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Vijay K. Arora Wilkes University E-mail: [email protected] Emerging Technologies Our Motivation and Economics Adam Smith, “An Enquiry into Nature and Causes of the Wealth of Nations” (1776) The wealth is created by laisse-faire economy and free trade John Maynard Keynes, “The General Theory of Employment, Interest, and Money” (1936) The wealth is created by careful government planning and government stimulation of economy 1990’s and Beyond The wealth is created by innovations and inventions 20th Century Paradigm Formulate a hypothesis or theory Accumulate data Do extensive experimentation and Check Publish if newsworthy Respect others’ work helping them to grow in the profession Demonstrate character ethics that puts community interests above personal aggrandizement 21st Century Paradigm Formulate a hypothesis or theory or design Make a prototype structure Patent it Raise 17 million dollars and start an IPO Sue your competitor for stealing your idea Demonstrate personality ethics that lubricates the process of human interaction for personal aggrandizement Gross world product and sales volumes Exponential Growth SIA roadmap Historical Trends New Technology generation every three years For each generation, memory density increase by 4 times and logic density increases by 2.5 times Rule of Two: In every two generations (6 years), the feature size decreased by 2, transistor current density, circuit speed, chip area, chip current and maximum I/O pins increased by 2 Research Scenario A comprehensive transport theory for quantum processes at nanosacle High-field distribution in quantum wells Optimization of the shape and size of quantum wells for high frequencies Quantum Computing: Multi-state logic by using quantum states Failure of Ohm’s Law: Re-assessment of the circuit theory principles Goals for High Speed Performance Large transistor current • Time constants • Interconnects • Cross talk Reduced transit time • Increased Mobility • High Saturation Velocity • Reduced Size RC and Transit Time Delays Source:Cadence Cadence Source: Interconnect Problems RC Time Delays RC time delay is increasing rapidly Wire resistance is rising Wires have larger cross-section … introduce coupling Electromigration imposes current limits System performance, area and reliability are determined by interconnect quality, not devices!!! Interconnect Performance 0.25 Decreasing Coupling Effect 0.5 Increasing Performance 1 Increased cross-section improves performance but also increases noise and capacitive and inductive coupling RC Delay Considerations R3 R2 R1 Cc layer m Cf Cf Co layer n Cf Cf R4 Cf Cs Cf layer m Cf Cs Cf substrate Cint = Cf + Cs + Co + Cload = Rint * ( Cint + Cc/(Cint+ Cc) ) = Rint * (Cint2 + Cint.Cc +Cc)/(Cint + Cc) • Cc depends on dimensional shrink due to increased in cross-section • In VLSI, make Cc becomes insignificant as possible, then = Rint * Cint Physical Effects Quantum Effects L D , a few nm High-Field Effects V 5V kV E 50 L 1m cm Field Broadening qED or qE k BT Nano-Scale Quantum Engineering D h p h 3m * k BT Bulk Semiconductors Lx , y , z D All 3 cartesian directions analog-type Density of States: 3 * 2 1 2me 1 dN gc (E) 4 2 E Eco 2 V dE h Quasi-Two-Dimensional QW Lz D Lx , y D z-direction digital-type x,y-directions analog-type ( k k ) 2 Enk Eco 2 x 2 y 2me * n 1, 2, 3,...... Density of States: n oz 2 2 2 oz * 2 2 me Lz E Eco 1 dN m gc2 ( E) Int A dE oz * e 2 AlGaAs/GaAs/AlGaAs Prototype Quantum Well Quasi-One-Dimensional QW L y , z D Lx D y, z-direction digital-type x-directions analog-type (QWW) 2 2 kx 2 2 Enk Eco m oy n oz * 2 me m, n 1, 2, 3,...... Density of States: o( y, z) * 2 2me Ly , z E ( E * 1/ 2 e 1 dN 2m g c1 ( E ) Lx dE 2 2 2 2 m n oz ) co oy 1 2 Quasi-Zero-Dimensional Quantum Well All 3 cartesian directions digital-type Quantum box (dot) Lx , y , z D Enk Ec ox m oy n oz 2 2 m, n, 1, 2, 3,...... 2 o( x, y , z ) * 2 2 me Lx , y , z 2 2 Quantum Well Wire Quantum Box (Dot) AlGaAs Quantum box Quantum wire GaAs inside Quantum Well Arrays Density of States DENSITY OF STATES ( 1026 eV-1m-3 ) 1 N ( E) Lx Ly Lz E E s 1.2 1.0 0.8 0.6 0.4 3D 2D 1D 0.2 0.0 0.0 0.2 0.4 0.6 E - Ec (eV) 0.8 1.0 Quantum Well with Finite Boundaries 1 L z 1 a P 1 2 2m * E a P 2 2 2 nz Z n z sin L z L z Triangular Quantum Well Approximate: Zn z nz 2 sin Ln Ln 2 Ln 2 zo an 0.53556 an Ai' n Exact: Z n ( z) 1 Ai' n z1o/ 2 z Ai z n o Quantum-Confined Mobility Degradation Changes in the Density of States QW bulk Lz D isotropic Lz D Changes in the relative strength each scattering interaction of Mobility Degradation Versus Quantum Confinement 0.7 0.6 2D / b 0.5 0.4 T=4K T = 77 K T = 300 K 0.3 0.2 0.1 0 0.1 -1 1 / Lz (nm ) 1 Gate-Field Confinement Mobility Degradation in a TQW MOBILITY (m 2 / V.s) 0.08 0.075 Theory Experiment 0.07 0.065 0.06 0.055 0.05 0.045 10 15 20 25 30 35 40 45 ELECTRIC FIELD (V / m) 50 Electron and Hole Mobility in Submicron CMOS Courtesy: Y. Taur and E. Novak, IBM Microelectronics, IEDM97 Invited Talk. Random Thermal Motion e h h e e h Ions e Electrons h Holes h vth 0 3k BT vth 105 m / s m* Quantum Emission Q Q e h o h h h Atoms h e Electrons h Holes e Q h h o qE Q o E o Q qE Randomness to Streamlining Velocity Vectors in Equilibrium Randomness: vd vth 0 Velocity Vectors in a Very High Field Streamlined: vd vth 2 vthˆ Saturation Velocity-Bulk v F1 vth F1/ 2 2 3D 2 k BT vth m* j 1 x Fj x Fermi Integral 0 ( j 1) 1 e Ec Normalized Fermi Energy k BT Saturation Velocity Limits vsat 8k BT vth * m vsat 2 3 h * 4m 3n 8 1 3 Non-degenerate limit Degenerate limit Saturation Velocity-Q2D v F1/ 2 vth 2 F0 2D F0 ln 1 e Ec k BT Ec Eco oz Saturation Velocity-Q1D v F0 vth F1/ 2 1 1D Ec k BT Ec Eco oy oz Modeling Transport dv qE v vth dt m* c =0 q c c E 1 e Transient Response: v m * t q c Steady State t c : vd E oE m* Quantum Emission qE Q o o Q qE Effective Collision time: eff o Q qEvth Q c c 1 e Q Effective collision length: o 1 e o 1-D Random Walk in a Bandgap semiconductor Modeling the Distribution f ( , E ) = 1 e x k BT qE k BT 1 1 e x 1 Q o o 1 e q E o E V o k B T Eco Vco o Q k BT Left-Right Asymmetry Itinerant Electron Population n x e e n( x ) e e 2 cosh ( ) Streamlining the Randomness 1 0.8 0.6 n +/n n-/n 0.4 0.2 0 0 0.5 1 1.5 2 2.5 Drift-Diffusion J ( x) n( x) q vth tanh dn q vth dx vd vth tanh Dn vth no Vt o q o q cn no mn* Vth mn* Drift Diffusion Drift Velocity Diffusion Coefficient k BT Vt q Single-Valley v-E Characteristics Velocity-Field Characterisitcs 2.0 10 5 Drift Velocity, vd (in m/sec) 3D 1.6 10 1.2 10 8.0 10 4.0 10 2D 5 5 1D 4 4 0 0 2 4 6 Normalized Electric Field, 8 10 Normalized Drift Velocity (vd /( 1/2 vth /2 )) Effect of Degeneracy (2-D) N ns D 2 1.6 1.4 1.2 1 0.8 D N=.01 0.6 N=.1 0.4 N=1 0.2 Non-Degen 0 0 4 8 12 16 20 h 2 m * k BT Mobility Degradation Diffusion Coefficient Degradation I-V Characteristics Microresistors Normalized I-V Characteristics 1.00 0.75 L=1 µm L=10 µm 0.50 L=100 µm 0.25 V/Vc 10.00 7.50 5.00 2.50 0.00 0.00 I/Isat Resistance Blow-Up 10 R/Ro (Experiment) R/Ro(Theory) r/Ro(Experiment) r/Ro(Theory) R/Ro 8 6 4 2 0 0 0.2 0.4 0.6 I/Isat 0.8 1 Multi-Valley Transport in GaAs Intervalley Electron Transfer Multi-Valley Transport in GaAs Velocity-Field Characteristics High-Frequency Transport j t E Edc o e E Edc dc Conductivity Degradation o o E hf ( E, ) ac Conductivity Degradation 2 2 1 eff Conclusions Quantum Confinement Transport properties function of confinement length in QW’s because of the change in the Density of States Relative strength of each scattering changes. Electrons tend to stay away from the interface as wave function vanishes near the interface Conclusions High-Field Driven Transport Electric field puts an order into otherwise completely random motion Higher mobility may not necessary lead to higher saturation velocity Saturation velocity is limited by Fermi /thermal velocity depending on degeneracy Saturation velocity is lowered by the quantum remission process RC time constants will dominate over transit time delay because of enhanced resistance Conclusions Failure of Ohm’s Law Effective resistance may rise dramatically as current approaches saturation level Familiar voltage divider and current divider rule may not be valid on submicron scales Golden Rule No matter what the size, make it smaller No matter what the speed, make it faster No matter what the function, make it larger No matter what the cost, make it cheaper No matter how little it heats up, make it cooler