Probabilistic modelling of performance parameters of Carbon Nanotube transistors

Probabilistic modelling of performance parameters of Carbon Nanotube transistors Department of Electrical and Computer Engineering By Yaman Sangar Amitesh Narayan Snehal Mhatre

Overview • Motivation • Introduction • CMOS v/s CNTFETs • CNT Technology - Challenges • Probabilistic model of faults • Modelling performance parameters: • ION / IOFF tuning ratio • Gate delay • Noise Margin • Conclusion

Overview • Motivation • Introduction • CMOS v/s CNTFETs • CNT Technology – Challenges • Probabilistic model of faults • Modelling performance parameters: • ION / IOFF tuning ratio • Gate delay • Noise Margin • Conclusion

MOTIVATION: Why CNTFET? • Dennard Scaling might not last long • Increased performance by better algorithms? • More parallelism? • Alternatives to CMOS - FinFETs, Ge-nanowire FET, Si-nanowire FET, wrap-around gate MOS, graphene ribbon FET • What about an inherently faster and less power consuming device? • Yay CNTFET – faster with low power

CNT is a tubular form of carbon with diameter as small as 1nm • CNT is configurationally equivalent to a 2-D graphene sheet rolled into a tube. Carbon Nanotubes

Single Walled CNT (SWNT) • Double Walled CNT (DWNT) • Multiple Walled CNT (MWNT) • Depending on Chiral angle: • Semiconducting CNT (s-CNT) • Metallic CNT (m-CNT) Types of CNTs

Properties of CNTs • Strong and very flexible molecular material • Electrical conductivity is 6 times that of copper • High current carrying capacity • Thermal conductivity is 15 times more than copper • Toxicity?

CNTFET • How CNTs conduct? • Gate used to electrostatically induce carriers into tube • Ballistic Transport

Simulation based Comparison between CMOS and CNT technology

Simulation based Comparison between CMOS and CNT technology Better delay

Simulation based Comparison between CMOS and CNT technology Better delay At lower power!

Major CNT specific variations CNT density variation Metallic CNT induced count variation CNT diameter variation CNT misalignment CNT doping variation • Unavoidable process variations • Performance parameters affected Challenges with CNT technology

CNT diameter variation CNT density variation • Current variation • Threshold voltage variation

CNT doping variation CNT Misalignment • Changes effective CNT length • Short between CNTs • Incorrect logic functionality • Reduction in drive current • May not lead to unipolar behavior

Metallic CNT induced count variation m-CNT m-CNT Current s-CNT s-CNT • Excessive leakage current • Increases power consumption • Changes gate delay • Inferior noise performance • Defective functionality Vgs

Removal of m-CNTFETs • VMR Technique : A special layout called VMR structure consisting of inter-digitated electrodes at minimum metal pitch is fabricated. M-CNT electrical breakdown performed by applying high voltage all at once using VMR. M-CNTs are burnt out and unwanted sections of VMR are later removed. • Using Thermal and Fluidic Process: Preferential thermal desorption of the alkyls from the semiconducting nanotubes and further dissolution of m-CNTs in chloroform. • Chemical Etching: Diameter dependent etching technique which removes all m-CNTs below a cutoff diameter.

Probabilistic model of CNT count variation due to m-CNTs Probability of grown CNT count • ps = probability of s-CNT • pm = probability of m-CNT • ps = 1 - pm • Ngs = number of grown s-CNTs • Ngm = number of grown m-CNTs • N = total number of CNTs

Conditional probability after removal techniques • Ns = number of surviving s-CNTs • Nm = number of surving m-CNTs • prs = conditional probability that a CNT is removed given that it is s-CNT • prm = conditional probability that a CNT is removed given that it is m-CNT • qrs= 1 - prs • qrm= 1 -prm

ION / IOFF is indicator of transistor leakage • Improper ION / IOFF → slow output transition or low output swing • Target value of ION / IOFF = 104 Effect of CNT count variation on ION / IOFF tuning ratio

Current of a single CNT • ICNT= ps Is+ pmIm • µ(ICNT) = psµ(Is)+ pmµ(Im) • ICNT =drive current of single CNT (type unknown) • Is =drive current of single s-CNT • Im = drive current of single m-CNT • ps = probability of s-CNT • pm = probability of m-CNT

Ns = count of s-CNT Nm = count of m-CNT Is,on = s-CNT current, Vgs = Vds = Vdd Is,off = s-CNT current, Vgs = 0 and Vds = Vdd Im = m-CNT current, Vds = Vdd ION / IOFF ratio of CNTFET

ION / IOFF ratio of CNTFET µ (Ns) = ps (1 - prs) N µ (Nm) = pm(1 - prm) N

Effect of various processing parameters on the ratio µ(ION) / µ(IOFF) • µ(ION) / µ(IOFF) is more sensitive to prm • µ(ION) / µ(IOFF) = 104 for prm > 1 – 10 -4 = 99.99 % for pm = 33.33% 1- prm

Effect of CNT count variation on Gate delay

= =

Plot of v/s = 0.3 N = 10 N = 20 N = 40 N = 30 N = 50

Plot of v/s N 0.9 0.8 0.6 0.4 0.2 N

Noise Margin of CNTFET

VIL and VIH pFET • Substituting= Vin, , and • = • Differentiating with respect to Vin and substituting -1 nFET

VIL and VIH For CMOS, For CNTFET, NML = VIL - 0 NMH = VDD – VIH

CONCLUSION • Modeled count variations and hence device current as a probabilistic function • Studied the affect of these faults on tuning ratio and gate delay • Inferred some design guidelines that could be used to judge the correctness of a process • Mathematically derived noise margin based on current equations – better noise margin than a CMOS

Probabilistic modelling of performance parameters of Carbon Nanotube transistors