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Papers by Sever Spanulescu

Research paper thumbnail of Reliability certification of semiconductor devices using Goldthwaite diagrams

SPIE Proceedings, 2000

ABSTRACT Beginning at observation that if a Goldthwaite diagram is draw a line (lambda) equals co... more ABSTRACT Beginning at observation that if a Goldthwaite diagram is draw a line (lambda) equals constant, all the curves of this diagrams are cutes in a point that are a value equal with that constant. If the constant is choose the maximum admissible value of failure rate multiplied by time of qualified life, the intersection of (lambda) line with the different (sigma) i curves, corresponding for a certain semiconductor devices, can determinate the value of median time tmi that corresponds t functioning temperature. In the laboratory was achieved accelerated aging for some semiconductor devices types. Parameters of accelerated aging were chosen so that they are not introducing any new failure mechanism non typical for normal functioning. Necessary time for accelerated aging test of this device was determinate using Arrhenius equation, for acceptance quality level 5 percent. For those devices, the time accelerated aging was determinate around on hundred hours. The value of failure rate certification was 102-103 Fits. The obtained results were validated therefore comparing then the results obtained using classical method for reliability testing, having the duration of 1000-200h. In this mode we can solve the problems of a long and expensive testing time before launching on the market a new devices.

Research paper thumbnail of Rayleigh scattering of X-ray and γ-ray by 2p electrons in ions and neutral atoms

The European Physical Journal D, 2016

Abstract Analytical formulae for the nonrelativistic 2p subshell Rayleigh scattering amplitudes a... more Abstract Analytical formulae for the nonrelativistic 2p subshell Rayleigh scattering amplitudes and cross section are obtained using the second order S-matrix element and the Coulombian Green function method, including multipoles and retardation. Relativistic kinematics effects are taking into account, allowing to remove the spurious poles that occur in a usual nonrelativistic calculation with retardation included. The nonrelativistic limit is obtained by removing the relativistic higher order terms in ω/m. A simple formula is also obtained for the total photoeffect cross section for a 2p electron. In the realistic case of ionized and neutral atoms, the screening effects were included by using an effective charge Zeff approach. A good agreement within 10% is found when comparing the predictions given by our analytical results for total photoionization cross section with the full relativistic numerical calculations in the case of 2p subshell for neutral atoms with 26 ≤ Z ≤ 92 and photon energies up to 100 keV. Graphical abstract

Research paper thumbnail of Spectral Method for Solving the Differential Equations Involved in Ab-Initio Treatment of Tunnel Transistors Structures

In lucrare este prezentată o nouă variantă a metodei spectrale de rezolvare a ecuaţiilor diferenţ... more In lucrare este prezentată o nouă variantă a metodei spectrale de rezolvare a ecuaţiilor diferenţiale cu condiţii la limită, aplicabilă la calcule ab-initio pentru tunelarea electronilor. Prin exprimarea potenţialului total în care se mişcă electronul ca o dezvoltare în serie după un anumit set de funcţii într-un spaţiu Hilbert, ecuatiile obtinute prin metoda colocatiei pot admite o integrare analitica initiala. Experimentele noastre numerice au aratat o îmbuntăţire importantă a preciziei datorită acestei prelucrări analitice suplimentare, ceea ce, împreună cu propritatea de evanescentă poate conferi metodei avantaje importante pentru calcule ab-initio.

Research paper thumbnail of Analysis of the Conduction Heat Transfer in Cantilevers under Steady State Cryogenic Conditions

arXiv: Materials Science, 2009

An accurate analysis of the conduction heat transfer in a cryogenic flask is made and some useful... more An accurate analysis of the conduction heat transfer in a cryogenic flask is made and some useful formulae are derived. Taking into account the temperature dependence of conductivity and tensile strength of the supporting rods for a helium cryostat, these formulae may provide more exact results than the the formulae based on simpler models. This allows the design of the supporting elements of a liquid helium cryostat with minimum cross-section (for minimizing the heat transfer)and proper mechanical resistance. Some examples of numerical results and tables are also presented.

Research paper thumbnail of Restaurarea statistică a informației cu aplicații în științele comunicării

Research paper thumbnail of Optimal basis set for ab-initio calculations of energy levels in tunneling structures, using the covariance matrix of the wave functions

The paper proposes a method to obtain the optimal basis set for solving the self consistent field... more The paper proposes a method to obtain the optimal basis set for solving the self consistent field (SCF) equations for large atomic systems in order to calculate the energy barriers in tunneling structures, with higher accuracy and speed. Taking into account the stochastic-like nature of the samples of all the involved wave functions for many body problems, a statistical optimization is made by considering the covariance matrix of these samples. An eigenvalues system is obtained and solved for the optimal basis set and by inspecting the rapidly decreasing eigenvalues one may seriously reduce the necessary number of vectors that insures an imposed precision. This leads to a potentially significant improvement in the speed of the SCF calculations and accuracy, as the statistical properties of a large number of wave functions in an large spatial domain may be considered. The eigenvalue problem has to be solved only few times, so that the amount of time added may be much smaller that the...

Research paper thumbnail of Statistical correlations in the demerit method with applications in nondestructive testing

SPIE Proceedings, 2001

12 In the paper, a new method of flaw evaluation in time for an organized production is presented... more 12 In the paper, a new method of flaw evaluation in time for an organized production is presented. A statistical correlation between the number of flows, the degree of gravity, the optimum production volume, the operators qualification level and their testing charge was established. The demerit method is a statistics one based on according a number of points to the defect types as function of their gravity degree. The `demerit' (term derived from French `sans merite') represents a mediation coefficient of the defects frequency pondered according to the assigned points. The `demerit' represents a synthetic complex and complete indicator, related to the defect number as well as to their gravity level.

Research paper thumbnail of Rayleigh scattering of x-ray and γ-ray by 1s and 2s electrons in ions and neutral atoms

Journal of Physics B: Atomic, Molecular and Optical Physics, 2011

Using the Coulomb-Green function method and considering the nonrelativistic limit for the two-pho... more Using the Coulomb-Green function method and considering the nonrelativistic limit for the two-photon S-matrix element, the right nonrelativistic 2s Rayleigh scattering amplitudes are obtained. Our result takes into account all multipoles, retardation and relativistic kinematics contributions, and the old dipole approximation result of Costescu [1] is retrieved as a limit case. The total photoeffect cross-section which is related to the

Research paper thumbnail of The second-order S -matrix element for the elastic scattering of photons by K-shell bound electrons: the nonrelativistic limit

Journal of Physics B: Atomic, Molecular and Optical Physics, 2007

In this paper, the right expressions of the fully nonrelativistic K-shell Rayleigh scattering amp... more In this paper, the right expressions of the fully nonrelativistic K-shell Rayleigh scattering amplitudes and cross-sections are obtained by using the Coulomb Green function method. Our analytical result has no spurious poles as the old nonrelativistic result with retardation [M. Gavrila and A.Costescu Phys. Rev. A 2, 1752 (1970)] presents. Taking into account the exact expression of the second order S-matrix element in the case of the elastic scattering of photons by K-shell bound electrons we obtain its nonrelativistic limit (valid for photon energies ω up to m Z

Research paper thumbnail of Improving the performances of the collocation method for numerically solving linear differential equations of the wavefunctions in large atomic systems

Research paper thumbnail of Elastic Photon Scattering and Photoeffect by K-Shell Electrons in Neutral Atoms *

A screening model based on nonrelativistic Hartree-Fock central field is elaborated for the K-she... more A screening model based on nonrelativistic Hartree-Fock central field is elaborated for the K-shell Rayleigh amplitudes and the total photoeffect cross section. It is valide in a large energy range from a few hundred eV up to hundreds of keV for intermediate and large atomic numbers. Multipoles, retardation as well as relativistic kinematics effects are taken into account. A good agreement with full relativistic numerical calculations is found.

Research paper thumbnail of Effects of a Supplementary Quadrature in the Collocation Method for Solving the Hartree Fock Equations in Ab-initio calculations

Abstract:- The collocation method for solving the Hartree-Fock equations of the self-consistent f... more Abstract:- The collocation method for solving the Hartree-Fock equations of the self-consistent field in large atomic and molecular systems is analyzed and a method for improving its performances by supplementary analytical and numerical quadrature is proposed. We used monomial and Chbyshev type trial functions and the collocation points were equidistant or Chebyshev polynomial roots. The singularities have been avoided by a function change and analytical expressions have been obtained for the most part of the integrated terms in the matrix elements, except the Hartree-Fock potential which is treated separately in a similar way. This a-priori analytical treatment ensures a greater speed and a lower condition number of the matrix necessary for the expansion’s coefficient calculus, with an important effect on the overall precision and speed. Some numerical results are presented and compared with well-known types of orbitals, demonstrating the performance increasing in terms of precisi...

Research paper thumbnail of Analysis of the radiative thermal transfer in planar multi-layer systems with various emissivity and transmissivity properties

The paper analyzes the radiative thermal transfer in a liquid helium cryostat with liquid nitroge... more The paper analyzes the radiative thermal transfer in a liquid helium cryostat with liquid nitrogen shielding. A infinite plane walls model is used for demonstrating a method for lowering the radiative heat transfer and the numerical results for two such systems are presented. Some advantages concerning the opportunity of using semi-transparent walls are analytically and numerically demonstrated.

Research paper thumbnail of Effects of a supplementary quadrature in the collocation method for solving the Hartree Fock equations in Ab-initio calculations

WSEAS Transactions on Mathematics archive, 2009

The collocation method for solving the Hartree-Fock equations of the self-consistent field in lar... more The collocation method for solving the Hartree-Fock equations of the self-consistent field in large atomic and molecular systems is analyzed and a method for improving its performances by supplementary analytical and numerical quadrature is proposed. We used monomial and Chbyshev type trial functions and the collocation points were equidistant or Chebyshev polynomial roots. The singularities have been avoided by a function change and analytical expressions have been obtained for the most part of the integrated terms in the matrix elements, except the Hartree-Fock potential which is treated separately in a similar way. This apriori analytical treatment ensures a greater speed and a lower condition number of the matrix necessary for the expansion's coefficient calculus, with an important effect on the overall precision and speed. Some numerical results are presented and compared with well-known types of orbitals, demonstrating the performance increasing in terms of precision and c...

Research paper thumbnail of Numerical evaluation and integration of higher transcendental Lauricella and Appell functions involved in photon-atom interactions

The triply differential cross-section for the inelastic Compton scattering of photons by K-shell ... more The triply differential cross-section for the inelastic Compton scattering of photons by K-shell bound electrons is expressed in closed form in terms of four high transcendental Lauricella functions FD of four variables and six parameters, all complex. In order to obtain the doubly differential cross-section, a numerical integration over the directions of the final electron is needed. The aim of this paper is to present a method for both evaluation and integration over the solid angle of Lauricella functions, valid for any photon energy and target's atomic number. While all the researchers seem to avoid even the evaluation of these functions, we present a new quadrature method, based on the analysis of the pathological behavior of the integrand near origin. Also, the solid angle integration process is achieved and discussed. Keeping the full form of the Lauricella functions allowed us to include in the doubly differential cross-section the exact dependence on the angles describi...

Research paper thumbnail of Analytical treatment of high transcendental functions involved in perturbation theory for inner shell electrons interaction with gamma-ray

This paper presents new analytical and numerical methods for handling the Appell and Gauss Hyperg... more This paper presents new analytical and numerical methods for handling the Appell and Gauss Hypergeometric functions involved in the relativistic elastic two photon scattering by inner shell electrons and in photoeffect and pair production processes. We find a possibility to reduce the number of needed Appell functions using their specific structure via recursion relationships. The oscillating nature of the integrand of the Appell functions in the high energy regime specific to γ -ray scattering is investigated and the solution for their accurate calculation on standard computer facilities is shown. The numerical results obtained using the presented methods were compared with other's authors results, displaying a very good agreement.

Research paper thumbnail of Analytical properties and numerical calculations of high transcendental functions involved in the relativistic amplitudes of two photon atomic processes

The high transcendental functions that occur in the relativistic expressions of the amplitudes of... more The high transcendental functions that occur in the relativistic expressions of the amplitudes of the two photon atomic processes are analytically treated taking advantage of their specific parameters values. We present some identities and recurrence relationships that allow reducing the number of needed Appell functions and transform their imaginary part in terms of Gauss hypergeometric functions. If the physical model takes into account only the terms up till the fourth power in αZ in the real part and the seventh power in the imaginary part, some transcendental functions may be reduced to elementary functions. The numerical results obtained using the presented methods were compared with other's authors results, displaying a very good agreement.

Research paper thumbnail of The calculus of the electric potential and field intensity in multiple electrodes lateral tunneling transistors with double gate

The paper presents an adaptive over-relaxation method for calculating the electric potential and ... more The paper presents an adaptive over-relaxation method for calculating the electric potential and field intensity, for a complex tunnel transistor structure involving a split gate and a shielding boundary. The accuracy and speed of the method has been numerically tested and found satisfactory for the study of such devices by calculating the tunneling currents for the obtained potential distribution.

Research paper thumbnail of Reliability certification of semiconductor devices using Goldthwaite diagrams

SPIE Proceedings, 2000

ABSTRACT Beginning at observation that if a Goldthwaite diagram is draw a line (lambda) equals co... more ABSTRACT Beginning at observation that if a Goldthwaite diagram is draw a line (lambda) equals constant, all the curves of this diagrams are cutes in a point that are a value equal with that constant. If the constant is choose the maximum admissible value of failure rate multiplied by time of qualified life, the intersection of (lambda) line with the different (sigma) i curves, corresponding for a certain semiconductor devices, can determinate the value of median time tmi that corresponds t functioning temperature. In the laboratory was achieved accelerated aging for some semiconductor devices types. Parameters of accelerated aging were chosen so that they are not introducing any new failure mechanism non typical for normal functioning. Necessary time for accelerated aging test of this device was determinate using Arrhenius equation, for acceptance quality level 5 percent. For those devices, the time accelerated aging was determinate around on hundred hours. The value of failure rate certification was 102-103 Fits. The obtained results were validated therefore comparing then the results obtained using classical method for reliability testing, having the duration of 1000-200h. In this mode we can solve the problems of a long and expensive testing time before launching on the market a new devices.

Research paper thumbnail of Rayleigh scattering of X-ray and γ-ray by 2p electrons in ions and neutral atoms

The European Physical Journal D, 2016

Abstract Analytical formulae for the nonrelativistic 2p subshell Rayleigh scattering amplitudes a... more Abstract Analytical formulae for the nonrelativistic 2p subshell Rayleigh scattering amplitudes and cross section are obtained using the second order S-matrix element and the Coulombian Green function method, including multipoles and retardation. Relativistic kinematics effects are taking into account, allowing to remove the spurious poles that occur in a usual nonrelativistic calculation with retardation included. The nonrelativistic limit is obtained by removing the relativistic higher order terms in ω/m. A simple formula is also obtained for the total photoeffect cross section for a 2p electron. In the realistic case of ionized and neutral atoms, the screening effects were included by using an effective charge Zeff approach. A good agreement within 10% is found when comparing the predictions given by our analytical results for total photoionization cross section with the full relativistic numerical calculations in the case of 2p subshell for neutral atoms with 26 ≤ Z ≤ 92 and photon energies up to 100 keV. Graphical abstract

Research paper thumbnail of Spectral Method for Solving the Differential Equations Involved in Ab-Initio Treatment of Tunnel Transistors Structures

In lucrare este prezentată o nouă variantă a metodei spectrale de rezolvare a ecuaţiilor diferenţ... more In lucrare este prezentată o nouă variantă a metodei spectrale de rezolvare a ecuaţiilor diferenţiale cu condiţii la limită, aplicabilă la calcule ab-initio pentru tunelarea electronilor. Prin exprimarea potenţialului total în care se mişcă electronul ca o dezvoltare în serie după un anumit set de funcţii într-un spaţiu Hilbert, ecuatiile obtinute prin metoda colocatiei pot admite o integrare analitica initiala. Experimentele noastre numerice au aratat o îmbuntăţire importantă a preciziei datorită acestei prelucrări analitice suplimentare, ceea ce, împreună cu propritatea de evanescentă poate conferi metodei avantaje importante pentru calcule ab-initio.

Research paper thumbnail of Analysis of the Conduction Heat Transfer in Cantilevers under Steady State Cryogenic Conditions

arXiv: Materials Science, 2009

An accurate analysis of the conduction heat transfer in a cryogenic flask is made and some useful... more An accurate analysis of the conduction heat transfer in a cryogenic flask is made and some useful formulae are derived. Taking into account the temperature dependence of conductivity and tensile strength of the supporting rods for a helium cryostat, these formulae may provide more exact results than the the formulae based on simpler models. This allows the design of the supporting elements of a liquid helium cryostat with minimum cross-section (for minimizing the heat transfer)and proper mechanical resistance. Some examples of numerical results and tables are also presented.

Research paper thumbnail of Restaurarea statistică a informației cu aplicații în științele comunicării

Research paper thumbnail of Optimal basis set for ab-initio calculations of energy levels in tunneling structures, using the covariance matrix of the wave functions

The paper proposes a method to obtain the optimal basis set for solving the self consistent field... more The paper proposes a method to obtain the optimal basis set for solving the self consistent field (SCF) equations for large atomic systems in order to calculate the energy barriers in tunneling structures, with higher accuracy and speed. Taking into account the stochastic-like nature of the samples of all the involved wave functions for many body problems, a statistical optimization is made by considering the covariance matrix of these samples. An eigenvalues system is obtained and solved for the optimal basis set and by inspecting the rapidly decreasing eigenvalues one may seriously reduce the necessary number of vectors that insures an imposed precision. This leads to a potentially significant improvement in the speed of the SCF calculations and accuracy, as the statistical properties of a large number of wave functions in an large spatial domain may be considered. The eigenvalue problem has to be solved only few times, so that the amount of time added may be much smaller that the...

Research paper thumbnail of Statistical correlations in the demerit method with applications in nondestructive testing

SPIE Proceedings, 2001

12 In the paper, a new method of flaw evaluation in time for an organized production is presented... more 12 In the paper, a new method of flaw evaluation in time for an organized production is presented. A statistical correlation between the number of flows, the degree of gravity, the optimum production volume, the operators qualification level and their testing charge was established. The demerit method is a statistics one based on according a number of points to the defect types as function of their gravity degree. The `demerit' (term derived from French `sans merite') represents a mediation coefficient of the defects frequency pondered according to the assigned points. The `demerit' represents a synthetic complex and complete indicator, related to the defect number as well as to their gravity level.

Research paper thumbnail of Rayleigh scattering of x-ray and γ-ray by 1s and 2s electrons in ions and neutral atoms

Journal of Physics B: Atomic, Molecular and Optical Physics, 2011

Using the Coulomb-Green function method and considering the nonrelativistic limit for the two-pho... more Using the Coulomb-Green function method and considering the nonrelativistic limit for the two-photon S-matrix element, the right nonrelativistic 2s Rayleigh scattering amplitudes are obtained. Our result takes into account all multipoles, retardation and relativistic kinematics contributions, and the old dipole approximation result of Costescu [1] is retrieved as a limit case. The total photoeffect cross-section which is related to the

Research paper thumbnail of The second-order S -matrix element for the elastic scattering of photons by K-shell bound electrons: the nonrelativistic limit

Journal of Physics B: Atomic, Molecular and Optical Physics, 2007

In this paper, the right expressions of the fully nonrelativistic K-shell Rayleigh scattering amp... more In this paper, the right expressions of the fully nonrelativistic K-shell Rayleigh scattering amplitudes and cross-sections are obtained by using the Coulomb Green function method. Our analytical result has no spurious poles as the old nonrelativistic result with retardation [M. Gavrila and A.Costescu Phys. Rev. A 2, 1752 (1970)] presents. Taking into account the exact expression of the second order S-matrix element in the case of the elastic scattering of photons by K-shell bound electrons we obtain its nonrelativistic limit (valid for photon energies ω up to m Z

Research paper thumbnail of Improving the performances of the collocation method for numerically solving linear differential equations of the wavefunctions in large atomic systems

Research paper thumbnail of Elastic Photon Scattering and Photoeffect by K-Shell Electrons in Neutral Atoms *

A screening model based on nonrelativistic Hartree-Fock central field is elaborated for the K-she... more A screening model based on nonrelativistic Hartree-Fock central field is elaborated for the K-shell Rayleigh amplitudes and the total photoeffect cross section. It is valide in a large energy range from a few hundred eV up to hundreds of keV for intermediate and large atomic numbers. Multipoles, retardation as well as relativistic kinematics effects are taken into account. A good agreement with full relativistic numerical calculations is found.

Research paper thumbnail of Effects of a Supplementary Quadrature in the Collocation Method for Solving the Hartree Fock Equations in Ab-initio calculations

Abstract:- The collocation method for solving the Hartree-Fock equations of the self-consistent f... more Abstract:- The collocation method for solving the Hartree-Fock equations of the self-consistent field in large atomic and molecular systems is analyzed and a method for improving its performances by supplementary analytical and numerical quadrature is proposed. We used monomial and Chbyshev type trial functions and the collocation points were equidistant or Chebyshev polynomial roots. The singularities have been avoided by a function change and analytical expressions have been obtained for the most part of the integrated terms in the matrix elements, except the Hartree-Fock potential which is treated separately in a similar way. This a-priori analytical treatment ensures a greater speed and a lower condition number of the matrix necessary for the expansion’s coefficient calculus, with an important effect on the overall precision and speed. Some numerical results are presented and compared with well-known types of orbitals, demonstrating the performance increasing in terms of precisi...

Research paper thumbnail of Analysis of the radiative thermal transfer in planar multi-layer systems with various emissivity and transmissivity properties

The paper analyzes the radiative thermal transfer in a liquid helium cryostat with liquid nitroge... more The paper analyzes the radiative thermal transfer in a liquid helium cryostat with liquid nitrogen shielding. A infinite plane walls model is used for demonstrating a method for lowering the radiative heat transfer and the numerical results for two such systems are presented. Some advantages concerning the opportunity of using semi-transparent walls are analytically and numerically demonstrated.

Research paper thumbnail of Effects of a supplementary quadrature in the collocation method for solving the Hartree Fock equations in Ab-initio calculations

WSEAS Transactions on Mathematics archive, 2009

The collocation method for solving the Hartree-Fock equations of the self-consistent field in lar... more The collocation method for solving the Hartree-Fock equations of the self-consistent field in large atomic and molecular systems is analyzed and a method for improving its performances by supplementary analytical and numerical quadrature is proposed. We used monomial and Chbyshev type trial functions and the collocation points were equidistant or Chebyshev polynomial roots. The singularities have been avoided by a function change and analytical expressions have been obtained for the most part of the integrated terms in the matrix elements, except the Hartree-Fock potential which is treated separately in a similar way. This apriori analytical treatment ensures a greater speed and a lower condition number of the matrix necessary for the expansion's coefficient calculus, with an important effect on the overall precision and speed. Some numerical results are presented and compared with well-known types of orbitals, demonstrating the performance increasing in terms of precision and c...

Research paper thumbnail of Numerical evaluation and integration of higher transcendental Lauricella and Appell functions involved in photon-atom interactions

The triply differential cross-section for the inelastic Compton scattering of photons by K-shell ... more The triply differential cross-section for the inelastic Compton scattering of photons by K-shell bound electrons is expressed in closed form in terms of four high transcendental Lauricella functions FD of four variables and six parameters, all complex. In order to obtain the doubly differential cross-section, a numerical integration over the directions of the final electron is needed. The aim of this paper is to present a method for both evaluation and integration over the solid angle of Lauricella functions, valid for any photon energy and target's atomic number. While all the researchers seem to avoid even the evaluation of these functions, we present a new quadrature method, based on the analysis of the pathological behavior of the integrand near origin. Also, the solid angle integration process is achieved and discussed. Keeping the full form of the Lauricella functions allowed us to include in the doubly differential cross-section the exact dependence on the angles describi...

Research paper thumbnail of Analytical treatment of high transcendental functions involved in perturbation theory for inner shell electrons interaction with gamma-ray

This paper presents new analytical and numerical methods for handling the Appell and Gauss Hyperg... more This paper presents new analytical and numerical methods for handling the Appell and Gauss Hypergeometric functions involved in the relativistic elastic two photon scattering by inner shell electrons and in photoeffect and pair production processes. We find a possibility to reduce the number of needed Appell functions using their specific structure via recursion relationships. The oscillating nature of the integrand of the Appell functions in the high energy regime specific to γ -ray scattering is investigated and the solution for their accurate calculation on standard computer facilities is shown. The numerical results obtained using the presented methods were compared with other's authors results, displaying a very good agreement.

Research paper thumbnail of Analytical properties and numerical calculations of high transcendental functions involved in the relativistic amplitudes of two photon atomic processes

The high transcendental functions that occur in the relativistic expressions of the amplitudes of... more The high transcendental functions that occur in the relativistic expressions of the amplitudes of the two photon atomic processes are analytically treated taking advantage of their specific parameters values. We present some identities and recurrence relationships that allow reducing the number of needed Appell functions and transform their imaginary part in terms of Gauss hypergeometric functions. If the physical model takes into account only the terms up till the fourth power in αZ in the real part and the seventh power in the imaginary part, some transcendental functions may be reduced to elementary functions. The numerical results obtained using the presented methods were compared with other's authors results, displaying a very good agreement.

Research paper thumbnail of The calculus of the electric potential and field intensity in multiple electrodes lateral tunneling transistors with double gate

The paper presents an adaptive over-relaxation method for calculating the electric potential and ... more The paper presents an adaptive over-relaxation method for calculating the electric potential and field intensity, for a complex tunnel transistor structure involving a split gate and a shielding boundary. The accuracy and speed of the method has been numerically tested and found satisfactory for the study of such devices by calculating the tunneling currents for the obtained potential distribution.