CMOS THz Wireline Communication 311
ing design geometries: the periodic pitch d = 15 µm, groove width a = 2.4
µm, line width w =5 µm, and the groove depth h = 6 µm. Their geometry
meanings are prese nted in Figure 14.1.
The capability of confining EM fie lds and crosstalk re duction can be eval-
uated by measuring the reflection coefficient S
11
and the crossta lk S
41
. The
THz signal is injected from one port into the directional co upler, and the re-
sulting S
41
will present the coupling. The SPP interconnect is measured on
CASCADE Microtech Elite-300 probe station and Agilent PNA-X (N5247A)
with the VDI providing signal source from 220 ∼ 325 GHz. Connectors, probe,
waveguides and cable loss ar e well calibrated before the on-wafer pr obe testing.
The measurement setup is shown in Figure 1 4.6 (c).
14.3 SRR Modulator
Future high-performance computers require wide-ba nd on-chip communica-
tion between memory and microprocessor cores. Demand is increasing for
tens of gigabits per second (>10Gbps) wireline communication, and the car-
rier fr equency has been pushed up to terahertz (THz) due to the ultra-wide
bandwidth utilization at this region [309]. Recently, millimeter-wave and THz
transceiver building blocks in CMOS have been reported [310]. Compared to
optical on-chip communication by optical I/O link, all components of THz I/O
link can be realized in CMOS. One critical block for on-chip communication
is the modulator whose implementation is conventionally realized by active
MOS transistors with inductive loadings [311, 312, 313]. The switching speed
is, however, ultimately limited by the capacitive latency in the oscillator tank.
On the other ha nd, the optical ring modulator with active switching region
[286] is a lso hard to tune and is susceptible under temperature fluctuation.
Recently, the split ring resonator (SRR) is demonstrated to realize on-chip
high-Q resonator [310]. Such a very compact magnetic metamater ial res onator
is conventiona lly realized as shown in Figure 14.8 along with equivalent cir-
cuits. As the magnetic res onance fre quency can be tuned by config uring the
inner rings of SRR (Figure 14.8(b)) with switches, modulation becomes pos-
sible. The modulated signal will be strongly rejected at normal resonation
region when the data bit is low with MOS switches turned off, while it can
propagate through the struc ture with low loss w he n the resona tion is shifted
to other frequency. In this case the data bit is high with MOS switches turned
on, and the inner rings are shorted to ground. However, directly incorporating
CMOS switches in the SRR ring will result in poor isolation with high loss.
In this work, we introduce a SRR-based sub-THz modulator with two
SRR unit-cells oppositely coupled as shown in Figure 14.9. As revealed in
EM-field analysis, the induced residue current in the SRR loop contributes
dominant radiation loss at THz, which can be effectively attenuated by the
stacked SRR configuration without scarifying additional area. Moreover, mul-
tiple CMOS switches are incorporated into the inner ring. As the switches
312 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
Ex
H
Cs
Cs
Ls
Lp
Cp
IN
OUT
M
Cs
Ls
IN
OUT
(d)
(e)
Cs
Cs
Ls
IN
OUT
(c)
Cp1
Lp1
(a)
(b)
Figure 14.8: The schematic of (a) conventional single SRR and (b)
stacking SRR structure; the equivalent circuit of (c) the sing le SRR,
(d) stacking SRR, and (e) the simplified version of (d).
are now isolative from the signal path, their capacitive influence as well as
distortion are minimized. As such, the data ra te is now la rgely dependent on
the performance of the SRR modulator instead of active devices.
The sing le SRR shown in Figure 14.8(a) is a common de sign to achieve the
negative permeability when the H-field is perpendicular to the SRR plane. In
traditional oscillator design, this structure is also referred to as the LC tank,
owing to its ability to store magnetic energy. Compared to other LC tank
structures in which transmission lines are employed, the single SRR provides
higher quality factor, lower loss with much compact area occupation. The
equivalent circuit is illustrated in Figure 14.8 (c). Here, components L
s
, C
s
denote the serial inductance and parasitic capacitance at the two terminals.
The magnetic resonance fr equency is therefor e determined by 1/
√
L
s
C
s
. One
critical drawback in single SRR is the radiation loss, which becomes domi-
nating especially at THz frequency. To verify this, a single SRR structure is
simulated in the standard 65-nm CMOS environment. Two 40-fF capacitor s
(C
s
) are incorporated to reduce the resonance frequency down to our concer n
(140GHz). The simulated body current (J
vo l
) is shown in Figure 14.10. O ne
can observe that the induced current distribution on the SRR loop is not
uniform. To be specific, the body curr ent tends to crowd toward the metal
surface, in much the same way resembling the proximity effect. Note that this
crowding gives a n increase in the e ffective resistance of the loop and introduces
CMOS THz Wireline Communication 313
0
1 1
1
0
1
0
0
1 1
1
0
1
0
High Speed Data
High Speed Data
On-state
Off-state
Proposed SRR Modulator
THz
Source
High Speed Data
Figure 14.9: Th e proposed mod ulator evolved from the stacked SRR
shown in Fig ure 14.1(b). Four MOS switches are incorporated con-
necting to the opening shape of both the two inner rings and achieve
the fu nctionality of modulation by a single data generator. The equiv-
alent views of the on/off state are also illustrated.
stronger electromagnetic interference to adjac ent conductive mediums, result-
ing in higher radiation loss which increases with frequency in a
√
f manner .
As such, single SRR has limited improvements at THz frequencies.
To further improve the quality factor of SRR structure, multiple layers
of SRR unit-cell can be periodically arranged or using the interleaving ar-
chitecture at the same metal plane. Due to more efficient area usage, the
interleaving structure is considered in this wor k to form a SRR unit-cell. In
fact, more SRR unit-cells can be stacked to achieve stronger isolatio n at mag-
netic resonation frequency. Here, we analyze the merit o f stacking SRR from
the perspective of its underlying physics. Note that in the case of a single SRR
structure, the electric dipole moment is excited, accompanying the excitation
of the magnetic dipole moment, leading to conside rably high radiation loss
[314]. Although the magnetic dipole has radiation losses as well, the radiation
losses of the magne tic dipole are much lower than those of the c orresponding
electric dipole. As such, to implement the low-loss magnetic metamaterial, the
induced curre nt residing toward the metal surface should be strongly attenu-
ated, i.e., the electric dipole moment induced by re sidual currents should be
greatly suppressed. To achieve this, an additional SRR unit-cell whose place-
ment is opposite with respect to the exiting SRR can be stacked to provide
opposite current. Such a twisted SRR excites the opposite direction of induced
currents for the existing SRR, and thus the induced curr ents of two twisted
314 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
(a)
(b)
Figure 14.10: (a) The simulated body current distribution of the sin-
gle SRR reson ator at magnetic resonance frequency (140 GHz), and
(b) the simu lated body current distribution of the stacked SRR res-
onator at magnetic resonance frequency (140 GHz).
SRRs neutralize each other. As such, the EM e ne rgy in this case is mainly
stored by the magnetic dipole, which inher ently has much lower loss than an
electric dipole at THz.
The layout of stacking SRR is shown in Figure 14.8 (b), in which the in-
terleaving SRR is realize d by the same metal layer to form an SRR unit-cell,
while such two unit-c ells are further stacked using the topmost two metal lay-
ers. The equivalent circuit is illustrated in Figure 14.8 (d), where components
L
s
, C
s
denote the serial inductance of the outer ring and parasitic capaci-
tance at the two terminals, while L
p
, C
p
represent the pa rallel inductance and
capacitance (due to opening) of the inner ring. The interac tion between the
two rings is evaluated by mutual coupling factor M, which is mainly governed
by their gap. The magnetic plasma region can be obtained by simplifying the
equivalent circuit of Figure 14.8 (d) and (e):
s
1
L
p1
C
p1
< ω <
s
1 + L
p1
/L
s
L
p1
C
p1
. (14.1)
Spec ific ally, when the EM wave travels into the medium with SRR struc-
ture the magnetic pla sma will be excited within the regio n defined by (14.1).
In this case, the EM energy cannot propa gate through the SRR and is almos t
perfectly reflected back with an equivalent open circuit es tablished.
With the strong attenuation obtained by the stacking SRR, the SRR-based
modulator is further proposed. Recall that while SRR naturally has a high
CMOS THz Wireline Communication 315
quality facto r over other resonato r structures, its stop band is sharper es pe-
cially for the stacking structure. Carr ier signal can thus pro pagate through
SRR a t frequencies slightly away from the magnetic resona nc e frequency. As
such, by instantaneously altering the magnetic resonance frequency, the func-
tionality of modulation can be achieved. Figur e 14.9 illustrates such a novel
concept. Here , the stacking SRR is e mployed owing to its higher quality factor.
The openings of the two inner rings are connected to multiple MOS transis-
tors whose gates are controlled to high speed data. The equivale nt circuit
of the proposed modulator is also illustrated at Figure 14.8(d), in which the
parallel inductances of inner rings L
p
is now modulated. According to (14.1),
the magnetic plasma region is alternatively chang ed as well, leading to the
modulation of resona nc e frequency. Physically, in the o ff state, the SRR acts
as a normal resonator and serves to isolate the incoming carrier signal, w hile
in the on state its resonance is shifted to the other frequency and the carrier
signal can propagate through the structure with low loss.
There ar e several merits owing to this structure. Fir stly, the MOS switches
are now isolated from the signal pa th, r esulting in less propagation loss since
the finite on-resistance of switches tend to de grade the insertion los s at high
frequency. Secondly, any pa rasitics of s w itches have be en absorb ed into the in-
ner rings and thus minimizes the influence on the signal transmission. Thirdly,
the disto rtions due to the nonlinear behavior of MOS switches during on/off
switching are strongly attenuated by SRR as well. Finally, the purely passive
structure is scalable to provide similar performance at higher carrier frequency
ranges (>300GHz), in which MOS transistors only have high loss w ith large
parasitics. All these features manifest the novel design of a potential candidate
to be suitable fo r ultra-high speed communications. Note that the bandwidth
of the modulator will increase by adding a transistor into the inner ring. This
can be verified by (1 4.1), in which the parallel capacitance C
s1
is increased
due to the incorporation of parasitics from MOS transistor. While the enlarged
bandwidth accommodates higher data rate transmission, the is olation of the
proposed SRR modulator will be degraded due to weaker magnetic plasma
resonation. As such, the dimension of MOS switches cannot be arbitrarily
large.
To verify the conjectures, an SRR-base d modula tor is designed as shown
in Figure 14.9 with silicon area of 40µm×67µe. Figure 14.9 also shows the
simplified vie w of the modulator in the on state. Now the SRR unit-cell has
been evolved to a sing le SRR, while such two unit-cells are further stacked.
Therefore, the induced current can still be effectively neutralized as well, and
the resulting resonance frequency will be increased. The induced current neu-
tralization will be presented in the next section. On the other hand, in the off
state the modulator evolves to a stacked SRR, as shown in Figure 14.9 as well.
Four MOS transisto rs with 40µm width are incorporated to form switches.
Extinction ratio plays a key role in ultra-high-speed communication since
the on/o ff state must be effectively distinguished. Conventiona l methods uti-
lize various equalization techniques to enlarge the eye opening by s acrificing
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