[IEEE 2011 69th Annual Device Research Conference (DRC) - Santa Barbara, CA, USA...
2
[1] Z. Chen and J. Appenzeller, IEDM, 2008; [2] T. Fang, et al., Appl. Phys. Lett., 2007; [3] C. Son and B. Ziaie, IEEE Trans. Biomed. Eng., 2008; [4] J.-B. Yau, et al., VLSI-TSA, 2011; [5] C. Shan, et al., Anal. Chem., 2009; [6] J. F. Kang, et al., Electrochem. & Solid- State Lett., 2005; [7] B. Fallahazad, et al., Appl. Phys. Lett., 2010; [8] K. Nagashio, et al., Appl. Phys. Lett., 2010. Graphene Quantum Capacitance Varactors for Wireless Sensing Applications S. J. Koester University of Minnesota-Twin Cities, 200 Union St. SE, Minneapolis, MN 55455 Ph : (612) 625-1316, FAX : (612) 625-4583, Email : [email protected] Introduction : The low density of states in graphene makes it possible for the quantum capacitance to be of the same order of magnitude as the oxide capacitance for experimentally achievable gate dielectric thicknesses [1]. This property, combined with the fact that the density of states varies as a function of energy, means that the capacitance in a metal-oxide-graphene capacitor can be tuned by varying the carrier concentration [2]. The very high mobility and zero band gap in graphene also allow it to remain conductive throughout the entire tuning range, making graphene an idea material to realize a high quality factor (Q) variable capacitor (varactor). If combined with an on-chip inductor to form an LC oscillator circuit, graphene varactors could enable a new class of ultra-compact sensors with wireless readout capability. Compared to MEMS-based varactors [3], the extremely-large capacitance per unit area of graphene varactors should allow orders-of-magnitude improvement in scalability, a vital feature for numerous applications including in vivo sensing where small size is critical. In this abstract, the device concept is described and simulated performance projections are provided. The main findings in this study are that wide frequency tuning ratios (> 50%) and high Q (> 40 at 1 GHz) are possible using realistic assumptions for the graphene properties, device dimensions and parasitic resistances. Device Description and Simulation Assumptions : The physical structure of the varactor is shown in Fig. 1. The cross-sectional geometry could vary depending upon the quantity to be sensed, and therefore may either utilize a standard top-gate geometry (Fig. 1(a), e.g., for sensing radiation-induced trapped charges in the buried oxide [4]) or an inverted geometry (Fig. 1(b) e.g., for sensing absorbed molecules, pH, etc. [5]). In either case, a multi-finger layout such as the one shown in Fig. 1(c) is likely to be needed to enable the capacitance to be increased while minimizing series resistance. A simple equivalent circuit model as shown in Fig. 2 has been utilized to analyze the potential performance of these devices. In this model, the relations in [2] were utilized for the quantum capacitance and the electron and hole concentrations, n and p, respectively. The channel resistance, R ch , was determined using the relation: R ch = 0.25 . (L g +2L ext )/(qμ(n + p))/W g /N fingers . The electron and hole mobilities, μ, were assumed to be equal, and μ was further assumed to be invariant with carrier concentration. Additional series resistance components associated with the contact and metallization (Au) resistances were also included in the model. Parallel conductance associated with gate leakage was further modeling assuming typical values for high-κ oxides on Si [6]. Simulation Results and Discussion : Simulations were performed at room temperature using the net carrier concentration, n net = n – p as the independent variable. Results at fixed frequency showing capacitance and quality factor plotted vs. n net are shown in Fig. 3. These simulations utilized an equivalent oxide thickness (EOT) of 0.7 nm, μ = 5000 cm 2 /Vs and contact resistance (R c ) of 500 Ω-μm. Additional parameters are shown in Fig. 3. The frequency tuning range was calculated assuming an ideal inductance, L, of 8.8 nH in series with the varactor circuit shown in Fig. 2. The results in Fig. 4 show that the frequency can be tuned by roughly 50% between n net = 5 x 10 11 cm -2 and 1 x 10 13 cm -2 , while maintaining Q > 88 over the entire tuning range. Again using the parameters in Fig. 3, the dependence of the varactor Q on various device parameters was calculated and the results are shown in Fig. 5. While the Q degrades with increasing L g and reduced R c and μ, reasonable values can be achieved using values already demonstrated in the literature [7]-[8]. Reducing EOT improves the tuning range (Fig. 6(a), and at extremely-small EOT values, tuning ranges approaching 100% can be achieved (Fig. 6(b)). Using high-κ-on-Si gate leakage values no degradation of Q was found even for gate leakage conductance values above 10 6 μS/cm 2 , demonstrating that scaling to very small EOT values is feasible. The form factor benefit of the graphene varactors is shown in Fig. 7. The plot shows that the high capacitance density of the graphene varactor allows frequencies comparable to MEMS based LC circuits, but with much smaller capacitor area. This capability is critical for wireless sensor scaling, since it allows the inductor to shrink while still allowing the tuning frequency range to be below the inductor self-resonance frequency. Finally, despite the fact that large voltages cannot be sustained across the gate oxide, with proper varactor/inductor matching, relatively high ac current levels can be sustained, as shown in Fig. 8. ______________________________________________________________________________________________________________________________________ 978-1-61284-244-8/11/$26.00 ©2011 IEEE 43
Transcript of [IEEE 2011 69th Annual Device Research Conference (DRC) - Santa Barbara, CA, USA...
![Page 1: [IEEE 2011 69th Annual Device Research Conference (DRC) - Santa Barbara, CA, USA (2011.06.20-2011.06.22)] 69th Device Research Conference - Graphene quantum capacitance varactors for](https://reader036.fdocuments.in/reader036/viewer/2022071809/575095061a28abbf6bbe33a4/html5/thumbnails/1.jpg)
[1] Z. Chen and J. Appenzeller, IEDM, 2008; [2] T. Fang, et al., Appl. Phys. Lett., 2007; [3] C. Son and B. Ziaie, IEEE Trans. Biomed.
Eng., 2008; [4] J.-B. Yau, et al., VLSI-TSA, 2011; [5] C. Shan, et al., Anal. Chem., 2009; [6] J. F. Kang, et al., Electrochem. & Solid-
State Lett., 2005; [7] B. Fallahazad, et al., Appl. Phys. Lett., 2010; [8] K. Nagashio, et al., Appl. Phys. Lett., 2010.
Graphene Quantum Capacitance Varactors for Wireless Sensing Applications S. J. Koester
University of Minnesota-Twin Cities, 200 Union St. SE, Minneapolis, MN 55455 Ph: (612) 625-1316, FAX: (612) 625-4583, Email: [email protected]
Introduction: The low density of states in graphene makes it possible for the quantum capacitance to be
of the same order of magnitude as the oxide capacitance for experimentally achievable gate dielectric
thicknesses [1]. This property, combined with the fact that the density of states varies as a function of energy,
means that the capacitance in a metal-oxide-graphene capacitor can be tuned by varying the carrier
concentration [2]. The very high mobility and zero band gap in graphene also allow it to remain conductive
throughout the entire tuning range, making graphene an idea material to realize a high quality factor (Q)
variable capacitor (varactor). If combined with an on-chip inductor to form an LC oscillator circuit, graphene
varactors could enable a new class of ultra-compact sensors with wireless readout capability. Compared to
MEMS-based varactors [3], the extremely-large capacitance per unit area of graphene varactors should allow
orders-of-magnitude improvement in scalability, a vital feature for numerous applications including in vivo
sensing where small size is critical. In this abstract, the device concept is described and simulated performance
projections are provided. The main findings in this study are that wide frequency tuning ratios (> 50%) and
high Q (> 40 at 1 GHz) are possible using realistic assumptions for the graphene properties, device dimensions
and parasitic resistances.
Device Description and Simulation Assumptions: The physical structure of the varactor is shown in
Fig. 1. The cross-sectional geometry could vary depending upon the quantity to be sensed, and therefore may
either utilize a standard top-gate geometry (Fig. 1(a), e.g., for sensing radiation-induced trapped charges in the
buried oxide [4]) or an inverted geometry (Fig. 1(b) e.g., for sensing absorbed molecules, pH, etc. [5]). In
either case, a multi-finger layout such as the one shown in Fig. 1(c) is likely to be needed to enable the
capacitance to be increased while minimizing series resistance. A simple equivalent circuit model as shown in
Fig. 2 has been utilized to analyze the potential performance of these devices. In this model, the relations in
[2] were utilized for the quantum capacitance and the electron and hole concentrations, n and p, respectively.
The channel resistance, Rch, was determined using the relation: Rch = 0.25.(Lg+2Lext)/(qµ(n + p))/Wg/Nfingers. The
electron and hole mobilities, µ, were assumed to be equal, and µ was further assumed to be invariant with
carrier concentration. Additional series resistance components associated with the contact and metallization
(Au) resistances were also included in the model. Parallel conductance associated with gate leakage was
further modeling assuming typical values for high-κ oxides on Si [6].
Simulation Results and Discussion: Simulations were performed at room temperature using the net carrier
concentration, nnet = n – p as the independent variable. Results at fixed frequency showing capacitance and
quality factor plotted vs. nnet are shown in Fig. 3. These simulations utilized an equivalent oxide thickness
(EOT) of 0.7 nm, µ = 5000 cm2/Vs and contact resistance (Rc) of 500 Ω-µm. Additional parameters are shown
in Fig. 3. The frequency tuning range was calculated assuming an ideal inductance, L, of 8.8 nH in series with
the varactor circuit shown in Fig. 2. The results in Fig. 4 show that the frequency can be tuned by roughly
50% between nnet = 5 x 1011
cm-2
and 1 x 1013
cm-2
, while maintaining Q > 88 over the entire tuning range.
Again using the parameters in Fig. 3, the dependence of the varactor Q on various device parameters was
calculated and the results are shown in Fig. 5. While the Q degrades with increasing Lg and reduced Rc and µ,
reasonable values can be achieved using values already demonstrated in the literature [7]-[8]. Reducing EOT
improves the tuning range (Fig. 6(a), and at extremely-small EOT values, tuning ranges approaching 100%
can be achieved (Fig. 6(b)). Using high-κ-on-Si gate leakage values no degradation of Q was found even for
gate leakage conductance values above 106 µS/cm
2, demonstrating that scaling to very small EOT values is
feasible. The form factor benefit of the graphene varactors is shown in Fig. 7. The plot shows that the high
capacitance density of the graphene varactor allows frequencies comparable to MEMS based LC circuits, but
with much smaller capacitor area. This capability is critical for wireless sensor scaling, since it allows the
inductor to shrink while still allowing the tuning frequency range to be below the inductor self-resonance
frequency. Finally, despite the fact that large voltages cannot be sustained across the gate oxide, with proper
varactor/inductor matching, relatively high ac current levels can be sustained, as shown in Fig. 8. ______________________________________________________________________________________________________________________________________
978-1-61284-244-8/11/$26.00 ©2011 IEEE 43
![Page 2: [IEEE 2011 69th Annual Device Research Conference (DRC) - Santa Barbara, CA, USA (2011.06.20-2011.06.22)] 69th Device Research Conference - Graphene quantum capacitance varactors for](https://reader036.fdocuments.in/reader036/viewer/2022071809/575095061a28abbf6bbe33a4/html5/thumbnails/2.jpg)
Lext LgLext
Gate high-κ dielectricgraphene
Lext LgLext graphene Wg
Gate
Gate high-κ dielectricgraphenesense charge
Nfingers
GateSiO2
SiSiO2
sense charge
high-κ dielectricgrapheneLg
SiSi
(a) (b) (c)(a) (b) (c)
Fig. 1 Schematic layout of graphene varactor sensor geometries. (a) Buried charge-trapping sensor geometry, (b) Surface sensor
design with buried gate electrode, (c) Top-view layout of multi-finger varactor geometry.design with buried gate electrode, (c) Top-view layout of multi-finger varactor geometry.
Simulation parameters160
15
Simulation parameters
EOT = 0.7 nm
Lg = 0.20 µm
Lext = 0.10 µm
120
160
f = 1 GHz
Qu
alit
y F
acto
r
10
15
Ca
pa
cita
nce
(p
F)COX
GLext = 0.10 µm
Wg = 20 µm
Nfingers = 120
µ = 5000 cm2/Vs
R = 500 Ω-µm40
80
Qu
alit
y F
acto
r
5
Ca
pa
cita
nce
(p
F)
CQ
GGL
Rseries RCH
Fig. 2. Equivalent circuit model
Rc = 500 Ω-µm
Ggl = 3500 µS/cm2
T = 300 K-1.0 -0.5 0.0 0.5 1.00
(b)
Qu
alit
y F
acto
r
Net Charge Concentration (1013
cm-2)
-1.0 -0.5 0.0 0.5 1.00
(a)
Ca
pa
cita
nce
(p
F)
Net Charge Concentration (1013
cm-2)Fig. 2. Equivalent circuit model
of varactor. Tuning occurs as the
quantum capacitance changes with
charge density in the graphene.
Fig. 3. Plot of (a) capacitance and (b) quality factor vs. net carrier concentration using the
parameters shown at right. Solid: with metal resistances, dashed: without metal resistances.
Net Charge Concentration (1013
cm-2)Net Charge Concentration (10
13 cm
-2)
charge density in the graphene. parameters shown at right. Solid: with metal resistances, dashed: without metal resistances.
Q = 100 L = 8.8 nH
100
f = 1 GHz
Qu
alit
y F
acto
r100
f = 1 GHz
Qu
alit
y F
acto
r
0.7
Q = 100 L = 8.8 nH
Fre
qu
en
cy (
GH
z)
nnet = 5 x 1011 cm-2nnet = 5 x 1011 cm-2
Qu
alit
y F
acto
r
Qu
alit
y F
acto
r
0.5
0.6
Fre
qu
en
cy (
GH
z)
1 x 1013 cm-2
1 x 1013 cm-2
10
(b)
Qu
alit
y F
acto
r
10
(a)
Qu
alit
y F
acto
r
0.1 1.0
0.5
Q = 88
Net Charge Concentration (1013
cm-2)
1 x 10 cm
Fig. 4. Resonant frequency vs. net
carrier concentration assuming an
0.1 1
Gate Length (µm)
0.2 0.4 0.6 0.8 1.0
EOT (nm)
Net Charge Concentration (10 cm )
ideal series inductor (L = 8.8 nH).
Q > 88 over the entire tuning range. 100
f = 1 GHz
Qu
alit
y F
acto
r
100
f = 1 GHz
Qu
alit
y F
acto
r
nnet = 5 x 1011 cm-2nnet = 5 x 1011 cm-2
0.7
0.8 L = 10 nH
Fre
que
ncy (
GH
z)
Qu
alit
y F
acto
r
Qu
alit
y F
acto
r
1 x 1013 cm-2
1 x 1013 cm-2
0.6
0.7
Fre
que
ncy (
GH
z)
10
(d)
Qu
alit
y F
acto
r
10
(c)
Qu
alit
y F
acto
r
1 x 1013 cm-2
0.4
0.5
EOT = 2.0 nm
EOT = 1.0 nm
EOT = 0.5 nm(a)
Fre
que
ncy (
GH
z)
100 1000
Contact Resistance (Ω-µm)
1000 10000
Mobility (cm2/Vs)
Fig. 5. Quality factor at f = 1 GHz for two carrier concentrations plotted vs. (a)
equivalent oxide thickness, (b) gate length, (c) mobility, and (d) contact resistance.
0.1 1
Net Charge Concentration (1013
cm-2)
100
Fre
qu
ency T
un
ing R
an
ge
(%
)
10-1
100
101
Graphene varactors from Fig. 7
100 nF
Ma
xim
um
RM
S C
urr
ent (A
)
9
1010
L = 4 nH
Ma
xim
um
Fre
que
ncy (
Hz)
Graphene varactor80
100
Fre
qu
ency T
un
ing R
an
ge
(%
)
10-4
10-3
10-2
10 100 nF
Ma
xim
um
RM
S C
urr
ent (A
)
1 nH
108
109
MEMs
varactorL = 400 nH
L = 40 nH
L = 4 nH
Ma
xim
um
Fre
que
ncy (
Hz)
60
Fre
qu
ency T
un
ing R
an
ge
(%
)
10-7
10-6
10-5
10-4
Vpp
(max) = 50 mV
100 µH100 fF
Ma
xim
um
RM
S C
urr
ent (A
)
106
107 L = 11 µH
Ma
xim
um
Fre
que
ncy (
Hz)
0.0 0.5 1.0 1.5 2.020
40
(b)
Fre
qu
ency T
un
ing R
an
ge
(%
)
105
106
107
108
109
1010
10-7M
axim
um
RM
S C
urr
ent (A
)
Frequency (Hz)
102
103
104
105
106
107
106M
axim
um
Fre
que
ncy (
Hz)
Capacitor Layout Area (µm2)
Fig. 6. (b) Plot of frequency vs. net Fig. 7. Max. frequency vs. varactor Fig. 8. Max. current vs. f for LC resonators
0.0 0.5 1.0 1.5 2.0
EOT (nm)
Fig. 6. (b) Plot of frequency vs. net
carrier concentration for 3 different
values of EOT. (b) Tuning range
plotted vs. EOT.
Fig. 7. Max. frequency vs. varactor
layout area for 3 L values. Values
from [3] are also shown.
Fig. 8. Max. current vs. f for LC resonators
where Vmax-pp = 50 mV. Graphene resonator
values from Fig. 7 are shown in blue.plotted vs. EOT. from [3] are also shown. values from Fig. 7 are shown in blue.
978-1-61284-244-8/11/$26.00 ©2011 IEEE 44
