Neuromorphic Engineering I. To do today. avlsi.ini.uzh.ch/classwiki. Book. A pidgin vocabulary. Neuromorphic Electronics? What is it all about?

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1 Neuromorphic Engineering I Time and day : Lecture Mondays, 13:15-14:45 Lab exercise location: Institut für Neuroinformatik, Universität Irchel, Y55 G87 Credits: 6 ECTS credit points Exam: Oral minutes at INI Labs: Group reports (max 3 persons). You must successfully complete at least 9 lab exercises. These exercises should include the first 3 labs (mandatory) and at least one of the last 2 labs. If you do all lab exercises, we will drop your 3 lowest lab grades. Grade: 70% exam + 30% lab exercises Taught by: Tobi Delbruck, Giacomo Indiveri, Shih-Chii Liu Teaching assistants: Christian Braendli and Hesham Elsayd To do today Arrange lab times Describe lab setup and classchip Introduce device physics avlsi.ini.uzh.ch/classwiki Book Available on Amazon 1 TD Course schedule Fall 2010 Introduction to neuromorphic avlsi. Device physics. 2 SCL Transistor properties below threshold. 3 SCL Transistor properties above threshold. 4 GI Static analog circuits. Current mirror, diff pair, transconductance amplifier, bump circuit. 5 GI Transconductance amplifier. 6 GI Current mode and winner-take-all circuits. 7 TD Linear systems: Follower integrator, follower differentiator. Small signal analysis I. Voltage amplifier. 8 TD Phototransduction in biological retinas. Adaptive photoreceptor. Small signal analysis II 9 TD Photoreceptor circuits. Logarithmic and adaptive photoreceptor. 10 SCL Synapses, excitatory and inhibitory. 11 SCL Silicon neurons. 12 SCL Long term storage in silicon. 13 TD Subthreshold noise in MOS transistors. A pidgin vocabulary Neuromorphic Electronics? What is it all about? (c) T. Delbruck, Inst. of Neuroinformatics 1

2 1947 Bardeen and Brattain The context A finished wafer G G S D D S holes electrons p + p + n + n + n well p well Constant ~$5/cm 2 Artificial real-world computation (or: How industry thinks of analog) Synchronous logic is ubiquitously used to implement Finite State Machines (FSMs) ADC Logic DAC External input Clock Combinational Logic (ANDs, ORs, inverters) State transition conditions Registers (memory elements) States Logic bus (many wires representing a digital symbol or state) (c) T. Delbruck, Inst. of Neuroinformatics 2

3 Natural computation The motivation Flies acrobatically Recognizes patterns Navigates Forages Communicates 10uW 10 6 neurons, 10 9 synapses 10 op/s/synapse J/op (synaptic activation) Digital silicon 10-7 to J/op (MAC) Biology is 10 8 to 10 4 times as efficient as digital silicon Core2 Quad Computer vs. Brain Cortex 1mm axon dendrite Device physics of membrane channels and transistors Anderson et al At the system level, brains are about 1 million times more power efficient than computers. Why? Cost of elementary operation (turning on transistor or activating synapse) is about the same. It s not some magic about physics. Computer Brain Fast global clock Self-timed Bit-perfect deterministic logical state Synapses are stochastic! Computation dances: digital analog digital Memory distant in time and space to computation Memory in synapses, at computation Fast high precision power hungry ADCs Low resolution adaptive data-driven quantizers Devices frozen on fabrication Constant adaptation and self-modification Transistor 40mV/e-fold Silicon has speed m electrons is 10 7 times m ions Biology has complex structures, self-modification, and wiring. 17 The fact that we can build devices that implement the same basic operations as those the nervous system uses leads to the inevitable conclusion that we should be able to build entire systems based on the organizing principles used by the nervous system. C. Mead, Proc. IEEE, 1990 f Engineering extremes - i + + A b o 1/ b 1 i 1 1 b Ab Brains do neither of these clearly. In practice we still do not know how in electronics to stride the middle ground very well. o (c) T. Delbruck, Inst. of Neuroinformatics 3

4 The subterranean group Biophysics of membrane channels History of NE Carver Mead (Caltech) Max Delbruck (Caltech) Moshe Eisenberg (from UPenn) Jim Hall (recalled early from Vietnam) Peter Leuger (Konstanz) Fred Sigworth Paul Mueller (UPenn) Fast forward to 1980 Physics of Computation Course Carver Mead Dick Feynman 1980 John Hopfield History of Neuromorphic Engineering The silicon retina Carver Mead s Misha Mahowald (c) T. Delbruck, Inst. of Neuroinformatics 4

5 1967 C. Mead M. Delbruck P. Mueller CSEM E. Vittoz The world of neuromorphic engineering 1980s C. Koch Mid to late 1990s Van Schaik R. Sarpeshkar B. Minch C. Diorio 26 P. Hasler S-C. Liu K. Boahen P.Julian Liu, 2005 Types of Neuromorphic chips Silicon retinas electronic models of retinas Silicon cochleas electronic models of cochleas Smart vision chips (e.g. tracking chips, motion sensors, presence sensors) Neural networks of spiking neurons Central pattern generators Models of specific systems: e.g. bat sonar echolocation, lamprey spinal cord for swimming, lobster stomatogastric ganglion, electric fishes Multichip systems that use spikes for interchip communication Scope Voltage source and picoammeter Power supply Power supply The lab setup Linux PC with Matlab+GPIB Potbox Voltmeter Current limit (c) T. Delbruck, Inst. of Neuroinformatics 5

6 Oscilloscope Keithley voltage source (230) and source-measure electrometer (236) Potbox Class chip ZIF socket Pots Class-chip design is open-sourced Test transistors (c) T. Delbruck, Inst. of Neuroinformatics 6

7 Follower + follower integrator Wide output range transconductance amplifier MOS transistors semiconductor device physics p+ p+ n+ n+ n- We need to understand enough about semiconductors and junctions to understand how MOS transistors work Insulators, conductors, semiconductors Crystal structure of silicon Band structure (valence, conduction, and forbidden bands) Holes and electrons Mechanisms of charge transport (diffusion & drift) Doping with donors and acceptors Fermi-Dirac distribution Law of mass action (np=n i2 ) p-n junction Reverse biased junction and its capacitance p- First look at semiconductors and transistors 46 Conductors, Semiconductors and Insulators The silicon lattice with an electron donor atom Covalent bonds Wave function of bound electron 48 (c) T. Delbruck, Inst. of Neuroinformatics 7

8 Energy Donors and Acceptors in the periodic table A P-N junction Mobile majority carriers Fixed ions Depletion region Space-charge region A P-N junction Electric field Diffusion of holes from p region Diffusion of electrons from n region In equilibrium, Drift = Diffusion for electrons and holes 51 Charges, fields, and potentials in a PN junction Charge density Electric field Electrostatic potential N D Q f E T kt q N A N N log( ) A D 2 ni Typically, the built-in voltage, T, is about 0.75V 52 MOS transistors use insulated gates to control barrier energies at PN surface junctions at source and drain V s V g V d n + n + p - Small Vgs, Vds=0 p+ p+ n+ n+ n p 53 Source Channel Drain (c) T. Delbruck, Inst. of Neuroinformatics 8

9 Energy Energy Energy levels V s V g ++++ V d n + n + Larger Vgs, Vds=0 V s V g V d n + n + Larger Vgs, Large Vds Source Channel Drain Source Channel Drain Measured FET IV relationship demonstrates Boltzmann distribution Closer look at silicon crystal structure and energy bands 58 The Diamond Structure of Silion Each atom is covalently bonded to 4 neighbors Bands arise from periodic strcture of crystal Wavefunctions of electron in a box A crystal is like a periodic box Only wavefunctions with discrete nonzero energies act like free particles Wavefunctions at forbidden energies die off exponentially Si dominates because it has a clean oxide interface: SiO 2 (c) T. Delbruck, Inst. of Neuroinformatics 9

10 Energy bands Electrons and holes Holes are bubbles in the valence band The electrons move, but it is easier to talk about the vacancy (the hole) moving, just like it is easier to talk about a bubble moving than about the water around it moving Quantum-mechanically, a hole acts just like an electron. The major difference is that holes have positive charge and the effective mass in silicon is 2.5 times larger for a hole than for an electron The meaning of energy in the band diagram E g =1.2eV=50kT The thermal energy Each degree of freedom of a system in thermal equilibrium has average energy kt/2 The thermal voltage kt/q is the voltage a single charge falls through to pick up the thermal energy kt kt/q=25mv=1/40v at room temperature kt/q is the natural scale of voltage for electronic systems in thermal equilibrium The Fermi-Dirac distribution States above Fermi level are occupied with Boltzman distribution ( E E f )/ kt p(occupied) e An intrinsic semiconductor Energy relative to Fermi level in kt units States at the Fermi level are ½ occupied States below Fermi level are unoccupied with Boltzman distribution Probability of occupation of a state ( E E)/ kt f p(unoccupied) e Band diagram Density of states Fermi-Dirac distribution Carrier concentrations (c) T. Delbruck, Inst. of Neuroinformatics 10

11 Donors and Acceptors in the periodic table Doping levels Concentration of Si is about /cm 3 Doping can vary from about /cm 3 to /cm 3 These doping levels still represent only a tiny fraction of the total atoms, from 10-8 to 10-4 A donor atom in the silicon lattice An n-type semiconductor Binding energy of electron is reduced from free atom binding energy (~0.5 ev) by silicon dielectric constant Si eV E binding 0.05eV 2kT 12 A p-type semiconductor The law of mass action: np=n i 2 In equilibrium, more holes means less electrons, and vice-versa. np=n 2 i n i is the intrinsic carrier density At room temperature n i is /cm 3, or about 1/10 13 Si atoms. n i increases with temperature (c) T. Delbruck, Inst. of Neuroinformatics 11

12 An electric field causes carriers to drift J m( E) qn Electron transport Drift and Diffusion Mobility The Einstein relation Current Flux J mqne Electric field Mobility Charge density for E that causes velocities much less than the thermal velocity of 100 km/s Mobility is a function of electric field A density gradient causes carriers to diffuse Current Flux Diffusion current J Dq n Diffusion constant Charge density Drift and diffusion are related by The Einstein relation Jdiffusion Dq n Jdrift D kt m q mqne Charges, fields, and potentials in a PN junction Charge density Electric field Electrostatic potential N D f Q E T kt q N A N N log( ) Typically, the built-in voltage, T, is about 0.75V A D 2 ni (c) T. Delbruck, Inst. of Neuroinformatics 12

13 Electrostatic potentials in a PN junction Band structure of a PN junction Electrostatic Potential: potential energy of positive charge f E Remember electron energy is UP in a band diagram f e Potential energy of negatively charged electron f e E f E i E i Carrier densities in a PN junction Carrier densities in a PN junction log scale n p linear scale p n i np=n i 2 n np=n i 2 depletion region both n and p are far below doping values n i depletion region both n and p are far below doping values I-V characteristics of a PN junction rectifier A reverse-biased PN junction +1V E original E applied f e E i E f E i What causes this reverse current? (c) T. Delbruck, Inst. of Neuroinformatics 13

14 +1V A reverse-biased PN junction +1V Reverse current comes from generated electron hole pairs in 3 regions E original E applied L diff E original E applied L diff Quasi E f 1V Quasi E f Quasi E f 1V Quasi E f Light Question What is capacitance of reverse-biased PN junction? L V A What happens when light shines on the junction? Which way does current flow? E original E applied C= Si /L As V increases, L increases. So, as V increases, C decreases L C Answer: light tries to forward bias the junction. V I-V characteristics of a PN junction rectifier A forward-biased PN junction -.25V What causes this forward current? E applied E original Quasi E f -.25V Quasi E f Exponential IV caused by Boltzmann distribution of carrier energies and imbalance of drift and diffusion currents (c) T. Delbruck, Inst. of Neuroinformatics 14

15 What was covered Insulators, conductors, semiconductors Crystal structure of silicon Band structure (valence, conduction, and forbidden bands) Holes and electrons Mechanisms of charge transport (diffusion & drift) Doping with donors and acceptors Fermi-Dirac distribution Law of mass action (np=n i2 ) p-n junction Reverse/forward biased junction and its capacitance in reverse bias Next week: Understanding how MOS transistors work in the subthreshold/weak inversion regime p+ p+ n+ n+ n p Properties of Materials (Si and Si0 2 ) (c) T. Delbruck, Inst. of Neuroinformatics 15