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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
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