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Sensitivity limitations of ellipsometry
Abstracts
W(ll0) in the photon energy range 15-32eV. The normal incidence data has been successfully interpreted in terms of bulk interband transitions with the help of a non-relativistic photoemission code [J F L Hopkinson, J B Pendry and D J Titterington, Comp Phys Commun, 19, 69 (1980)]. The code was used to generate band structures and photocurrent calculations at some of the experimental photon energies. Refinements to the interpretation have been made with the help of a fully relativistic APW band structure calculation FN Egede Christensen and B Feuerbacher, Phys Rev, B10, 2349 (1980)].
calculate the pure-error sum-of-squares which gives a measure of the goodness-of-fit; such sampling also reduces the effects of noise and reduces the correlated errors in the results. (b) The uniqueness of the fit--it is important to check whether different initial estimates of the optical parameters for the fitting yield unequivocal conclusions; if there is not a reliable global minimum or if the sensitivity matrix is ill-conditioned recursive experimental design can show how to modify critically the range of measurements, and how much reduction of experimental noise is necessary to obtain reliable parameters.
The unoccupied states of Ta(001) studied by inverse photoemission
Empirical tight binding cluster method for semiconductor surface structures
I R Collins and P T Andrews, Department of Physics, University of
Liverpool, Oxford St, PO Box 147, Liverpool L69 3BX, UK
J N Carter, V M Dwyer and B W Holland, Department of Physics,
University of Warwick, Coventry CV4 7AL, UK The energy and dispersion of unoccupied states in tantalum in the FH direction and the dispersion of the unoccupied surface states in the ~1~,1direction on the (001) surface have been measured with angle resolved inverse photoemission. The bulk features were interpreted by comparison with Ta [I Petroff and C R Viswanathan, Phys Rev, B4, 799 (1971)1 and W IN E Christensen and B Feuerbacher, Phys Rev, B10, 2349 (1974)] band structure and W photocurrent [A D Laine, PhD Thesis, University of Liverpool (1986)] calculations. The bulk bands corresponded well with the calculations when some allowance was made for relativistic effects. Unoccupied surface states were identified in the 17"/~I direction by comparing 20 eV photon energy IPE spectra from clean and hydrogen dosed surfaces. An unoccupied hydrogeninduced adsorbate state was also observed. The surface states lay in bulk symmetry gaps and were in fair agreement with slab calculations [H Krakauer, Phys Rev, B30, 6834 (1984)] but differed in some respects from the results of previous measurements made with 9.7eV photons [R A Bartynski and T Gustafsson, Phys Rev, B35, 939 (1987)].
A cluster method for determining the structure of semiconductor surfaces by energy minimization and applicable to both ideal surfaces and those with defects, is presented. The cluster contains all those atoms that are assumed to undergo displacements from their bulk positions together with the neighbours required to give a reasonable local bonding environment for each displaced atom. The one-electron energy is obtained by diagonalizing a tight binding Hamiltonian whose matrix elements are determined empirically. It is shown by calculations for the Si(lll)-(2 × 1), Si(100)-(2 x 1) and GaAs(110)-(1 x 1) surfaces that the structures converge rapidly with increasing cluster size and give results close to those obtained by similar calculations on ideal infinite surface models.
Electronic structure of V-Si interfaces N V Rees and C C Matthai, Department of Physics, University
College, PO Box 78, Cardiff CFI IXL, UK Sensitivity limitations of ellipsometry D M Spink, J M Noras and C B Thomas, School of Electrical Engineering, University of Bradford, Bradford BD7 1DP, UK Spectroscopic and comparison ellipsometry are useful qualityassessment tools for monitoring thicknesses and optical properties of epitaxial structures and thin films both during growth and between treatments and manufacturing processes. Ellipsometry can be used to make fundamental measurements of dielectric properties in order to obtain data on defect and impurity concentrations and distributions in planar structures, and to locate and probe interfaces. Reduction of the experimental data to provide reliable information of this nature involves a difficult and sometimes unstable inverse-problem. Here we report on statistical approaches to parameter estimation, which provide checks on the accuracy and interpretation of results and also permit the design of optimal measurement strategies. Least-squares fitting of data to models leaves two main questions. (a) The magnitudes and correlations of errors in the derived parameters--analysis of the covariance matrix shows how badly conditioned is any particular problem: it is necessary to over-sample data in order to 430
At room temperatures, the deposition of V on Si leads to simple chemisorption followed by polycrystalline growth of V metal. At high temperatures (550°C) VSi 2 is formed on the Si surface. There is also evidence of an intermixed compound of average surface composition of VSi at lower temperatures (350°C). We use the iterative extended Huckel method to study the electronic structure ofV interstitials in the Si surface layer and of the VSi2-Si interface.
Multiple oxidation states on AI(lll) C F McConville*, D L Seymour, S Bao'i" and D P Woodruff,
Physics Department, University of Warwick, Coventry CV4 7AL, UK Previous studies of the initial stages of oxidation of AI(I 11) have highlighted the complexity of this system with suggested overlayer and underlayer chemisorption in addition to local oxide formation. Here we present the results of a new experimental study using synchrotron radiation photoemission from the A1 2p levels at
W(ll0) in the photon energy range 15-32eV. The normal incidence data has been successfully interpreted in terms of bulk interband transitions with the help of a non-relativistic photoemission code [J F L Hopkinson, J B Pendry and D J Titterington, Comp Phys Commun, 19, 69 (1980)]. The code was used to generate band structures and photocurrent calculations at some of the experimental photon energies. Refinements to the interpretation have been made with the help of a fully relativistic APW band structure calculation FN Egede Christensen and B Feuerbacher, Phys Rev, B10, 2349 (1980)].
calculate the pure-error sum-of-squares which gives a measure of the goodness-of-fit; such sampling also reduces the effects of noise and reduces the correlated errors in the results. (b) The uniqueness of the fit--it is important to check whether different initial estimates of the optical parameters for the fitting yield unequivocal conclusions; if there is not a reliable global minimum or if the sensitivity matrix is ill-conditioned recursive experimental design can show how to modify critically the range of measurements, and how much reduction of experimental noise is necessary to obtain reliable parameters.
The unoccupied states of Ta(001) studied by inverse photoemission
Empirical tight binding cluster method for semiconductor surface structures
I R Collins and P T Andrews, Department of Physics, University of
Liverpool, Oxford St, PO Box 147, Liverpool L69 3BX, UK
J N Carter, V M Dwyer and B W Holland, Department of Physics,
University of Warwick, Coventry CV4 7AL, UK The energy and dispersion of unoccupied states in tantalum in the FH direction and the dispersion of the unoccupied surface states in the ~1~,1direction on the (001) surface have been measured with angle resolved inverse photoemission. The bulk features were interpreted by comparison with Ta [I Petroff and C R Viswanathan, Phys Rev, B4, 799 (1971)1 and W IN E Christensen and B Feuerbacher, Phys Rev, B10, 2349 (1974)] band structure and W photocurrent [A D Laine, PhD Thesis, University of Liverpool (1986)] calculations. The bulk bands corresponded well with the calculations when some allowance was made for relativistic effects. Unoccupied surface states were identified in the 17"/~I direction by comparing 20 eV photon energy IPE spectra from clean and hydrogen dosed surfaces. An unoccupied hydrogeninduced adsorbate state was also observed. The surface states lay in bulk symmetry gaps and were in fair agreement with slab calculations [H Krakauer, Phys Rev, B30, 6834 (1984)] but differed in some respects from the results of previous measurements made with 9.7eV photons [R A Bartynski and T Gustafsson, Phys Rev, B35, 939 (1987)].
A cluster method for determining the structure of semiconductor surfaces by energy minimization and applicable to both ideal surfaces and those with defects, is presented. The cluster contains all those atoms that are assumed to undergo displacements from their bulk positions together with the neighbours required to give a reasonable local bonding environment for each displaced atom. The one-electron energy is obtained by diagonalizing a tight binding Hamiltonian whose matrix elements are determined empirically. It is shown by calculations for the Si(lll)-(2 × 1), Si(100)-(2 x 1) and GaAs(110)-(1 x 1) surfaces that the structures converge rapidly with increasing cluster size and give results close to those obtained by similar calculations on ideal infinite surface models.
Electronic structure of V-Si interfaces N V Rees and C C Matthai, Department of Physics, University
College, PO Box 78, Cardiff CFI IXL, UK Sensitivity limitations of ellipsometry D M Spink, J M Noras and C B Thomas, School of Electrical Engineering, University of Bradford, Bradford BD7 1DP, UK Spectroscopic and comparison ellipsometry are useful qualityassessment tools for monitoring thicknesses and optical properties of epitaxial structures and thin films both during growth and between treatments and manufacturing processes. Ellipsometry can be used to make fundamental measurements of dielectric properties in order to obtain data on defect and impurity concentrations and distributions in planar structures, and to locate and probe interfaces. Reduction of the experimental data to provide reliable information of this nature involves a difficult and sometimes unstable inverse-problem. Here we report on statistical approaches to parameter estimation, which provide checks on the accuracy and interpretation of results and also permit the design of optimal measurement strategies. Least-squares fitting of data to models leaves two main questions. (a) The magnitudes and correlations of errors in the derived parameters--analysis of the covariance matrix shows how badly conditioned is any particular problem: it is necessary to over-sample data in order to 430
At room temperatures, the deposition of V on Si leads to simple chemisorption followed by polycrystalline growth of V metal. At high temperatures (550°C) VSi 2 is formed on the Si surface. There is also evidence of an intermixed compound of average surface composition of VSi at lower temperatures (350°C). We use the iterative extended Huckel method to study the electronic structure ofV interstitials in the Si surface layer and of the VSi2-Si interface.
Multiple oxidation states on AI(lll) C F McConville*, D L Seymour, S Bao'i" and D P Woodruff,
Physics Department, University of Warwick, Coventry CV4 7AL, UK Previous studies of the initial stages of oxidation of AI(I 11) have highlighted the complexity of this system with suggested overlayer and underlayer chemisorption in addition to local oxide formation. Here we present the results of a new experimental study using synchrotron radiation photoemission from the A1 2p levels at