A Proposed Confinement Modulated Gap Nanowire Transistor Based

Apr 13, 2012 - Nolan , M.; O'Callaghan , S.; Fagas , G.; Greer , J. C. Silicon nanowire band gap modification Nano Lett. 2007, 7, 34– 38. [ACS Full ...
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A Proposed Confinement Modulated Gap Nanowire Transistor Based on a Metal (Tin) Lida Ansari,* Giorgos Fagas, Jean-Pierre Colinge, and James C. Greer Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork, Ireland S Supporting Information *

ABSTRACT: Energy bandgaps are observed to increase with decreasing diameter due to quantum confinement in quasione-dimensional semiconductor nanostructures or nanowires. A similar effect is observed in semimetal nanowires for sufficiently small wire diameters: A bandgap is induced, and the semimetal nanowire becomes a semiconductor. We demonstrate that on the length scale on which the semimetal−semiconductor transition occurs, this enables the use of bandgap engineering to form a field-effect transistor near atomic dimensions and eliminates the need for doping in the transistor’s source, channel, or drain. By removing the requirement to supply free carriers by introducing dopant impurities, quantum confinement allows for a materials engineering to overcome the primary obstacle to fabricating sub-5 nm transistors, enabling aggressive scaling to near atomic limits. KEYWORDS: Ab initio calculations, electronic structure, electron transport, gray tin, nanowire transistor, quantum confinement

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to be narrow to permit full depletion of carriers; this constraint is completely consistent with the goal of continued transistor miniaturization.11 Nonetheless, for channels with sub-5 nm gate lengths, the number of semiconductor atoms in the channel and source/drain regions for semiconductor nanowires is typically on the order of a few hundred to thousand, and introduction of even a few dopant atoms introduces extremely high doping levels. Issues of dopant segregation to the nanowire surface, increased random dopant fluctuations,12 and dopant levels decoupling from the energy bands due to confinement resulting in suppressed dopant activation8,12 immediately arise. For these reasons, it is highly desirable to develop a transistor technology that is dopant free and that is compatible with current silicon-based nanofabrication technology. Column IV of the periodic table contains the elements carbon, silicon, germanium, tin, and lead. Crystalline C, Si, and Ge have a diamond structure with strong covalent bonds and are insulators or semiconductors. The stable phase of Pb is metallic and has a face centered cubic (fcc) crystal structure. Crystalline Sn bonds are borderline between covalent and metallic. Below a temperature of 13.2 °C, Sn crystals have a diamond cubic structure with a zero bandgap (gray tin or α-tin) as shown in Figure 1; see also refs 13 and 14. When heated, tin undergoes a phase transition at 13.2 °C and becomes metallic white tin.13 However, growth of perfect epitaxial layers of gray tin on CdTe and InSb substrates at room temperature has been

rowing computing and communication requirements continue to motivate the miniaturization of electronic devices. Fundamental physical constraints, materials limitations, and exponentially rising manufacturing costs have, however, rendered traditional scaling increasingly challenging, and worldwide there is an intensive search for new materials and novel device solutions. By engineering a material’s shape in nanometer lengths, it is possible to tailor bandgap energies1,2 and to change, for example, an indirect gap semiconductor to a direct bandgap.3,4 Exciting progress has been achieved toward the fabrication of electronic devices at scales approaching fundamental limits set by atom sizes. Ultrathin metal-oxide semiconductor field-effect transistors (MOSFETs) with multiple gates5 and gate all-around silicon nanowire devices with a mere 3 nm diameter6 have demonstrated electrostatic control over the channel, thus promising an avenue for continued miniaturization and opening the possibility to continue to follow Moore’s ‘law’. Recently, the introduction of high-doping concentration of a single carrier type in the source, channel, and drain regions of nanowire-like structures led to the demonstration of junctionless nanowire transistors (JNTs).7 This design offers one of the few solutions to engineer out difficulties related to aggressive scaling of the traditional (bulk or nanoengineered) MOSFETs, and the physical operation of these transistors with a gate length down to 3 nm has been studied.8 In JNTs, variability issues due to the formation of p−n junctions are avoided,9 and short-channel effects are strongly suppressed owing to the absence of depletion regions associated with the junctions and related space charges in the channel region.10 The JNT design imposes a constraint on the cross-section of the channel region © 2012 American Chemical Society

Received: November 19, 2011 Revised: April 13, 2012 Published: April 13, 2012 2222

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energy bands. This creates metallic source and drain regions and a semiconducting channel. For the lengths scales we are interested in, we demonstrate this is readily achievable using semimetal nanowires. First-principles approaches based on density functional theory (DFT) provide an accurate description of the geometry and electronic structure of nanowires, and as a result, a clear understanding of the properties of materials as their dimensionality is changed from three- to one-dimensional through nanofabrication is obtained. For technical details of the DFT calculations, we refer the reader to the Supporting Information, Section a. The electronic structure of SnNWs derived from the diamond cubic crystal structure is studied with the axis of the nanowire oriented along the ⟨100⟩, ⟨110⟩, or ⟨111⟩ crystallographic directions and for varying nanowire diameters. Surface dangling bonds are bonded to hydrogen hence passivating surface states.26 Cross-sectional views of the smallest nanowires investigated are shown in Figure 2a. Note that approximate exchange−correlation functions typically used within DFT method tend to underestimate bandgaps, suggesting that the nanowire diameters we discuss are a lower limit to achieving a desired bandgap. However, the bandgap underestimation by DFT is not as pronounced in this specific case, with our calculations agreeing with GW predictions for the density of states at the Fermi level,24 consistent with angular resolved photoemission spectra.17 Atomic positions are allowed to relax within the firstprinciple calculations leading to energetically stable structures, and at these stable geometries, the electronic band structures for the SnNWs are calculated. In contrast to the characteristic semimetal band structure of bulk tin as shown in Figure 1, in the nanowires, a bandgap emerges that increases with decreasing diameter. Various sub-bands are illustrated in Figure 2b-i to b-vi along the first Brillion zone of one-dimensional structure. Band structures are depicted for the ⟨100⟩ and ⟨110⟩ orientations and for three different diameters. The formation of the bandgap is attributable to the well-known phenomena of quantum confinement. The electronic structure corresponding to the ⟨100⟩ orientation indicates the formation of a direct bandgap at all diameters considered. However, as shown in Figure 2b-iv to b-vi for the ⟨110⟩ orientation, the quantum confinement effect induces an indirect bandgap for relatively large diameters, and the bandgap becomes direct in this case as the diameter approaches 1.15 nm. The magnitude of the bandgap observed is smaller in the ⟨110⟩ nanowires than in those with ⟨100⟩ orientation. More importantly, the ⟨110⟩oriented Sn nanowire remains semimetal for diameters larger than 3.9 nm, in which case, it displays similar characteristics as bulk α-tin. The variation of the bandgap energy in a SnNW is shown in Figure 3 as a function of the nanowire diameter. The smaller the diameter of a wire, the more of a relative increase in the bandgap is seen. In addition to the diameter dependence, the Sn bandgap depends on the crystal orientation of the nanowire. As illustrated in Figure 3, larger bandgap energies are found in nanowires with the ⟨100⟩ orientation, followed by ⟨111⟩ and then by ⟨110⟩. The bandgap energy vanishes for a SnNW with ⟨110⟩ orientation when the diameter is greater than approximately 4 nm. The CMGT utilizes the electronic structure properties of the nanowires described in the previous section. The CMGT consists of a SnNW with varying cross section. In the central region, the cross section is small enough for the tin to become

Figure 1. The semimetallic band structure of bulk Sn with diamond crystal structure is shown along the various symmetry lines of the first Brillion zone (the Fermi level is taken at zero energy) calculated from density functional theory. Note that although metastable α-tin bulk phase is a semimetal, there is a vanishing density of states at the Fermi level.

reported,15,16 and processing is possible without a phase transition up to 115 °C.17 A high stability of gray tin has been achieved when encapsulated in nanotubes.18 Carbon, germanium, and tin are all compatible with silicon fabrication technologies and are commonly introduced within nanoelectronic processing to create mechanical strain in silicon devices.19,20 Antimony, arsenic, bismuth, and graphite together with α-tin form the semimetal group of elements. A semimetal to semiconductor transition has been observed in bismuth and antimony nanowires, and this transition can be identified with the formation of an energy bandgap due to quantum confinement.21−23 Due to the fact that there is a vanishing density of states at the Fermi level in α-tin, the material, although a semimetal, is already akin to a semiconductor in the bulk phase as demonstrated experimentally17 and by the GW approximation.24 Hence the material is an ideal candidate for manipulating the semimetal to semiconductor transition in nanowires, as we will demonstrate. In this study, we apply first-principle electronic structure methods25 to determine the electronic structure and electrical properties of tin nanowires (SnNWs) with the diamond crystal structure. The effect of nanowire orientation and diameter on the electronic structure is determined. It is shown that tin, consistent with other semimetals, exhibits a transition from semimetal to semiconductor as the diameter of the nanowire is decreased. The bandgap energy Eg can be larger than 2 eV at diameters below 2 nm. Based on the different electronic properties of Sn in both the bulk and the nanowire forms, a new candidate for future “end-of-the-roadmap” transistors is introduced that relies only on the use of bandgap engineering via nanofabrication and relies solely on the properties of a single material, tin, when patterned on the nanoscale. The resulting proposal for a transistor design, the confinement modulated gap transistor (CMGT), follows by forming the source, channel, and drain regions using atoms of a single element, unlike in conventional MOSFETs which require dopant atoms to define different device regions. The electronic and electrical properties of the channel are engineered by varying the nanowire cross-section to achieve modulation of the 2223

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Figure 2. (a) Cross sections of Sn nanowires grown along the (a-i) ⟨100⟩, (a-ii) ⟨110⟩, and (a-iii) ⟨111⟩ crystallographic directions. (b) Energy band diagrams for SnNWs oriented along the ((b-i) to (b-iii)) ⟨100⟩ and ((b-iv) to (b-vi)) ⟨110⟩ crystallographic directions; from top to bottom the nanowire diameter decreases as indicated. The opening of a confinement-induced energy gap is observed. The horizontal dashed line shows the position of the Fermi level. The effective masses at the Γ-point for the smallest SnNWs in the various orientations were calculated by taking the second derivative of energy bands with respect to the momentum vector (for more details see the Supporting Information, Section f).

semiconducting and defines a channel region. The cross section is then increased on either side of the channel to form a metallic source and drain. The channel region is surrounded by a gate stack, as in a gate all-around MOSFET (Figure 4). Details are described in the Supporting Information, Section b. In a regular semiconductor transistor, source and drain require

heavy doping to supply large quantities of carriers (electrons in the case of an n-channel device). In the CMGT, source and drain do not require doping since they consist of semimetallic tin. On the other hand, the channel situated between source and drain exhibits a bandgap determined by the nanowire diameter and orientation. A similar concept for two-dimen2224

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Electron transport is described within the Landauer formalism and is based on the assumption that transport along the channel region is coherent,29 i.e., inelastic scattering is negligible within the short length of the channel whose resistance is dominated by the interface to the larger cross sectional areas of the source and drain. The electronic transmission and, hence, the current are calculated from the first-principles Hamiltonian in the DFT implementation with the method of the nonequilibrium Green’s function (NEGF) [ref 30 see also the Supporting Information, Sections c and d]. The output characteristic of the drain current versus the drain-to-source voltage (ID versus VDS) of the CMGT is plotted in Figure 5a at various gate voltages. As seen in the graph, the

Figure 3. Bandgap energy as a function of nanowire diameter for wires grown along different crystallographic directions.

Figure 4. Atomic scale illustration of the structure which has been used to simulate the confinement modulated gap transistor. All surface dangling bonds are saturated by hydrogen. The ring around the channel indicates an isopotential surface from the application of gate bias.

sional confinement has been suggested for graphene nanoribbon FETs.27 However, the smaller bandgap of graphene nanoribbons, the smaller length scales required to produce a large gap in grapheme as well as interband coupling at higher bias voltages leads to increased off-currents potentially diminishing the usefulness of these transistors as switches. There are also additional challenges related to the planar geometry and surface termination of the edges.28 In this work we perform state-of-the-art transport simulations of a ⟨110⟩-oriented SnNW channel with 1 nm in diameter and with a gate length Lg = 2.3 nm. It should be noted that the physical channel length in the off-state is approximately 4.1 nm as estimated from the local density of states (see Supporting Information). This is in contrast to conventional MOSFETs in which the depletion region at the p−n junctions shortens the effective gate length. The oxide isolating the channel from the gate electrode is modeled as a continuum characterized by a dielectric constant of κHfO2 = 25 corresponding to, for example, 1 nm hafnium oxide.

Figure 5. (a) Output characteristic of confinement modulated gap transistor. (b) ID−VGS characteristic of confinement modulated gap transistor in log scale for drain voltages of 50 mV and 0.4 V. The inset shows the curves in linear scale. A work function of zero volts is implied for the gate electrode, but a simple recalibration of the gate voltage will reveal device operation for different gate metal choices. The subthreshold slope is estimated to be 72.6 mV/dec at room temperature.

CMGT works as a conventional transistor in terms of its response to the gate or bias voltages. The device is strongly turned ‘off’ at zero gate voltage, and applying positive gate voltages turns the switch ‘on’. We note that the source−drain tunneling current is suppressed due to the larger physical channel length compared to conventional MOSFETs. The current−voltage characteristics in Figure 5a demonstrate that bandgap engineering based on different cross sections for the source, drain, and channel region can be used to fabricate a dopant-free, monomaterial transistor. 2225

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(2) Ma, D. D. D.; Lee, C. S; Au, F. C. K.; Tong, S. Y.; Lee, S. T. Small diameter silicon nanowire surfaces. Science 2003, 299, 1874−1877. (3) Sun, X.; Liu, J.; Kimerling, L. C.; Jurgen, M. Room-temperature direct bandgap electroluminesence from Ge-on-Si light-emitting diodes. Opt. Lett. 2009, 34, 1198−1200. (4) De Boer, W. D. A. M.; Timmerman, D.; Dohnalova, K.; Yassievich, I. N.; Zhang, H.; Buma, W. J.; Gregorkiewicz, T. Red spectral shift and enhanced quantum efficiency in phonon-free photoluminescence from silicon nanocrystals. Nat. Nanotechnol. 2010, 5, 878−884. (5) Colinge, J. P. Multiple-gate SOI MOSFETs. Solid State Electron. 2004, 48, 897−905. (6) Singh, N.; Buddharaju, K. D.; Manhas, S. K.; Agarwal, A.; Rustagi, S. C.; Lo, G. Q.; Balasubramanian, N.; Kwong, D. L. SiGe nanowire devices by top-down technology and their applications. IEEE Trans. Electron Devices 2008, 55, 3107−3118. (7) Colinge, J. P.; et al. Nanowire transistors without junctions. Nat. Nanotechnol. 2010, 5, 225−229. (8) Ansari, L.; Feldman, B.; Fagas, F.; Colinge, J. P.; Greer, J. C. Simulation of junctionless Si nanowire transistors with 3 nm gate length. Appl. Phys. Lett. 2010, 97, 062105. (9) Dehdashti Akhavan, N.; Ferain, I.; Razavi, P.; Yu, R.; Colinge, J. P. Random dopant variation in junctionless nanowire transistors. In Proceedings of 2011 IEEE International SOI Conference, Tempe, Arizona, October 3−6, 2011; IEEE: Washington, D.C.. (10) Lee, C. W. et al. Short channel junctionless nanowire transistors. In Proceedings of 2010 International Conference on Solid State Devices and Materials (SSDM 2010), The University of Tokyo, Tokyo, Japan, September 22-24, 2010; SSDM: Tokyo, Japan, 2010; pp 1044−1045. (11) Ferain, I.; Colinge, C. A.; Colinge, J. P. Multigate transistors. Nature 2011, 479, 2−8. (12) Rurali, R.; Aradi, B.; Frauenheim, T.; Gali, A. Donor levels in Si nanowires determined by hybrid-functional calculations. Phys. Rev. B 2009, 79, 115303. (13) Paul, W. Band structure of the intermetallic semiconductors from pressure experiments. J. Appl. Phys. 1961, 32, 2082. (14) Cheong, B. H.; Chang, K. J. First-principles study of the structural properties of Sn under pressure. Phys. Rev. B 1991, 44, 4103−4108. (15) Farrow, R. F. C.; et al. The Growth of metastable, heteroepitaxial films of alpha-Sn by metal beam epitaxy. J. Cryst. Growth 1981, 54, 507−518. (16) John, P.; Miller, T.; Chiang, T. C. Core-level photoemission studies of the a-Sn/InSb(100) heterostructure system. Phys. Rev. B 1989, 39, 3223−3229. (17) Höchst, H.; Hernández-Calderón, I. Angular resolved photoemission of InSb(001) and heteroepitaxial films of α-Sn(001). Surf. Sci. 1983, 126, 25−31. (18) Wang, B.; Ouyang, G.; Yang, Y. H.; Yang, G. W. Anomalous thermal stability of cubic tin confined in a nanotube. Appl. Phys. Lett. 2007, 90, 121905. (19) Wang, G. H. et al. Realization of silicon-germanium-tin (SiGeSn) source/drain stressors by Sn implant and solid phase epitaxy for strain engineering in SiGe channel P-MOSFETs. In 2008 International Symposium on VLSI Technology, Systems and Applications; IEEE: Washington, D.C., 2008; pp 128−129. (20) Koh, S. M.; et al. N-channel MOSFETs with embedded siliconcarbon source/srain stressors formed using cluster-carbon implant and excimer-laser-induced solid phase epitaxy. IEEE Electron Device Lett. 2008, 29, 1315−1318. (21) Heremans, J.; et al. Bismuth nanowire arrays: synthesis and galvanomagnetic properties. Phys. Rev. B 2000, 61, 2921−2930. (22) Zhang, Z.; Sun, X.; Dresselhaus, M. S.; Ying, J. Y.; Heremans, J. Electronic transport properties of single-crystal bismuth nanowire arrays. Phys. Rev. B 2000, 61, 4850−4861. (23) Heremans, J.; Thrush, C. M.; Lin, Y. M.; Cronin, S. B.; Dresselhaus, M. S. Transport properties of antimony nanowires. Phys. Rev. B 2001, 63, 085406.

A key electrical parameter of a transistor to evaluate its performance is the subthreshold slope (SS) [see the Supporting Information, Section e]. The dependence of the drain−source current on gate voltage for the proposed CMGT is plotted in semilog scale in Figure 5b. The subthreshold slope extracted from this graph is 72.6 mV/dec at room temperature comparable to values commonly found in multigate silicon transistors.31 As for other comparisons, this ideal value does not reflect any degradation which may arise from possible dielectric−channel interface states. In summary, our results confirm a semimetal-to-semiconductor transition in SnNWs arising from quantum confinement in nanowires. Below a threshold diameter that depends on the wire orientation, a bandgap is induced and increases in value with decreasing diameter. The semiconducting property of SnNWs implies that Sn is yet another (and likely the last) group IV element for which transistor channels are possible. Indeed, the design of a dopant-free, monomaterial field effect transistor is demonstrated. The drain−source current voltage characteristic of the confinement modulated gap transistor shows that the subthreshold slope and the on/off ratio are 72.6 mV/dec and up to 104, respectively. That such figures can be achieved at essentially molecular length scales in a conceivably manufacturable design bodes well for continued nanoelectronic miniaturization and compares favorably to what can be achieved in Si nanowire FETs with similar dimensions7 but without the need to impose stringent requirements on doping of nanoscale materials. The influence of manufacturability issues, such as channel length variations and surface roughness, is the same as in other nanoscale FET proposals. Critically, the CMGT devices do not lead to impurity scattering decreasing mobility for high doping concentrations nor to suffering from dopant fluctuation and activation problems that are deemed insurmountable on the few nanometer length scale.

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ASSOCIATED CONTENT

S Supporting Information *

More details about electronic structure calculations, Gate all around geometry, local density of states along the channel axis, transmission and conductance characteristics of the channel, together with some of the device performance parameters, and the effective electron and hole masses are provided in the Supporting Information section. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was funded by Science Foundation Ireland under the Principal Investigator grant no. 06/IN.1/I857. We thank the SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support.

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REFERENCES

(1) Guichard, A. R.; Barsic, D. N.; Sharma, S.; Kamins, T. I.; Brongersma, M. L. Tunable light emission from quantum-confined excitons in TiSi2-catalyzed silicon nanowires. Nano Lett. 2006, 6, 2140−2144. 2226

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(24) Rhohlfing, M.; Krüger, P.; Pollmann, J. Role of semicore d electrons in quasiparticle band-structure calculations. Phys. Rev. B 1998, 57, 6485−6492. (25) DFT OpenMX code; http://www.openmx-square.org/ (26) Nolan, M.; O’Callaghan, S.; Fagas, G.; Greer, J. C. Silicon nanowire band gap modification. Nano Lett. 2007, 7, 34−38. (27) Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Chemically derived, ultrasmooth graphene nanoribbon semiconductors. Science 2008, 29, 1229−1232. (28) Son, Y. W.; Cohen, M. L.; Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803. (29) Datta, S. Electronic Conduction in Mesoscopic Systems; Cambridge University Press: Cambridge, U.K., 1996. (30) Ozaki, T.; Nishio, K.; Kino, H. Efficient implementation of the non-equilibrium Green function method for electronic transport calculations. Phys. Rev. B 2010, 81, 035116. (31) Colinge, J. P. FinFETs and Other Multi-Gate Transistors; Springer: New York, 2007.

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