ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 07 Jul 2020 03:15:11 GMT2020-07-07T03:15:11Z50371- Spreading resistance analysis based on the method of regularisationhttps://scholarbank.nus.edu.sg/handle/10635/62805Title: Spreading resistance analysis based on the method of regularisation
Authors: Choo, S.C.; Leong, M.S.; Lee, Y.T.
Abstract: The method of regularisation is applied to recover, from spreading resistance (SR) measurement data, the dopant profiles of a variety of pn junction structures in which carrier spilling effects are significant. These structures range from those of several microns thick to submicron structures. A comparison is made of two methods of deriving the dopant profile: a direct method which inverts the measured SR profile directly to yield the dopant profile, and an indirect method, which derives the dopant profile from the "on-bevel" carrier profile. It is shown that while the two methods give similar results for the thick structures, the direct method is more accurate for the thin structures, particularly in determining the location of the metallurgical junction. The computation times required by both methods of a 486DX-33 computer are of the order of an hour. Sufficient details of the methods are provided for them to be implementable by users of the spreading resistance technique.
Fri, 01 Jan 1993 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628051993-01-01T00:00:00Z
- Extraction of semiconductor dopant profiles from spreading resistance data: An inverse problemhttps://scholarbank.nus.edu.sg/handle/10635/62175Title: Extraction of semiconductor dopant profiles from spreading resistance data: An inverse problem
Authors: Choo, S.C.; Leong, M.S.; Liem, C.B.T.; Kong, K.C.
Abstract: The traditional method of solving, on a layer-by-layer basis, the inverse problem of extracting resistivity vaues from spreading resistance measurements is found to produce wildly oscillatory, physically unacceptable resistivity profiles in the case of p-type silicon structures, where a resistivity-dependent probe contact radius is used in conjunction with the probe calibration data. These oscillations are manifestations of the fact that the inverse problem has non-unique solutions; they occur because the problem is inherently ill-posed. The well-known Tikhonov regularisation technique, which converts the present set of highly non-linear integral equations to an equivalent variational problem, is applied to stabilise the solution. Tests are performed on a variety of simulated profiles, and they reveal the existence of an optimum value for the regularisation parameter that is to be used with a second difference expression for the stabiliser of the cost function. When applied to measured spreading resistance data, the technique is found to produce results of reconstruction that are stable and physically reasonable.
Mon, 01 Jan 1990 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/621751990-01-01T00:00:00Z
- On space-charge recombination in pn junctionshttps://scholarbank.nus.edu.sg/handle/10635/80867Title: On space-charge recombination in pn junctions
Authors: Choo, S.C.
Thu, 01 Feb 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/808671996-02-01T00:00:00Z
- Theory of surface photovoltage in a semiconductor with a Schottky contacthttps://scholarbank.nus.edu.sg/handle/10635/68445Title: Theory of surface photovoltage in a semiconductor with a Schottky contact
Authors: Choo, S.C.
Abstract: An analytical theory of surface photovoltage is developed for a semiconductor with a Schottky contact. The theory is able to predict, for light with small to large absorption coefficients, the photon flux required to yield a specified photovoltage, taking into account the three current components that describe the internal behaviour of the semiconductor, namely, the surface current, the space-charge recombination current and the bulk diffusion current. Detailed modelling of these current components is done with the help of exact numerical solutions of the drift-diffusion transport equations. The validity of the theory is confirmed by comparison with exact numerical solutions over a wide range of doping concentrations and minority-carrier lifetimes.
Sun, 01 Jan 1995 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/684451995-01-01T00:00:00Z
- Improved variational method for spreading resistance calculationshttps://scholarbank.nus.edu.sg/handle/10635/62322Title: Improved variational method for spreading resistance calculations
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: An improved version of the variational method has been developed for spreading resistance calculations, based on a different source function from one used previously. This new version is capable of great accuracy, yielding results which for most practical purposes can be regarded as indistinguishable from those obtained from the exact method using the mixed boundary value approach. At the same time, it retains the main advantage, namely, speed of computation, of the variational method. Thus, in its present form, the variational method can be used in place of the exact method for accurate determination of both the correction factors and the source current density, especially where speed of computation is an important consideration. © 1986.
Wed, 01 Jan 1986 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/623221986-01-01T00:00:00Z
- On space-charge recombination in pn junctionshttps://scholarbank.nus.edu.sg/handle/10635/62525Title: On space-charge recombination in pn junctions
Authors: Choo, S.C.
Thu, 01 Feb 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/625251996-02-01T00:00:00Z
- Numerical investigation of subpicosecond electrical pulse generation by edge illumination of silicon transmission-line gapshttps://scholarbank.nus.edu.sg/handle/10635/62505Title: Numerical investigation of subpicosecond electrical pulse generation by edge illumination of silicon transmission-line gaps
Authors: Zhou, X.; Tang, T.; Seah, L.S.; Yap, C.J.; Choo, S.C.
Abstract: The phenomena involved in the subpicosecond electrical pulses generated by edge illumination of a charged coplanar transmission line on silicon substrate are investigated theoretically using a two-dimensional numerical model. The calculated terminal current, which is related to the observed electrical signal, is interpreted as being due to the dielectric relaxation of the space-charge field based on an equivalent circuit model. The pulse dependence (including amplitude, delay, rise time, and shape) on the wavelength of the laser source is investigated in terms of light penetration and the generated photocarriers. The frequency limit of the laser pulse train is determined theoretically for different carrier lifetimes. The simulation results are in qualitative agreement with experimental observations, and the dielectric-relaxation interpretation is consistent with other theories based on the full-wave analysis and the Monte Carlo model.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/625051998-01-01T00:00:00Z
- On the calculation of spreading resistance correction factorshttps://scholarbank.nus.edu.sg/handle/10635/62528Title: On the calculation of spreading resistance correction factors
Authors: Choo, S.C.; Leong, M.S.; Kuan, K.L.
Abstract: It is shown that the calculations of spreading resistance correction factors for graded structures can be readily carried out by using a simple recurrence formula for the integration factor that occurs in Schumann and Gardner's multilayer theory. The number of layers that can be used in the practical application of this theory has hitherto been limited by the computer core size requirement, because the earlier method of calculating the integration factor requires the inversion of a 2N × 2N matrix for an N-layer approximation. The use of the recurrence formula effectively removes this constraint. In terms of computation time, the recurrence-formula method is also very efficient. The economy thus achieved both in computation time and in core size requirement makes it possible now to make spreading resistance correction a routine matter, without having to resort to such measures as Hu's interpolation and space partitioning scheme. © 1976.
Thu, 01 Jul 1976 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/625281976-07-01T00:00:00Z
- Spreading resistance calculations for graded structures based on the uniform flux source boundary conditionhttps://scholarbank.nus.edu.sg/handle/10635/81216Title: Spreading resistance calculations for graded structures based on the uniform flux source boundary condition
Authors: Leong, M.S.; Choo, S.C.; Wang, C.C.
Abstract: In the approximate calculations of spreading resistance correction factors, two different types of boundary conditions over the source region have hitherto been assumed, viz., a uniform flux distribution, and the specific flux distribution that obtains in the classical solution for the infinitely thick slab. This paper presents results of a theory which has been derived for multilayer structures by using the uniform source flux distribution. The results given include those obtained for a series of exponentially-graded structures of varying steepness in the resistivity profile, whose thickness h1 ranges from 0.1 to 10 times the circular source contact radius, a. The results show that, as a rule, for an insulating substrate and (h′1/a) < 0.5, the uniform flux assumption leads to correction factors which differ at most by about 3% from those derived from the infinitely-thick slab flux assumption, while for a conducting substrate and (h′1/a) = 0.1 to 10, there is a difference of about 8%. Whatever the nature of the resistivity profile studied, it has been found that the difference is never greater than about 8%. © 1977.
Tue, 01 Mar 1977 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812161977-03-01T00:00:00Z
- Spreading resistance analysis based on the method of regularisationhttps://scholarbank.nus.edu.sg/handle/10635/81213Title: Spreading resistance analysis based on the method of regularisation
Authors: Choo, S.C.; Leong, M.S.; Lee, Y.T.
Abstract: The method of regularisation is applied to recover, from spreading resistance (SR) measurement data, the dopant profiles of a variety of pn junction structures in which carrier spilling effects are significant. These structures range from those of several microns thick to submicron structures. A comparison is made of two methods of deriving the dopant profile: a direct method which inverts the measured SR profile directly to yield the dopant profile, and an indirect method, which derives the dopant profile from the "on-bevel" carrier profile. It is shown that while the two methods give similar results for the thick structures, the direct method is more accurate for the thin structures, particularly in determining the location of the metallurgical junction. The computation times required by both methods of a 486DX-33 computer are of the order of an hour. Sufficient details of the methods are provided for them to be implementable by users of the spreading resistance technique. © 1993.
Fri, 01 Jan 1993 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812131993-01-01T00:00:00Z
- The role of source boundary condition in spreading resistance calculationshttps://scholarbank.nus.edu.sg/handle/10635/81260Title: The role of source boundary condition in spreading resistance calculations
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: Solutions are presented for the current density distribution at an equipotential disc electrode in contact with a slab backed by a perfect conductor. These exact solutions provide a basis for testing the validity of the two forms of source current density distribution assumed in approximate calculations of spreading resistance correction factors, viz. a uniform distribution and the distribution given by the classical solution for the infinitely thick slab. By using the latter distribution and the power loss definition for spreading resistance, a new correction factor integral has been obtained. Correction factors have been calculated by using this integral and those given by Schumann and Gardner, by Lee and by assuming a uniform current distribution. Except for Schumann and Gardner's method, all the methods yield results consistent with those obtained for the current density distributions. In the case of Schumann and Gardner's method, the correction factors obtained for thin slabs agree closely with those given by the exact method, despite the fact that the assumed source current distribution is in gross disagreement with the exact distribution. The close agreement in correction factors is fortuitous and is a consequence of the definition that Schumann and Gardner used for the spreading resistance. For a slab with a perfectly insulating substrate, exact solutions are not available. A comparative study has therefore been made in this case between the correction factors obtained by the four approximate methods themselves. The overall conclusion is that of the approximate methods, the uniform current density method is the most satisfactory from the point of view of self-consistency and overall accuracy. © 1978.
Sat, 01 Jul 1978 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812601978-07-01T00:00:00Z
- The spreading resistance of a homogeneous slab on a high-resistivity substrate: Mixed boundary value solutionshttps://scholarbank.nus.edu.sg/handle/10635/81261Title: The spreading resistance of a homogeneous slab on a high-resistivity substrate: Mixed boundary value solutions
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: The range of applicability of the mixed boundary value method for calculating spreading resistance is extended to a homogeneous slab with a disc contact source and backed by a substrate of arbitrary, but finite resistivity. Solutions are presented in terms of the spreading resistance correction factors and the source current density distributions for a slab of varying thickness and with various high resistivity substrates. In particular, the results for a thin slab indicate that, as the substrate resistivity increases, more and more of the source current is concentrated near the edge of the disc electrode. A comparison is made of the source current density and potential corresponding to the mixed boundary value method with those given by the uniform flux and the variable flux (power-loss) method. It is found that, except for large slab thicknesses, the source potential distributions for a slab with a high resistivity substrate are not strongly influenced by the particular form of the source current density distribution assumed in either the uniform flux or the variable flux method. In consequence, both these two methods yield correction factors which agree quite closely with those derived from the mixed boundary value method. © 1982.
Wed, 01 Sep 1982 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812611982-09-01T00:00:00Z
- The resistance of an infinite slab with a disc electrode as a mixed boundary value problemhttps://scholarbank.nus.edu.sg/handle/10635/81258Title: The resistance of an infinite slab with a disc electrode as a mixed boundary value problem
Authors: Leong, M.S.; Choo, S.C.; Tay, K.H.
Abstract: We consider the resistance of an infinite slab of material with a disc contact source on one side and with current collected over the entire back plane. By imposing the boundary condition of a constant potential over the source region, the problem becomes one of mixed boundary conditions, requiring the solution of a pair of dual integral equations. These equations are solved in terms of a Fredholm integral equation of the second kind. Calculations of the resistance are performed for values of slab thicknesses ranging from 0·05 to 4 times the disc contact radius, and the solutions obtained agree closely with Foxhall and Lewis' electrolytic tank measurements. The results are used to establish the range of validity of two approximate methods previously proposed for correction factor calculations in spreading resistance measurements on semiconductor device structures. © 1976.
Sat, 01 May 1976 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812581976-05-01T00:00:00Z
- Spreading resistance calculations by the use of Gauss-Laguerre quadraturehttps://scholarbank.nus.edu.sg/handle/10635/81214Title: Spreading resistance calculations by the use of Gauss-Laguerre quadrature
Authors: Choo, S.C.; Leong, M.S.; Hong, H.L.; Li, L.; Tan, L.S.
Abstract: The Gauss-Laguerre quadrature is proposed as a numerical method for calculating the correction factor integrals that occur in spreading resistance calculations. The method is very efficient in terms of computation time and memory storage, requiring only 33 integrand values for each integral evaluation. The accuracy of the method has been investigated for a variety of graded structures, and found to be better than 5%. As a test of its practical utility, the method has been used in the correction of the spreading resistance profile of a practical buried layer structure, and it has been found that the CPU time taken to correct the entire profile of 57 data points is 1.0 min on an IBM 1130 System with a 16K word (16 bit) memory or 0.4 sec on a UNIVAC 1100/10 Multiprocessor System with a 393K word (36 bit) memory. These times are a factor of 6 to 8 less than those required by using the previously proposed adaptive Simpson's rule to compute the correction factor integrals. © 1978.
Mon, 01 May 1978 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812141978-05-01T00:00:00Z
- Spreading resistance calculations by the variational methodhttps://scholarbank.nus.edu.sg/handle/10635/81215Title: Spreading resistance calculations by the variational method
Authors: Choo, S.C.; Leong, M.S.; Tan, L.S.
Abstract: In this paper the variational principle is applied to the calculations of spreading resistance for both homogeneous and inhomogeneous slabs on a perfectly conducting substrate, using a linear combination of two types of source flux distributions, namely, a uniform flux distribution and the classical form of the distribution for the infinitely thick slab. It is found that, as a rule, a linear combination of these two source distributions yields values of correction factors which agree much more closely with those derived from the exact constant potential approach than any given by previous approximate methods based on either of the source distributions. The variational method is not only accurate but also computationally efficient, being only a factor of three slower than any of the earlier approximate methods. © 1981.
Mon, 01 Jun 1981 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812151981-06-01T00:00:00Z
- Theory for the determination of backside contact resistance of semiconductor wafers from surface potential measurementshttps://scholarbank.nus.edu.sg/handle/10635/81273Title: Theory for the determination of backside contact resistance of semiconductor wafers from surface potential measurements
Authors: Tan, L.S.; Leong, M.S.; Choo, S.C.
Abstract: We present a method for the calculation of the potential on the surface of a homogeneous semiconductor slab with a disc source electrode on part of the front surface and a resistive contact over the backside of the entire slab. The imposed boundary condition of a constant potential over the source region gives rise to a pair of dual integral equations, which is transformed into a Fredholm integral equation of the second kind and subsequently solved using a simple numerical integration. The potential distributions on the surface of the slab are calculated for contact-to-semiconductor resistivity ratio in the range of 0 to 1 and for slab thickness ranging from 0.1 to 5x the radius of the disc contact. The results, which are directly applicable to the microelectronic test pattern NBS-3[1], show that there is a strong dependence of the surface potential distribution on the backside contact resistivity. A hitherto used two-dimensional model, with a strip source contact and restricted to the special case of a perfectly conducting backside contact, is shown to provide gross overestimates of the corresponding surface potentials when compared to the present method. © 1998 Elsevier Science Ltd. All rights reserved.
Mon, 06 Apr 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812731998-04-06T00:00:00Z
- The spreading resistance of an inhomogeneous slab with a disc electrode as a mixed boundary value problemhttps://scholarbank.nus.edu.sg/handle/10635/81262Title: The spreading resistance of an inhomogeneous slab with a disc electrode as a mixed boundary value problem
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: This paper presents a treatment of the mixed boundary value problem that arises in determining the spreading resistance of an inhomogeneous slab backed by a perfectly conducting substrate. It is shown that the inhomogeneity enters into the problem through the weight function of a pair of dual integral equations, and that this function is the same as the integration factor that occurs in previous approximate solutions based on assumed source current distributions. Except for the difference in the weight function, the dual integral equations are similar to those for the homogeneous slab. Calculations are performed for structures with exponential resistivity profiles, and the results used to determine the accuracy of three approximate methods currently available for spreading resistance calculations on semiconductor device structures. © 1979.
Fri, 01 Jun 1979 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812621979-06-01T00:00:00Z
- Theory of surface photovoltage in a semiconductor with a Schottky contacthttps://scholarbank.nus.edu.sg/handle/10635/81276Title: Theory of surface photovoltage in a semiconductor with a Schottky contact
Authors: Choo, S.C.
Abstract: An analytical theory of surface photovoltage is developed for a semiconductor with a Schottky contact. The theory is able to predict, for light with small to large absorption coefficients, the photon flux required to yield a specified photovoltage, taking into account the three current components that describe the internal behaviour of the semiconductor, namely, the surface current, the space-charge recombination current and the bulk diffusion current. Detailed modelling of these current components is done with the help of exact numerical solutions of the drift-diffusion transport equations. The validity of the theory is confirmed by comparison with exact numerical solutions over a wide range of doping concentrations and minority-carrier lifetimes. © 1995.
Fri, 01 Dec 1995 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812761995-12-01T00:00:00Z
- Theory of the photovoltage at semiconductor surfaces and its application to diffusion length measurementshttps://scholarbank.nus.edu.sg/handle/10635/81278Title: Theory of the photovoltage at semiconductor surfaces and its application to diffusion length measurements
Authors: Choo, S.C.; Tan, L.S.; Quek, K.B.
Abstract: This paper presents an analytical theory of the steady-state surface photovoltage, which takes into account recombination in the surface space charge region and at surface states, as well as bulk diffusion in the semiconductor. For a given wavelength of light used in the photo-excitation, the theory is able to predict the photon flux required to yield a specified surface photovoltage. The validity of the theory has been established by means of detailed comparison with exact numerical solutions. It is shown that for an Si specimen space charge recombination plays an important role in determining the surface photovoltage, particularly at photovoltages of the order 0.1 times the thermal voltage or less. The theory is applied to a rigorous examination of the validity of two standard test methods of the American Society for Testing and Materials for measuring the minority carrier diffusion length, which are based on the surface photovoltage. It is found that while the method due to Goodman works well in general and even in the presence of large surface recombination, the method due to Quilliet and Gosar does not always give the correct value of diffusion length, because of the importance of recombination in the space charge region and at the surface states-it does so only under certain restrictive conditions, i.e. the material must have a doping concentration greater than 1015 cm-3 and a long minority carrier lifetime (> 10 μs), with a surface in depletion (but not in inversion) at equilibrium and a very low surface recombination velocity. © 1992.
Sun, 01 Mar 1992 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812781992-03-01T00:00:00Z
- Theory of surface photovoltage in a semiconductor with deep impuritieshttps://scholarbank.nus.edu.sg/handle/10635/81277Title: Theory of surface photovoltage in a semiconductor with deep impurities
Authors: Choo, S.C.; Tan, L.S.; See, H.H.
Abstract: A recent theory of the surface photovoltage is extended to a semiconductor with deep impurities, whose concentration NT ≤ 0.1|N1|, where N1 is the net concentration of shallow impurities. Numerical solutions, which have been obtained for both n-type and p-type Si with gold as an example of a deep impurity, are used to guide the development of the theory. By approximating the gold acceptor and donor levels as two independent levels, expressions are derived for the relationships between the surface photovoltage and the splitting of the quasi-Fermi potentials νSC in the surface space charge region, and between νSC and the photon flux density in terms of recombination in the space charge region and at surface states, as well as carrier diffusion in the bulk. From these expressions, a complete theory is built up which is capable of predicting the photon flux density required to yield a specified photovoltage for a given wavelength of light. The theory is shown to agree well with the numerical solutions. In particular, it explains the unexpectedly large surface photovoltage observed from the numerical solutions for n-type gold-doped Si with NT = 0.1|N1|. As an application of the theory, it is shown that Goodman's surface photovoltage method will yield the appropriate minority carrier diffusion lengths in the bulk regions of n-type and p-type gold-doped Si material. © 1993.
Thu, 01 Jul 1993 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812771993-07-01T00:00:00Z
- The contact resistance at the interface between a disc electrode and an infinite slab: Mixed-boundary-value solutionshttps://scholarbank.nus.edu.sg/handle/10635/81244Title: The contact resistance at the interface between a disc electrode and an infinite slab: Mixed-boundary-value solutions
Authors: Choo, S.C.; Leong, M.S.; Low, W.C.
Abstract: We consider the contact-resistance problem that arises when a circular-disc electrode is in imperfect contact with a semiconductor slab, the imperfect contact being modelled by an infinitely thin layer of resistive material at the interface between the disc electrode and the slab. The resulting mixed-boundary-value problem is solved through the use of basis functions that satisfy the boundary conditions outside the source region identically. Calculations of the source current-density and the total slab resistance (including the effect of the contact resistance) are performed for homogeneous slabs of different thicknesses and with different substrate resistivities, for a wide range of values of the contact resistivity of the interface layer. The results obtained show that the presence of a contact resistance tends to make the source current density distribution more uniform. They also confirm the existence of upper and lower bounds for the difference between the total slab resistance and the layer contact-resistance, as predicted by Foxhall and Lewis. Although applied only to slabs of uniform resistivity, the method can be readily extended to slabs of nonuniform resistivity. © 1986.
Thu, 01 May 1986 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/812441986-05-01T00:00:00Z
- Spreading resistance calculations by the variational methodhttps://scholarbank.nus.edu.sg/handle/10635/62807Title: Spreading resistance calculations by the variational method
Authors: Choo, S.C.; Leong, M.S.; Tan, L.S.
Abstract: In this paper the variational principle is applied to the calculations of spreading resistance for both homogeneous and inhomogeneous slabs on a perfectly conducting substrate, using a linear combination of two types of source flux distributions, namely, a uniform flux distribution and the classical form of the distribution for the infinitely thick slab. It is found that, as a rule, a linear combination of these two source distributions yields values of correction factors which agree much more closely with those derived from the exact constant potential approach than any given by previous approximate methods based on either of the source distributions. The variational method is not only accurate but also computationally efficient, being only a factor of three slower than any of the earlier approximate methods. © 1981.
Mon, 01 Jun 1981 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628071981-06-01T00:00:00Z
- The contact resistance at the interface between a disc electrode and an infinite slab: Mixed-boundary-value solutionshttps://scholarbank.nus.edu.sg/handle/10635/62854Title: The contact resistance at the interface between a disc electrode and an infinite slab: Mixed-boundary-value solutions
Authors: Choo, S.C.; Leong, M.S.; Low, W.C.
Abstract: We consider the contact-resistance problem that arises when a circular-disc electrode is in imperfect contact with a semiconductor slab, the imperfect contact being modelled by an infinitely thin layer of resistive material at the interface between the disc electrode and the slab. The resulting mixed-boundary-value problem is solved through the use of basis functions that satisfy the boundary conditions outside the source region identically. Calculations of the source current-density and the total slab resistance (including the effect of the contact resistance) are performed for homogeneous slabs of different thicknesses and with different substrate resistivities, for a wide range of values of the contact resistivity of the interface layer. The results obtained show that the presence of a contact resistance tends to make the source current density distribution more uniform. They also confirm the existence of upper and lower bounds for the difference between the total slab resistance and the layer contact-resistance, as predicted by Foxhall and Lewis. Although applied only to slabs of uniform resistivity, the method can be readily extended to slabs of nonuniform resistivity. © 1986.
Thu, 01 May 1986 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628541986-05-01T00:00:00Z
- Spreading resistance calculations by the use of Gauss-Laguerre quadraturehttps://scholarbank.nus.edu.sg/handle/10635/62806Title: Spreading resistance calculations by the use of Gauss-Laguerre quadrature
Authors: Choo, S.C.; Leong, M.S.; Hong, H.L.; Li, L.; Tan, L.S.
Abstract: The Gauss-Laguerre quadrature is proposed as a numerical method for calculating the correction factor integrals that occur in spreading resistance calculations. The method is very efficient in terms of computation time and memory storage, requiring only 33 integrand values for each integral evaluation. The accuracy of the method has been investigated for a variety of graded structures, and found to be better than 5%. As a test of its practical utility, the method has been used in the correction of the spreading resistance profile of a practical buried layer structure, and it has been found that the CPU time taken to correct the entire profile of 57 data points is 1.0 min on an IBM 1130 System with a 16K word (16 bit) memory or 0.4 sec on a UNIVAC 1100/10 Multiprocessor System with a 393K word (36 bit) memory. These times are a factor of 6 to 8 less than those required by using the previously proposed adaptive Simpson's rule to compute the correction factor integrals. © 1978.
Mon, 01 May 1978 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628061978-05-01T00:00:00Z
- Improved variational method for spreading resistance calculationshttps://scholarbank.nus.edu.sg/handle/10635/80583Title: Improved variational method for spreading resistance calculations
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: An improved version of the variational method has been developed for spreading resistance calculations, based on a different source function from one used previously. This new version is capable of great accuracy, yielding results which for most practical purposes can be regarded as indistinguishable from those obtained from the exact method using the mixed boundary value approach. At the same time, it retains the main advantage, namely, speed of computation, of the variational method. Thus, in its present form, the variational method can be used in place of the exact method for accurate determination of both the correction factors and the source current density, especially where speed of computation is an important consideration. © 1986.
Wed, 01 Jan 1986 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/805831986-01-01T00:00:00Z
- Contact resistance calculations based on a variational methodhttps://scholarbank.nus.edu.sg/handle/10635/80338Title: Contact resistance calculations based on a variational method
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.; Goh, T.L.
Abstract: Noble's variational method is used to solve the contact resistance problem that arises when a circular disc source electrode is in contact with a semiconductor slab through an infinitesimally thin layer of resistive material. The method assumes that the source current density distribution J(r) has the form K1(1 - r2)-μ + K2(1 - r2) 1 2 + K3(1 - r2) 3 2, where the parameters K1, K2, K3 and μ are determined by variational principles. Calculations of the source current density and the total slab resistance, performed for a wide range of contact resistivities, show that the results are practically indistinguishable from those derived from an exact mixed boundary value method proposed earlier by us. Whilst this method of using an optimised μ is very accurate, it is computationally slow. By fixing μ at a constant value of 1 4, we find that we can drastically reduce the computation time for each calculation of the total slab resistance to 1.5 s on an Apple II microcomputer, and still achieve an overall accuracy of 1%. Tables of the abscissas and weights required for implementation of the numerical scheme are provided in the paper. © 1988.
Fri, 01 Jul 1988 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/803381988-07-01T00:00:00Z
- Analytical approximations for diffused junctions under high-level conditionshttps://scholarbank.nus.edu.sg/handle/10635/80297Title: Analytical approximations for diffused junctions under high-level conditions
Authors: Choo, S.C.; Yamasaki, H.
Abstract: A theoretical sutdy is made of the applicability of a previously-proposed diffused-junction model to diffused junctions with varying degrees of steepness in the impurity profile. This is done by comparing the predictions of the model with the exact numerical solutions obtained for a series of silicon p+n diffused junctions, ranging from very gradual junctions to the infinitely steep or ideal step junctions, and with the lightly-doped side of the junction in each case under high-level injection conditions. The results indicate that the range of validity of the model extends from those gradual junctions which are typically found in high-power thyristor structures to relatively steep diffused junctions similar to those that can occur in the emitter regions of UHF transistors. © 1976.
Wed, 01 Sep 1976 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/802971976-09-01T00:00:00Z
- Numerical investigation of subpicosecond electrical pulse generation by edge illumination of silicon transmission-line gapshttps://scholarbank.nus.edu.sg/handle/10635/80844Title: Numerical investigation of subpicosecond electrical pulse generation by edge illumination of silicon transmission-line gaps
Authors: Zhou, X.; Tang, T.; Seah, L.S.; Yap, C.J.; Choo, S.C.
Abstract: The phenomena involved in the subpicosecond electrical pulses generated by edge illumination of a charged coplanar transmission line on silicon substrate are investigated theoretically using a two-dimensional numerical model. The calculated terminal current, which is related to the observed electrical signal, is interpreted as being due to the dielectric relaxation of the space-charge field based on an equivalent circuit model. The pulse dependence (including amplitude, delay, rise time, and shape) on the wavelength of the laser source is investigated in terms of light penetration and the generated photocarriers. The frequency limit of the laser pulse train is determined theoretically for different carrier lifetimes. The simulation results are in qualitative agreement with experimental observations, and the dielectric-relaxation interpretation is consistent with other theories based on the full-wave analysis and the Monte Carlo model.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/808441998-01-01T00:00:00Z
- On the calculation of spreading resistance correction factorshttps://scholarbank.nus.edu.sg/handle/10635/80870Title: On the calculation of spreading resistance correction factors
Authors: Choo, S.C.; Leong, M.S.; Kuan, K.L.
Abstract: It is shown that the calculations of spreading resistance correction factors for graded structures can be readily carried out by using a simple recurrence formula for the integration factor that occurs in Schumann and Gardner's multilayer theory. The number of layers that can be used in the practical application of this theory has hitherto been limited by the computer core size requirement, because the earlier method of calculating the integration factor requires the inversion of a 2N × 2N matrix for an N-layer approximation. The use of the recurrence formula effectively removes this constraint. In terms of computation time, the recurrence-formula method is also very efficient. The economy thus achieved both in computation time and in core size requirement makes it possible now to make spreading resistance correction a routine matter, without having to resort to such measures as Hu's interpolation and space partitioning scheme. © 1976.
Thu, 01 Jul 1976 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/808701976-07-01T00:00:00Z
- An efficient numerical scheme for spreading resistance calculations based on the variational methodhttps://scholarbank.nus.edu.sg/handle/10635/61803Title: An efficient numerical scheme for spreading resistance calculations based on the variational method
Authors: Choo, S.C.; Leong, M.S.; Sim, J.H.
Abstract: This paper presents a simple and efficient numerical scheme for evaluating the correction factor integrals that arise in the variational method. The scheme is a modification of one recently proposed by Berkowitz and Lux for the uniform flux method. The abscissae and the weights required for the integration are given in a form which allows the numerical scheme to be readily implemented. Using this scheme, it takes, on an average, 0.8 sec to compute one value of correction factor on an Apple II Microcomputer. For a slab of varying thickness, backed by either a perfectly conducting or a high resistivity substrate, the correction factors obtained agree with those derived from the exact constant-potential method to within 1%. © 1983.
Mon, 01 Aug 1983 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/618031983-08-01T00:00:00Z
- A multilayer correction scheme for spreading resistance measurementshttps://scholarbank.nus.edu.sg/handle/10635/54450Title: A multilayer correction scheme for spreading resistance measurements
Authors: Choo, S.C.; Leong, M.S.; Hong, H.L.; Li, L.; Tan, L.S.
Abstract: This paper presents a method for computing the correction factor integral that arises in Schumann and Gardner's multilayer theory for spreading resistance measurements. From a detailed analysis of the integrand, a numerical scheme has been devised in which the integration is carried out with typically less than 150 integrand values and most of the functional values needed in the integration are pre-calculated and stored. The numerical scheme has been implemented on both an IBM 1130 System and a Univac 1106 Time Sharing System, and used to correct the spreading resistance profile of a buried layer structure. The results indicate that routine application of the multilayer theory is now practicable on either a minicomputer or a time sharing system. © 1977.
Sat, 01 Oct 1977 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/544501977-10-01T00:00:00Z
- A multilayer exponential model for spreading resistance calculationshttps://scholarbank.nus.edu.sg/handle/10635/54451Title: A multilayer exponential model for spreading resistance calculations
Authors: Choo, S.C.; Leong, M.S.
Abstract: A new multilayer approach to spreading-resistance correction-factor calculations is proposed, based on the approximation of the graded resistivity profile by a series of exponential functions. The existence of a recurrence formula for the integration factor in the correction factor integral makes the proposed model a practical alternative to Schumann and Gardner's staircase model. Although a factor of 3 slower in terms of computation time, the exponential model yields results much closer to the true profile than the staircase model, particularly in cases where the profile has very steep gradient but where the available measurement data points are sparse. © 1979.
Sun, 01 Apr 1979 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/544511979-04-01T00:00:00Z
- The spreading resistance of a homogeneous slab on a high-resistivity substrate: Mixed boundary value solutionshttps://scholarbank.nus.edu.sg/handle/10635/62865Title: The spreading resistance of a homogeneous slab on a high-resistivity substrate: Mixed boundary value solutions
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: The range of applicability of the mixed boundary value method for calculating spreading resistance is extended to a homogeneous slab with a disc contact source and backed by a substrate of arbitrary, but finite resistivity. Solutions are presented in terms of the spreading resistance correction factors and the source current density distributions for a slab of varying thickness and with various high resistivity substrates. In particular, the results for a thin slab indicate that, as the substrate resistivity increases, more and more of the source current is concentrated near the edge of the disc electrode. A comparison is made of the source current density and potential corresponding to the mixed boundary value method with those given by the uniform flux and the variable flux (power-loss) method. It is found that, except for large slab thicknesses, the source potential distributions for a slab with a high resistivity substrate are not strongly influenced by the particular form of the source current density distribution assumed in either the uniform flux or the variable flux method. In consequence, both these two methods yield correction factors which agree quite closely with those derived from the mixed boundary value method. © 1982.
Wed, 01 Sep 1982 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628651982-09-01T00:00:00Z
- The resistance of an infinite slab with a disc electrode as a mixed boundary value problemhttps://scholarbank.nus.edu.sg/handle/10635/62863Title: The resistance of an infinite slab with a disc electrode as a mixed boundary value problem
Authors: Leong, M.S.; Choo, S.C.; Tay, K.H.
Abstract: We consider the resistance of an infinite slab of material with a disc contact source on one side and with current collected over the entire back plane. By imposing the boundary condition of a constant potential over the source region, the problem becomes one of mixed boundary conditions, requiring the solution of a pair of dual integral equations. These equations are solved in terms of a Fredholm integral equation of the second kind. Calculations of the resistance are performed for values of slab thicknesses ranging from 0·05 to 4 times the disc contact radius, and the solutions obtained agree closely with Foxhall and Lewis' electrolytic tank measurements. The results are used to establish the range of validity of two approximate methods previously proposed for correction factor calculations in spreading resistance measurements on semiconductor device structures. © 1976.
Sat, 01 May 1976 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628631976-05-01T00:00:00Z
- The role of source boundary condition in spreading resistance calculationshttps://scholarbank.nus.edu.sg/handle/10635/62864Title: The role of source boundary condition in spreading resistance calculations
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: Solutions are presented for the current density distribution at an equipotential disc electrode in contact with a slab backed by a perfect conductor. These exact solutions provide a basis for testing the validity of the two forms of source current density distribution assumed in approximate calculations of spreading resistance correction factors, viz. a uniform distribution and the distribution given by the classical solution for the infinitely thick slab. By using the latter distribution and the power loss definition for spreading resistance, a new correction factor integral has been obtained. Correction factors have been calculated by using this integral and those given by Schumann and Gardner, by Lee and by assuming a uniform current distribution. Except for Schumann and Gardner's method, all the methods yield results consistent with those obtained for the current density distributions. In the case of Schumann and Gardner's method, the correction factors obtained for thin slabs agree closely with those given by the exact method, despite the fact that the assumed source current distribution is in gross disagreement with the exact distribution. The close agreement in correction factors is fortuitous and is a consequence of the definition that Schumann and Gardner used for the spreading resistance. For a slab with a perfectly insulating substrate, exact solutions are not available. A comparative study has therefore been made in this case between the correction factors obtained by the four approximate methods themselves. The overall conclusion is that of the approximate methods, the uniform current density method is the most satisfactory from the point of view of self-consistency and overall accuracy. © 1978.
Sat, 01 Jul 1978 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628641978-07-01T00:00:00Z
- The spreading resistance of an inhomogeneous slab with a disc electrode as a mixed boundary value problemhttps://scholarbank.nus.edu.sg/handle/10635/62866Title: The spreading resistance of an inhomogeneous slab with a disc electrode as a mixed boundary value problem
Authors: Leong, M.S.; Choo, S.C.; Tan, L.S.
Abstract: This paper presents a treatment of the mixed boundary value problem that arises in determining the spreading resistance of an inhomogeneous slab backed by a perfectly conducting substrate. It is shown that the inhomogeneity enters into the problem through the weight function of a pair of dual integral equations, and that this function is the same as the integration factor that occurs in previous approximate solutions based on assumed source current distributions. Except for the difference in the weight function, the dual integral equations are similar to those for the homogeneous slab. Calculations are performed for structures with exponential resistivity profiles, and the results used to determine the accuracy of three approximate methods currently available for spreading resistance calculations on semiconductor device structures. © 1979.
Fri, 01 Jun 1979 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628661979-06-01T00:00:00Z
- Theory for the determination of backside contact resistance of semiconductor wafers from surface potential measurementshttps://scholarbank.nus.edu.sg/handle/10635/62871Title: Theory for the determination of backside contact resistance of semiconductor wafers from surface potential measurements
Authors: Tan, L.S.; Leong, M.S.; Choo, S.C.
Abstract: We present a method for the calculation of the potential on the surface of a homogeneous semiconductor slab with a disc source electrode on part of the front surface and a resistive contact over the backside of the entire slab. The imposed boundary condition of a constant potential over the source region gives rise to a pair of dual integral equations, which is transformed into a Fredholm integral equation of the second kind and subsequently solved using a simple numerical integration. The potential distributions on the surface of the slab are calculated for contact-to-semiconductor resistivity ratio in the range of 0 to 1 and for slab thickness ranging from 0.1 to 5x the radius of the disc contact. The results, which are directly applicable to the microelectronic test pattern NBS-3[1], show that there is a strong dependence of the surface potential distribution on the backside contact resistivity. A hitherto used two-dimensional model, with a strip source contact and restricted to the special case of a perfectly conducting backside contact, is shown to provide gross overestimates of the corresponding surface potentials when compared to the present method. © 1998 Elsevier Science Ltd. All rights reserved.
Mon, 06 Apr 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/628711998-04-06T00:00:00Z