U.S. patent application number 10/765578 was filed with the patent office on 2004-11-18 for voltage-variable capacitor with increased current conducting perimeter.
Invention is credited to York, Robert A..
Application Number | 20040227176 10/765578 |
Document ID | / |
Family ID | 26841755 |
Filed Date | 2004-11-18 |
United States Patent
Application |
20040227176 |
Kind Code |
A1 |
York, Robert A. |
November 18, 2004 |
Voltage-variable capacitor with increased current conducting
perimeter
Abstract
A parallel-plate, voltage-variable capacitor is designed to have
an increased current conducting perimeter relative to its area. In
one approach, the perimeter is increased by changing the shape of
the plates. In another approach, the varactor is implemented by a
number of disjoint plates, which are coupled in parallel.
Inventors: |
York, Robert A.; (Santa
Barbara, CA) |
Correspondence
Address: |
FENWICK & WEST LLP
SILICON VALLEY CENTER
801 CALIFORNIA STREET
MOUNTAIN VIEW
CA
94041
US
|
Family ID: |
26841755 |
Appl. No.: |
10/765578 |
Filed: |
January 26, 2004 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10765578 |
Jan 26, 2004 |
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10144185 |
May 10, 2002 |
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6683341 |
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60337364 |
Dec 5, 2001 |
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Current U.S.
Class: |
257/312 ;
257/E27.049 |
Current CPC
Class: |
H01L 27/0808
20130101 |
Class at
Publication: |
257/312 |
International
Class: |
H01L 027/108 |
Claims
What is claimed is:
1. A parallel plate varactor comprising: a bottom electrode; a top
electrode; a dielectric layer sandwiched between the bottom
electrode and the top electrode, wherein a permittivity of the
dielectric layer varies according to an electric field applied to
the dielectric layer; the bottom electrode, dielectric layer, and
top electrode are integrated on a substrate; and an overlap between
the bottom electrode, dielectric layer, and top electrode defines
an active region for the varactor; and wherein, for at least one of
the electrodes: a resistance of the active region of the electrode
is significantly higher than a resistance of a bulk region of the
electrode; the active region has a lateral area A, the electrode
has a current conducting perimeter P; and a ratio R of the
perimeter P to a square root of the area A is at least 2.0.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 10/144,185, "Voltage-Variable Capacitor with
Increased Current Conducting Perimeter," by Robert A. York, filed
May 10, 2002; which claims priority under 35 U.S.C. .sctn. 119(e)
to U.S. Provisional Patent Application Serial No. 60/337,364,
"Ferroelectric Varactor Design," by Robert A. York, filed Dec. 5,
2001. The subject matter of all of the foregoing is incorporated
herein by reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] This invention generally relates to voltage-variable
capacitors (varactors) of a parallel plate design.
[0004] 2. Description of the Related Art
[0005] Capacitors are a basic building block for electronic
circuits and voltage-variable capacitors (varactors) have the added
flexibility that their capacitance can be tuned by changing a bias
voltage across the capacitor. Dielectric materials which have a
permittivity that depends on the applied electric field can be used
to form such varactors. Varactors have an added advantage that they
can be easily integrated with other components, particularly if the
dielectric layer is a thin film. One common approach to
voltage-variable varactors is the "parallel-plate" configuration,
in which the voltage-variable dielectric is sandwiched between two
electrodes. For example, in an integrated varactor, one electrode
may be a bottom conducting layer, the dielectric may be a
ferroelectric thin film deposited over the bottom electrode, and
the top electrode may be a metal layer.
[0006] In the parallel-plate configuration, the capacitance of the
varactor is determined in part by the area of overlap of the top
electrode, the dielectric layer and bottom electrode. For
convenience, this area shall be referred to as the active region of
the varactor. In many designs, the active region is determined
mainly by the size and shape of the two electrodes; the dielectric
layer is made large enough so that it does not additionally limit
the active region. Thus, the varactor is designed for a specific
capacitance by adjusting the lateral dimensions of the top and/or
bottom electrodes. The active region typically is square-shaped (or
close to square-shaped) although other shapes, including circular,
may also be used.
[0007] The electrodes have some finite resistance. This resistance
leads to loss and also limits the operating bandwidth of the
varactor. For example, the electrode resistance in series with the
varactor's capacitance forms an RC combination with a certain time
constant. Higher resistance means longer RC time constant and lower
cutoff frequency. The resistance typically is reduced by increasing
the thickness of the metal films forming the electrodes. However,
limitations in the fabrication process can place an upper limit on
the maximum thickness of the electrodes. Increasing the thickness
of the electrodes can also be costly since, for various reasons,
the bottom electrode may be made from an expensive refractory metal
such as platinum, palladium, iridium and related compounds. For
these reasons, the electrode thicknesses are constrained. This, in
turn, limits the sheet resistance and the current handling capacity
of the varactor as a result of effects such as electromigration
and/or Joule-heating. Hence, the conventional parallel-plate design
is not particularly well suited for implementing low-loss,
high-current varactors.
SUMMARY OF THE INVENTION
[0008] The present invention overcomes the limitations of the
related art by providing a parallel-plate varactor in which the
current conducting perimeter of the active region for at least one
electrode is increased relative to the area of the active region.
The current conducting perimeter is that portion of the geometrical
perimeter which supports current flow between the active region and
the rest of the electrode. In one approach, the current conducting
perimeter is increased by changing the shape of the active region,
for example by using a long skinny active region rather than a
square one. In another approach, the active region is implemented
by a number of disjoint subregions, termed "cells," which are
coupled in parallel. The cells together have the area required to
implement a certain capacitance but subdividing the active region
into cells increases the total current conducting perimeter.
[0009] Increasing the current conducting perimeter addresses the
problems with conventional parallel-plate designs. The increased
perimeter results in more paths for current to move between the
dielectric layer and the bulk regions of the electrodes, thus
reducing the resistance of the electrodes. This same effect also
increases the current handling capacity of the varactor.
Furthermore, these gains are achieved without having to increase
the electrode thickness, although doing so may result in even
further gains.
[0010] In one implementation, a parallel plate varactor includes a
bottom electrode, a top electrode and a dielectric layer sandwiched
between the top electrode and the bottom electrode. The
permittivity of the dielectric layer varies according to an
electric field applied to the dielectric layer. The active region
of the varactor is defined by an overlap between the top electrode,
the dielectric layer and the bottom electrode. For at least one of
the electrodes, the resistance of the active region of the
electrode is significantly higher than a resistance of a bulk
region of the electrode. Furthermore, the active region has a
lateral area A, the electrode has a current conducting perimeter P,
and a ratio R of the perimeter P to a square root of the area A is
at least 2.0.
[0011] In one embodiment, the dielectric layer is a
voltage-variable thin film (e.g., based on a ferroelectric
material) and the high resistance electrode is a refractory metal.
Examples of voltage-variable ferroelectric thin films include
barium titanate, strontium titanate and barium strontium titanate.
Examples of refractory metals include platinum, palladium, iridium,
nickel, tungsten, or ruthenium.
[0012] In one particular aspect of the invention, the active region
includes one or more rectangular cells. The active region of the
bottom electrode has a higher sheet resistance than the active
region of the top electrode. For example, platinum may be used for
the bottom electrode, barium strontium titanate as the dielectric
layer and gold for the top electrode. Furthermore, for each cell,
the current conducting perimeter of the bottom electrode includes
at least three sides of the cell and the current conducting
perimeter of the top electrode includes the fourth side of the
cell.
BRIEF DESCRIPTION OF THE DRAWING
[0013] The invention has other advantages and features which will
be more readily apparent from the following detailed description of
the invention and the appended claims, when taken in conjunction
with the accompanying drawing, in which:
[0014] FIGS. 1A and 1B are a top view and cross-sectional view,
respectively, of a varactor according to the present invention.
[0015] FIG. 2 is a top view of an active region having multiple
cells.
[0016] FIG. 3 is a top view of another varactor having multiple
cells.
[0017] FIGS. 4A-4C are top view and cross-sectional view pairs,
illustrating fabrication of one cell of the varactor of FIG. 3.
[0018] FIG. 5 is a diagram of a resistive model for the cell of
FIG. 3.
[0019] FIG. 6 is a graph of cutoff frequency for the varactor of
FIG. 3 as a function of capacitance and of number N of cells.
[0020] FIGS. 7A and 7B are graphs of excess current conducting
perimeter as a function of electrode length for N=1 and N=4 cells,
respectively.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0021] FIGS. 1A and 1B are a top view and cross-sectional view,
respectively, of a voltage-variable capacitor (varactor) 100
according to the present invention. The varactor 100 includes a
bottom electrode 110, a top electrode 140 and a layer 120 of
dielectric material sandwiched between the top electrode and the
bottom electrode. The top electrode 140, the dielectric layer 120
and the bottom electrode 110 form a parallel plate capacitor. The
active region 150 of the capacitor is defined by the overlap
between the top electrode 140, the dielectric layer 120 and the
bottom electrode 110. The varactor 100 in FIG. 1 is drawn with a
specific shape for the electrodes 110, 140, dielectric layer 120
and active region 150. However, this is not meant as a limitation.
FIG. 1 is intended to be a general depiction of a varactor 100 with
electrodes 110, 140, dielectric layer 120 and active region 150.
Furthermore, varactor 100 shows the most relevant layers 110, 120,
140, but this is not meant to imply that other layers do not exist.
For example, additional layers located between those shown may be
used for various purposes according to conventional techniques.
Examples include layers to increase adhesion, to provide a
diffusion barrier, or to improve the Schottky barrier height.
[0022] The dielectric layer 120 is voltage-variable in the sense
that the dielectric material has a field-dependent electrical
permittivity. Thus, the capacitance of the varactor can be changed
by changing the voltage applied across the dielectric layer 120. By
changing the voltage applied across the two electrodes 110,140, the
electric field within the dielectric layer 120 is also changed.
This, in turn, changes the dielectric constant of the dielectric
layer 120, thus changing the capacitance of the varactor. 100. This
invention is not specific to a particular choice of dielectric
material or film thickness or fabrication sequence. Examples of
dielectric materials include ferroelectric materials. The
dielectric layer 120 preferably exhibits a field-dependent
permittivity in a (non-hysteretic) paraelectric state over a useful
temperature range (e.g., -30 C to +90 C).
[0023] Two factors which can limit the performance of a varactor
are the resistance of the varactor and the current handling
capacity of the varactor. Higher resistance results in higher ohmic
losses and also results in a lower operating bandwidth (e.g., due
to a longer RC time constant). Lower current handling capacity
limits the applications in which a varactor can be used.
[0024] In addition to the active region 150, electrodes also have a
"bulk" region, which is the portion of the electrode away from the
active region. Typically, the resistance of the bulk region is
relatively insignificant relative to that of the active region. For
example, if an electrode is narrow in the active region and then
opens up into a wide area (e.g., a bonding pad), the wide area is
part of the bulk region of the electrode and typically will have
minimal resistance compared to the narrow portion.
[0025] In varactor 100, the active region of one or both electrodes
110, 140 has a resistance that is significantly higher than the
resistance of the bulk region of the electrode 110, 140. For
example, the active region of the electrode may be thinner than the
bulk region or it may be made from a different material with lower
conductivity. In both of these examples, the sheet resistance of
the active region is significantly higher than that of the bulk
region and, therefore, the overall resistance is also higher.
Alternately, the active region and bulk region may have a similar
sheet resistance but the lateral geometry causes the active region
to have a significantly higher resistance compared to the bulk
region. In any event, in varactor 100, the active region of the
high-resistance electrode is a significant, if not dominant,
contributor to the overall resistance of the varactor, resulting in
the unwanted effects described previously.
[0026] Varactor 100 reduces these effects by increasing the
"current conducting" perimeter of the active region 150 relative to
the area of the active region. The "current conducting" perimeter
is that portion of the perimeter which supports current flow
between the active region and the rest of the electrode. For
example, referring to electrode 110 in FIG. 1, the geometrical
perimeter includes sides 152A-D. However, the current conducting
perimeter only includes sides 152B-D and not side 152A. This is
because, for electrode 110, current can flow from the active region
150 through sides 152B, C or D to the bulk of the electrode.
However, there is no current path from the active region through
side 152A.
[0027] Increasing the current conducting perimeter increases the
number of current paths between the active region and the bulk of
the electrode. The increased current conducting perimeter results
in less resistance through the high resistance electrode (assumed
to be electrode 110 in the above example) and therefore less
resistance overall since the high resistance electrode makes a
significant contribution to the overall resistance. The increased
perimeter also results in better current handling capacity. The
current conducting perimeter can be increased in a number of
different ways and this effect can be quantified using a number of
different measures.
[0028] In one approach, the effect is quantified by the ratio
R=P/sqrt(A) (1)
[0029] where P is the current conducting perimeter of the active
region, A is the lateral area of the active region and sqrt( ) is
the square root operator. For a square electrode in which the
current conducting perimeter is one half of the geometrical
perimeter, the ratio R=2.0. For comparison, a rectangular active
region with a 2:1 aspect ratio in which half of the geometrical
perimeter is current conducting has a ratio R=3 /sqrt(2)=2.13. A
circular active region with 50% conducting perimeter has a ratio
R=sqrt(.pi.)=1.77. A square active region with three sides
conducting has a ratio R=3.
[0030] One way to increase the current conducting perimeter for
rectangular shaped active regions (assuming that the fraction of
the geometrical perimeter that is current conducting remains
constant) is to increase the aspect ratio of the rectangle. The use
of long, narrow electrodes (and active regions) results in an
increased perimeter compared to a more square shaped active region
of the same area.
[0031] This effect is even more pronounced if the fraction of the
geometrical perimeter that is current conducting also increases as
the aspect ratio increases. For example, in one approach, two long
sides and one short side of the rectangular active region are
current conducting. The ratio R for this type of rectangular active
region with aspect ratio m (i.e., the active region is L.times.mL
where L is some length, m.gtoreq.1) is given by
R=(2m+1)/sqrt(m) (2)
[0032] This function has a minimum at m=1 (i.e., square shaped
active region) and increases with increasing m.
[0033] The active region can have shapes other than rectangular.
For example, circular or disc-shaped active regions are sometimes
used. However, rectangular active regions are generally easier to
lay out and manufacture. In addition, they typically have more
current conducting perimeter than a circular or disc-shaped active
region of equal area.
[0034] Another way to increase the perimeter of an active region is
to implement the active region as a number of disjoint subregions,
which shall be referred to as cells. FIG. 2 is a top view of an
active region 150 having N cells 250A-N. Each cell 250 behaves as a
"mini varactor" and the multiple mini varactors are coupled in
parallel to form the overall varactor. An active region made up of
multiple cells generally will have a higher R ratio than a
comparable active region made up of a single cell.
[0035] For example, assume that a one cell design has an area A,
current conducting perimeter P and capacitance C. The corresponding
R=P/sqrt(A). All else being equal, the capacitance C is directly
proportional to the area A. Now assume that the capacitance C is
implemented as an active region having N cells, each of which is
the same shape and design as the original cell. Each cell is a
1/sqrt(N) scaled version of the original cell. Therefore, each cell
has an area of A/N and a current conducting perimeter of P/sqrt(N).
The total area for all N cells is A (and therefore the capacitance
is the same as for the one cell design) and the total current
conducting perimeter is P sqrt(N). The corresponding R=sqrt(N)
P/sqrt(A). In other words,
R(N)=sqrt(N)R(1) (3)
[0036] where R(1) is the R ratio for the one cell design and R(N)
is the R ratio for the N cell design. The R ratio has been
increased by a factor of sqrt(N) by moving from a one cell active
region to an N cell active region.
[0037] Both principles discussed above may be applied to a given
design, although at times tradeoffs between the two may be
required. For example, consider the design of a varactor with an
active region of area L.sup.2, L>1. Assume that the minimum
feature size is 1. Table 1 shows four possible designs for this
varactor, listed in increasing order of R ratio. In all of the
designs, the cells are rectangular in shape and it is assumed that
two long sides and one short side of each cell is current
conducting.
1TABLE 1 Four Designs for a Varactor of Area L.sup.2 Total Current
Conducting Active Region Total Area Perimeter R Ratio 1 cell of
L.sup.2 3 L 3 dimension L .times. L 1 cell of L.sup.2 (2 L.sup.2 +
1) 2 L + 1/L dimension L.sup.2 .times. 1 L cells of L.sup.2 L(2 L +
1) 2 L + 1 dimension L .times. 1. L.sup.2 cells of L.sup.2 3
L.sup.2 3 L dimension 1 .times. 1.
[0038] Table 1 is consistent with the general notion that it is
preferable to have a larger number of cells, even if they are
square in shape. The number of cells, however, can be constrained
by other factors, for example limits in lithographic capability,
current-handling considerations, and materials limitations. For
example, in some cases where small capacitance values are required,
the minimum realizable feature size may dictate that only
single-cell designs are feasible. In this case, a long, narrow
active region is preferred to an active region that is more square
in shape. As another example, although long, narrow active regions
are generally preferred, beyond a certain aspect ratio, incremental
gains that result from further increasing the aspect ratio may be
offset by other effects, for example increased resistance in the
other electrode (i.e., the low resistance electrode). Generally
speaking, significant gains can be realized by moving from an
aspect ratio of 1:1 to 2:1, moderate gains for aspect ratios in the
range of 2:1 to 10:1, and diminishing returns for aspect ratios
beyond about 10:1. Hence, all other factors being equal, aspect
ratios in the range of 2:1 to 10:1 are generally preferred.
[0039] In one implementation, the dielectric layer 120 is a thin
film and the entire varactor is integrated on a substrate. Examples
of suitable voltage-variable thin film materials include barium
titanate, strontium titanate, and composites of the two (e.g.,
barium strontium titanate). The materials may also include small
concentrations of one or more dopants to modify certain properties.
Standard IC fabrication methods may be used to fabricate the
integrated varactor. To reduce costs, inexpensive insulating
substrates are usually preferred, including but not limited to
high-resistivity silicon (HR Si), crystalline sapphire
(Al.sub.2O.sub.3), aluminum nitride (AlN), quartz and glass. These
substrates are polished for low surface roughness for compatibility
with growth of smooth ferroelectric films with high breakdown
fields. This approach results in low-cost, small size, reliable
components which are suitable for mass production and for
integration with other circuit elements.
[0040] Thin-film varactors can be used in a variety of applications
such as radio-frequency (RF) or wireless electronics,
voltage-controlled oscillators, impedance matching networks,
tunable filters, and numerous other applications. A thin-film
varactor is attractive because it can be easily integrated
alongside other active and passive electrical components on many
different host substrates, including semiconductors (such as
silicon, gallium arsenide, silicon carbide, gallium nitride, etc.)
and insulators (such as glass, quartz, sapphire, etc.). However,
thin-film ferroelectric materials have a high intrinsic capacitance
density, which means that typical capacitance values for RF circuit
designs will be realized by small active regions. In addition,
processing steps for ferroelectric materials can require conditions
that limit the choice of materials for the electrode(s). High
temperature processing may limit electrode materials to those with
high melting points which also do not oxidize easily. Examples of
such materials include platinum and other refractory metals such as
palladium and tungsten, but generally exclude commonly used
conductors such as gold, copper and aluminum. Unfortunately, these
materials typically have higher resistivity and can also be quite
expensive. This in turn can lead to high ohmic losses and high
current densities. Hence, the principles described above for
reducing resistance and current densities are especially suited for
these devices.
[0041] As one example, these varactors can be used in RC tuning
circuits for RF applications, such as mobile phones. While specific
numbers will vary by application, 2:1 capacitance variations and
capacitances in the range of 0.01 pF to 10 nF are not unheard of.
Similarly, DC control voltages may be in the range of -100 to +100
volts, depending on the film thickness and the specific
application. The varactors preferably are operated at voltages that
are less than half their intrinsic breakdown voltage.
[0042] FIG. 3 is a top view of an example thin-film ferroelectric
varactor 300 having multiple cells 350A-N. In this varactor, the
ferroelectric layer 120 is a barium strontium titanate (BST) thin
film. The bottom electrode has two parts which shall be referred to
as the bottom electrode layer 112 and the bottom contact layer 114.
These two layers 112, 114 are in electrical contact with each
other. Each layer may include one or more types of materials,
although they are shown and will be described as single layers of
material in this example. The active region (i.e., each cell 350)
is defined by the lateral overlap of the bottom electrode layer
112, the BST film 120 and the top electrode layer 140. The bottom
electrode layer 112 is platinum in this example because it must be
compatible with BST processing. The bottom contact layer 114 is a
thick metal layer (e.g., gold) that provides electrical connection
with reduced resistance to the bottom electrode layer 1 12. The top
electrode 140 could be formed from the same thick metal layer or a
separately deposited metal layer. In this example, it is assumed to
be the same gold layer.
[0043] In FIG. 3, the full lateral extent of the top electrode 140
and the bottom contact layer 114 are visible. The BST film 120 is
an eight-sided shape which is partially hidden by top electrode
140. Five of the eight sides are fully visible, two of the eight
sides are partially visible and one side is obscured by top
electrode 140. The bottom electrode layer 112 is rectangular in
shape but extends beyond what is visible in FIG. 3. It is partially
hidden by portions of the ferroelectric 120, bottom contact layer
114 and top electrode 140.
[0044] FIGS. 4A-4C are pairs of top view and cross-sectional view,
illustrating fabrication of one cell 350 of varactor 300. In FIG.
4A, the bottom electrode layer 112 has been deposited on a
substrate. In this example, layer 112 is a thin layer of platinum.
Platinum is selected for compatibility with the BST processing and
a thin layer is preferred since platinum is expensive. The layer
112 contains N disjoint subregions, each corresponding to one of
the cells 350. In one approach, platinum is deposited across the
entire substrate, the desired subregions are then masked, and the
material in the unmasked regions are removed. What remains is the N
subregions. In an alternate approach, a liftoff layer is deposited
in areas other than the desired subregions, platinum is deposited
across the substrate, and removal of the liftoff layer also removes
the platinum from the unwanted areas. Other patterning techniques
may be used.
[0045] In a next step, the BST film 120 is grown on top of the
platinum layer 112. Conventional growth and patterning techniques
may be used. Like layer 112, the BST film 120 contains N separate
subregions, one for each cell 350. The film 120 overlaps the
electrode layer 112. The result is shown in FIG. 4B. In the top
view, the hidden portions of the bottom electrode layer 112 are
shown by dashed lines.
[0046] In a final step, a gold layer is deposited and patterned to
form both the top electrode 140 and the bottom contact layer 114 as
shown in FIG. 4C. In the top view, the dashed lines indicate
portions of the lower layers which are hidden by this gold layer.
The bottom contact layer 114 overlaps with the bottom electrode
layer 112, thus providing an electrical path to all of the disjoint
subregions in layer 112. The gold layer 114,140 is thicker than the
platinum layer 112 and gold is a better conductor than platinum. As
a result, the platinum resistance is a significant, if not
dominant, contribution to the overall resistance of the
varactor.
[0047] The cells 350 making up the active region are rectangular in
shape with dimension W.times.L in FIG. 4C. Each of the top
electrode 140, bottom electrode layer 112 and BST film 120 entirely
overlaps cell 350. Three sides of the cell 350 are defined by the
top electrode 140. The fourth side is defined by the bottom
electrode layer 112. The top electrode 140 and bottom contact layer
114 provide external contacts to the varactor. For example, they
may lead to other circuit components or to external connections,
such as bonding pads.
[0048] The top electrode 140 and bottom electrode (layers 112 and
114) preferably are thick and good conductors in order to reduce
sheet resistance and current densities. However, in this particular
example, bottom electrode layer 1 12 is relatively thin and a poor
conductor (i.e., platinum), as a result of processing requirements
imposed by the BST layer 120. However, the bottom contact layer 114
is relatively thick and a good conductor (gold). Thus, it is
advantageous to place the bottom contact layer 114 in close
proximity to the cells 350, in order to minimize the resistance
resulting from the platinum layer 112. Top electrode 140 is also
thick and a good conductor to minimize sheet resistance.
[0049] The use of multiple, narrow top electrodes 140 in close
physical proximity to the bottom contact layer 114 results in a
geometry with increased device perimeter for a given active area
and with low resistance paths from the active region to external
contacts. This geometry reduces ohmic losses and current densities
in the device contacts, thus improving the electrical performance
of the varactor. In particular, the layers are laid out so that the
current conducting perimeter of the platinum layer 112 is
relatively large. Two long sides and one short side of the
rectangular active region are current conducting for a total
current conducting perimeter of 2L+W for platinum layer 112.
[0050] FIG. 5 is a diagram of a resistive model for the cell 350.
Resistances in the bulk regions of the bottom contact layer 114 and
top electrode 140 are assumed to be negligible. Assuming that
current flows from the top electrode 140 to the bottom contact
layer 114, the current encounters the impedances shown in Table
2.
2TABLE 2 Impedances in the Resistive Model of FIG. 5 Symbol
Description Expression R.sub.access Resistance from bulk of top
electrode R.sub.access = r.sub.1d/W 140 to active area of top
electrode R.sub.top Average resistance through active area
R.sub.top = r.sub.1L/(3 W) of top electrode Z.sub.varactor
Impedance of ferroelectric material Z.sub.vavactor = 1/(y.sub.dWL)
R.sub.side Resistance from side of active area of R.sub.side =
r.sub.bg/L bottom electrode layer 112 to bulk of bottom contact
layer 114 R.sub.end Resistance from end of active area of R.sub.end
= r.sub.bg/W bottom electrode layer 112 to bulk of bottom contact
layer 114 where r.sub.1 = sheet resistance of top electrode 140 (in
.OMEGA./square) r.sub.b = sheet resistance of bottom electrode
layer 112 (in .OMEGA./square) y.sub.d = g.sub.d + j.omega.c.sub.d =
admittance density of BST film 120 g.sub.d = ferroelectric
conductance density (S/m.sup.2) c.sub.d = ferroelectric capacitance
density (F/m.sup.2). Quantities d, W, L and g are the lengths shown
in FIG. 5. Specifically, cell 350 is defined by the rectangle with
width W and length L. The length g is the distance from the cell
350 to the bulk of bottom contact layer 114. The distance d is the
distance from the cell 350 to the bulk of top electrode 140.
[0051] An approximate expression for the impedance of the cell 350
is then 1 Z i n r t W ( d + L 3 ) + r b g 2 L + W R S + 1 y d WL (
4 )
[0052] R.sub.s is the equivalent series resistance for the cell.
The series resistance consists of R.sub.access and R.sub.top
coupled in series with the parallel combination of R.sub.side,
R.sub.end and R.sub.side. The resistance contribution from the
bottom electrode layer 112 is usually the dominant term due to the
materials and thickness differences described above. Furthermore,
this model highlights the important feature that the resistance
contribution from the bottom electrode layer 112 is a direct
function of the quantity 2L+W, which is the current conducting
perimeter. Thus, the series resistance of the cell can be reduced
by increasing the current conducting perimeter.
[0053] Considering only electrode losses (i.e., assuming
g.sub.d=0), the cutoff frequency for the cell is given by 2 f c 1 2
r b c d g ( 2 L + W A ) ( 6 )
[0054] where A is the area of the cell. The cutoff frequency is a
measure of performance. Higher cutoff frequencies are usually
preferred. Assuming the series resistance is dominated by the
contribution from the bottom electrode layer 112, the cutoff
frequency is approximately showing the dependence on the current
conducting perimeter and on the perimeter to area ratio. Thus, to
realize a varactor with a high cutoff frequency (i.e., a low series
resistance), devices with large R ratios and/or current conducting
perimeters are preferred. The R ratio and/or current conducting
perimeter can be increased using the techniques described
previously, for example by increasing the aspect ratio of the cells
and/or by increasing the number of cells. Note that the
cutoff-frequency of N identical capacitors connected in parallel is
the same as that of the individual capacitors. Thus a
multiple-contact geometry like that shown in FIG. 3 can provide low
resistive loss and high cutoff frequency for a given varactor
capacitance.
[0055] For example, if a varactor has N cells, each of which is
W.times.L as shown in FIG. 3, then the total area of the active
region will be A=NWL. The N cells are connected in parallel, so the
total resistance for the varactor will be 1/N of the resistance for
one cell. Referring to Eqn. 4, dividing the expression for the
series resistance by N and making use of the equation A=NWL yields
a total series resistance of 3 R s = r t L A ( d + L 3 ) + r b gL 2
NL 2 + A ( 7 )
[0056] FIG. 6 is a graph of cutoff frequency for the varactor of
FIG. 3 as a function of capacitance and of the number N of cells,
for N=1, 2, 3, and 4. The cells are assumed to be the same shape
for all designs. In this example, if a 0.2 pF capacitor were
desired, FIG. 6 shows that the cutoff frequency can be increased by
75% using a three-cell design instead of a one-cell design.
[0057] Current handling is another factor that limits the
performance of varactors. If the electrodes are made from metal
films, there are two failure mechanisms which typically will limit
the current densities in the electrodes. One is electromigration
failures, in which momentum transfer from the mobile charges to the
metal atoms is sufficient to tear the material apart. The other is
Joule heating, in which high current densities create large thermal
gradients that degrade the metal or neighboring materials. In each
case, the current density J in the metal film must be kept below
some critical value J.sub.c. The value J.sub.c varies according to
the type of metal, the method of deposition, and the local
environment. Mathematically,
J<J.sub.c (8)
[0058] J.sub.c may be on the order of 10.sup.6 A/cm.sup.2. The
amount of AC current that will flow in the varactor is a function
of the RF voltage and impedance. If the peak AC voltage swing is
denoted by V.sub.max, the peak AC current is
I.sub.max=j.omega.CV.sub.max (9)
[0059] For the cell of FIG. 3, Eqn. 9 implies the following
inequalities for the top and bottom electrodes, respectively 4 I
max t c W < J c I max t b ( 2 L + W ) < J c ( 10 )
[0060] where t.sub.c and t.sub.b are the thicknesses of the top
electrode 140 and bottom electrode layer 112, respectively.
[0061] According to the first inequality in Eqn. 10, the width W
must satisfy 5 W > W min = I max t c J c ( 11 )
[0062] The constraint on length L is slightly more complicated
since the current density in the bottom contact is set by the
quantity (2L+W), and also since the length-width product LW=A is
set by the desired capacitance value of the cell. Substituting
W=A/L in the second inequality in Eqn. 10 and then manipulating
results in 6 2 L + A L - I max t b J c > 0 ( 12 )
[0063] This inequality will be satisfied by large values of L (in
which case the 2L term is large) or for small values of L (in which
case the A/L term is large). However, the small value solutions
typically are less interesting because they represent the case
where two short sides and one long side of a rectangular cell are
current conducting (i.e., the case where L in FIG. 4C is small and
W is large). A valid cell design has values of W and L that satisfy
Eqns. 11 and 12 as well as the equality LW=A, where A is set by the
desired capacitance of the cell. There is no guarantee that a valid
cell design exists.
[0064] The quantity on the left in Eqn. 12 can be thought of as the
"excess" current conducting perimeter beyond what is needed to keep
the current density in the bottom electrode below the threshold
current density. It is a measure of how close to the current
handling limit the varactor design is. The larger the quantity, the
farther away from the limit is the design. There is no guarantee
that there is a realizable length in the range
L<L.sub.max=A/W.sub.min that will satisfy Eqn. 12. If there is
not, one possible solution is to increase the metal thicknesses
until a realizable design is achieved. However, the bottom
electrode layer 112 is typically made from an expensive refractory
material such as platinum. Hence, it is desirable to minimize the
electrode thickness in order to reduce the amount of expensive
metal required. It is also desirable to keep this thickness small
in order to avoid lithography problems resulting from non-planar
topology.
[0065] Hence, the approach described above is an attractive
alternate solution. That is, the current density can be reduced by
increasing the current conducting perimeter of the active region,
while maintaining the same area. One way to do this is to increase
the number of cells. If there are N cells, then the area and peak
current in each cell is reduced by 1/N. Therefore, Eqn. 12 becomes
7 2 L + A NL - I max t b J c N > 0 ( 13 )
[0066] FIGS. 7A and 7B are graphs of excess current conducting
perimeter (i.e., the lefthand side of Eqn. 13) as a function of
length L for N=1 and N=4 cells, respectively. These graphs are
plotted only for values of L which satisfy the inequality
L<L.sub.max=A/W.sub.min. In other words, the graphs plot the
excess current conducting perimeter only for allowable values of
stripe length L. In order to be a valid cell design, the excess
perimeter must be greater than zero (Eqn. 13) and the resulting
cell design must also have acceptable resistive loss (generally,
lower resistive losses are achieved by higher values of L, as
discussed previously). In FIG. 7A, the only values of L which
satisfy Eqn. 13 are low values of L, but these probably have
unacceptable resistive loss. Thus, it is likely that an acceptable
1-cell design does not exist. In FIG. 7B, larger stripe lengths
also satisfy Eqn. 13, suggesting that a valid 4-cell design likely
does exist.
[0067] Although the invention has been described in considerable
detail with reference to certain preferred embodiments thereof,
other embodiments will be apparent. For example, the shapes of the
top and bottom electrodes in FIG. 3 could be switched. As another
example, the electrodes and active regions can take shapes other
than rectangular, for example circular, semicircular or serpentine.
In these cases, the design objective of increasing perimeter would
still favor the use of multiple cells, but the exact resistive
model and design equations would be different than those presented
herein although the principles illustrated would still be
applicable. As a final example, it is not necessary that all cells
have exactly the same size and shape. A mix of cells of different
dimensions and/or shapes could also be used to increase the
varactor perimeter. Therefore, the scope of the appended claims
should not be limited to the description of the preferred
embodiments contained herein.
* * * * *