) hierarchy. We focus here on adaptive mesh MHD. The scheme is based on making a significant advance in the divergence-free reconstruction of vector fields. In that sense, it complements the earlier work of Balsara and Spicer (1999) where we discussed the divergence-free time-update of vector fields which satisfy Stoke's law type evolution equations. Our advance in divergence-free reconstruction of vector fields is such that it reduces to the total variation diminishing (TVD) property for one-dimensional evolution and yet goes beyond it in multiple dimensions. Divergence-free restriction is also discussed. An electric field correction strategy is presented for use on AMR meshes. The electric field correction strategy helps preserve the divergence-free evolution of the magnetic field even when the time steps are sub-cycled on refined meshes. The above-mentioned innovations have been implemented in Balsara's RIEMANN framework for parallel, self-adaptive computational astrophysics which supports both non-relativistic and relativistic MHD. Several rigorous, three dimensional AMR-MHD test problems with strong discontinuities have been run with the RIEMANN framework showing that the strategy works very well.Comment: J.C.P., figures of reduced qualit

Optikai modellek fejlesztése sokösszetevős anyagrendszerek ellipszometriai vizsgálatához = Optical model development for ellipsometric study of many-compound materials

Az ellipszometria olyan optikai módszer, amely felületközeli, roncsolásmentes, in situ vizsgálatokat tesz lehetővé. A technológiába bekerülő összetett rétegek törésmutatója általában nem ismert, vagy éppen az a meghatározandó mennyiség. Ebben az esetben a törésmutatót diszperziós formulákkal, vagy az ún. effektív közeg közelítéssel (vagy egyszerre mindkettővel) határozhatjuk meg. Van lehetőség olyan paraméterek meghatározására is, amelyek egy-egy mikroszkópikus szerkezeti tulajdonsággal (pl. sávszélesség ill. szemcseméret, különböző fázisok) kapcsolatba hozhatók. Ebben a munkában az egy- és polikristályos CdTe (amely egy igéretes fotovoltaikus anyag) ion implantációval keltett hibasűrűségének az optikai tulajdonságaira való hatását vizsgáltuk. A CdTe optikai tulajdonságainak kritikus pont struktúráinak szélességét a kontrollált roncsoltság függvényében határoztuk meg. Az effektív roncsoltság mint egyetlen paraméter szerinti parametrizációt kerestük, amely elegendő az összes minta és a kritikus pontok szélességének szimultán leírásához. Ez a parametrizáció szolgálhat adatbázisul a különböző feltételek között leválasztott CdTe filmek optikai tulajdonságainak fitteléséhez. Ezen az úton nyílik lehetőség a CdTe gyártásközi, valósidejű ellenőrzésére. | Ellipsometry is an optical method which makes possible near-surface, non-destructive, in-situ studies. However, the refractive index of the coumpound materials in the technology is usually unknown or just the only question. In this case, the refractive index can be determined using dispersion formula or the so called effective medium approximation, or both. There is a possibility to determine parameters which can be coupled with microscopical structural properties (such as band gap or grain size or different phases). In this project, we studied the effects of defect density caused by ion implantation on the optical properties of single and polycrystalline CdTe, which is a promising photovoltaic material. The widths of the critical point structures in the optical properties of CdTe were determined as a function of the controlled defect density. We seeked a parameterization of the optical properties with a single parameter – an effective defect density -- that is sufficient to modify all critical point widths simultaneously and describe the optical properties for the full set of samples. This parameterization can serve as a database to fit the optical properties of CdTe films during different growth conditions. In this way, it will be possible to use real time optical measurements of CdTe during its fabrication and processing