WO2009108175A1

WO2009108175A1 - Carbon nanotube capacitor structures and methods

Info

Publication number: WO2009108175A1
Application number: PCT/US2008/013624
Authority: WO
Inventors: Mark M. Budnik; Eric W. Johnson; Joshua D. Wood
Original assignee: The Lutheran University Association, Inc. D/B/A Valparaiso University
Priority date: 2007-12-12
Filing date: 2008-12-12
Publication date: 2009-09-03

Abstract

Structures and methods utilizing vertically grown carbon nanotubes (CNTs) in the formation of carbon nanotube capacitors (CNCAP) are provided. In various embodiments, the CNCAP structures include variously dense CNT bundles or walls as replacements for traditional inter-metal layer interconnects, utilizing various CNT diameters, inter-CNT spacing and CNT length.

Description

CARBON NANOTUBE CAPACITOR STRUCTURES AND METHODS

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. provisional application Ser. No. 61/007,598, filed on December 12, 2007, which is hereby incorporated by reference in its entirety.

BACKGROUND OF THE DISCLOSURE

1. Field of the Disclosure

[0002] The present disclosure relates generally to methods and apparatus associated with carbon nanotube capacitor structures and specifically to carbon nanotube capacitor structures providing high capacitance per unit area with respect to conventional metal-oxide-semiconductor and metal-insulator-metal capacitors.

2. Description of the Background of the Disclosure

[0003] Capacitors are important components in analog, digital, and mixed-signal circuits. They are used in a number of applications including decoupling circuits (the suppression of supply voltage variation due to transients in operating currents) and analog signal processing (in switched capacitor circuits, for example).

[0004] Traditional semiconductor capacitors are based upon a parallel plate structure. One such traditional semiconductor capacitor, a metal-oxide-semiconductor capacitor (MOSC) uses a metal-oxide-semiconductor field effect transistor (MOSFET) to create the capacitor. The MOSFET' s gate functions as one electrode, its source and drain region function as the second electrode, and the gate dielectric serves as the capacitor dielectric. Another semiconductor capacitor in use is the metal-insulator-metal capacitor (MIM). The MIM is fabricated in higher levels of metal with a thin dielectric material (often SiO₂). The capacitance C of the MOSC and MIM devices is approximated by the equation: C = A e/d where A is the area of each parallel plate, d is the thickness of the dielectric, and ^e is the dielectric permittivity.

[0005] The International Technology Roadmap for Semiconductors (ITRS) forecasts the capacitance per unit area of MOSC and MIM devices will increase from 7fF/μm² and 4fF/μm² in 2008 to l lfF/μm² and 10fF/μm² in 2018, respectively. As capacitor component dimensions are scaled down, the decreasing parallel plate area of the MOSC and MIM capacitors will result in a reduction in capacitance. Reducing the dielectric thickness, d, can offset the decrease in parallel plate area A, but this will lead to higher leakage currents.

[0006] New capacitor structures for use in nanotechnology applications are being developed. One such capacitor structure uses carbon nanotubes (CNTs) to create capacitors. CNTs are cylinders of very small diameter typically formed by rolling very thin sheets of graphite. When rolled correctly, a CNT can exhibit metallic properties. When CNTs are rolled with a single wall, ballistic transport of electrons is possible in the presence of small and moderate electric fields. As such, bundles of single-walled CNTs are being used between traditional metal interconnects in integrated circuit technology at the nanoscale level. When CNT bundles, or vias, are connected to opposing polarities (operating voltage and ground, respectively), a carbon nanotube capacitor (CNCAP) is formed.

[0007] Further, horizontal CNCAP structures are known, as shown in U.S. Patent Application No. 11/640,691 to Budnik et al.

[0008] In many signal transmission applications, it is desirable to minimize the capacitance between parallel CNT bundles. However, in typical CNCAP structures, the capacitance between parallel CNT bundles is exploited to achieve very high values of capacitance per unit area as compared to traditional MOSC and MIM capacitors. SUMMARY OF THE DISCLOSURE

[0009] In one aspect of the disclosure, a carbon nanotube capacitor (CNCAP) structure is provided that includes an anode, a cathode, a plurality of substrates, an array of carbon nanotubes (CNTs) aligned substantially perpendicular to and interconnected between the plurality of substrates, wherein each CNT or CNT bundle of the array is selectively coupled to parallel, yet alternately charged first and second electrodes.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 illustrates a perspective view of a vertical carbon nanotube capacitor (CNCAP);

[0011] FIG. 2 is a top view of a cross-section of a vertical CNCAP structure;

[0012] FIG. 3 illustrates a top cross-sectional view of a rotated version of the CNCAP structure of FIG. 2;

[0013] FIG. 4 is a partial perspective view of the CNCAP structure of FIG. 3;

[0014] FIG. 5 is a partial top view of a cross-section on its side of the vertical CNCAP of FIG. 1;

[0015] FIG. 6 is a top cross-sectional view of a dense, vertical CNCAP structure;

[0016] FIG. 7 is a top cross-sectional view of a sparsely packed, vertical CNCAP structure;

[0017] FIG. 8 is a schematic circuit diagram of an equivalent circuit of vertical, parallel, metallic, single-walled CNTs;

[0018] FIG. 9 is a three-element model of a CNCAP;

[0019] FIG. 10 is a graph illustrating the equivalent series resistance (ESR) of each of the CNCAP structures of FIGS. 2-4, 5-6 and 7 as a function of contact resistance; [0020] FIG. 11 is a graph illustrating the capacitance per unit area of various parallel-plate approximations and computer simulations of a vertical CNCAP structure as a function of CNCAP bundle dimensions L_S/DE and LSPACE, where L_SJDE ⁼ LSPACE-

[0021] FIG. 12 illustrates a top cross-sectional view of a pseudo-parallel plate CNCAP structure; and

[0022] FIG. 13 illustrates a top cross-sectional view of an interleaved CNCAP structure as shown in FIGS. 2-4, with electrical connections.

DETAILED DESCRIPTION

[0023] While the present disclosure may be embodied in many different forms, several specific embodiments are discussed herein with the understanding that the present disclosure is to be considered only as an exemplification of the principles of the disclosure, and it is not intended to limit the disclosure to the embodiments illustrated.

[0024] Referring to FIG. 1, a vertical carbon nanotube capacitor (CNCAP) structure 20 is shown. The CNCAP structure 20 includes two vertical interterconnects 22, via-like structures, which each include bundles of vertical CNTs 23. The vertical interconnects 22 may include vertical CNTs 23 bundled in a variety of shapes and patterns, including but not limited to hexagonal, square, random, quasi-random, and sparsely packed bundles. The CNTs 23 of one of the vertical interconnects 22 are connected at respective bases thereof to an electrode 24 and at respective top ends thereof to an electrode 25. The CNTs 23 of the other interconnect 22 are also connected at respective bases thereof to an electrode 26 and at respective top ends thereof to an electrode 27.

[0025] The CNCAP structure 20 shown in FIG. 1 has its bundles of CNTs 23 formed in aligned arrays, extending substantially uniformly in a direction substantially perpendicular to the various substrates 24-27 to which one or more of the CNTs 23 may be connected. In the embodiment shown in FIG. 1 , the CNCAP structure 20 has a capacitance Cvi_a that is achieved when the two bundles of CNTs 23 are alternately connected to opposing electrodes, forming a cathode and an anode, to achieve a relatively high value of capacitance per unit area.

[0026] FIG. 2 shows a cross-section of a vertical CNCAP structure 30, CNCAPl. The electrostatic coupling capacitance C_c is shown between one CNT (anode Al) and one CNT (cathode Cl). If the CNCAP structure 30 as shown in FIG. 2 is rotated about 45°, the anode CNTs, as designated by A1-A4, and the cathode CNTs, as designated by C and Cl, can be aligned longitudinally, as seen in FIG. 3. The CNCAP structure 30 includes vertical CNTs in interconnects 32, similar to the vertical interconnects 22, where each CNT of the interconnects 32 is connected as a via between two substrates, capacitor electrodes 34 and 36, as shown in FIG. 4. This alignment may allow the top and/or bottom of each vertical CNT to be connected to parallel, yet alternately connected capacitor electrodes 34 and 36. This alternate connection of electrodes, forming a cathode and an anode with a capacitance C_f, can be seen in a top cross- sectional view in FIG. 13.

[0027] In FIG. 3, the area bounded by the dotted line surrounding cathode Cl containing 1/4 of anodes A1-A4, is about 50nm². This area may also contain four of the electrostatic coupling capacitors Cc from FIG. 3 (where only one Cc is shown). A typical value for the diameter of a single-walled CNT is about lnm. Illustratively, using about a 4nm distance between nearest neighbor anode-cathode CNTs, the number of CNTs/μm² can be calculated. The CNCAP structure 30, CNCAPl, utilizes about two CNTs/50nm², and the total CNTs/μm² will be about 40,000.

[0028] A top view on its side of the vertical CNT interconnects 22 of FIG. 1 , is shown in FIG. 5. As shown, the diameter of a single-walled CNT is about lnm. The footprints of the vertical interconnects 22 are about lOnm by about lOnm. This footprint dimension can be expressed as the CNT bundle side length L_SIDE- The number of CNTs per vertical CNT bundle is:

CNTs I bundle ^« {L$IDE ^ ^^nm) ■ [0029] The vertical interconnects 22 are spaced a distance of about lOnm, which can be expressed as L_SPACE, and there are approximately 100 CNTs per vertical CNT interconnect 22. Such embodiments of vertical CNT interconnects 22 are relatively dense. For an inter-bundle distance of LS_PACE (not always equal to L_SI_DE), the number of CNCAP electrodes per unit area is given by

Number of Anodes _ Number of Cathodes \μm μm² μm² 2(L₈IDE + L_SPACE)²

[0030] In FIG. 6, a CNCAP structure 40, CNCAP2, includes a network of the relatively dense CNT bundles of FIG. 5, vertical CNT interconnects 42, similar to the vertical interconnects 32. The CNT bundles are alternately connected to base electrodes 44 and/or top electrodes (not shown) to form anodes (A) and cathodes (C) of the CNCAP structure 40. With the same vertical CNT interconnect dimensions (L_SIDE equaling about lOnm) as used in CNCAP structure 30, CNCAPl, and the same distance between interconnects (L_SPACE equaling about lOnm), the number of electrodes/μm² can be calculated. A unit cell of the vertical CNT interconnects is about 20nm by about 20nm and contains approximately 100 CNTs. This geometry results in about 2,500 electrodes/μm² (about 1,250 anodes and about 1,250 cathodes).

[0031] Similar to the CNCAP structure 40, a CNCAP structure 50, CNCAP3, is shown in FIG. 7 and includes of a network of vertical CNT interconnects 52. In this embodiment, the CNT bundles are alternately connected to base electrodes 54 and/or top electrodes (not shown). However, rather than using relatively dense vertical CNT bundles, the CNCAP structure 50 is composed of sparse vertical CNT bundles, with only about four CNTs per approximately a lOOnm² bundle area. The CNCAP structure 50, CNCAP3, has about 2,500 electrodes/μm², but may allow for greater inter-CNT distances.

[0032] FIG. 8 shows an equivalent circuit of two vertical, parallel, single-walled, metallic CNTs, such as those described in the CNCAP structure 20. The quantum capacitance, C_Q, is approximately 40OaF per about lμm of CNT length (vertical height). The inductance, L, of the CNTs is approximately 4nH/μm. Rc is the CNT-metal interconnect contact resistance at the top and the base of each CNT, where each CNT is connected to electrodes, such as capacitor electrodes 34 and 36 in the CNCAP structure 30, CNCAPl.

[0033] The resistance, R, can be approximated by the equation:

where RQ is the quantum resistance (6.45kΩ), ^ is the length of the CNT, ^_mfp,i_Ow is the CNT low-bias mean free path (approximately 1.6μm), V is the voltage drop across the CNT, and Io is approximately 25μA. A typical value of the height of a CNCAP's vertical CNTs, ^ , is about lμm. In an illustrative CNCAP, the voltage across each CNT is about OV. In one embodiment, a CNCAP is used in integrated circuits near the end of the International Technology Roadmap for Semiconductors (ITRS), with operating voltages at about 0.5 V. If the maximum voltage drop across the CNTs is allowed to be about 10OmV, an illustrative CNT resistance can be approximated as:

R = (6.45*Ω)f 1 + J^=-] + I∞ϋ£ = 14.5/fcΩ v \ \ .6μm) 25μA

[0034] For relatively short vertical CNT interconnects, the contact resistance, Rc, at the top and base of each CNT may be important to electrical modeling of the whole CNCAP structure. However, in some embodiments, the vertical CNT interconnects can be partially buried in their metallic electrode contacts, achieving relatively small contact resistances (much less than RQ). While in some instances Rc could be neglected, here the contact resistance is taken into account when calculating the equivalent series resistance of the CNCAP structures 30, 40, and 50 (CNCAPl, CNCAP2, and CNCAP3, respectively).

[0035] A variety of techniques to manufacture vertical CNTs are known to those skilled in the art, including, for example, chemical vapor deposition (CVD), as described in, for example, L. Zhu, Y. Sun, J. Xu, Z. Zhang, D. W. Hess, C. P. Wong, "Aligned carbon nanotubes for electrical interconnect and thermal management," Proc. Electronic Components and Technology, vol. 1, pp. 44-50, June 2005. Other illustrative techniques to produce CNTs include, for example, arc discharge, laser ablation, high pressure carbon monoxide, and plasma enhanced CVD, some of which are described in, for example, U.S. Patent Nos. 7,132,714, 7,282,191, and 7,288,321. Many manufacturing processes for growing CNTs onto a substrate layer take place in a vacuum and/or with process gases, as is understood by those skilled in the art.

[0036] The present disclosure is further illustrated by the following examples, which should not be construed as limiting in any way.

EXAMPLES

[0037] To determine the capacitance per unit area of the CNCAP structure 30, CNCAPl, a capacitance Cc is calculated between any two opposite polarity CNTs. With a CNT length, ^ ,of about lμm, a CNT diameter of about lnm, and approximately 4nm of spacing between the anode and cathode nearest neighbors, Cc is about 15.6aF. For larger values of ^ , Cc (and ultimately the capacitance per unit area, C_CNCAPI) scales linearly.

[0038] Using the equivalent circuit of FIG. 8, the actual capacitance between two opposite polarity CNTs in the CNCAP structure 30 is the series equivalent of two C_Q and Cc- Therefore, the net capacitance between two opposite polarity nearest neighbor CNT electrodes in the CNCAP structure 30, CNCAPl, is approximately:

-1

C NET ^~ I = 14. 5aF

400αF \5.6aF 40OaF J

[0039] With four parallel C_NET capacitors for every anode, the total capacitance per unit area is about 4(14.5aF)/50nm² or about 58aF/50nm². Converting this to μm², the capacitance per unit area C_c = C_CNCAPI of the CNCAP structure 30, CNCAPl, is about l,160fF/μm². In one embodiment, and taking into consideration the ratio of metallic, single-walled CNTs to semiconducting, single-walled CNTs, statistically, 1/3 of single-walled CNTs are metallic. Therefore, in this example, the capacitance per unit area of the CNCAP structure 30, CNCAPl, can be approximated as: μm 3 ^ μm J

[0040] This very high capacitance per unit area of about 387fF/μm² is more than an order of magnitude beyond the International Technology Roadmap for Semiconductors (ITRS) expectations for MOSC and MIM devices as forecast for the year 2018 (forecasts of l lfF//μm² and 10fF/μm², respectively).

[0041] To calculate the equivalent series inductance (ESL) and ESR of the CNCAP structure 30, CNCAPl, as shown in the three-element model circuit of FIG. 9, remembering that the CNCAP structure 30 utilizes about 2 CNTs/50nm², giving it about 40,000 CNTs per μm² (about 20,000 anodes and about 20,000 cathodes), the ESL is:

ESL_CNCAP\ -

# anodes * ){ % Metallic j ; and ,

ESL_CNCAPλ = [ ^4nH If —!— ) = 0.6pH/μm² C^NCApy ^ 20, 000 Λ 0.33 J '

[0042] The ESR of the CNCAP structure 30, CNCAPl, as a function of Rc and the percentage of metallic single- walled CNTs is plotted as shown in FIG. 10 and given by the equation:

[0043] To determine the capacitance per unit area of the CNCAP structure 40, CNCAP2, using a parallel plate approximation, it is recalled that the CNCAP structure 40, with L_SI_DE ⁼ LsP_ACE ⁼ 10nm, may include about 1,250 anodes and about 1,250 cathodes per μm². With the electrode CNT density approaching 100 CNTs/lOOnm², and a CNT length, t , of about lμm, the electrostatic coupling capacitance between electrodes (Cc₂ in FIG. 6) is about 35aF. For larger values of ^ , the capacitance per unit area Cc₂ ⁼ C_CNCAP2 generally scales linearly. Neglecting the effects of the fringe CNT bundles on the fringe of the CNCAP structure 40, CNCAP2, each anode has an electrostatic coupling capacitance between itself and its four nearest-neighbor cathode bundles. Again considering the fraction of metallic CNTs:

≤SSEffiL = (% metallic){anodes){^≡^^-\capacitance) μm² \ anode J^v . ^

[0044] This parallel-plate approximation of the capacitance per unit area of CNCAP structure 40, CNCAP2, can be simulated for different dimensions of L_SID_E and L_SPA_CE- AS L_SIDE and L_SPACE are decreased below 0.5μm, simulations performed on the CNCAP structure 40, CNCAP2, using FastCap, a 3-D capacitance extraction computer program, show an increase in C_CN_CAP2- These simulations can be seen in FIG. 11. Previous simulations by others, however, show that C_CN_CAP2, even at L_SI_DE and L_SPACE dimensions of 10nm, remains consistent with the parallel-plate approximations.

[0045] Assuming that only the CNTs on the edges of each of the vertical electrode bundles contribute to the capacitance, there are approximately 100,000 CNTs/μm² in the CNCAP structure 40, CNC AP2. The equivalent series inductance can be approximated as:

ESL_CC_NN_CC_AA_FP₂2 = = 2If ^JH " I μ*m²

[0046] Using the same equation as used above for the CNCAP structure 30, CNCAPl, the ESR of the CNCAP structure 40, CNC AP2, is plotted as a function of Rc, as shown in FIG. 10.

[0047] Finally, to determine the capacitance per unit area of the CNCAP structure 50, CNCAP3, it is recalled that the CNCAP may include about 1,250 anodes and about 1,250 cathodes per μm². With an electrode CNT density of only about four CNTs/lOOnm² and a CNT length, ^ , of about lμm, the electrostatic coupling capacitance between electrodes (Cc3 in FIG. 7) is about 3OaF. The capacitance per unit area of the CNCAP structure 50, CNCAP3, is calculated to be:

[0048] Given only about four CNTs/bundle, the total number of CNTs/μm² is about 10,000. The ESL of the CNCAP structure 50, CNCAP3, is:

^{ESL ^} _C ^C _N ^N _C ^C _A ^A _P ^P ₃ ⁱ = I ^ - 5^000- J If (^ — 0. !3—3 J J = 2ApH I ' μm²

[0049] As with the CNCAP structures 30 and 40 (CNCAPl and CNCAP2, respectively), the ESR of the CNCAP structure 50, CNCAP3, is calculated and plotted in FIG. 10 as a function of Rc-

[0050] The footprint of the embodiments of CNCAPs of the present disclosure may take several different forms. While the CNCAP structures 30, 40 and 50 (CNCAPl, CNCAP2, and CNC AP3, respectively) may be directly implemented, a simpler, vertical pseudo-parallel plate version 60 of a CNCAP may be implemented with capacitance Cpp, as shown in FIG. 12.

[0051] For each of the CNCAP structures 30, 40 and 50 (CNCAPl, CNCAP2, and CNCAP3, respectively), the electrical models developed in the above illustrative example show that vertical CNCAPs only about lμm in height produce capacitances per unit area from about 50fF/μm to about 387fF/μm², significantly higher than the 4fF/μm² to 7fF/μm² achievable today in conventional metal-oxide-semiconductor capacitors and metal-insulator-metal capacitors. The electrical models as shown above illustrates that vertical CNCAP structures can become viable circuit components.

[0052] It is contemplated that the parts and features of any one of the embodiments of the vertical CNCAP structures described can be interchanged with the parts and features of any other of the embodiments without departing from the spirit of the disclosure. The foregoing description describes merely exemplary embodiments of the present disclosure and is not intended to be exhaustive or to limit the disclosure to the precise form disclosed. As will be understood by those skilled in the art, the disclosure may be embodied in other specific forms, or modified or varied in light of the above teachings, without departing from the spirit, novelty or essential characteristics of the present disclosure. Accordingly, the present disclosure of the present disclosure is intended to be illustrative, but not limiting, of the scope of the disclosure. All patents, patent publications, and other references cited herein are incorporated herein by reference in their entirety.

Claims

WHAT IS CLAIMED IS:

1. A carbon nanotube capacitor comprising: an first electrode; a second electrode; a plurality of substrates; and an array of carbon nanotubes (CNTs) aligned substantially perpendicular to and interconnected between the plurality of substrates; wherein each CNT of the array is selectively coupled to parallel, yet alternately charged first and second electrodes.

2. The carbon nanotube capacitor of claim 1, wherein the first electrode is an anode and the second electrode is a cathode.

3. The carbon nanotube capacitor of claim 2, wherein the carbon nanotube capacitor is single-walled.

4. The carbon nanotube capacitor of claim 1 , wherein each of the first electrode and the second electrode includes an array of carbon nanotubes (CNTs) aligned perpendicular to and interconnected between the plurality of substrates, and wherein the carbon nanotubes (CNTs) in the array are densely packed.

5. The carbon nanotube capacitor of claim 1, wherein each of the first electrode and the second electrode includes an array of carbon nanotubes (CNTs) aligned perpendicular to and interconnected between the plurality of substrates, and wherein the carbon nanotubes (CNTs) in the array are sparsely packed.

6. A method of forming a carbon nanotube capacitor, comprising the steps of: providing a first electrode; providing a second electrode; providing a plurality of substrates; providing an array of carbon nanotubes (CNTs) aligned substantially perpendicular to and interconnected between the plurality of substrates, wherein each CNT of the array is selectively coupled to parallel, yet alternately charged first and second electrodes.