Circuit Modeling and Performance Analysis of GNR@SWCNT Bundle Interconnects

In this paper, the single-walled carbon nanotube(SWCNT) with graphene nanoribbon(GNR)inside, namely GNR@SWCNT, is proposed as alternative conductor material for the interconnect applications. The equivalent circuit model is established, and the circuit parameters extracted analytically. By virtue of the equivalent circuit model, the signal transmission performance of GNR@SWCNT bundle interconnect is evaluated and compared with its Cu and SWCNT counterparts. The optimal repeater insertions in glo...     

单根多壁碳纳米管的电学测试

提出了一种制备多壁碳纳米管的简单方法。以乙醇为碳源，利用催化化学气相沉积工艺制备了碳纳米管。用较为简单的设备在较低的反应温度下，在基底上生长了取向多壁碳纳米管阵列。利用扫描电子显微镜内部的纳米操纵仪对单根碳纳米管进行操纵，并测试了单根多壁碳纳米管的电学特性。     

单根多壁碳纳米管的电学测试

提出了一种制备多壁碳纳米管的简单方法。以乙醇为碳源,利用催化化学气相沉积工艺制备了碳纳米管。用较为简单的设备在较低的反应温度下,在基底上生长了取向多壁碳纳米管阵列。利用扫描电子显微镜内部的纳米操纵仪对单根碳纳米管进行操纵,并测试了单根多壁碳纳米管的电学特性。     

Physical Modeling of Temperature Coefficient of Resistance for Single- and Multi-Wall Carbon Nanotube Interconnects

Equivalent circuit models are presented for the resistance of single- and multi-wall carbon nanotubes (MWCNs) that capture various electron-phonon scattering mechanisms as well as changes in the number of conduction channels as a function of temperature. For single- and few-wall nanotubes, the temperature coefficient of resistance (TCR) is always positive and increases with length. It reaches 1/(T-200 K) for lengths much larger than the electron mean free path, where T is the temperature in kelvin. For MWCNs with large diameters (>20 nm), TCR varies from -1/T to +0.66/(T-200 K) as the length varies from zero to very large values     

A Novel Approach for Stability Analysis in Carbon Nanotube Interconnects

This letter introduces a new method for stability analysis of carbon nanotube (CNT) interconnects based on transmission line modeling and using the Nyquist stability criterion for the first time. Using this new method, the degree of relative stability for CNT bundle interconnects, versus the length of bundle and the diameter of each individual CNT, has been obtained. The obtained results show that with increasing the length of the CNT bundle and the diameter of each individual CNT interconnect, the relative stability increases, and the system becomes more stable.      

High-Frequency Analysis of Carbon Nanotube Interconnects and Implications for On-Chip Inductor Design

This paper presents a rigorous investigation of high-frequency effects in carbon nanotube (CNT) interconnects and their implications for the design and performance analysis of high-quality on-chip inductors. A frequency-dependent impedance extraction method is developed for both single-walled CNT (SWCNT) and multiwalled CNT (MWCNT) bundle interconnects. The method is subsequently verified by comparing the results with those derived directly from the Maxwell's equations. Our analysis reveals for the first time that skin effect in CNT (particularly MWCNT) bundles is significantly reduced compared to that in conventional metal conductors, which makes them very attractive and promising material for high-frequency applications, including high-quality (Q) factor on-chip inductor design in high-performance RF/mixed-signal circuits. It is shown that such unique high-frequency properties of CNTs essentially arise due to their large momentum relaxation time (leading to their large kinetic inductance), which causes the skin depths to saturate with frequency and thereby limits resistance increase at high frequencies in a bundle structure. It is subsequently shown that CNT-based planar spiral inductors can achieve more than three times higher Q factor than their Cu-based counterparts without using any magnetic materials or Q factor enhancement techniques.     

A Paradigm of Carbon Nanotube Interconnects in Microelectronic Packaging

Carbon nanotube (CNT) arrays/films were transferred onto copper substrates via eutectic tin/lead (SnPb) solder pastes. The morphologies, thermal stabilities, adhesion to substrates, and electrical properties of the as-transferred CNT arrays were studied. The CNT arrays generated negligible expansion or contraction below 250°C. The adhesion of CNT arrays to the substrate was significantly improved by the transfer process. An ohmic contact was formed between the transferred CNT arrays and the Sn-Pb solder. Four-probe electrical measurements yielded the resistance of the as-transferred CNT films under the electrode to be around 0.0056 Ω, from which the resistivity of each individual CNT tube was calculated to be 2.44 × 10⁻⁴ Ω cm.     

Electromigration Studies of Cu/Carbon Nanotube Composite Interconnects Using Blech Structure

The electromigration (EM) properties of pure Cu and Cu/carbon nanotube (CNT) composites were studied using the Blech test structure. Pure Cu and Cu/CNT composite segments were subjected to a current density of $hbox{1.2} times hbox{10}^{6} hbox{A/cm}^{2}$. The average void growth rate of Cu/CNT composite sample was measured to be around four times lower than that of the pure copper sample. The average critical current-density–length threshold products of the pure Cu and Cu/CNT composites were estimated to be 1800 and 5400 A/cm, respectively. The slower EM rate of the Cu/CNT composite stripes is attributed to the presence of CNT, which acts as trapping centers and causes a decrease in the diffusion of EM-induced migrating atoms.      

Schottky-Barrier Carbon Nanotube Field-Effect Transistor Modeling

The theoretical performance of carbon nanotube field-effect transistors (CNFETs) with Schottky barriers (SBs) is examined by means of a general ballistic model. A novel approach is used to treat the SBs at the metal-nanotube contacts as mesoscopic scatterers by modifying the distribution functions for carriers in the channel. Noticeable current reduction is observed compared to previous ballistic models without SBs. Evanescent-mode analysis is used to derive a scale length and the potential profile near the contacts for radially symmetric CNFET structures. Band-to-band tunneling current and ambipolar conduction are also treated. The effects of different device geometries and different nanotube chiralities on the drain-current are studied using this simple model. Quantum conductance degradation due to SBs is also observed     

Performance Modeling for Single- and Multiwall Carbon Nanotubes as Signal and Power Interconnects in Gigascale Systems

Using physics-based circuit models, the performances of carbon nanotube (CNT) interconnects, both single- and multiwall (SWNT and MWNT), are benchmarked against their copper counterparts at a realistic operating temperature (100degC). The models used capture various electron phonon scattering mechanisms and the dependence of quantum conductance on temperature and diameter. It is demonstrated that any performance comparison between CNT and copper wires needs to be done at realistic temperatures because changes in temperature affect copper and CNT interconnects quite differently. The results of this paper demonstrate that a hybrid system of copper/SWNT/MWNT offers the highest performance enhancement for interconnects.     

Nonlinear Characterization and Modeling of Carbon Nanotube Field-Effect Transistors

We report for the first time to our knowledge large-signal measurements performed at 600 MHz and in time domain on carbon nanotube field-effect transistors (CNFETs) using a large-signal network analyzer. To overcome the very high mismatch between the high CNFET impedance and the basic 50-$Omega$ configuration of the setup, the output impedance was matched with the help of an experimental active load–pull configuration. Hence, we were able to observe under large-signal conditions the nonlinear behavior of CNFETs. Static measurements and continuous-wave ${ S}_{ ij}$-parameter measurements were made for many different biases. They were used in order to determine a nonlinear electrical model that has been validated thanks to the nonlinear measurements. The developed model opens the way for electrical CNFET circuit simulation and nonlinear applications of these devices.      

一个用于VHSIC连接线瞬态分析的电路模拟器

本文介绍了一个可对含连接线的电路进行瞬态分析的电路模拟器,该模拟器是在SPICE基础上经修改扩充而成的,连接线的处理采用了文献[1]的方法.文中介绍了方法的基本原理,讨论了数值Laplace反变换时参数的选择与误差的控制.实际VHSIC电路的试算结果表明,该模拟器是相当有效的.     

Electrothermal Analysis of Breakdown in Carbon Nanofiber Interconnects

To elucidate the observed current capacity behavior, a model is developed that takes into account heat transport through the entire carbon nanofiber interconnect test structure and breakdown location. The model also includes variations in contact location with the support material. The resulting predicted heat dissipation and current capacity are completely consistent with experimental data.     

Design and Performance Modeling for Single-Walled Carbon Nanotubes as Local, Semiglobal, and Global Interconnects in Gigascale Integrated Systems

Based on physical models, distributed circuit models are presented for single-walled carbon nanotubes (SWCNs) and SWCN bundles that are valid for all voltages and lengths. These models can be used for circuit simulations and compact modeling. It is demonstrated that by customizing SWCN interconnects at the local, semiglobal, and global levels, several major challenges facing gigascale integrated systems can potentially be addressed. For local interconnects, monolayer or multilayer SWCN interconnects can offer up to 50% reduction in capacitance and power dissipation with up to 20% improvement in latency if they are short enough (<20 mum). For semiglobal interconnects, either latency or power dissipation can be substantially improved if bundles of SWCNs are used. The improvements increase as the cross-sectional dimensions scale down. For global interconnects, bandwidth density can be improved by 40% if there is at least one metallic SWCN per 3-nm² cross-sectional area     

Modeling, Analysis, and Design of Graphene Nano-Ribbon Interconnects

Graphene nanoribbons (GNRs) are considered as a prospective interconnect material. A comprehensive conductance and delay analysis of GNR interconnects is presented in this paper. Using a simple tight-binding model and the linear response Landauer formula, the conductance model of GNR is derived. Several GNR structures are examined, and the conductance among them and other interconnect materials [e.g., copper (Cu), tungsten (W), and carbon nanotubes (CNTs)] is compared. The impact of different model parameters (i.e., bandgap, mean free path, Fermi level, and edge specularity) on the conductance is discussed. Both global and local GNR interconnect delays are analyzed using an RLC equivalent circuit model. Intercalation doping for multilayer GNRs is proposed, and it is shown that in order to match (or better) the performance of Cu or CNT bundles at either the global or local level, multiple zigzag-edged GNR layers along with proper intercalation doping must be used and near-specular nanoribbon edge should be achieved. However, intercalation-doped multilayer zigzag GNRs can have better performance than that of W, implying possible application as local interconnects in some cases. Thus, this paper identifies the on-chip interconnect domains where GNRs can be employed and provides valuable insights into the process technology development for GNR interconnects.      

Modeling and Analysis of On-Chip Single and H-tree Distributed RLC Interconnects

This paper presents novel methods for modeling and analysis of on-chip Single and H-tree distributed resistance inductance capacitance interconnects. The matrix pade-type approximation and scaling and squaring methods are employed for the numerical estimation of delay in single interconnect, and H-tree interconnects. The proposed models, which are based on these methods, provide rational function approximation for obtaining a passive interconnect model. Multiple single input single output model approximated transfer functions are developed for H-tree interconnects structure. With the equivalent reduced order lossy interconnect transfer functions, finite ramp responses are obtained, and line delay is estimated for various line lengths, input ramp rise times, source resistances, parasitic capacitances and load capacitances. In order to demonstrate the accuracy of proposed models, the estimated 50 % delay values are compared with the standard HSPICE W-element model and are found to be in good agreement. The proposed models worst case 50 % delay errors of single interconnect are 0.27 and 0.24 % respectively, while the worst case 50 % delay errors of H-tree structure are 5.73 and 3.94 % respectively.     

Exploring the Performance Limit of Carbon Nanotube Network Film Field‐Effect Transistors for Digital Integrated Circuit Applications

Carbon nanotube (CNT) network thin film field‐effect transistors (TFTs), which used to be considered as low cost and low performance transistors for display driving or flexible electronics, have recently been used to construct digital integrated circuits (ICs). However, few studies have focused on exploring how optimal CNT TFTs can be achieved according to transistor standards in digital applications. In this work, sub‐micrometer TFTs based on high‐quality and high‐purity solution‐derived CNT films are fabricated and the potential performance restriction due to the switching‐off property of these transistors is explored. Specifically, subthreshold swing (SS) severely degrades upon scaling down the channel length or increasing the CNT density in TFTs, and a tradeoff between peak transconductance (g_m) and SS in CNT TFTs due to the random orientation distribution of CNTs has been observed in experiments and proven by theoretical simulations. A well‐designed balance between g_m and SS is necessary to build CNT TFTs with SS of 120 mV dec^?1 and g_m of 150 µS µm^?1 to meet device requirements in digital ICs powered by a supplied voltage, V_DD, lower than 2.0 V.     

乙醇化学气相沉积法制备多壁碳纳米管

介绍了采用浮动催化剂法，利用乙醇化学气相沉积法制备多壁碳纳米管。采用二茂铁作为催化剂先体，乙醇作为碳源，利用石英基底收集产物。催化剂先体二茂铁的蒸汽在载气的作用下被带到高温区（800℃），二茂铁在高温区分解形成铁纳米催化剂颗粒，这些催化剂颗粒催化生长出多壁碳纳米管。利用扫描电子显微镜、（高分辨）透射电子显微镜对制备的多壁碳纳米管都进行了表征。实验结果表明，制备的多壁碳纳米管均匀性好，石墨化程度较高。