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References
1 MARCATILI, E. A. J.: 'Slab-coupled waveguides', Bell Syst. Tech. J.,
1974, 53, pp. 645-674
2 FURLTA, H., NODA, H., and IHAYA, A.: 'Novel optical waveguide for
integrated optics', Appl. Opt., 1974, 13, pp. 322-326
3 PENG, s. T., and OLINER, A. A.: 'Leakage and resonance effects on
strip waveguides for integrated optics', Trans. Inst. Electron.
Commun. Eng. Japan, 1978, E61, pp. 151-154
4 OLINER, A. A., and PENG, s. T.: 'A new class of leaky modes on open
dielectric waveguides'. IEEE Microwave Symposium Digest, 1979,
pp. 569-571
5 KOSHIBA, M., and SUZUKI, M.: 'Equivalent network analysis of dielectric thin-film waveguides for optical integrated circuits and its
applications', Radio Sci., special issue on theory of optical fiber,
circuits and propagation in Japan, to be published
6 OHTAKA, M., MATSUHARA, M., and KUMAGAi, N.: 'Analysis of the
guided modes in slab-coupled waveguides using a variation
method', IEEE J. Quantum Electron., 1976, QE-12, pp. 378-382
7 YEH, c , HA, K., DONG, s. B., and BROWN, w. p.: 'Single-mode optical
waveguides', Appl. Opt., 1979, 18, pp. 1490-1504
8 YASUURA, K., SHIMOHARA, K., and MIYAMOTO, T. : 'Numerical analysis
of a thin-film waveguide by mode-matching method', J. Opt. Soc.
Am., 1980, 70, pp. 183-191
9 PELOSI, P. M., VANDENBULCKE, P., WILKINSON, C. D . W., a n d DE LA
RUE, R. M.: 'Propagation characteristics of trapezoidal cross-section
ridge optical waveguides: an experimental and theoretical investigation', Appl. Opt., 1978, 17, pp. 1187-1193
10 GALLAGHER, i. G.\ 'Mode dispersion of trapezoidal cross-section
dielectric optical waveguides by the effective-index method', Electron. Lett., 1979, 15, pp. 734-736
11 MIYAMOTO, T.: 'Numerical analysis of a rib optical waveguide with
trapezoidal cross section', Opt. Commun., 1980, 34, pp. 35-38
By correlating the TCL evaluation with the fraction of good
devices for both broad area and stripe geometry laser
configurations, TCL is shown to be an effective nondestructive
screening technique for rake lines.
The LPE laser material considered in this investigation was
prepared for the 0-83 j/m laser used in the FT-3 transmitter
subsystem. It has the usual four-layer double heterostructure
with a Te-doped n-ternary layer. Starting from the /i-GaAs
substrate, the layers have the following compositions:
(i) n-Al x Ga,_ x As (x = 0-34-0-44); (ii) p-Al v Gax_ v As (v =
0-00-0-10);(iii)p-AlxGa, _xAs (x = 0-34-0-44), and (iv)p-GaAs.9
The thickness of the Ge-doped p-type active layer (ii) is
0-10-0-20//m and the total thickness of the p-layers is ~ 1-8 /im.
For TCL evaluation the DH laser slice is mounted epitaxial
side up on a PIN silicon photodiode, and the electron beam of
the SEM is scanned over the top of the slice. In order to form a
high quality TCL image of rake lines in the thin active layer,
the electron beam must penetrate to the active layer but fall
short of the substrate. If the electron beam reaches the n-GaAs
substrate and produces a substantial amount of cathodoluminescence emission, the TCL image of the active layer will be
degraded. Thus, for a total p-layer thickness of 1-8 /.im the
accelerating voltage should be 20-30 kV, 10 with a beam current of 10~ 7 -10~ 6 A. A rigorous explanation of TCL and how
the active layer is imaged is given by Reference 6. Fig. 1 compares the TCL image of a slice having severe rake lines with the
almost featureless backscattered electron (BSE) image of the
top surface of the slice. In this instance the separation between
rake lines varies from 5 to 40 /im.
0013-5194/81/080283-02$!. 50/0
TRANSMISSION CATHODOLUMINESCENCE
AS A SCREENING TECHNIQUE FOR
RAKE LINES IN (Al, Ga)As DH LASER
MATERIAL
Indexing terms: Semiconductor materials & devices, Electron
microscopy
The use of transmission cathodoluminescence (TCL) as a
nondestructive screening technique for rake lines in (Al,
Ga)As double heterostructure laser material is reported here
for the first time. TCL evaluation is shown to correlate well
with the fraction of good devices for both broad area and
stripe geometry laser configurations.
The incidence of rake lines1 3 in the active layer of (Al, Ga)As
double heterostructure (DH) laser material can be a prominent
and deleterious growth defect in liquid phase epitaxial (LPE)
material grown with a Te-doped n-ternary layer by a technique
similar to that described by Dawson. 4 Rake lines, which
typically occur normal to the direction of LPE slider movement, indicate the absence of an active layer every 5 to 125 nm.
Other workers 2 - 3 have reported separations between rake lines
of 100-200 ^m. The presence of rake lines usually results either
in devices which do not operate in a lasing mode or in devices
with threshold currents elevated by tens to several hundred per
cent.2
In the present investigation we demonstrate for the first time
that transmission cathodoluminescence (TCL) 5 can be extended to reveal rake lines in thin active layers of (Al, Ga)As
DH laser material. 6 Several other techniques have been used in
the past to identify rake lines. These include the nondestructive
technique of scanning photocurrent, 3 - 7 and the destructive
techniques of photoluminescence (PL) 1 3 and cylinder lap. 2 - 6
Since the incidence and severity of rake lines can vary throughout a given slice, the need for a nondestructive screen to determine the extent of the problem is obvious. In addition to being
nondestructive, TCL has higher resolution than scanning
photocurrent, takes advantage of the magnification and depth
of field of the scanning electron microscope (SEM), and allows
the detection of a variety of crystalline8 and growth defects.6
ELECTRONICS LETTERS
16th April 1981
Vol.17
No. 8
Fig. 1 Comparison of TCL image of DH laser material having severe
rake lines with almost featureless backscattered electron (BSE) micrograph of top surface of slice. Micron bar represents 1(X) fim
After TCL evaluation a portion of the slice was processed
into broad area devices (250 x 380 urn2) for room temperature
pulse testing of the light-output/current characteristic. The
pulse width was 100 ns with a repetition rate of 1 kHz; the
current density was varied to a maximum of 2 kA/cm 2 .
Although overly optimistic results might be obtained with
broad area devices due to lasing within filaments not representative of the bulk material, others 11 have obtained reasonable
correlation with stripe geometry devices. For the purpose of
the present comparison between TCL evaluation and broad
area lasers, only the fraction of lasers with a threshold current
density Jth < 2 kA/cm 2 is considered.
The results are shown in Table 1. With the exception of one
slice, those slices identified by TCL as having rake lines did not
have any lasers with Jlh < 2 kA cm 2 while those without rake
lines had a relatively high fraction of good lasers. These data
are consistent with that of Nash et al.2 in which significant
increases in threshold current density are observed with increasing severity of rake lines. In the case of slices E and J,
which had a somewhat lower fraction of good devices than the
rest of the slices exhibiting no rake lines, an intense mottled (or
spotted) pattern 6 was observed in the TCL image. A particular
slice evaluated by TCL was found to have a moderate density
of rake lines over half of its area. This slice was processed into
285
proton-bombarded 5 ^m stripe geometry lasers with the stripe
perpendicular to the rake lines. These devices were tested for
their CW electro-optical characteristics at 30 and 65°C. The
half containing rake lines gave very poor devices; those which
lased typically had threshold currents 20% greater than those
from the half without rake lines. The fraction of good devices
after the test at 65°C was 0-40 for the half without rake lines
compared to 005 for the half containing rake lines. TCL evaluation of another slice revealed three quadrants to be free of
rake lines while the fourth had a moderate density of them.
Table 1 CORRELATION BETWEEN TCL RAKE LINE
EVALUATION AND FRACTION OF GOOD
BROAD AREA LASERS
Slice
TCL*
Fraction good
A
B
C
D
E
F
G
H
1
J
K
S
S
M
M
N
N
N
N
N
N
N
0
0
0
0-33
0-40
0-70
0-60
0-63
0-60
0-40
0-75
* Notation refers to the presence of rake lines: S = strong
(separation < 100 fxm), M = moderate (separation > 100 ^m),
N = none
This slice was also processed into proton-delineated stripe
geometry lasers for CW electro-optical characterisation. The
quadrant containing rake lines did not have any devices which
operated in a lasing mode while for the remaining three quadrants the average fraction of good devices was 0-55.
Rake line growth defects in the active layer of (Al, Ga)As
DH laser material have been revealed for the first time using
transmission cathodoluminescence. On the basis of the comparison presented above between TCL evaluation and device
properties, TCL has been shown to be a suitable nondestructive screening technique for rake lines. By screening the
as-grown material immediately after growth, it is possible to
make rapid adjustments in the LPE technique to improve the
material quality. The removal of laser material containing rake
lines from further processing should result in a substantial
avoidance of cost in wafer fabrication and device assembly.
TCL evaluation can also detect slices which have widely
spaced rake lines, and the laser cavities can then be aligned
parallel to the rake lines for enhanced yield. In addition, this
investigation has reaffirmed the disastrous effect which rake
lines have on device properties.
Acknowledgments: The authors thank A. E. Bakanowski, R. C.
Vehse, and B. W. Hakki for comments on the manuscript and
useful discussions. The technical assistance of Mrs. E. Homan
is gratefully acknowledged. The authors are also indebted to
M. C. Tamargo, R. I. Kunkel, and B. J. Gross for providing the
LPE grown laser material, to W. R. Holbrook for processing
the broad area lasers, and to K. Y. Lee for the use of his laser
testing instrumentation.
C. A. GAW
C. L. REYNOLDS, JUN.
Bell Laboratories
Reading, Pa. 19604, USA
5 CHIN, A. K., TEMKIN, H., and ROEDEL, R. j . : 'Transmission cathodo-
luminescence: a new SEM technique to study defects in bulk semiconductor samples', Appl. Phys. Lett., 1979, 34, pp. 476-478
6 GAW, C. A., NYGREN, S. F., REYNOLDS, C. L., JUN., a n d ANTHONY, P. J.:
in preparation
7 ANTHONY, p. J., SCHUMAKER, N. E., and LEE, J. w.: unpublished
8 CHIN, A. K., KERIMIDAS, V. G., JOHNSTON, W. D., JUN., MAHAJAN, S.,
and ROCCASECCA, D. D.: 'Evaluation of defects and degradation in
GaAs-GaAlAs wafers using transmission cathodoluminescence', J.
Appl. Phys., 1980, 51, pp. 978-983
9 HARTMAN, R. L., and KOSZI, L. A. : 'Characterization of (Al, Ga)As
injection lasers using the luminescence emitted from the substrate',
J. Appl. Phys., 1978, 49, pp. 5731-5744
10 WELLS, o. c.: 'Scanning electron microscopy' (McGraw-Hill, NY,
1974), p. 44
11 ANTHONY, P. J.: private communication
0013-5194/81/080285-02$! .50/0
ANALYSIS OF NOISE, SENSITIVITY AND
DYNAMIC RANGE IN DIGITAL FILTERS
USING MULTIPLIER EXTRACTION
APPROACH
Indexing terms: Filters, Signal processing
The evaluation of sensitivity, roundoff noise and dynamic
range of digital filters involves the calculation of a number of
substructure transfer functions. A method of calculating these
substructure transfer functions based upon the multiplier extraction approach is proposed. This new method requires
only the evaluation of a series of determinants and thus
avoids the need for matrix inversion.
Introduction: A useful measure for determining the performance of a digital filter structure is the sensitivity of the filter
transfer function H{z) with respect to variation of the multipliers within the structure. Several authors 1 ' 2 have shown by
means of Tellegen's theorem and the inter-reciprocity of transposed networks that the sensitivity of a filter transfer function
with respect to a multiplier am is given by
dH(z)
(z)Hml(z)
(1)
where Hlm(z) is the substructure transfer function between a
signal Xx{z) applied at the filter input and that measured at the
output of multiplier am, and Hml(z) is the substructure transfer
function between a signal applied at the output of multiplier am
and that measured at the filter output, Yi(z), with the filter
input Xi(z) set to zero.
Jackson3 showed that a good estimate of the power spectral
density of the roundoff noise in a digital filter containing
(n — 1) multipliers numbered 2 through n is given by
Ny(co) =
(2)
23rd February 1981
References
1 NASH, F. R., DIXON, R. W., BARNES, P. A., a n d SCHUMAKER, N. E.:
'Laser-excited photoluminescence of three-layer GaAs doubleheterostructure laser material', Appl. Phys. Lett., 1975, 27, pp.
234-237
2 NASH. F. R., WAGNER. w. R., and BROWN, R. L.: 'Threshold current
variations and optical scattering losses in (Al, Ga)As doubleheterostructure lasers', J. Appl. Phys., 1976, 47, pp. 3992-4005
3 LOGAN, R. A., SCHUMAKER, N . E., HENRY, C. H., a n d MERRITT, F. R.:
"Doping effects on rake line formation in LPE growth of
A l ^ G a ^ A s DH lasers', ibid., 1979, 50, pp. 5970-5977
286
L. R.: 'Near-equilibrium
LPE growth of
4 DAWSON,
GaAs-Gaj-jAl^As double heterostructures', J. Cryst. Growth,
1974, 27, pp. 86-95
where Ny(a>) is the roundoff noise power density at frequency
co and o\ is the variance of the roundoff noise at the output
of multiplier k. The dynamic range constraints which a filter
must satisfy if overflow of its internal registers is to be avoided
are given by 3
\Hlk(e*°)\\p<l
= 2, 3 , . . . , n
(3)
where Hik(ei<o)\\p is t n e Lp norm of Hlk{ei<o). The appropriate
value of p is determined by assumed conditions on the spectra
of the input signals to the filter. In order to analyse these
dynamic range constraints, it is necessary to evaluate the Lp
norms of H^e*10) in eqn. 3.
ELECTRONICS LETTERS
16th April 1981
Vol.17
No. 8
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