Advanced nanoelectronics

Advanced NANOELECTRONICS Nano and Energy Series Editor: Sohail Anwar PUBLISHED TITLES Advanced Nanoelectronics Razali Ismail, Mohammad Taghi Ahmadi, and Sohail Anwar Computational Nanotechnology: Modeling and Applications with MATLAB® Sarhan M Musa Nanotechnology: Business Applications and Commercialization Sherron Sparks Nanotechnology: Ethical and Social Implications Ahmed S Khan Advanced NANOELECTRONICS Edited by Razali Ismail Mohammad Taghi Ahmadi Sohail Anwar Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business MATLAB® and Simulink® are trademarks of The MathWorks, Inc and are used with permission The MathWorks does not warrant the accuracy of the text or exercises in this book This book’s use or discussion of MATLAB® and Simulink® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® and Simulink® software CRC Press Taylor & 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http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface vii Acknowledgments xi Editors xiii Contributors xv Chapter Fundamentals of Quantum Nanoelectronics .1 Jeffrey Frank Webb and Mohammad Taghi Ahmadi Chapter Carbon-Based Materials Concepts and Basic Physics 49 Mohammad Taghi Ahmadi, Jeffrey Frank Webb, Razali Ismail, and Moones Rahmandoust Chapter Carbon Nanotube Field Effect Transistor Model 83 Mohammad Taghi Ahmadi and Razali Ismail Chapter Carbon Nanotube Circuit Analysis and Simulation 119 Desmond C Y Chek and Razali Ismail Chapter Graphene Nanoribbon Field Effect Transistors 149 Noraliah Aziziah Amin, Mohammad Taghi Ahmadi, and Razali Ismail Chapter Carrier Transport, Current–Voltage Characteristics of BGN 163 Seyed Mahdi Mousavi, Meisam Rahmani, Hatef Sadeghi, Mohammad Taghi Ahmadi, and Razali Ismail Chapter Bilayer Graphene Nanoribbon Transport Model 187 Hatef Sadeghi, Seyed Mahdi Mousavi, Meisam Rahmani, Mohammad Taghi Ahmadi, and Razali Ismail Chapter Trilayer Graphene Nanoribbon Field Effect Transistor Modeling 207 Meisam Rahmani, Hatef Sadeghi, Seyed Mahdi Mousavi, Mohammad Taghi Ahmadi, and Razali Ismail v vi Contents Chapter Graphene Nanoribbon Transistor Model: Additional Concepts 239 Mahdiar Ghadiry, Mahdieh Nadi, and Asrulnizam Abd Manaf Chapter 10 Silicon Nanowire Field Effect Transistor Modeling 257 Amir Hossein Fallahpour and Mohammad Taghi Ahmadi Chapter 11 Silicon Nanowires/Nanoneedles: Advanced Fabrication Methods 287 Habib Hamidinezhad and Yussof Wahab Chapter 12 Top-Down Fabrication of ZnO NWFETs 331 Suhana Mohamed Sultan, Peter Ashburn, and Harold M H Chong Chapter 13 Quantum Mechanical Effects in Nanometer Scale Strained Si/‌Si1−x Gex MOSFETs 357 Kang Eng Siew and Razali Ismail Chapter 14 Nanoelectronics Research and Commercialization in the United States 379 Sohail Anwar Appendix��������������������������������������������������������������������������������������������������������������� 389 Glossary����������������������������������������������������������������������������������������������������������������407 Index 415 Preface Nanoelectronics refers to the technology of electronic devices, especially transistors, whose dimensions range from atoms to 100 nm Such transistors are so small that the interatomic interactions and quantum mechanical properties need to be studied extensively This book provides research information regarding advanced nanoelectronics concepts, focusing primarily on the aspects of modeling and simulation It develops and applies numerical algorithms to investigate nanodevices While theories based on classical physics have been very successful in helping experimentalists design microelectronic devices, new approaches based on quantum mechanics are required to accurately model nanoscale transistors and to predict their characteristics even before they are fabricated The book is organized into 14 chapters Chapter  introduces the basic ideas related to quantum theory required for understanding nanoscale structures found in n­ anoelectronics The key principles of quantum theory are briefly explained, ­followed by an explanation of the basic quantum theory of electrons relevant to nanoelectronics A brief outline of standard solid state physics is presented and how this has to be extended to account for the electronic properties of nanoscale s­ ystems is also shown At the end of the chapter, these fundamental theoretical ideas are applied to nanostructures such as graphenes, carbon nanotubes, quantum wells, quantum dots, and quantum wires Chapter highlights some of the key concepts required to understand nanotransistors The quantum theory of solids and the Fermi–Dirac distribution function are introduced, followed by the application of these concepts to three-dimensional ­materials in the nondegenerate and degenerate limits Quasi two-dimensional and one-dimensional devices are then considered These concepts are applied to the ­carbon nanotube (CNT) A comprehensive study of the CNT is presented Chapter describes the carbon nanotube field effect transistor (CNTFET) model in detail The key concepts relevant to quantum electronic and semiconductor physics, which were presented in Chapters and 2, provide the background for this chapter The types of CNTFET are first discussed, followed by the CNTFET design Next, the CNTFET models used are reviewed The chapter goes on to describe how CNTFET models are developed Carrier statistics are formulated and results presented Circuit theory in electronic textbooks relies heavily on Ohm’s law Ohm’s law enjoyed its superiority in the performance assessment of all conducting materials until it was discovered that the carrier velocity cannot increase indefinitely with the increase of electric field, and eventually saturates to a value that leads to current saturation Chapter discusses the application of nonohmic law to CNTFET circuits The ultimate goal of this chapter is to verify the application of nonohmic law to the CNTFET circuit by comparing the theoretical results with the Hspice simulation results This chapter concludes with a discussion of two quality measures, which indeed examine the overall performance of CNTFET in logic gates, comparing it with that of the logic gates made of state-of-the-art metal–oxide–semiconductor field effect transistor (MOSFET) vii viii Preface Chapters through focus on graphene This unzipped form of CNT is the recently discovered allotrope of carbon that has gained a tremendous amount of ­scientific and technological interest Prototype structures showing good performance for transistors, interconnects, electromechanical switches, infrared emitters, and biosensors have been demonstrated The graphene nanoribbon (GNR) MOSFET (GNRFET) has been developed and used as a possible replacement to overcome the CNT chirality challenge In recent years, single-layer graphene (SLG) has attracted a great deal of interest Chapter reviews and discusses the theoretical physics related to GNR, SLG, and GNRFET Chapter describes bilayer graphene nanoribbon (BGN) The carrier density and temperature effects on mobility of carriers in BGNs are explored Further, variation of gate voltage during the device operation and its effect on mobility are discussed, and a numerical mobility model is presented based on channel conductance Chapter continues with the discussion on BGN models The BGN carrier statistics and ballistic conductance in the nondegenerate and the degenerate limits are presented The proposed model shows good agreement with experimental data Since a BGN field effect transistor (BGNFET) can be shaped by using graphene bilayers with an external controllable voltage that is perpendicular to the layers, its application as a future field effect transistor channel is expected to be widespread Chapter presents trilayer graphene nanoribbon (TGN) In this chapter, a tightbinding method for the band structure of TGN in the presence of a perpendicular electric field is employed An analytical model of ABA-stacked TGN carrier statistics incorporated with a numerical solution in the degenerate and nondegenerate regimes is presented Simulated results based on the presented model indicate that this model can be approximated by degenerate and nondegenerate approximation in some numbers of normalized Fermi energy Chapter provides additional GNR transistor modeling concepts Analytical models for surface potential, lateral electric field, and length of saturation in the saturation region are presented The behavior of the GNR transistor in the saturation region is also studied In order to achieve downscaling of devices, the use of new material or structure should be explored Nanowire is one such candidate A silicon nanowire (SiNW) is an elongated crystalline or amorphous silicon with the diameter ranging from ten to hundred nanometers and a length of several micrometers Researchers have focused on SiNWs because of their unique properties being significantly different from those of bulk silicon The electronic band gap of SiNW is adjustable with the nanowire diameter Chapters 10 through 12 focus on SiNW Chapter 10 describes the modeling and simulation of SiNW, while Chapter 11 describes its properties and growth techniques Experimental results obtained are also discussed ZnO nanowires are generally fabricated using bottom-up technology and require the use of tedious pick and place method and electron beam lithography, which limits their use in large area and low-cost applications Chapter 12 provides a new perspective of top-down fabrication technique to produce highly oriented and reproducible nanowires with different channel lengths in defined locations on a larger processing scale One of the most popular new material technologies is strained technology Strained technology changes the properties of device materials rather than changing Preface ix the device geometry Chapter 13 presents a comprehensive knowledge of the stress technology using Si/Si1-xGex materials In addition, it provides a useful threshold voltage model using the quantum mechanical effect approach Although nanoelectronics have the potential for numerous applications, they face technical and economic challenges A major obstacle is the long time period from research to commercialization This gap must be addressed by industry, government, and academia Chapter 14 discusses the triple helix models involving universities, industries, and government, which can help bridge this gap and lower the barriers to nanoelectronics commercialization Finally, the book concludes with an Appendix containing the MATLAB® codes used to generate some of the figures, followed by a Glossary of terms used in the chapters concerning nanoelectronics The Glossary is not comprehensive and does not list every technical term used to describe advanced nanoelectronics However, effort has been made to include important terms It is hoped that this book will serve as a useful source of technical and scientific information for professionals, researchers, and scientists who want to know about topics that deal with advanced nanoelectronics Razali Ismail MATLAB® and Simulink® are registered trademarks of The MathWorks, Inc For ­product information, please contact: The MathWorks, Inc Apple Hill Drive Natick, MA 01760-2098 USA Tel: 508 647 7000 Fax: 508-647-7001 E-mail: info@mathworks.com Web: www.mathworks.com i G High k Pd Pd Sio2 P+ Si FIGURE 3.15  Illustration of the CNT capacitor device ≤ VD ≤ VDsat α=1 2.5 α> λD ≈ 10 nm A1 A1 γ0 B1 B1 A2 γ2 γ1 A2 A2 B2 A3 γ3 B γ3 A3 B3 A3 B3 (a) ABA B1 γ1 A2 γ1 A γ0 B1 γ4 B2 γ4 A1 γ5 A2 γ1 A2 B2 A3 B3 A3 B3 (b) ABC FIGURE 8.5  Structures of TGN with (a) ABA (Bernal) stacking and (b) ABC ­(rhombohedral) stacking A2 B2 B1 B2(A3) A1(B3) B3 B1(A2) A1 B1(A2) B2(A3) A3 γ1 γ4 A2 A1 γ2/2 γ3 γ3 B2 γ4 B3 A1(B3) γ1 A3 B1 (b) (a) FIGURE 8.6  (a) Lattice structure of ABC-stacked TGN and (b) schematic of the unit cell of ABC-stacked TGN x Source Gate SiO2 GNR Drain tox tG L FIGURE 9.1  Schematic cross section of a top-gated GNRFET [9] Typical device para­ meters are doping concentration N = × 1016 m−2, tOX = nm, L = 20 nm, and wG = nm < x < LE tOX Source x tG t < x < ∆L Gate Oxide Es GNR EOX1 Oxide Gate EOX2 tOX Ex Drain L FIGURE 9.6  Schematic cross section of a DG-GNRFET [9] Typical device parameters are doping concentration Nd = × 1016 m−2, tOX = nm, L = 20 nm, and wG = nm tOX Source Gate  1 Oxide x tG GNR y tOX Drain Oxide Gate L FIGURE 9.11  Schematic cross section of a DG-GNRFET VGS S G D VDS FIGURE 10.6  Schematic of a nanowire transistor with gate dielectric ZQ Rox Rwire tox FIGURE 10.7  Schematic of a nanowire cross section with gate dielectric 2.5 I (μA) VGS = −0.8 1.5 0.5 VGS = −0.6 VGS = −0.4 VGS = −0.2 −0.8 −0.6 −0.4 V (V) −0.2 FIGURE 10.8  Current–voltage characteristics in a nanowire compared with the published data taken from Ref [49] Element Si O Au Cu C Wt.% 4.6 At.% 58.2 73.3 15.8 6.3 13.6 9.1 19.1 C Cu Cu Cu Au Au Si Si (a) Energy (keV) 10 Count (arb unit) Count (arb unit) Au Element Si O Au Cu C Wt.% 80.8 4.7 At.% 75.8 12.4 11.3 3.2 4.7 7.1 (b) Cu C Cu O Cu Energy (keV) 10 FIGURE 11.15  The corresponding EDX spectra of Au-catalyzed SiNWs grown by VSS mechanism at 320°C (a) tip and (b) stem of the nanowire QMEs strained, VDS = 0.05 V QMEs strained, VDS = 0.5 V QMEs strained, VDS = V Control strained, VDS = 0.05 V Control strained, VDS = 0.5 V Control strained, VDS = V 1.8 Surface potential, V 1.6 1.4 1.2 0.8 0.6 0.4 0.2 10 15 20 Channel length, L (nm) 25 30 FIGURE 13.12  Surface potential variation along the channel for 30 nm channel length with 20% germanium content, respectively, for conventional and quantum tensile strained Si The solid curves obtained by the quantum approach and the dashed represent the conventional strained Si 0.6 0.5 Threshold voltage, Vth (V) 0.4 0.3 0.2 0.1 QMEs conventional MOS Conventional MOS QMEs strained frac = 0.2 Control strained frac = 0.2 QMEs strained frac = 0.4 Control strained frac = 0.4 −0.1 −0.2 −0.3 −0.4 20 40 60 80 Channel length, L (nm) 100 120 FIGURE 13.13  Threshold voltage variation along the channel, ­comparing conventional MOSFETs, and conventional and quantum strained Si model, for  ­germanium content 0.2 and 0.4 0.4 Threshold voltage, Vth (V) 0.35 0.3 0.25 0.2 0.15 QMEs strained, L = 30 nm Control strained, L = 30 nm QMEs strained, L = 50 nm Control strained, L = 50 nm QMEs strained, L = 100 nm Control strained, L = 100 nm 0.1 0.05 10 15 Strained thin film thickness, Tsi (nm) 20 FIGURE 13.15  Plot of threshold voltage performance as the function of strained Si ­thickness for L = 30, 50, and 100 nm for 30% germanium content in Si1−xGex substrate [...]... p­ ublished various articles on the subject His current research interest is in the ­emerging area of nanoelectronics devices focusing on the use of carbon-based materials and novel device structure He is presently with the Universiti Teknologi Malaysia as a ­professor and head of the Computational Nanoelectronics Research Group He is a member of the IEEE Electron Devices Society (EDS) Mohammad Taghi... Wave Equation Treatment of Many Electron Systems 18 1.3.2 Electrons in Unbounded Space 19 1.3.2.1 One-Dimensional Problem 19 1.3.2.2 Three-Dimensional Problem .20 17 18 Advanced Nanoelectronics 1.3.3 Electrons in Space Bounded by Infinite Potentials 21 1.3.4 One-Dimensional Space Bounded by an Infinite Well 21 1.4 Electrons in Periodic Structures 23 1.4.1 Solid... explained in the classical framework concerned blackbody radiation and the photoelectric effect These will now be explained briefly—a more detailed account is given in Bohm (1951) and Hund (1974) 20 Advanced Nanoelectronics 1.2.1  Experimental Results beyond Classical Physics 1.2.1.1  Blackbody Radiation All materials emit electromagnetic radiation over a wide frequency range Thus, a cavity will be filled... discovered that beams of FIGURE 1.1  Young’s double slit experiment A plane wave incident on the slits from the left is diffracted at each slit leading to the interference pattern on the screen 22 Advanced Nanoelectronics electrons were also diffracted by the crystal, as though they were waves rather than particles A diffraction pattern on a screen sensitive to electrons was observed consistent with... 1.2.3.2  Heisenberg Uncertainty Principle An important implication of the mathematical description of quantum behavior is the Heisenberg uncertainty principle, formulated in 1927 (Heisenberg, 1927) 24 Advanced Nanoelectronics It states that there is a limit to the accuracy with which the position and momentum of a particle* can be simultaneously measured The principle is expressed mathematically as DpDx... physically, the overall motion is determined by vg, which does not exceed c, as required by Einstein’s relativity theory that limits particles of finite mass such as electrons from exceeding c 26 Advanced Nanoelectronics sinc[Δkx] π π −π Δkx1 =− π 2 Δkx2 =π 2 Δkx FIGURE 1.3  A measure of the width of a wave packet Insight into the Heisenberg uncertainty principle can be gained from the wave packet... energy of the quantum system Schrödinger’s equation can also be written using the Hamiltonian energy operator: H =- 2 2m — 2 + V (r, t ) (1.16) This operator will be discussed in the following 28 Advanced Nanoelectronics The boundary conditions are that Ψ and its derivative are continuous at boundaries This can be expressed by Y s1,i (rbi , t ) = Y s2,i (rbi , t ), (1.17) —Y ¢ s1,i (rbi , t ) n(rbi... finding a particle in a small volume dV ­centered at r is ρ(r, t) = |Ψ(r, t)|2dV, and the probability of finding it in a region R is P = ÚR | Y (r, t ) |2 dV = ÚR Y * (r, t )Y (r, t ) dV , (1.27) 30 Advanced Nanoelectronics where * denotes the complex conjugate Since the existing particle must be somewhere in space, we also have ÚR =• Y * (r, t )Y (r, t ) dV = 1 (1.28) This is used to normalize the solutions... λn for an observable We have seen that the corresponding eigenfunction Ψi can be expressed using Equation 1.32 From Equations 1.30 and 1.32, the probability of obtaining λn in a measurement is 32 Advanced Nanoelectronics 2 P(ln ) = ÚY y *ndV = P(ln ) = Ú( amy m )y ndV * 2 (1.38) Invoking orthonormality yields from this the simple result P(ln ) = | an |2 (1.39) This expresses the algorithmic relation... make quantum theory more intelligible and pays attention to the development of a coherent ontology for quantum theory; * Ontology is concerned with discovering the nature or essence of things 34 Advanced Nanoelectronics a  major feature brought out by Bohm and Hiley is the importance of wholeness, which is not very often discussed in standard textbooks on quantum theory More details can be found in