Graphene Nanoribbon as a Field Effect Transistor

GRAPHENE NANORIBBON AS A FIELD EFFECT TRANSISTOR AND PERFORMANCE ANALYSIS AGAINST FINFET

 

Abstract-

      Graphene is a widely considered to be one of the most promising semiconductor materials for the future. Graphene is by itself a semimetal with a zero bandgap. [4] Graphene has a unique structure, unlike other form of carbon. Graphene is one layer of carbon atoms in the shape of a hexagon in a honeycomb. [4] This forms a 2 dimensional structure arrangement of carbon-carbon atoms bonding in a sp2hybridization.  Due to its one of a kind electric spectrum, there has been a rise of interest in studying the properties and characteristics of graphene. The motivation for this topic came across while studying Schrodinger’s equation in class. Until recently, the preferred material for semiconductor was Silicone. In the recent years however, there has been a slowdown in the processing power and silicone is on the verge of being phased out as a semiconducting material of choice. Graphene has all the potential to overtake silicone as a preferred choice for semiconductor. There are however many challenges with graphene which need to be looked at. One of the major challenges with graphene is edge irregularities. Edge irregularities are caused during the fabrication process. As the graphene ribbons get smaller and smaller, the edge irregularities become more pervasive problem. This study will help us to understand detailed structure of graphene nanoribbons as a field effect transistor and compare its performance against a Fin field effect transistor.

Introduction-

       Carbon based field-effect transistors in the nano-scale have emerged as a next big alternative to the traditional silicone based FETs due to their exceptional electrical properties due to the improving fabrication techniques. [1] One of the most well researched transistors are Carbon nanotube FET (CNTFET) and Graphene nanoribbon FET(GNRFET). [1] To know more about graphene as a field-effect transistor, first we need to understand the structure of graphene. Due to the wonderful properties of graphene, a small change in making a GNR changes the electrical properties of GNR. [2] Since the fabrication technology of GNRFETs is still in very rudimentary stage, the way the transistor is modelled plays an important role for next-gen graphene circuits. [1]

      In this paper, the main topics that we will cover are as follows:

Studying the graphene nanoribbon structure.

Learning about the defects in the fabrication techniques leading to defects in the GNR

Developing a SPICE model for GNRFET and FINFET. Running simulations using an XOR gate and find the results.

Comparing the performance of both the field effect transistors to find out the overall better performing transistor.

 Graphene Structure-

       Graphene nanoribbons are single layered nanoribbons of graphite; the electronic model have been modelled by the necessary boundary conditions using the Schrodinger’s equation. [2] Like other semiconducting materials, the electrical properties of graphene will change as the device shrinks to the nanoscale. In this case concepts of quantum mechanics such as quantum confinement and edge effect are considered. [4] In these models, it is observed that the GNR with arm chair shape are either metallic or semiconducting depending on their widths. [2] These are also called (AGNR) arm chair graphene nanoribbon. On the other hand, the graphene nano ribbons with zig zag shaped edges are metallic or semi conducting in nature regardless of the widths. [2] These are called as (ZGNR) zig zag graphene nano ribbons. Graphene nanoribbons are currently manufactured using two major processes. It is either Peeling or Unzipping. Unzipping technique is a complicated procedure. Here the carbon nanotubes are suspended in concentrated sulphuric acid followed by KMNO4 solution for at least an hour at room temperature. [3] Following this procedure the nanoribbon is highly soluble in water and other solvents. We then see an opening of nanotubes along a line similar to the unzipping of graphite oxide. [3] In the figure below we can see the unzipping process in progress.

Fig 1. Graphene sheets

Graphene Properties and Methods of Fabrication

       Graphene has zero bandgap; this means it is a brilliant conductor of electricity. [1] Although graphene sheets are not very useful. Graphene has to be cut into narrow strips called ribbons. [1] The width must be less than 10nm comparable to De Broglie’s wavelength. [1] It is proven that the width is inversely proportional to the energy bandgap. [1] Dimer lines N are used to define the width. There are two varieties of graphene nano ribbon, one is the Schottky barrier type and the other is the metal oxide semiconductor type. [1] The SB type of FET has metallic contacts with a graphene channel. The MOSFET-type has doped regions with electrons and holes. [1] The region doped with electrons results in N-type and the regions doped with holes results in P-type graphene nano ribbon FET. It is observed that the MOSFET have faster switching speeds and are much better than the SB-type GNRFET in certain applications. [1]

  

Fig 2. Unzipping process of Graphene nanoribbons from Single walled Carbon nanotube.

        GNR are fabricated using many methods as discussed above like lithography, chemical processes and unzipping. [1] The lithography method produces graphene nanoribbons around 20nm wide. It is also noted that the edges are uneven. [1] Chemical synthesis can narrow down GNR to 2nm wide. However, the current fabrication techniques are not efficient enough to mass produce GNR circuits. [1] Researchers have found the mobility of electrons through approx. 2nm GNR to be 171-189cm2/V s. The mean free path (MFP) is equal to the length of the channel for GNR sizes less than 1.5nm. [1] Here a ballistic transport is observed. [1] It means that the mobility is extremely good. [1]

Fig3. Armchair and Zig Zag Graphene nanoribbons with their corresponding bandgap

       It is interesting to note that the armchair Carbon nano tube (A-CNT) when unzipped turns into a zig zag Graphene nanoribbon (Z-GNR) and vice versa. As we see in the image below, the bandgap for armchair GNR is not zero whereas in case of zigzag GNR the bandgap is zero. This suggests that the Z-GNR is metallic in nature and A-GNR is semi metallic. These unique properties make the graphene so appealing to the researchers, merely changing the chirality; the results obtained.

Graphene nanoribbon as a field-effect transistor-

         We read above about the graphene structure, types and its electrical properties. As far as the current technology goes, it is extremely difficult to fabricate GNRFETs that have conductance at room temperature. [7] The main challenge is it make a GNRFET with enough bandgap at room temperature that is approximately 1nm wide. Since it is not possible to make a physical GNRFET that small, we can simulate the electromagnetic properties of GNRFETs to learn more about their performance. [7]

Fig4- Graphene Field effect transistor.

           In the figure above we can see a single layer sheet of graphene that can be graphene nanoribbon with width W and Length L between two dielectric substrates, in this case SiO2. [7] The thickness being h and dielectric constant as ɛd. A gate voltage Vg is applied. [7]

Edge Roughness-

         In theory, GNRFETs with no Line Edge roughness exist. But in reality, GNRFET with perfectly smooth edges are extremely rare. [5] It is important to understand the effects of edges on the overall performance of the device. The effects of edge roughness on device performance has been studied at the material level. [5] How it affects the performance of the GNRFET is still to be found. [5] It is reported that the carrier transport is heavily depended on the edge shapes, this affects the properties of the transistor. [5]

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           Even with the technology today, the effects of edge roughness are visible in the simulations as reported in [6] Due to gap states induced in the bandgap region, the current during the off period is increased. This causes leakage current in the off stage. [6] This significantly reduces the on current. [6] In case of SB-type GNRFET, the band gap near the start of the channel improves the quantum transport. In case of a MOSFET, quantum transmission decreases because of the carrier transport with less than perfect edges. [6]

Fig5- The effect of edge roughness on I-V characteristics in case of Schottky barrier GNRFET and MOSFET GNRFET

Performance Analysis

        The circuit model was implemented in HSPICE. To make the results comparable, we implemented digital logic XOR gate and performed power and leakage current analysis and compared the results of GNRFET and FinFET. This circuit will be common to both the simulations.

         First, we implemented FinFET with parameters NFIN = 2, LCH = 12nm W = 6nm using the default setting provided from [8].

Fig 6. 2 bit XOR gate using CMOS

Input

Output

A

B

0

0

0

0

1

1

1

0

1

1

1

0

Table1- Logic of XOR gate

    We have the following results. For this analysis we are using the model provided on ptm.asu website.[8]

Fig7- The results for dynamic power and leakage current for FINFET

Here we can see that the dynamic power= 351.6097 from= 0 to= 9.0000n

leakage current= 6.7303u from= 6n to= 9n.

Fig8- The 2 input nodes ‘a’ and ‘b’

Fig9- The resulting output of the nodes ‘a’ and ‘b’ in XOR gate

        The last two images show that the XOR logic gate is working and that the performance analysis is successful. Next we will perform the SPICE simulation for GNRFET and compare the results.

Code for HSPICE

* cmos XOR

* model file

.lib ‘./PTM-MG/models’ PTM10hp

.temp 25

.global vdd vcc gnd

* Power Supply

Vvdd vdd 0 0.7v

Vvcc vcc 0 0

.param LM=6.0nm

.param wid=2*len

.param len=2*LM

XpI1 nA A vdd vdd pfet W=wid L=len nfin=2

XnI1 nA A vcc vcc nfet W=wid L=len nfin=2

XpI2 nB B vdd vdd pfet W=wid L=len nfin=2

XnI2 nB B vcc vcc nfet W=wid L=len nfin=2

* main circuit

Xp1 uj nA vdd vdd pfet W=wid L=len nfin=2

Xp2 out B uj uj pfet W=wid L=len nfin=2

Xp3 vj nB vdd vdd pfet W=wid L=len nfin=2

Xp4 out A vj vj pfet W=wid L=len nfin=2

Xn1 wj A out out nfet W=wid L=len nfin=2

Xn2 0 B wj wj nfet W=wid L=len nfin=2

Xn3 xj nA out out nfet W=wid L=len nfin=2

Xn4 0 nB xj xj nfet W=wid L=len nfin=2

.option post

* load capacitance

*c1 out 0 5pf

* dynamic input for 1 input variable

Vtest1 A 0 DC PULSE(0 Vdd 2ns 0.01ns 0.01ns 2ns 4ns)

Vtest2 B 0 DC PULSE(0 Vdd 1ns 0.01ns 0.01ns 1ns 2ns)

.tran .1ps 9ns

.print tran v(a) v(b) v(~a) v(~b) v(out) i(vmain)

.measure dynpower avg power from 0n to 9n

.measure tran leakage_current rms I(Vvdd) FROM=6n TO=9n

.print leakage_current

.end

         Now we perform the same for GNRFET, in this case we consider the following parameters. LCH = 32nm W = 6nm , N= 10, TOX = 0.95nm and Supply voltage  = 0.5V – 0.7 V. For these parameters we get the following results. For the GNRFET model we make use of the model provided on the nanohub.org website. [9]

Fig10- The results for dynamic power and leakage current for GNRFET

       Here we can see that the dynamic power= 5.8201e-007 from= 0e to= 9e-009 and the leakage current= 5e-007 from= 6e-009 to= 9e-009.

Fig 11- The input node ‘a’ and ‘b’ for GNRFET

Code HSPICE

* GNRFET XOR

* model file

*.lib ‘./PTM-MG/models’ PTM10hp

*For optimal accuracy, convergence, and runtime

.options POST

.options AUTOSTOP

.options INGOLD=2     DCON=1

.options GSHUNT=1e-12 RMIN=1e-15

.options ABSTOL=1e-5  ABSVDC=1e-4

.options RELTOL=1e-2  RELVDC=1e-2

.options NUMDGT=4     PIVOT=13

.param   TEMP=27

*Include relevant model files

.lib ‘./GNRFET_model/MOS-GNRFET/gnrfet.lib’ GNRFET

*Supplies and voltage params:

.param Supply=0.5

.param Vg=’Supply’

.param Vd=’Supply’

* Define power supply

Vdd     Drain     Gnd     Vd

Vss     Source    Gnd     0

Vgg  Gate   Gnd   Vg

Vsub    Sub       Gnd     0

*Inverter

XGNRpI1 nA A Vdd Vdd gnrfetpmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNRnI1 nB B Vss Vss gnrfetnmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR1 uj nA vdd vdd gnrfetnmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR2 out B uj uj gnrfetnmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR3 vj nB vdd vdd gnrfetnmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR4 out A vj vj gnrfetnmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR5 wj A out out gnrfetpmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR6 0 B wj wj gnrfetpmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR7 xj nA out out gnrfetpmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

XGNR8  0 nB xj xj gnrfetpmos nRib=6 n=10 L=32n Tox=0.95n sp=2n dop=0.001 p=0

.option post

* load capacitance

c1 out 0 5pf

* dynamic input for 1 input variable

Vtest1 A 0 DC PULSE(0 Supply 2ns 0.01ns 0.01ns 2ns 4ns)

Vtest2 B 0 DC PULSE(0 Supply 1ns 0.01ns 0.01ns 1ns 2ns)

.tran .1ps 9ns

.GRAPH  V(out)

.measure dynpower avg power from 0n to 9n

.measure tran leakage_current rms I(vdd) FROM=6n TO=9n

.end

Results-

        In the table below, the summarized results of the simulations are provided. Using the model files from ptm.asu and nanohub.org for FINFET and GNRFET respectively. The final results are as follows.

Leakage current and dynamic power

Performance of GNRFET and FINFET

GNRFET

FINFET

Dynamic Power

5.8201e-007 

351.6097

Leakage Current

5.0000e-007

6.7303

        In the above SPICE-simulations model of GNRFET and FINFET, we can see that the dynamic power in case of GNRFET is low. The results signify that graphene nanoribbons field effect transistor are better in terms of dynamic power. It is also noted that the leakage current in case of Fin field effect transistor is more. The leakage current in an ideal circuit is supposed to be as low as possible.

Conclusion-

        In conclusion, we discussed the Graphene structure. We also looked at graphene nanoribbon as a field effect transistor. We also looked as the fabrication techniques for graphene nanoribbons. The problems arising from the current fabrication techniques. We also looked at the defects that are caused from fabrication and otherwise. From the simulations performed, it is evident that GNRFET is more efficient than FINFET. However, it is also important to understand that the current technology is not sufficient to mass produce graphene nanoribbons. It is also expensive to produce graphene nanoribbons from graphene sheets. For now, FINFET is a semiconductor material for choice. For the future, it is safe to say that graphene will take over as a semiconducting material due to the advancement in fabrication technology.

Figure Table and references

 

References

Ying-Yu Chen1, A. R. (2013). A SPICE-Compatible Model of Graphene Nano-Ribbon Field-Effect Transistors Enabling Circuit-Level Delay and Power Analysis Under Process Variation. EDAA.

Young-Woo Son, 1. M. (2006). Energy Gaps in Graphene Nanoribbons. The American Physical Society.

Dmitry V. Kosynkin, A. L. (2009). Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons. Nature.

Jingwei Bai, Y. H. ( 23 July 2010). Fabrication and electrical properties of graphene nanoribbons. Elsevier.

Youngki Yoon and Jing Guo, Y. Y. (N/A). Effect of Edge Roughness in Graphene Nanoribbon Transistors .

Youngki Yoon, Seokmin Hong, Giuseppe Iannaccone, and Jing Guo, . (2008). Performance Comparison of Graphene Nanoribbon Schottky Barrier and MOS FETs. IEEE Xplore.

Yangbing Wu1, D. G. (n.d.). Modeling of Graphene Nanoribbon FET and Analysis of Its Electrical Properties . IEEE Xplore.

PTM. (n.d.). http://ptm.asu.edu/.

By Ying-Yu Chen1, M. G. (2013). https://nanohub.org/resources/17074. NanoHUB .