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Vijay K. Arora Wilkes University E-mail: varora@wilkes.edu

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Emerging Technologies

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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

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20 th 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

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21 st 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

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Gross world product and sales volumes

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Exponential Growth SIA roadmap

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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

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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

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Goals for High Speed Performance Large transistor current Time constantsTime constants InterconnectsInterconnects Cross talkCross talk Reduced transit time Increased MobilityIncreased Mobility High Saturation VelocityHigh Saturation Velocity Reduced SizeReduced Size

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RC and Transit Time Delays Source: Cadence

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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!!!

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Increased cross-section improves performance but also increases noise and capacitive and inductive coupling 1 0.5 0.25 Increasing Performance Decreasing Coupling Effect Interconnect Performance

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substrate layer m Cs Cf Cc R1R1 R2R2 Cf layer m Co Cf R3R3 layer n R4R4 Cint = Cf + Cs + Co + Cload = Rint * ( Cint + Cc/(Cint+ Cc) ) = Rint * (Cint 2 + 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 RC Delay Considerations

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Physical Effects Quantum Effects High-Field Effects Field Broadening

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Nano-Scale Quantum Engineering

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Bulk Semiconductors All 3 cartesian directions analog-type Density of States:

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Quasi-Two-Dimensional QW z-direction digital-type x,y-directions analog-type Density of States:

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AlGaAs/GaAs/AlGaAs Prototype Quantum Well

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Quasi-One-Dimensional QW y, z-direction digital-type x-directions analog-type (QWW) Density of States:

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Quasi-Zero-Dimensional Quantum Well All 3 cartesian directions digital-type Quantum box (dot)

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Quantum Well Wire Quantum Box (Dot)

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Quantum Well Arrays

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Density of States

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Quantum Well with Finite Boundaries

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Triangular Quantum Well Approximate: Exact:

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Quantum-Confined Mobility Degradation Changes in the Density of States Changes in the relative strength of each scattering interaction

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Mobility Degradation Versus Quantum Confinement

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Gate-Field Confinement Mobility Degradation in a TQW

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Electron and Hole Mobility in Submicron CMOS Courtesy: Y. Taur and E. Novak, IBM Microelectronics, IEDM97 Invited Talk.

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Random Thermal Motion

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Quantum Emission

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Randomness to Streamlining Velocity Vectors in Equilibrium Randomness: Velocity Vectors in a Very High Field Streamlined:

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Saturation Velocity-Bulk Fermi Integral Normalized Fermi Energy

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Saturation Velocity Limits Non-degenerate limit Degenerate limit

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Saturation Velocity-Q2D

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Saturation Velocity-Q1D

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Modeling Transport Transient Response: =0

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Quantum Emission Effective Collision time: Effective collision length :

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1-D Random Walk in a Bandgap semiconductor

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Modeling the Distribution

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Left-Right Asymmetry Itinerant Electron Population

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Streamlining the Randomness

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Drift-Diffusion Drift Velocity Diffusion Drift Diffusion Coefficient

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Single-Valley v-E Characteristics

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Velocity-Field Characterisitcs

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Effect of Degeneracy (2-D)

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Mobility Degradation

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Diffusion Coefficient Degradation

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I-V Characteristics Microresistors

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Resistance Blow-Up

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Multi-Valley Transport in GaAs Intervalley Electron Transfer

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Multi-Valley Transport in GaAs Velocity-Field Characteristics

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High-Frequency Transport dc Conductivity Degradation ac Conductivity Degradation

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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

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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

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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

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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

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