bit input 1 bit input N reference reference bit input 1 bit input N 1386/31 Fig. 3 SC0RPI0N-1N cell and DAC NOT the corresponding bit inputs). A prototype of this version has been successfully implemented. The SCORPION DAC family maintains high speed with increasing bit resolution since the capacitance seen by each amplifier remains fixed. The convoluted feedback of the structure also tends to maintain speed. Both versions feature low ratio sensitivities, and all ratios are integers. Another property of these DACs is that they grow linearly in size with the bit resolution rather than exponentially. Acknowledgments: The authors are grateful to Mr. S. Chu and Dr. M. Milkovic of General Electric R&D and Prof. D. Gisser of Rensselaer Polytechnic Institute for their comments and discussions. References 1 SINGH, S. P., PRABHAKAR, A., and BHATTACHARYYA, A. B.: 'C-2C ladder voltage dividers for application in all-MOS A/D convertors', Electron. Lett., 1982,18, pp. 537-538 2 3 4 5 6 SINGH, S. P., PRABHAKAR, A., and BHATTACHARYYA, A. B.: 'Modified C-2C ladder voltage divider for application in PCM A/D convertors\ ibid., 1983,19, pp. 788-789 GHAUSI, M. s., and LAKER, K. L.: 'Modern filter design' (PrenticeHall, Inc., Englewood Cliffs, 1981) GOBET, c , and KNOB, A.: 'Noise analysis of switched capacitor networks', IEEE Trans., 1983, CAS-30, pp. 37-43 LAM, K. K. K., and COPELAND, M. A.: 'Noise-cancelling switchedcapacitor (SC) filtering technique', Electron. Lett., 1983, 19, pp. 810-811; Comment and Reply: 1984, 20, pp. 545-546 TEMES, G. c , and HAUG, K. : 'Improved offset-compensation schemes for switched-capacitor circuits', ibid., 1984, 20, pp. 508-509 R. M. PAYTON 24th September 1986 M. SAVIC Electrical, Computer & Systems Engineering Department Rensselaer Polytechnic Institute Troy, NY 12181, USA 8 WATANABE, K., and FUJIWARA, K.: 'Offset-compensated switched- NEW ANALYTICAL SOLUTION FOR A CURRENT/VOLTAG.E CHARACTERISTIC OF SPACE-CHARGE-LIMITED CURRENTS WITH A NONLINEAR VELOCITY-FIELD RELATIONSHIP of drift velocity saturation. The new solution is used also to obtain thefirst-ordercorrection to the Mott-Gurney law.6 For the one-dimensional problem the current/voltage characteristic of the ideal trap-free insulator is obtained by solving the system of equations 7 ERICKSSON, s., and CHEN, K.: 'Offset-compensated switched- capacitor leapfrog filters', ibid., 1984, 20, pp. 731-733 capacitor circuits', ibid., 1984, 20, pp. 780-781 j = pv(F) e dF/dx = p (1) Indexing terms: Semiconductor devices and materials, Current/ with boundary conditions voltage characteristic We present a new analytical solution for a current/voltage characteristic of space-charge-limited currents in materials with a nonlinear velocity-field relationship. Unlike previously reported results, this solution describes a gradual transition between the regimes of constant mobility and fieldindependent drift velocity. Considerable attention has been paid in the literature to the derivation and experimental verification of the current/voltage characteristic of space-charge-limited currents (SCLCs) in materials with a nonlinear velocity-field (v-F) relationship.1"9 In particular, it was found that an analytical solution is possible when the velocity v is a power function of the electric field Fi-3~5-8 or when the F(v) dependence has a polynomial form.2-6 In this letter we report a new analytical solution based on the Trofimenkoff's v-F relationship.10 Unlike the earlier solutions the new result allows us to trace the gradual transition between the regimes of constant mobility and that 1322 (2) F dx= V (3) In these equations ; is the current density, p is the space charge, e denotes the absolute dielectric permittivity, L is the thickness of the sample and V is the applied voltage. The co-ordinate x is taken from the virtual cathode (x = 0) along the current lines and the sign convention is such that all quantities are positive. As in previous investigations of this problem,1"9 we neglect the diffusion current component and adopt the virtual cathode approximation expressed by eqn. 2. This approach is natural to the analysis of the strong field effects.2-6 The velocity-field dependence used in the present work is10 (4) ELECTRONICS LETTERS 4th December 1986 Vol. 22 No. 25 where // 0 is the low-field mobility and Fc denotes the critical field. We note that for this model the F(v) dependence is not polynomial and hence the general formalism of Reference 2 does not apply. After the space charge p is excluded from eqns. 1 and 4 the Poisson equation takes the form F(l + F/F;.)'1 dF = (j/e[i0) dx (5) Integrating and using the boundary condition eqn. 2 we find x = (e^0 F2/j)lF/Fc - In (F/Fc + 1)] F(L) (7) \xdF o or, after x is substituted from expr. 6, (8) where y = F(L)/FC denotes the normalised anode field. The current density is found from eqn. 6 by putting x = L: (9) Eqns. 8 and 9 present the current/voltage characteristic of an SCLC in the parametric form with the normalised anode field as a parameter. The result is plotted in Fig. 1 together with two asymptotic lines which are obtained by considering the following limiting cases. In the low-field region F(L) <^ Fc, then eqns. 8 and 9 give LFc(2y/3-y2/lS = V2 JMG (10) (11) (12) — 8eA*o TaT The first term corresponds to the Mott-Gurney law,6 while the second introduces the first-order correction due to the nonlinearity of the v — F relationship. In the strong-field limit F(L)$> Fc, so that eqns. 8 and 9 lead to (6) Integrating by parts in eqn. 3 and once again using the virtual cathode approximation eqn. 2 we have = LF(L)- where j=js = 2vseV/L2 (13) where vs = n0 Fc denotes the saturation velocity. This is the expected result for the regime of complete velocity saturation. The gradual transition between the regimes described by eqns. 12 and 13 is illustrated in Fig. 1. The transition occurs in the vicinity of V = (16/9)LFC corresponding to jMG=js. The same equations describe SCLCs in materials with shallow traps after £ is changed to e9, where 6 -^ 1 is the ratio of the mobile to trapped charge densities.6 In conclusion, we have found a new analytical solution for the SCLC in materials with a nonlinear v — F dependence which describes the gradual transition between the low-field and strong-field limits. G. S. GILDENBLAT S. S. COHEN Department of Electrical Engineering Pennsylvania State University University Park, PA 16802, USA 8th October 1986 References 1 DACEY, G. c : Phys. Rev., 1953,90, p. 759 2 LAMPERT, M. A.: J. Appl. Phys., 1958, 29, p. 1082 3 GREGORY, B. L., and JORDAN, A. G.: Phys. Rev. A, 1964,134, p. 1378 4 LEE, D. H., and NICOLET, M. A.: Solid-State Electron., 1965, 8, p. 182 5 DENDA, s., and NICOLET, M. A.: J. Appl. Phys., 1966,37, p. 2412 6 LAMPERT, M. A., and MARK, P.: 'Current injection in solids' (Academic Press, New York, 1970) 7 WINTLE, H. J.: J. Appl. Phys., 1972,43, p. 2927 8 SHARMA, Y. K., and SRIVASTAVA, B. B.: Solid-State Electron., 1974, Thus in this region the current density can be presented as Sov. Phys. Semicond., 1978,12, p. 565 10 TROFIMENKOFF, F. N.: Proc. IEEE, 1965, 53, p. 1765 JUG 1 20 1 ' J /i N=TVN — 1-5 — 7 //- i 10 0-5 _ / 2V —*y/ / / / Indexing terms: Optical fibres, Single-mode fibres, Fibre characteristics / / — - oo y y / -10 4 -15 - -20 / / -10 - 0 - 5 NON-GAUSSIAN MODEL FOR FUNDAMENTAL-MODE FIELD IN SINGLE-MODE OPTICAL FIBRES / ! -0-5 17, p.1214 9 GILDENBLAT, G. SH., KARACHENTSEV, A. YA., a n d POTASHEV, YTJ. N . : i 00 0-5 log V, 10 1-5 U.L 3/11 Fig. 1 Normalised current/voltage characteristic (solid line) described by eqns. 8 and 9 Normalised current and voltage are defined as JN = jL/e(i0 Ff and VN = V/LFC Broken line represents Mott-Gurney law. Dotted line corresponds to regime of complete velocity saturation described by eqn. 13 ELECTRONICS LETTERS 4th December 1986 Vol. 22 The model fits the fundamental-mode field better than the Gaussian distribution. It reduces the differences, caused by non-Gaussian field shapes, among methods for measuring mode field radius. Formulas are provided for calculating Petermann's mode field radius from lateral offset, pinhole scan and VAMFF data. The fundamental-mode field radius (MFR) is usually determined by fitting a model to measurements of near-field lateral offset power transmission, pinhole scan of far-field power or far-field cumulative power. If the model is not exact, the different measurement methods will yield slightly different fits to the model, and consequently different MFRs, even with perfect data. The fundamental-mode field is approximately Gaussian in the centre, but its tails decay exponentially. For step-index fibres the deviation from Gaussian becomes significant as the wavelength increases. For dispersion-shifted and dispersionflattened fibres the deviation is significant at all wavelengths. No. 25 1323

1/--страниц