J-QE/24/2//
17793
Capacitance Free Generation
and
Detection
of
Subpicosecond Electrical Pulses
on
Coplanar Transmission
Lines
Daniel R. Grischkowsky
Mark B. Ketchen
C.-C. Chi
lrl N. Duling, III
Naomi
J.
Halas
Jean-Marc Halbout
Paul
G.
May
Reprinted from
IEEE
JOURNAL
OF
QUANTUM ELECTRONICS
Vol. 24, No. 2, February 1988
IEEE JOURNAL OF QUANTUM ELECTRONICS,
VOL.
24,
NO.
2,
FEBRUARY
1988
221
Capacitance
Free
Generation
and
Detection
of
Subpicosecond
Electrical
Pulses
on
Coplanar
Transmission
Lines
DANIEL
R.
GRISCHKOWSKY, MEMBER, IEEE, MARK B. KETCHEN, MEMBER, IEEE, C.-C. CHI,
IRL
N.
DULING, III, NAOMI
J.
HALAS, JEAN-MARC HALBOUT, MEMBER, IEEE,
AND
PAUL
G.
MAY
(Invited Paper}
Abstract-Based on a reanalysis
of
previous work and new experi-
mental measurements, we conclude that the parasitic capacitance at
the generation site
is
negligible for sliding contact excitation
of
small
dimension coplanar transmission lines.
T
HE generation
of
short electrical pulses via optical
methods has for some time been performed by driv-
ing Auston switches (photoconductive gaps) with short
laser pulses [ 1]. The generated electrical pulse is deter-
mined
by
the laser pulse, the carrier lifetime in the semi-
conductor, the capacitance
of
the switch, and the char-
acteristic impedance
of
the electrical transmission line.
The same techniques can also measure the resulting elec-
trical pulses by sampling methods. Recent work utilizing
photoconductive gaps has generated and measured sub-
picosecond electrical pulses [2). This large reduction in
the generated pulsewidth demonstrates the ultrafast ca-
pability
of
the Auston switches and calls for an under-
standing
of
the fundamental limits
of
their generation and
detection processes.
Stimulated by recent direct measurements [3], [4]
of
the
carrier lifetime in ion-implanted silicon-on-sapphire
(SOS), we have reanalyzed the results
of
[2). Based on
this analysis, we have come to the conclusion that, for the
so-called "sliding-contact" method
of
excitation [2], [5],
to first order the capacitance
of
the photoconductive switch
at the generation site
is
zero. This conclusion
is
further
supported by an experimental measurement
of
an ultra-
short electrical pulse using the double sliding-contact
method
of
generation and detection [6] where, to first or-
der, the capacitances at both the generation and detection
sites are zero. This measurement
is
in excellent agreement
with a theoretical analysis which assumes that the dura-
tion
of
the generated electrical pulse was limited only by
the laser pulsewidth and the carrier lifetime. This conclu-
sion removes one
of
the most severe limitations, associ-
Manuscript received June 9, 1987; revised August 7, 1987. This work
was supported in part
by
the U.S. Office
of
Naval Research.
D.
R.
Grischkowsky,
M.
B.
Ketchen, C.-C. Chi, I.
N.
Duling, III,
J.-M. Halbout, and
P.
G. May are with the IBM T. J. Watson Research
Center, Yorktown Heights,
NY
10598.
N. J. Halas was with the IBM T. J. Watson Research Center, Yorktown
Heights,
NY
10598. She is now with AT&T Bell Laboratories, Holmdel,
NJ
07733.
IEEE Log Number 8717793.
ated with the circuit parameters, on the generation
of
ul-
trashort electrical pulses by photoconductive switches.
The remaining limitations are the carrier lifetime, where
recent progress has been made [4], and the laser pulse-
width itself.
We will briefly review the initial experiment and its
analysis to provide the background for this recent ad-
vance. The geometry
of
the experimental arrangement [2]
is
illustrated in Fig. l(a). The 20 mm long transmission
line had a design impedance
of
100 0 and consisted
of
three parallel 5
µm
aluminum lines separated from each
other by 10
µm.
The de resistance
of
a single 5
µm
line
was
200
0.
The transmission line, composed
of
a 0.5
µm
thick
Al
film, was fabricated on an undoped silicon-on-
sapphire (SOS) wafer, which was heavily implanted with
0 + ions to ensure the required short carrier lifetime.
The laser source is a compensated, colliding-pulse,
passively mode-locked dye laser producing 80
fs
pulses
at a 100 MHz repetition rate. The measurements were
made with the standard excite and probe arrangement for
the beams
of
optical pulses. The time delay between the
exciting and sampling beams was mechanically scanned
by
moving an air-spaced retroreftector with a computer-
controlled stepping motor synchronized with a multichan-
nel analyzer. The measured subpicosecond electrical pulse
with an excellent signal-to-noise ratio
is
shown in Fig.
l(b). For this result, the spatial separation between the
exciting and sampling beams was approximately 50
µm,
while the laser spot diameters were
10
µm.
Our initial analysis [2]
of
this pulse followed Auston's
theory [1], which is extremely general and applies to
practically any transmission line configuration. The the-
ory only assumes (for both the generation and detection
sites) a conductance, given by the convolution
of
the laser
pulse and the carrier lifetime, charging a capacitance.
Each capacitance C discharges with time constant
ZC
where Z
is
approximately the transmission line imped-
ence. The numerical
fit
shown as the solid line in Fig.
1 (b) was obtained with the following parameters. The
conductances
of
both the sliding contact generation site
and the sampling gap site g
1
(t)
and g
2
(t),
respectively,
were assumed to be given by the convolution
of
the laser
pulse (allowing for its spatial extent) with
an
exponential
0018-9197/88/0200-0221$01.00 © 1988 IEEE
222
IEEE JOURNAL OF QUANTUM ELECTRONICS,
VOL.
24,
NO.
2,
FEBRUARY
1988
0
Sl.lOING
CONTACT"
9 1.0
"'
i.:
u
DETECTION
(a)
0 4 8 12
TIME
DELAY
(p
■
ec)
(b)
Fig. I. Experimental geometry
of
(2]. (b) Measured electrical pulse (dots)
compared to theory
of
[2] with
tc
= 250 fs,
C,c
= 1 fF,
and
C, = 4 fF.
response function describing the carrier lifetime
tc.
For
this initial analysis,
tc
was assumed to be 250 fs. An in-
tuitive argument presented in
[2]
led to the values
of
the
capacitance at the generation site
Csc
= 1 fF and at the
sampling site to be
Cs
= 4 fF.
As
can be seen, the
fit
is
reasonably good, with the exception that the leading edge
of
the calculated pulse rises much faster than the experi-
ment. Later analysis indicated that the shortness
of
the
assumed carrier lifetime ( compared to the measured pulse)
was responsible for this deviation. A recent direct mea-
surement
of
the carrier lifetime for heavily implanted
SOS
obtained the value
of
tc
= 600
fs
[3], and thereby con-
firmed this situation. This measurement forced the fol-
lowing reanalysis
of
the generation process for the elec-
trical pulse.
We
will now discuss some general aspects
of
transmis-
sion line theory
in
the quasi-static limit (QSL) for which
the wavelengths involved are large compared to the trans-
verse dimensions
of
the line. For this case, the number
of
transverse electromagnetic (TEM) modes
is
one less than
the number of metal lines making up the transmission line.
Consequently, a two-line transmission line has a single
propagating TEM mode. In the QSL, the electric field dis-
tribution
of
this mode
is
the same as for the static case
when the lines are equally and oppositely charged. Any
pulse propagating on this line can be described mathe-
matically as a Fourier sum
of
single frequency compo-
nents, all with this same TEM modal distribution. Like-
wise, a transient "purely electric" pulse
of
a limited
spatial extent can be considered to be the sum
of
two
counterpropagating pulses with the same spatial extent.
For this "stationary" electrical pulse, the zero H field
comes from the superposition
of
the two counterpropa- .
gating pulses where the E fields add, but the H fields sub-
tract. The
key
point in the argument to follow
is
that for
sliding-contact excitation, the resulting electrical tran-
sient
is
equivalent to the superposition
of
two
counterpropagating electrical pulses due
to
the zero H field
and to the excellent match
of
the E field lines to the prop-
agating TEM mode. This essentially perfect coupling
eliminates the parasitic capacitance (and inductance) at
the excitation site.
Consideration
of
the sliding-contact excitation site
shows that, to first order, charge
is
simply transferred from
one line to the other, creating a symmetrical field distri-
bution with respect to the two lines. During the excitation
process, a current
flow
is
induced between the lines. Lo-
calized charge accumulations
of
opposite sign build up on
the segments
of
the two metal lines under the laser exci-
tation spot, creating a dipolar field distribution similar to
that illustrated in Fig. 2(a). The response time
of
this field
pattern
is
approximately the time required for electromag-
netic radiation to cross the separation between the two
lines. For the simplified quasi-static picture to apply, this
time should be short compared to either the laser pulse
duration or the carrier lifetime, whichever is longer. This
is
simply a restatement that the wavelengths involved
should be large compared to the transverse dimensions
of
the line. Because the electric field lines
of
the TEM mode
have the same pattern as the de field lines [illustrated
in
Fig. 2(a)] when the lines are equally and oppositely
charged [7], the sliding-contact excitation
is
well matched
to the TEM mode. The major part
of
generated field pat-
tern is the same as this TEM mode which
is
perfectly cou-
pled to the line.
A most important feature
of
a coplanar transmission line
(of negligible thickness) on an infinite dielectric half-space
is
that for a constant voltage between the two conducting
lines, the electric field lines are the same as for the lines
immersed in free space [8]. This result
is
due to the geo-
metric symmetry with respect to the dielectric boundary
and
is
a consequence
of
the fact that
no
electric field lines
cross this boundary. The effect
of
the dielectric (with di-
electric constant
e)
is to increase the surface charge den-
sity on the conductors in contact with the dielectric to
ec,
0
where a
0
is
the surface charge density in free space. How-
ever, because there
is
a polarization surface charge den-
sity
of
( e - 1
)c,
0
of
the opposite sign, the net surface
charge remains a
0
, keeping the electric field the same.
Consequently, the main effect
of
the dielectric
is
to in-
crease the distributed line capacitance. This increase will
now be evaluated following the procedure
of
[8]. Con-
sider the capacitance per unit length
of
the line to be C
0
in free space. In the dielectric medium, the surface charge
density
is
ECJo,
but for the side
of
the line in free space,
the surface charge density remains a
0
• Therefore, for the
same voltage between the lines, the charge has increased
by
( 1 + e)
/2,
and the corresponding capacitance has in-
creased to C = ( l + e) C
0
/ 2. Because we assume the
dielectric medium has a magnetic permeability equal to
unity, the inductance
Lo
per unit length does not change
in the presence
of
the dielectric.
The predicted group velocity can now be evaluated fol-
lowing the logic
of
[8]. For the transmission line
in
free
GRISCHKOWSKY
et
al.:
CAPACITANCE
FREE
GENERATION & DETECTION
OF
ELECTRICAL PULSES
223
I 0
05
0
·.:
.·
··'
......
(a)
(b)
,\
•'
. '
..
I
'.
'
\
4 8
TIME DELA\'
(psec)
(c)
Vo
12
Fig. 2. (a) Electrical field lines for the propagating TEM mode (differen-
tial mode)
of
a two-line transmission line in a uniform dielectric and on
the surface
of
a uniform dielectric. (b) Equivalent circuit for sliding-
contact excitation
of
a two-line transmission line. (c) Measured electrical
pulse (dots)
of
(2)
compared to theory with
r,
= 600 fs, C,, = 0, and
C,
= 1 fF.
space, the group velocity v
8
is
given by v
8
=
(1
/ (
Lo
C
0
))
1
7
2
= c [9], [ 1
O].
In the presence
of
the di-
electric, the capacitance has increased to ( 1 + e
)C
0
/2,
while the inductance remained the same. This situation
gives the result v
8
=
c(2
/ ( e + 1) )
1
/
2
• The low-fre-
quency dielectric constants
of
sapphire are 9.4 for the or-
dinary ray and
11.
6 for the extraordinary ray [
11]
. These
values give the corresponding group velocities
of
c
/2.28
and
c/2.51,
which bracket our measured value
[2]
of
c
/2
.45 obtained on sapphire
of
unknown orientation. This
good agreement confirms the validity
of
the quasi-static
approximation and shows that the TEM mode remains a
good approximation for this split dielectric case, even
though it
is
no longer an exact solution. Consequently, all
of
the above arguments also apply to the split dielectric
case, i.e., sliding-contact excitation produces a field dis-
tribution which matches the propagating mode
of
the line,
and thereby the parasitic capacitance at the generation site
is
negligible.
An
equivalent circuit illustrating this situation
is
shown
in Fig. 2(b) where the photoconductance g
1
(t)
created by
the laser excitation
is
connected directly across the char-
acteristic (resistive) impedance
Zo
in either direction. The
infinite capacitances simply illustrate that the line extends
without end in both directions. Because this circuit has no
capacitance at the generation site, the voltage pulses
launched
in
both directions down the line are given
by
V(t)
= V
0
Zo/(Zo
+ 1 / g
1
(t)
). For our case where
V(t)
<< V
0
, this result simplifies to
V(t)
= V
0
Z
0
g
1
(t).
Con-
sequently, the generated electrical pulse has the same time
dependence as the conductance g
1
(
t).
We again numerically analyzed the measured electrical
pulse
of
Fig. l(b), but with the following parameters. The
conductances g
1
(t)
and g
2
(t)
were obtained
as
before,
except now the carrier lifetime is known to be 600 fs. The
capacitance at the generation site was set equal to zero,
Csc
= 0. Thus, the capacitance at the sampling site was
the only adjustable parameter to be determined by nu-
merically fitting to the measured pulse. With the opti-
mized value
Cs
= 1 fF,
we
obtained the excellent agree-
ment with theory shown
as
the solid line in Fig. 2(c). For
this situation, the actual generated electrical pulse was
calculated and
is
shown in Fig. 3 to have a pulsewidth
of
only 0.52 ps. The sharp rising edge is due to the short
laser pulse excitation, while the slower falling edge
of
the
pulse is due to the 600
fs
carrier lifetime. This pulse is
directly proportional to g
1
(t)
in accordance with the anal-
ysis
of
the equivalent circuit
of
Fig. 2(b).
The good agreement between theory and experiment in
Fig. 2(c) gave
us
confidence in our new understanding
of
the pulse generation process and suggested
as
a further
confirmation the experiment illustrated in Fig. 4(a). This
more symmetrical arrangement
is
called the double slid-
ing-contact and has no observable capacitance [6]. It is to
be noted that
we
used a two-line transmission line, so that
the above arguments about matching to the propagating
TEM mode are more precise. The electrical pulse
is
gen-
erated
as
before, but here the sampling measurement
is
also made by shorting the transmission line with the sam-
pling laser pulse. For this case, the two laser beams are
mechanically chopped at incommensurate frequencies and
the signal
is
measured
as
a modulation
of
the photocurrent
on the transmission line at the sum
of
the two chopping
frequencies. Because to first order this arrangement has
no
capacitance at both the generation and sampling sites,
the measured electrical pulse had a pulsewidth
of
only
0.85
ps
compared to the previous measurement
of
1.
1
ps
using a sampling gap. This measurement was made on a
smaller geometry coplanar line with line dimensions
of
1.2
µm
separated
by
2.4
µm.
The design impedance was
100
0 and the bias was 1.5 V. In order
to
compare to
theory, the conductances g
1
(
t)
and g
2
((t)
were obtained
as
before with the carrier lifetime
of
600 fs, but
now
the
capacitances at both the generation and sampling sites
were set to zero. The resulting
fit
to the data is shown
as
the solid line in Fig. 4(b). This theoretical prediction
is
equivalent to the autocorrelation
of
the electrical pulse
shown in Fig. 3. The agreement between theory and ex-
periment showing the sharpness
of
the peak
of
the pulse
is
good. This extremely sharp peak is due to the sharp
leading edge
of
the generated electrical pulse in Fig. 3.
However, the data in Fig. 4(b) definitely show a faster
time dependence than the calculations which only assume
an excitation pulse
of
130
fs
(the square root
of
the
sum
of
the squares
of
the laser pulsewidth plus the transit time
due to the
10
µm
diameter spot size) and the 600
fs
carrier
lifetime.
224
IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 24,
NO.
2,
FEBRUARY 1988
1.0
,i\
I\
05
0 Z 4 6
TIME
(psec)
Fig. 3. Generated electrical pulse.
~•=;;•
.,..
EXCITING
SAMPLING
:::;
I 0
;;:
;:
t..,
ii,
t;
;.; 0 5
"'
"'
>
~
"'
0
BEAM
BEAM
"DOUBLE
SLIDING
CONTACT"
(a)
;,
4 6
TIME DELAY
(psec)
(b)
°'
Of-----
4 6
TIME DELAY (
psec)
(c)
IZ
Fig. 4. (a) Experimental geometry for double sliding contact. (b) Mea-
sured electrical pulse (dots) compared to theory with
tc
= 600 fs,
C.«
=
0 fF, and
C,
= 0 fF. (c) Measured electrical pulse (dots) compared to
theory with le = 400 fs,
C,c
= 0 fF, and C, = 0 fF.
Because the 600
fs
data were obtained by reflectivity
measurements [3], [4], it is natural to assume that they
were a surface-sensitive measure
of
the carrier lifetime.
However, a recent analysis [12) has shown that this was
not the case, and that for a 0.5
µm
thick layer
of
silicon
on a sapphire substrate, the main component on the signal
obtained with 620
nm
light was due to the induced change
in
the optical length
of
the silicon, due to the change in
the index
of
refraction. This thin-film, interference-en-
hanced signal can
be
as
much
as
20 times larger than the
comparable change
in
reflectivity from the single surface
of
a thick silicon wafer. Consequently, the measurements
of
the carrier lifetime
of
[3],
[4]
are representative
of
the ·
entire silicon
film
and not just the surface layer.
As
such,
it
is
possible that the relevant carrier lifetime for opto-
electronic pulse generation and measurement could be
'-'
ii,
t;
~
0.5
:.,
"'
>
~
I
i \
\
\
\.
,
.•
f,1
o~---
~-====-
0 4 8
IZ
TIME DELAY
(psec)
Fig. 5. Measured electrical pulse (dots) compared to theory with,,. = 400
fs,
C_,..
= 0 fF, and
C.,
= 2.5 fF.
shorter due to their surface sensitivity and the presence
of
additional traps at the surface.
This conjecture was tested
by
reanalyzing the data
of
Fig. 4, using a carrier lifetime
of
400 fs, which appears
to give a significantly better
fit
as shown
in
Fig. 4(c). The
capacitances were,
of
course, kept equal
to
zero.
In order to provide more information
on
this point,
we
compare a calculation to some recently measured high
signal-to-noise data shown
in
Fig. 5. This pulse was gen-
erated
by
sliding-contact excitation
of
a two-line trans-
mission line consisting
of
5
µm
lines separated
by
10
µm,
and was detected with a side gap similar
to
that shown in
Fig.
1.
As
previously mentioned, the zero capacitance ar-
gument
is
more precise for this two-line case. The theo-
retical comparison shown
as
the solid line
in
the figure
fits
the rising edge and the main pulse itself exceedingly well.
The deviation on the falling edge is thought to be due to
resistive line effects. Again, this was
fit
with a
130
fs
ex-
citation pulse, a 400
fs
carrier lifetime, zero capacitance
at the generation site, and for this gap, a 2.6 fF capaci-
tance. These parameters correspond to a generated elec-
trical pulse
of
only 0.45 ps with a shape similar to that
shown
in
Fig.
3.
In summary, by reanalyzing the first experiment to gen-
erate subpicosecond pulses using photoconductive
switches,
we
have shown that to first order, the sliding-
contact generation site has
no
capacitance. This conclu-
sion
is
further supported by a double sliding-contact ex-
periment where, to first order, neither the generation nor
the detection site has any capacitance. This result
re-
moves the parasitic capacitance
of
the electrical circuit
as
one
of
the major difficulties to short electrical pulse gen-
eration using photoconductive switches.
ACKNOWLEDGMENT
D.
R.
Grischkowsky would like to acknowledge stim-
ulating and informative discussions with D. H. Auston,
H.
Melchior, and
M.
J.
W.
Rodwell concerning this work.
REFERENCES
[l]
D.
H. Auston, "Impulse response ofphotoconductors
in
transmission
lines,"
IEEE
J.
Quantum Electron., vol. QE-19, pp. 639-648, 1983.
[2] M.
B.
Ketchen, D. Grischkowsky, T. C. Chen, C.-C. Chi, I. N.
Duling, III, N.
J.
Halas, J.-M. Halbout, J. A. Kash, and G. P. Li,
''Generation
of
subpicosecond electrical pulses on coplanar transmis-
sion
lines,"
Appl. Phys. Lett., vol. 48, pp. 751-753, 1986.
[3]
F. E. Doany,
D.
Grischkowsky, and C.-C. Chi,
"Carrier
lifetime
