Simulation of Graphene Nanoribbon Field-Effect Transistors
Summary (1 min read)
I. INTRODUCTION
- I N THE last decade, carbon nanotubes (CNT) have attracted extraordinary interest for their extremely interesting physical and electrical properties [1] and their potential as an alternative to silicon as channel material for transistors beyond complimentary metal-oxide-semiconductor technology [2] .
- Two-dimensional graphene is a zero-gap material, which makes it not suitable for transistor applications.
- Experiments on graphene-based devices [5] and graphene nanoribbon field-effect transistors [6] (GNR-FETs) have appeared only very recently and demonstrate limited capability to modulate the conductance of a graphene channel at room temperature.
- For short-channel transistors, only a 3-D simulation is suitable for an accurate evaluation of the electrostatics and of intraband and interband tunneling.
II. PHYSICAL MODEL AND RESULTS
- The authors approach is based on the self-consistent solution of the 3-D Poisson and Schrödinger equations with open boundary conditions [12] , which is able to take into account fully ballistic transport, in order to outline the higher limits of device performance, as well as elastic scattering due to line edge roughness.
- The considered double-gate GNR-FETs have the structure depicted in the inset of Fig. 1 .
- If only elastic band-to-band tunneling can occur (as assumed in their simulation), the excess of holes in the channel lowers the channel potential, increasing the OFF current and S, as shown in Fig. 1 : the lower the energy gap and the higher the V DS , the higher the HIBL effect.
- As can be seen in Fig. 2 (a), the three devices behave as transistors but show very different behavior, even if they differ by only one carbon atom along the channel width.
- Rough edge scattering strongly affects the ON current and the transconductance suppressing it by about 30% with respect to fully ballistic transistors.
III. CONCLUSION
- A simulation study of GNR-FETs has been performed by means of the self-consistent solution of the 3-D Poisson and Schrödinger equations with open boundary conditions within the NEGF formalism.
- Edge states have been considered at the lateral ends of the nanoribbon using the model proposed in [7] .
- GNR-FETs exhibit performance similar to CNT-FETs, also showing significant band-to-band tunneling when small gap devices are considered and large V DS is applied.
- GNR-FETs are more robust than CNT-FETs with respect to variability of the channel chirality, and edge roughness seems to play a useful averaging effect.
- Finally, the authors suggest that periodic strain could in principle represent an alternative to etching for inducing an energy gap in graphene.
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Cites background from "Simulation of Graphene Nanoribbon F..."
...Page 23 of 57 Yet large enough ION/IOFF will require the fabrication of very narrow ribbons with atomically precise edges.[229] Transmission electron microscopy (TEM) has recently proven that unsupported zig-zag and armchair ribbon edges were stable in ambient conditions in vacuum....
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References
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"Simulation of Graphene Nanoribbon F..." refers background in this paper
...Electrons in graphene behave as massless fermions [4] and ex hibit high mobility up to10(4) cm(2)/Vs at room temperature [3]....
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...[3] demonstrated the possibility of fabr icating stable single atomic layer graphene sheets, with remarkable electrical properties, that have brought new ex citation to the field of carbon electronics....
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"Simulation of Graphene Nanoribbon F..." refers background in this paper
...Energy gap can however be induced by means of lateral confinement [4], realized for example by lithography defini-...
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4,471 citations
"Simulation of Graphene Nanoribbon F..." refers background or methods in this paper
...Edge states have been considered at the lateral ends of the nanoribbon using the model proposed in [7]....
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...Recent theoretical works have shown that graphene nanoribbons have an energy gap that has an oscillating behavior as a function of width, with average roughly proportional to the inverse width, and that edge states play a very important role in inhibiting the existence of fully metallic nanoribbons [7]....
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...The Hamiltonian is taken from [7], in which edge states at the nanoribbon lateral ends have been considered....
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Frequently Asked Questions (14)
Q2. What is the effect of rough edge scattering on the ON current?
Rough edge scattering strongly affects the ON current and the transconductance suppressing it by about 30% with respect to fully ballistic transistors.
Q3. What is the effect of periodic strain on the GNR?
GNR-FETs are more robust than CNT-FETs with respect to variability of the channel chirality, and edge roughness seems to play a useful averaging effect.
Q4. What is the simplest approach to the GNRFET?
Their approach is based on the self-consistent solution of the 3-D Poisson and Schrödinger equations with open boundary conditions [12], which is able to take into account fully ballistic transport, in order to outline the higher limits of device performance, as well as elastic scattering due to line edge roughness.
Q5. How much S is pronounced in the GNR-FET?
For VDS = 0.5 V, the authors observe a pronounced degradation of S, with S = 191 mV/dec for the GNR-FET and almost 250 mV/dec for the CNT-FET.
Q6. How do the authors determine the energy gap in a periodic strain pattern?
In order to evaluate whether a periodic strain pattern can allow to engineer the GNR gap, the authors have computed the energy gap in a (24,0) GNR (W = 5.86 nm), multiplying the overlap integral of the element of the Hamiltonian in correspondence to the couple of atoms in the middle of the GNR by a “strain factor” σ : σ is larger than 1 for compressive strain, andsmaller than 1 for tensile strain.
Q7. What is the effect of chirality on the transfer of GNRs?
The authors also found that electrostatic periodic potential modulation with a peak-to-peak value of a few volts is not sufficient to induce the required gap of a few hundred millivolts.
Q8. What is the performance of the GNR-FETs?
GNR-FETs exhibit performance similar to CNT-FETs, also showing significant band-to-band tunneling when small gap devices are considered and large VDS is applied.
Q9. What is the gm of the GNR-FET?
In strong inversion, the transconductance gm at VDS = 0.1 V is 3600 and 6100 µS/µm for the GNR-FET and the CNTFET, respectively, whereas at VDS = 0.5 V, the authors obtain gm = 4800 µS/µm for the GNR and a gm = 8760 µS/µm for the CNT.
Q10. How do the authors determine the effect of chirality on the transfer characteristics of a GNR?
The authors have considered the impact of line edge roughness in a (16,0) GNR-FET device, by randomly decoupling carbon atoms on the lateral boundaries of the GNR.
Q11. What is the problem with the gap?
The problem is that the gap is still largely dependent on the chirality: the (16,0) GNR (W = 1.87 nm) has the largest gap (Egap = 0.71 eV), whereas the (14,0) (W = 1.62 nm) has the smallest gap (Egap = 0.13 eV).
Q12. What is the effect of the rough edge scattering on the transfer characteristics of a GNR?
As a consequence, the (16,0) device shows the best gate control over the channel potential, whereas the (14,0) shows the worst: the energy gap is so small that elastic band-to-band tunneling occurs at the source and current is dominated by GIDL.
Q13. What is the difference between the two GNRs?
From the aforementioned simulations, it is clear that lateral confinement way beyond state-of-the-art etching capabilities would be needed to obtain adequate Egap.
Q14. What is the effect of chirality on the transfer of a GNR?
It is known that a variability of the chirality of fabricated CNTs yields metallic nanotubes useless for transistor applications.