graphene based interconnect modelling...5b. bala tripura sundari 1,2,3,4,5electronics and...

Proceedings of SARC-ITR International Conference, 04th May-2014, Chennai, India, ISBN: 978-93-84209-14-8

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GRAPHENE BASED INTERCONNECT MODELLING

1SUJOY SENGUPTA, 2DEV ARAVIND S.R., 3VIMAL RICHARSON, 4SOMEESHWAR, 5B. BALA TRIPURA SUNDARI

1,2,3,4,5Electronics and Communication Engineering Department, Amrita University

Abstract- Graphene Interconnects are considered as a future material for system on chip interconnects and Field-Effect Transistors. This paper introduces a comprehensive analysis of Graphene interconnects based on a quantum approach. Graphene nanoribbons (GNR) has been modeled using tight-binding model and the conductance of Graphene interconnect has been derived using Landauer formula. The model takes into account the effective mobility due to holes and electrons. The model discusses the impact of different parameters like mean free path, band gap and Fermi level on interconnect performance. The paper provides an insight on the operation of Graphene Interconnect. Keywords- Boltzmann Equation, Graphene Nanoribbons (GNR), Hamiltonian, Interconnect. I. INTRODUCTION Graphene is considered as one of the strong contenders for the post silicon electronic industry. The recent developments made in Graphene research have shown some of the remarkable electrical and thermal properties which make it suitable for Field Effect transistor and Interconnect fabrication [1]. It has been shown that Graphene has high current density [1], high thermal conductivity [2] and long mean free path [2]. Graphene has a high mobility and is ambipolar that is the conduction is carried by both electrons and holes Graphene Nanoribbons are the building block of Graphene CNTs, Graphite etc. [3] Graphene Nanoribbons has a hexagonal structure as shown in the Fig. 1. Graphene shows an unusual Quantum hall effect and also shows a Berry phase of 2π [1]. Recently Graphene Nanoribbons have been fabricated which shows large momentum relaxation time which encourages use of Graphene interconnects for system on chip. The electronic band structures of Graphene zigzag and armchair structures have been discussed along with the conductivity and the behavior under the influence of a strong electric field. The Graphene interconnect conductivity has been modeled using Landauer formula and considering tight binding model of Graphene. The model has been used for frequency analysis of Graphene interconnect by introducing the effective mobility which considers the mobility due to both electrons and holes. The model does a detailed analysis of the parameter variations on the performance of interconnect. The effect of mean free path and band-gap on the electric field has been discussed. The Boltzmann equation has been used to find the conductivity of the sheet considering both the electrons and holes. The skin depth has been derived

using the electric field equation and the frequency analysis has been done. II. BAND STRUCTURE OF GRAPHENE

Graphene based Interconnect Modelling


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III. MODELLOING GRAPHENE INTERCONNECT CONDUCTANCE The electrical conductance [8] of graphene Nanoribbons is given by



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In our model we are considering both electrons and holes for conduction. So the net conduction of a layer of Graphene is given by

IV. SKIN DEPTH OF GNR From the previous section it can be seen that the mean free path for Graphene is high so graphene is susceptible to skin effect. Due to skin effect the current distributes in the graphene nanoribbons which results in increase in the resistance at higher frequencies. The electric field is assumed to be constant when the mean free path is comparable to the skin depth. In this case the device follows ordinary ohm’s law. For graphene nanoribbons the skin depth is comparable to the mean free path. The electrons no longer travel under constant electric field between the collisions and the current gets affected from the potential at other points.



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CONCLUSION The graphene Nanoribbons interconnect has been modeled in this paper using quantum mechanical approach. The Graphene sheet resistance was found out to be decreasing as the GNR width increases. The band structure of graphene give rise to Armchair and Zigzag structures which are semiconductor or metallic. The skin depth of graphene Nanoribbons were found to be optimum when compared to the modern day interconnect materials. Skin Depth shows a strong dependence on frequency.

The application of graphene interconnect in electronic devices is needed to be investigated and the properties of Graphene like high mobility, ambipolar nature needed to be exploited for future uses. REFERENCES

[1] Y. Awano,"Graphene for VLSI: FET and interconnect applications", IEDM Tech. Dig., pp.1 -4 2009.

[2] Behnam Ashkan, Lyons Austin S., Myung, “Transport in Nanoribbon Interconnects Obtained from Graphene Grown by Chemical Vapour Deposition”, in Nano Lett., 12 (9), pp. 4424–4430, Aug. 1, 2012.

[3] Chuan Xu,Hong Li, Banerjee K., “Modeling, Analysis, and Design of Graphene Nano-Ribbon Interconnects”, ,” IEEE trans. Electron devices, Vol.58, No. 3, pp.1567-1578, Aug, 2009.

[4] Areshkin Denis A., Gunlycke Daniel, White Carter T., “Ballistic Transport in Graphene Nanostrips in the Presence of Disorder: Importance of Edge Effects,” in Nano lett., pp.204-210, Nov 8, 2006.

[5] Sarkar Deblina, Xu Chuan, Li Hong, Banerjee Kaustav, “High-Frequency Behaviour of Graphene-Based Interconnects—Part I: Impedance Modelling,” IEEE trans. Electron devices, Vol.58, No. 3, Mar, 2011.

[6] Vadim V. Cheianov and Vladimir I. Fal’ko “Selective transmission of Dirac electrons and ballistic magnetoresistance of n-p junctions in graphene”, Phys. Rev B74 0414403, 17 July, 2006.

[7] Murali, Raghunath, “Resistivity of Graphene Nanoribbon Interconnects”, IEEE Electron Device Letters, Vol.30, pp.611-613, Jun, 2009.

[8] Supriyo Dutta, “Quantum Transport: Atom to Transistor”

graphene based interconnect modelling...5b. bala tripura sundari 1,2,3,4,5electronics and...

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