Electronics B. Joel Voldman. Massachusetts Institute of Technology

Transcription

1 Electronics B Joel Voldman Massachusetts Institute of Technology JV: 2.372J/6.777J Spring 2007, Lecture 7E 1

2 Outline > Elements of circuit analysis > Elements of semiconductor physics Semiconductor diodes and resistors The MOSFET and the MOSFET inverter/amplifier > Opamps TODAY JV: 2.372J/6.777J Spring 2007, Lecture 7E 2

3 Elements of semiconductor physics > Discrete molecules (e.g., hydrogen atom) have discrete energy levels that the electrons can occupy Determined via quantum mechanics > Adding a discrete amount of energy to the electrons (via light, thermal energy, etc.) can excite an electron from its ground state to an excited state E (ev) E (0 ev) E 5 (0.54 ev) E 4 (0.85 ev) E 3 (1.51 ev) E 2 (3.40 ev) E 1 (13.6 ev) Paschen series Balmer series Lyman series Hydrogen (n = 3, 1 = 1) p orbital 6 allowed levels > Different atoms have different number of filled states All the action typically happens at the highest unoccupied state > Two distinct molecules have identical and independent energylevel structures (n = 2) 8 electrons (n = 1) 2 electrons (n = 3, 1 = 0) s orbital 2 allowed levels Silicon Adapted from Figures 2.1 and 2.6 in Razeghi, M. Fundamentals of Solid State Engineering. 2nd ed. New York, NY: Springer, 2006, pp. 48 and 59. ISBN: Razeghi, Fundamentals of Solid State Engineering JV: 2.372J/6.777J Spring 2007, Lecture 7E 3

4 Elements of semiconductor physics > Atoms packed into a lattice behave differently than discrete atoms > Their discrete energy levels coalesce into continuous energy bands > There may be many energy bands for the molecule > We don t care about the ones that are filled and inaccessible > We care about the highest one with electrons 6 L3 Γ 2' Γ 2' 4 Electron energy p s 4N empty states 2N2N filled states L 1 Γ Γ Si Γ 25' X 1 Γ 25' L 3, X 4 X 1 L 1 L 2' Energy Gap Isolated Si atoms Decreasing atom spacing Si lattice spacing Adapted from Figure 2.5 in: Pierret, Robert F. Semiconductor DeviceFundamentals. Reading, MA: AddisonWesley, 1996, p. 28. ISBN: Γ Γ L Λ Γ X U,K Σ Γ Wave Vector k Figure 1 on p. 559 in: Chelikowsky, J. R., and M. L. Cohen. "Nonlocal Pseudopotential Calculations for the Electronic Structure of Eleven Diamond and Zincblende Semiconductors." Physical Review B 14, no. 2 (July 1976): Razeghi, Fundamentals of Solid State Engineering O pencourseware ( Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. JV: 2.372J/6.777J Spring 2007, Lecture 7E 4

5 Elements of semiconductor physics > The highest normally filled set of electronic states is the valence band > The lowest normally empty set of electronic states is the conduction band > An energy gap separates these states > At T=0 K, all the valence band states are filled > A filled band cannot conduct electricity This is an insulator 6 L L 1 0 L 3, Si Γ 2' Γ 2' Γ 15 Γ 15 Γ 25' X 1 Γ 25' 6 X 1 L 8 1 L 2' 10 Γ Γ L Λ Γ X U,K Σ Γ Energy Gap Figure by MIT OpenCourseWare. Figure 1 on p. 559 in: Chelikowsky, J. R., and M. L. Cohen. "Nonlocal Pseudopotential Calculations for the Electronic Structure of Eleven Diamond and Zincblende Semiconductors." Physical Review B 14, no. 2 (July 1976): Razeghi, Fundamentals of Solid State Engineering X 4 Wave Vector k T=0 K conduction band energy gap valence band JV: 2.372J/6.777J Spring 2007, Lecture 7E 5

6 Elements of semiconductor physics JV: 2.372J/6.777J Spring 2007, Lecture 7E 6 > T>0 K, electrons have thermal energy (~kt) > At equilibrium, the only way for an electron to cross the energy barrier is to be thermally excited > The number of electrons that can do this is increases with thermal energy (and thus T) decreases with larger bandgap > The thermally excited electrons give rise to electrons > The resulting empty states in the valence band give rise to holes Behave similar to electrons but with opposite charge and different mass electrons holes T=0 K T=300 K

7 JV: 2.372J/6.777J Spring 2007, Lecture 7E 7 Key terminology > Energy gap E G (1.1 ev in silicon at RT) > Si atom concentration = 5x10 22 /cm 3 > The number of carriers in intrinsic Si is related to Probability distribution function of energies» This obeys FermiDirac statistics Allowable states > ~10 9 (prob of being filled) x ~10 19 (density of states) = ~10 10 (carriers) > n i is the intrinsic carrier concentration the equilibrium concentration of holes and electrons in the absence of dopants ~1.5x10 10 cm 3 at RT This is a material property > n is the concentration [#/cm 3 ] of electrons > p is the concentration [#/cm 3 ] of holes n n i i E k e 2 = p Every thermally generated electron leaves behind a hole i G B T

8 Key terminology JV: 2.372J/6.777J Spring 2007, Lecture 7E 8 > Intrinsic carrier concentration of Si, Ge, and GaAs Ge Si GaAs Intrinsic carrier concentration (cm 3 ) Adapted from Figure 2.20 in: Pierret, Robert F. Semiconductor Device Fundamentals. Reading, MA: AddisonWesley, 1996, p. 54. ISBN: T (K)

9 JV: 2.372J/6.777J Spring 2007, Lecture 7E 9 Doped semiconductors > Dopants: substitutional impurity atoms introduced having one different valence than the semiconductor > Acceptor dopant concentrations are N A [#/cm 3 ] ptype material Boron (3 valence electrons) > Donor dopant concentrations are N [#/cm 3 ] ntype material Phosphorous (5 valence electrons) > These introduce new energy levels close to valence or conduction bands (~0.05 ev) > Dopant concentrations >> n i D Si Si Si Si Si Si Adapted from Figure 7.5 in: Razeghi, M. Fundamentals of Solid State Engineering. 2nd ed. New York, NY: Springer, 2006, p ISBN: P T=0 K Si Si

10 JV: 2.372J/6.777J Spring 2007, Lecture 7E 10 Doped semiconductors > Energy to ionize << kt (at RT) > We assume all dopants are ionized at RT E c E D ntype dopant E v T = 0 T > 0 K T = 300 K E c ptype dopant E A E v Adapted from Figure 2.13 in: Pierret, Robert F. Semiconductor Device Fundamentals. Reading, MA: AddisonWesley, 1996, p. 38. ISBN:

11 Main results JV: 2.372J/6.777J Spring 2007, Lecture 7E 11 > Donors or acceptors are fully ionized > Define n 0 and p 0 as the electron and hole concentrations at equilibrium > n 0 and p 0 follow a massaction law N N e D A D A D N N h N N A N N D A np = n i N A = p N = n n= p D

12 Main results JV: 2.372J/6.777J Spring 2007, Lecture 7E 12 > Overall, silicon is neutral Can use to determine n 0 and p 0 > Carrier concentrations typically vary over many orders of magnitude Can use this to simplify > Ex: n i ~ cm 3 N A, N D ~ cm 3 > In a given material at equilibrium N A > 100N D (ptype) N D > 100N A (ntype) Charge neutrality requires: N n = N p A 0 D 0 N n N p A For ptype material: p N n 0 0 D 0 0 A 2 2 i ni n = = p 0 N A

13 Main results JV: 2.372J/6.777J Spring 2007, Lecture 7E 13 > Therefore, the equilibrium majority carrier concentration is determined by the net doping and the minority carrier concentration is determined by the n 0 p 0 product. > For typical numbers, minority carrier concentration is much less majority carrier concentration n ptype p n 0 0 = = 0 N N n N A 2 i A ~ p = N = 10 cm 10 3 ( 10 cm ) 2 i NA 10 cm A A cm 17 3 n = = = 10 2 n p ntype 0 0 = = cm N n N 3 3 D 2 i D

14 JV: 2.372J/6.777J Spring 2007, Lecture 7E 14 > We can do various things to create excess carriers Shine light Apply electric fields > Excess carriers (n, p ) represent a departure from equilibrium > Excess holes and electrons are created in pairs > Excess carriers recombine exponentially in pairs, governed by lifetime The minority carrier lifetime Excess carriers Recombination rate n = n n p = p p Generally, n = p 0 0 dn n dt τ m m n ()~ t n (0) e τ t Electronhole pair (EHP)

15 Excess carriers > GaAs w/ N A =p 0 =10 15 cm 3 > GaAs n i = 10 6 cm p(t) > Therefore, n 0 = 10 3 cm 3 > Create EHP/cm 3 and calculate carrier concentrations over time Carrier concentrations (cm 3 ) n(t) p 0 Adapted from Figure 4.7 in: Streetman, Ben G., and Sanjay Kumar Banerjee. Solid State Electronic Devices. 6th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2006, p ISBN: time (ns) JV: 2.372J/6.777J Spring 2007, Lecture 7E 15

16 JV: 2.372J/6.777J Spring 2007, Lecture 7E 16 Drift and diffusion of carriers > Carriers in semiconductors obey a drift/diffusion flux relation > Drift: carriers move in an electric field > Diffusion: carriers move in a concentration gradient > For ptype material n is small drift current is small n can be big diffusion current dominates J Electric field [V/cm] drift diffusion ( μ E ) = q n D n n e n n Mobility [cm 2 /Vs] Diffusivity [cm 2 /s] Carrier concentration [cm 3 ] Drift Figure 3.1b) in: Pierret, Robert F. Semiconductor Device Fundamentals. Reading, MA: AddisonWesley, 1996, p. 76. ISBN:

17 Outline JV: 2.372J/6.777J Spring 2007, Lecture 7E 17 > Elements of circuit analysis > Elements of semiconductor physics > Semiconductor diodes and resistors > The MOSFET and the MOSFET inverter/amplifier > Opamps

18 JV: 2.372J/6.777J Spring 2007, Lecture 7E 18 The semiconductor diode > A pn junction has very different concentrations of carriers in the two regions, creating a diffusive driving force > At equilibrium diffusive driving force = electric field in the vicinity of the junction > In order to set up this electric field, the ionized donors and acceptors are relatively depleted of mobile carriers near the junction the spacecharge layer (SCL) or depletion region x n0 X J0 φ x p0 E ptype ntype ntype substrate ptype region Oxide Adapted from Figure 14.1 in: Senturia Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: , Stephen D. Microsystem Design.

19 The exponential diode JV: 2.372J/6.777J Spring 2007, Lecture 7E 19 > An external voltage modifies the net potential drop across the space charge layer > Forward bias reduces the barrier to diffusion, leading to an increase in current > Reverse bias increases the barrier, so only current is due to minority carriers generated in or near the spacecharge layer p Equilibrium I N n E c E v Oxide Metal ptype region I D E c E v ntype substrate V D I P _ Adapted from Figure 14.2 in: Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: Forward bias Adapted from Figu re 6.1 in: Pierret, Robert F. Semiconductor Device Fundamentals. Reading, MA: AddisonWesley, 1996, p ISBN:

20 Ideal Exponential Diode Analysis JV: 2.372J/6.777J Spring 2007, Lecture 7E 20 > Linear changes in voltage lead to exponential changes in carrier concentrations Forward bias The total current is qv e D kbt ID = I0 e 1 Current (A) V B Reverse blocking Reverse breakdown Voltage (V) Adapted from Figure 14.3 in: Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN:

21 JV: 2.372J/6.777J Spring 2007, Lecture 7E 21 The JunctionIsolated Diffused Resistor > The structure is a diode, but with two contacts > The diode action prevents currents into the substrate provided the diode is always reverse biased > The conductivity is controlled by doping > The resistor value is determined by geometry desired undesired Oxide distributed diode ptype region Metal ntype substrate resistor v v Adapted from Figure14.7 in: Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN:

22 Outline JV: 2.372J/6.777J Spring 2007, Lecture 7E 22 > Elements of circuit analysis > Elements of semiconductor physics > Semiconductor diodes and resistors > The MOSFET and the MOSFET inverter/amplifier > Opamps

23 MOSFET Structure JV: 2.372J/6.777J Spring 2007, Lecture 7E 23 > The MOSFET exploits the concept of a fieldinduced junction > The electric field between the gate and the channel region of the substrate can either increase the surface concentration (accumulation) or deplete the surface and eventually invert the surface Source Gate Drain Oxide D Channels ptype substrate n regions G B Body Adapted from Figure in: Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: S

24 MOSFET qualitative operation JV: 2.372J/6.777J Spring 2007, Lecture 7E 24 > With D & S grounded, backtoback diodes prevent current flow between D & S > To reduce barrier, apply positive voltage to G (w.r.t. D & S) > At some threshold voltage, this will form an nchannel inversion layer that will connect D & S

25 JV: 2.372J/6.777J Spring 2007, Lecture 7E 25 > Need V GS >V T for device to turn on > As V DS increases, current will flow between D & S > As V DS increases, voltage between G and D decreases > When V DS gets too big, one side of channel pinches off, preventing further increases in current D G MOSFET Characteristics S D I D (µa) G S triode D V DS I D,sat V GS = 3 V saturation G V GS = 4 V V GS = 2 V Adapted from Figure in: Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: S e e e e e e nchannel V DS =0 V DS >0 V > V V DS GS T

26 Different kinds of MOSFETs JV: 2.372J/6.777J Spring 2007, Lecture 7E 26 S S G B G B pchannel D Enhancement D D Depletion D G B nchannel G B S S Adapted from Figure in: Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN:

27 JV: 2.372J/6.777J Spring 2007, Lecture 7E 27 Largesignal and smallsignal MOSFET models > Electrical engineers use circuit models to analyze circuits involving MOSFETS > Can use either full nonlinear characteristics > Or linearized smallsignal model Different models include different components G G D S K/2(V V ) GS Simple largesignal model, in saturation D C gv m gs r 0 GS Tn 2 S Simple smallsignal model, in saturation

28 Outline JV: 2.372J/6.777J Spring 2007, Lecture 7E 28 > Elements of circuit analysis > Elements of semiconductor physics Semiconductor diodes and resistors The MOSFET and the MOSFET inverter/amplifier > Opamps

29 Operational Amplifiers opamps > Let someone else design a highperformance amplifier > Basic structure and transfer characteristic v 0 V Signal path sat _ v Slope A 0 v 0 v v v Differential amplifier Highgain amplifier Output amplifier V sat v _ V S Output A DIP/SO Package 1 8 v v V S v 0 Inverting input A Noninverting input A GND 2 7 _ A B _ Top view Output B Inverting input B Noninverting Input B Adapted from Figures and in Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: LM158 JV: 2.372J/6.777J Spring 2007, Lecture 7E 29

30 Ideal and nonideal behavior JV: 2.372J/6.777J Spring 2007, Lecture 7E 30 > We do first analysis using ideal linear model > Opamp data sheets have pages and pages of limitations > A sampling Input offset voltage v off : zero volts at input gives nonzero output Frequency limitations: opamps can only amplify up to a maximum frequency 0 ( ) v () s = A() s v () s v () s where As As () = s s 0 0 0

31 The Inverting Amplifier JV: 2.372J/6.777J Spring 2007, Lecture 7E 31 V s V s R 1 R 2 v v v v R 1 R 2 A(v v ) V o V o Assume opamp draws no current Use Nodal analysis: KCL: 0 Vs v v V = R R 1 2 V = A(0 v ) Vo R2 1 = Vs R 1 R 1 1 A R 1 2 V V o s A R2 = R 1 1 0

32 Short method for analyzing opamps JV: 2.372J/6.777J Spring 2007, Lecture 7E 32 > Assume linear region operation This implies that the two inputs are essentially at the same voltage (but never exactly equal) > Assume zero currents at both inputs > Analyze the external circuit with these constraints > Check to verify that the output is not at either saturation limit (±V S )

33 More opamp configurations JV: 2.372J/6.777J Spring 2007, Lecture 7E 33 V s _ V 0 R 1 R 2 v = v = V 2 Vs = V0 R 2 R 1 V V = S R R 2 S R Noninverting Adapted from Figure in Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN:

34 More opamp configurations JV: 2.372J/6.777J Spring 2007, Lecture 7E 34 R 1 I s _ V 0 Adapted from Figure in Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: Transimpedance amplifier V0 = 1 R I S

35 Integrator JV: 2.372J/6.777J Spring 2007, Lecture 7E 35 C R 1 _ v C _ Vs _ V 0 Adapted from Figure in Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: V0 = Vs ( t) dt R C 1

36 Differentiator R 1 C _ Vs _ V 0 Adapted from Figure in Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers, 2001, p ISBN: The differentiator is less "ideal" Vs 0 V = 1 R1 sc V0 = sr1c V s JV: 2.372J/6.777J Spring 2007, Lecture 7E 36 0