A High Density Carbon Nanotube Capacitor for Decoupling Applications Mark M. Budnik, Arijit Raychowdhury, Aditya Bansal, Kaushik Roy July 27, 2006 Mark M. Budnik, Arijit Raychowdhury, Aditya Bansal, Kaushik Roy July 27, 2006

A High Density Carbon Nanotube Capacitor Introduction to Decoupling Capacitors Carbon Nanotube Capacitor Physical Structure Carbon Nanotube Electrical Model Carbon Nanotube vs. Conventional Capacitors Capacitance per Unit Area Leakage per Unit Area Conclusions

Introduction to Decoupling Capacitors Decoupling capacitors are used to reduce supply voltage variations in advanced processors i (t) Input Voltage + -

Integrated Decoupling Capacitor Structure t A A

Traditional Decoupling Capacitors Problems Parallel plate topology - low capacitance / unit area Expensive die area High leakage current Algorithm placement Improvements? Improve dielectric material - limited Increase area - more expensive, more leakage Decrease dielectric thickness - more leakage Increase number of layers - unproven

Carbon Nanotube Capacitor Alternative Metallic, single wall carbon nanotubes Offer large surface area to volume ratio ~ 1nm  1m 1m

Carbon Nanotube Capacitor (CNCAP) CC CC CC CC AA AA AA AA C = Cathode A = Anode

CNCAP Electrical Model Parallel CNTsCNCAP Model Front End R/2L/2 R/2 CQCQ CGCG Front End R/2L/2 R/2 CQCQ CGCG CQCQ CQCQ C Cathode Anode L R CTCT

Capacitance Per Unit Area Separation 2 nm 3 nm 4 nmC 22.8 aF / µm 18.1 aF / µm 15.6 aF / µm C T 20.4 aF / µm 16.6 aF / µm 14.4 aF / µm 4xC T 81.6 aF / µm 66.4 aF / µm 57.6 aF / µm Capacitor Technology 2018 MOS CNCAP, s=2nm CNCAP, s=3nm CNCAP, s=4nm ITRS Capacitance ( fF / µm 2 ) CNT Layers Capacitance ( fF / µm 2 ) ,710 1,660 1,160

Capacitance Leakage Per Unit Area Capacitor Technology 2018 MOS CNCAP, s=2nm CNCAP, s=3nm CNCAP, s=4nm Capacitance ( fF / µm 2 ) 11 2,710 1,660 1,160 Leakage Current ( / µm 2 ) < 20 fA 1.83 µA 27.5 pA fA I LEAK

Conclusions Traditional MOS parallel plate capacitors Limited in ability to serve as decoupling capacitors Limited improvements for the forseeable future Metallic, single wall carbon nanotubes High surface area to volume ratio Small inter-tube spacing can result in appreciable capacitance per unit length May be placed in multiple layer bundles 3-D carbon nanotube capacitor structure High capacitance per unit area ( >> 11fF / µm 2 as a function of the number of layers) Low leakage current per unit area ( < 1fA / µm 2 for inter-tube spacing of 4nm)