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A proposed numerical solution for the diffusion equation
346
World Abstracts on Microelectronics and Reliability
from the PSG with high phosphorus concentration in the form of the pentoxide.
Shallow impurity states in semiconductors: absorption cross-sections, excitation rates and capture cross-sections. W. W. ANDERSON. Solid-St. Electron. 18, 235 (1975). Shallow impurity state wave functions are derived for both a coulomb and 8-function binding potential within the effective mass formalism of Kohn. These wave functions, along with the Bloch functions of a perfect crystal are then used to obtain analytic expressions for photon spectral absorption cross-sections, thermal photon excitation rates, and carrier radiative capture cross-sections into the shallow centers. The calculated absorption cross-sections are in satisfactory agreement with both magnitude and spectral shape of experimentally measured cross-sections. The absorption cross-sections are such as to make the centers very sensitive to thermal photon excitation over a wide range of temperatures or center ionization energies. Finally, it is shown that radiative carrier trapping is normally negligible for shallow centers. Advances in solid planar dopant sources for silicon. J. J. STESLOW, J. E. RAPP and P. L. WHITE. Solid-St. Technol. (1975) p. 31. Planar diffusion sources have been utilized in the semiconductor industry since 1970. As silicon wafer diameters increase, the importance of these sources have increased correspondingly. This is due to their ability to produce uniform concentration of dopant both across and between silicon wafers. Acceptance of planar diffusion sources has been slowed by suspicion of impurities in these sources and by reactivation cycles necessitated by the composition of these sources. A new high purity boron source void of these problems has been developed which should advance the use of planar diffusion sources. Looking inside semiconductor devices. G. L. MILt.ER and D. A. H. ROBINSON. Bell Laboratories Record. February 1975. p. 129. Bell Labs research scientists have devised a simple method for measuring and displaying the distribution of impurities in semiconductors. The impurity "profile" is plotted directly on an x-y chart recorder while the measurement is being carried out, making this new method useful during research, development, and production of semiconductor devices having stringent materials requirements. A theoretical and experimental study of recombination in silicon p--n Junctions. P. ASHBURN, D. V. MORGAN and M. J. HOWES. Solid-St. Electron. 18, 569 (1975). This paper describes the results of a numerical solution of the one-dimensional transport equations as applied to p-n junctions. Generation-recombination is included in the model, and the method of solution is based on that of De Marl. The modifications of Choo are included to allow the solution of problems involving heavy recombination. Theoretical current-voltage characteristics are presented for both uniform and non-uniform distributions of recombination centres, and a comparison is made with experimental results on carbon implanted, silicon, p-n diodes. The dependence of the I/V characteristics on activation energy, capture cross sections, and density of recombination centres is described. Good agreement between theory and experiment is obtained, and the results suggest that the I/V characteristics can be described by the sum of two independant components of current. The first component is the generation-recombination current with an exp (eV/mkT) dependence, and the second is the diffusion current with an exp (eV/kT) dependance. A proposed numerical solution tot the diffusion equation. A. CHRYSSAFIS and R. J. HARRINGTON. Int. J. Electron. 38, 465 (1975). Both one and two-dimensional diffusion
equations are treated numerically, on a purely mathematical basis with the aid of a digital computer. One and two-dimensional models are considered to represent the n-region of a p-n junction. The impurity profile is assumed to be exponential, resulting in drift fields of constant magnitude. In the two-dimensional analysis the already existing one-dimensional theory of the mechanism for minority carriers is extended to respond to the requirements of the boundary conditions. Furthermore, the lateral dimension, and the position of the metal contact are taken into account. A qualitative description of the variation of reverse switching times with the variation of some physical parameters characterizing the models, as well as a range of possible solutions, are provided. A doped oxide diltnsion source. E. M. JULEFF. Microelectronies 6, 21 (1975). Planar integrated circuit technology requires various high temperature heat treatments in the fabrication of devices on single crystal silicon substrates. Such processes include: wet and dry thermal oxidations; epitaxy and diffusions. These treatments can produce imperfections detrimental to final device performance, and a reduction in the number of such steps is advantageous to device manufacture. In particular, standard diffusion methods involving a high temperature pre-deposit and subsequent drive can generate a high density of imperfections such as dislocations and precipitates. In addition, concentrations of dopant below the solid-solubility limit for silicon at a specific temperature are difficult to control. A new solid-solid diffusion technique from doped SiO2 grown by the low temperature decomposition of tetraethylorthosilicate and an alkoxide of the dopant, described by Scott and Olmstead, has several advantages over the stahdard methods. For example, since the doped SiO2 is grown at ~< 850°C essentially no conversion of the substrate occurs until drive temperature. Thus, no high concentration of dopant builds up in the substrate prior to drive and subsequently no dislocation generation or precipitation will occur. During drive, however, the doped oxide is depleting in a predictable manner providing good control and reproducibility.
Avalanche injection into the oxide in silicon gatecontrolled devices--l. Theory. C. BULUCEA. Solid-St. Electron. 18, 363 (1975). The avalanche injection into the oxide region of silicon gate-controlled devices is analysed in some detail, in terms of the physical theory of hot electrons in silicon as developed by Bartelink, Moll and Meyer. Numerically computed universal plots are given for the calculation of the hot-carrier injection ratio (avalanche-induced gate current over junction current) at given maximum interface electric field at breakdown. Features such as barrier reflexion due to transverse momentum of electrons, non-normal orientation of the electric field and Schottky barrier lowering have been incorporated in the analysis. Values of the hot-carrier injection ratio in positive-gate biased p*-n diodes (electron injection) calculated in this theory range between 4.3 × 10 4 and 4.7 × 10 3 for maximum interface electric fields at breakdown between 1.0 × 10 ~ V/cm and 1.4 × 106 V/cm, if the fitting parameters of the above quoted physical theory are used. The defect structure of silver-doped CdSt. H. R. VYDYANATH and F. A. KROOER. J. Phys. Chem. Solifts 36, 509 (1975). High-temperature Hall effect measure'ments are carried out on CdS doped with 2.5 × 1017 - 2-3 × 102° Ag cm 3 under various cadmium and sulfur pressures. At high pod and low silver concentrations, Ag acts as a donor. At higher concentrations self compensation occurs. An
World Abstracts on Microelectronics and Reliability
from the PSG with high phosphorus concentration in the form of the pentoxide.
Shallow impurity states in semiconductors: absorption cross-sections, excitation rates and capture cross-sections. W. W. ANDERSON. Solid-St. Electron. 18, 235 (1975). Shallow impurity state wave functions are derived for both a coulomb and 8-function binding potential within the effective mass formalism of Kohn. These wave functions, along with the Bloch functions of a perfect crystal are then used to obtain analytic expressions for photon spectral absorption cross-sections, thermal photon excitation rates, and carrier radiative capture cross-sections into the shallow centers. The calculated absorption cross-sections are in satisfactory agreement with both magnitude and spectral shape of experimentally measured cross-sections. The absorption cross-sections are such as to make the centers very sensitive to thermal photon excitation over a wide range of temperatures or center ionization energies. Finally, it is shown that radiative carrier trapping is normally negligible for shallow centers. Advances in solid planar dopant sources for silicon. J. J. STESLOW, J. E. RAPP and P. L. WHITE. Solid-St. Technol. (1975) p. 31. Planar diffusion sources have been utilized in the semiconductor industry since 1970. As silicon wafer diameters increase, the importance of these sources have increased correspondingly. This is due to their ability to produce uniform concentration of dopant both across and between silicon wafers. Acceptance of planar diffusion sources has been slowed by suspicion of impurities in these sources and by reactivation cycles necessitated by the composition of these sources. A new high purity boron source void of these problems has been developed which should advance the use of planar diffusion sources. Looking inside semiconductor devices. G. L. MILt.ER and D. A. H. ROBINSON. Bell Laboratories Record. February 1975. p. 129. Bell Labs research scientists have devised a simple method for measuring and displaying the distribution of impurities in semiconductors. The impurity "profile" is plotted directly on an x-y chart recorder while the measurement is being carried out, making this new method useful during research, development, and production of semiconductor devices having stringent materials requirements. A theoretical and experimental study of recombination in silicon p--n Junctions. P. ASHBURN, D. V. MORGAN and M. J. HOWES. Solid-St. Electron. 18, 569 (1975). This paper describes the results of a numerical solution of the one-dimensional transport equations as applied to p-n junctions. Generation-recombination is included in the model, and the method of solution is based on that of De Marl. The modifications of Choo are included to allow the solution of problems involving heavy recombination. Theoretical current-voltage characteristics are presented for both uniform and non-uniform distributions of recombination centres, and a comparison is made with experimental results on carbon implanted, silicon, p-n diodes. The dependence of the I/V characteristics on activation energy, capture cross sections, and density of recombination centres is described. Good agreement between theory and experiment is obtained, and the results suggest that the I/V characteristics can be described by the sum of two independant components of current. The first component is the generation-recombination current with an exp (eV/mkT) dependence, and the second is the diffusion current with an exp (eV/kT) dependance. A proposed numerical solution tot the diffusion equation. A. CHRYSSAFIS and R. J. HARRINGTON. Int. J. Electron. 38, 465 (1975). Both one and two-dimensional diffusion
equations are treated numerically, on a purely mathematical basis with the aid of a digital computer. One and two-dimensional models are considered to represent the n-region of a p-n junction. The impurity profile is assumed to be exponential, resulting in drift fields of constant magnitude. In the two-dimensional analysis the already existing one-dimensional theory of the mechanism for minority carriers is extended to respond to the requirements of the boundary conditions. Furthermore, the lateral dimension, and the position of the metal contact are taken into account. A qualitative description of the variation of reverse switching times with the variation of some physical parameters characterizing the models, as well as a range of possible solutions, are provided. A doped oxide diltnsion source. E. M. JULEFF. Microelectronies 6, 21 (1975). Planar integrated circuit technology requires various high temperature heat treatments in the fabrication of devices on single crystal silicon substrates. Such processes include: wet and dry thermal oxidations; epitaxy and diffusions. These treatments can produce imperfections detrimental to final device performance, and a reduction in the number of such steps is advantageous to device manufacture. In particular, standard diffusion methods involving a high temperature pre-deposit and subsequent drive can generate a high density of imperfections such as dislocations and precipitates. In addition, concentrations of dopant below the solid-solubility limit for silicon at a specific temperature are difficult to control. A new solid-solid diffusion technique from doped SiO2 grown by the low temperature decomposition of tetraethylorthosilicate and an alkoxide of the dopant, described by Scott and Olmstead, has several advantages over the stahdard methods. For example, since the doped SiO2 is grown at ~< 850°C essentially no conversion of the substrate occurs until drive temperature. Thus, no high concentration of dopant builds up in the substrate prior to drive and subsequently no dislocation generation or precipitation will occur. During drive, however, the doped oxide is depleting in a predictable manner providing good control and reproducibility.
Avalanche injection into the oxide in silicon gatecontrolled devices--l. Theory. C. BULUCEA. Solid-St. Electron. 18, 363 (1975). The avalanche injection into the oxide region of silicon gate-controlled devices is analysed in some detail, in terms of the physical theory of hot electrons in silicon as developed by Bartelink, Moll and Meyer. Numerically computed universal plots are given for the calculation of the hot-carrier injection ratio (avalanche-induced gate current over junction current) at given maximum interface electric field at breakdown. Features such as barrier reflexion due to transverse momentum of electrons, non-normal orientation of the electric field and Schottky barrier lowering have been incorporated in the analysis. Values of the hot-carrier injection ratio in positive-gate biased p*-n diodes (electron injection) calculated in this theory range between 4.3 × 10 4 and 4.7 × 10 3 for maximum interface electric fields at breakdown between 1.0 × 10 ~ V/cm and 1.4 × 106 V/cm, if the fitting parameters of the above quoted physical theory are used. The defect structure of silver-doped CdSt. H. R. VYDYANATH and F. A. KROOER. J. Phys. Chem. Solifts 36, 509 (1975). High-temperature Hall effect measure'ments are carried out on CdS doped with 2.5 × 1017 - 2-3 × 102° Ag cm 3 under various cadmium and sulfur pressures. At high pod and low silver concentrations, Ag acts as a donor. At higher concentrations self compensation occurs. An