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ECSE-6290 Semiconductor Devices and Models II Lecture 7

ECSE-6290 Semiconductor Devices and Models II Lecture 7. Prof. Shayla Sawyer Bldg. CII, Rooms 8225 Rensselaer Polytechnic Institute Troy, NY 12180-3590 Tel. (518)276-2164 Fax. (518)276-2990 e-mail: sawyes@rpi.edu. June 2, 2014. June 2, 2014.

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ECSE-6290 Semiconductor Devices and Models II Lecture 7

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  1. ECSE-6290Semiconductor Devices and Models IILecture 7 Prof. Shayla Sawyer Bldg. CII, Rooms 8225 Rensselaer Polytechnic Institute Troy, NY 12180-3590 Tel. (518)276-2164 Fax. (518)276-2990 e-mail: sawyes@rpi.edu June 2, 2014 June 2, 2014 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html 1 1

  2. Lecture Outline • Bipolar Junction Transistor • Physics of Operation • Junction Biasing • Solution of Diffusion Equation • Base Current Components

  3. Bipolar Junction Transistor • pn junction: supply of majority carriers with forward bias is high • pn junction: supply of minority carriers with reverse bias is low: need enhancement • Can place a forward biased pn junction very close to a reverse biased pn junction • Minority carrier population is now under electrical control: bias applied by nearby forward junction

  4. Bipolar Junction Transistor • Current-controlled device • Controlling signal: Base current • Controlled signal: Collector current • BJT as • Amplifier: Current or voltage gain • Switch: Logic or power switch What are the names of the regions or operation modes that define amplifier or switching action?

  5. Bipolar Junction Transistor

  6. Bipolar Junction Transistor • Forward biased emitter, reverse biased collector junction (active) • Arrows show direction of current flow

  7. Bipolar Junction Transistor Thermal Equilibrium Cut-Off • Increase both barriers • Depletes base region • Few electrons in the base • Charge transfer of electrons is • inhibited by barriers

  8. Bipolar Junction Transistor Saturation Forward Active • Makes signal amplification possible • Inject electrons into base • Sweeps nearby electrons • out of base (depletion • region) • Positive bias to both junction • Lowering both barriers • Huge increase in base density • Easy flow between junctions

  9. Bipolar Junction Transistor Reverse Active (prototype) Saturation Superposition of forward active and reverse active modes Injection at the same time IC >0 Under the line is stored charge Emitter: depleted at junction Base: swept away at emitter side, injection at collector side Collector: hole from base injected Cut-off Forward Active Same as reverse active (prototype) bias switched Minority carriers in base lowered

  10. Bipolar Junction Transistor With this configuration can reverse active and normal active modes be interchanged? What is the advantage of this?

  11. Bipolar Junction Transistor Forward Active Mode • Mechanisms for base emitter current in active biased transistor • Recombination of injected electrons with majority carrier holes in quasi neutral base • Recombination in base-emitter space charge region • Holes injected into the emitter • Generation within BC space charge region

  12. Bipolar Junction Transistor • Solution of Diffusion Equation yields terminal I-V characteristics for (saturation and active) • Assumptions: • Both junctions obey ideal diode equation • Low-level injection • Uniformly doped base, emitter and collector General Solution: Continuity equation Neutral base region From x=0 to x=W, injected minority carrier distribution

  13. Bipolar Junction Transistor • C1 and C2 are dependent on the boundary conditions of np(0) and np(WB) with boundary conditions at two edges:

  14. Bipolar Junction Transistor • Electron current at the emitter edge and collector edge given by: saturation X=0 saturation X=W

  15. Bipolar Junction Transistor • Forward active mode • VBC<0 contribution np=0 • Base Transport Factor • Fraction of electron current reaching the collector

  16. Bipolar Junction Transistor • When WB << Ln, transistor action occurs, T  1 and reduces to Where QB (injected excess base charge)= When WB >> Ln, T  0 and transistor action is lost!

  17. Bipolar Junction Transistor Base Current Components: • Carrier Recombination (IB1) Minimize IrB implies WB  and base lifetime n  • Since n >> ni2/NA, Uniformly doped base T = (|InE| – |IrB|)/|InE| = 1 – (|IrB|/|InE|) T = sech(WB/Ln)  1 – [WB2/(2Ln2)]

  18. Bipolar Junction Transistor Holes recombine Base Current Components: • Injection into Emitter (IB2) (a) Long Emitter (b) Short Emitter uniformly doped emitter

  19. Bipolar Junction Transistor Base Current Components: • Recombination within EB space charge region (IB3) – important at low biases IrE (1/)exp(qVBE/mkT) where m ~ 2, 1/ = 1/nSRH + 1/nA and nA = 1/GnND2 nA is Auger recombination: inverse of avalanche multiplication Gn is the recombination rate

  20. Bipolar Junction Transistor Base Current Components: • Generation within BC space charge region (IB4) Ipgen = ICO = -qACniWBC/SC  VBC1/2/SC

  21. Lecture Outline • Bipolar Junction Transistor • Device Parameters • Emitter Injection Efficiency • Base Transport Factor • Output Characteristics • Common-Base Configuration • Common-Emitter Configuration

  22. Bipolar Junction Transistor

  23. Bipolar Junction Transistor Terminal Currents • IE = InE + IpE + IrE IC = InC + ICO IB = IE – IC = IBi = IrB + IpE + IrE + ICO = (InE – InC) + IpE + IrE + ICO • Note IE = IC + IB InE=Electron diffusion current injected at emitter-base junction InC=Electron diffusion current reaching collector IrB=Loss of electron current recombining in the base IpE=Hole diffusion current at emitter- base junction IrE=Recombination current at emitter- base junction ICO=Reverse current at collector base junction

  24. Bipolar Junction Transistor Current Gains • Common–Base Current Gain 0 (= hFB)  IC/IE =(InE/IE)(InC/InE)(InC/IC) = T M 0   T where   InE/IE is emitter injection efficiency, T  InC/InE is base transport factor and M  InC/IC is collector collection efficiency Typically,   1, T  1 and M  1 so 0 close to 1 Small–Signal  (= hfb)  dIC/dIE

  25. Bipolar Junction Transistor Current Gains • Common–Emitter Current Gain 0 (= hFE)  IC/IB = 0/(1 - 0) >> 1 Small–Signal  (= hfe)  dIC/dIB • When 0 = 0.99, 0 = 99 When 0 = 0.998, 0 = 499 • Since ICBO = ICO|IE=0 is reverse current at the collector base junction when IE is zero and ICEO = ICO|IB=0,is reverse current at the collector base junction when IB is zero ICEO = ICBO /(1 - 0)

  26. Emitter Injection Efficiency Design NDE >> NAB (n+/p for EB junction) so that   1 ~ Number of holes in the emitter (from the base) times its diffusion length must be much less the number of electrons (going to the base) times its diffuion length

  27. Base Transport Factor • When  > 0.995  1, 0  T and 0  T/(1 - T)  (2Ln2/WB2) -1 For high-voltage power transistors, the current gain is often limited by T due to the wide base region • At high collector current densities, T  1 because of increasing drift current component so 0 becomes  limited and 0   and 0  /(1 - )

  28. Base Transport Factor • When T > 0.995  1 (e.g., for high-speed BJTs where WB  0.1Ln), 0   and Gummel number: number of base dopant atoms (per cm2) in the quasi neutral region. 0  1/Nb’  Base ion dose (for implanted BJTs) Base ion dose  lead to 0 

  29. Gummel Number • The disadvantage of a low base charge (in a prototype design) is the invalidation of the low injection approximation near the base emitter junction • High injection degrades performance • How do you solve this problem? • Control of the Gummel Number for high gain transistor is extremely important.

  30. Current Gain • Current Gain varies with collector current • At low IC, recombination current dominates and 0  IC/IB  exp(qVBE/kT)/ exp(qVBE/mkT)  exp[(qVBE/kT)(1-1/m)]  IC(1-1/m) • At moderate IC, diffusion dominates and 0  max • At high IC, high-level injection occurs in base,  0  IC-1 (Webster Effect)

  31. Bipolar Junction Transistor Gummel Plot: Collector and Base Current on logarithmic scale with base- emitter bias Note: β0=IC/IB Current gain shown 4 regions • Low current IB ~ exp(qVBE/mkT) • Ideal • Base Resistance • High-Level Injection

  32. Emitter Resistance • Transconductance gm dIC/dVBE = (q/kT)IC gm IC for BJT (vs. gm ID1/2 for MOSFET) gm(BJT) > gm(MOSFET) (better driver!) • High gm demands low emitter resistance RE to prevent VBE de-biasing since gmx= gmi/ (1 + REgmi) Thick metallization is placed over emitter diffusion regions to decrease RE

  33. Example Problem • Example problem: Assume that the data in Figure 6.4 was measured on a prototype npn transistor with a base width xB=0.5 μm. Find the Gummel Number for the transistor and find the acceptor doping. • Calculate the value of base-emitter voltage necessary to cause the electron density at the emitter edge of the base to be 1% of the base dopant density. Assume Dn~22 cm2s-1, ni at room temperature is 1.45 x 1010 cm-3.

  34. Output Characteristics • a)normal or forward active mode with VBE varying (injected electrons increase) and VBC fixed • b) normal or forward active mode with VBE fixed and VBC varying (depletion width widening into the base) first taking out injected electrons, then minority carrier electrons in the base • c) Saturation mode: No current, flat, charge stored in base, with current still some charge stored • d) Open emitter (less the ordinary reverse current) Open base (more)

  35. Bipolar Junction Transistor Common-Base Config. • Since 0  1, IC  IE  f(VCB), remaining constant when VCB  0 • As VCB increases to the value of VBCBO, the current increases rapidly (avalanche breakdown of collector base junction) • BVCBO may also occur because of punchthrough due to low base doping

  36. Bipolar Junction Transistor Common-Emitter Config. • 0 >> 1, IC  with VCB  • Base width modulation meaning the width is dependent on voltage (Early Effects) leads to finite output conductance • To reduce the influence of collector base voltage on collector current, the magnitude of VA should be increased • Increase ratio of base majority charge per unit area to the small signal capacitance (how?) • Reduces movement of base collector boundary into the base region • Note: balance between Early voltage and current gain

  37. Lecture Outline • Bipolar Junction Transistor • Base Resistance • Exponentially Doped Base • Bandgap Narrowing • Base Transit Time • Webster Effect

  38. Base Resistance • Emitter base current is spread over the active region of the emitter • Base current decreases continuously as we move toward the center line • Current crowding toward the perimeter of the emitter increases with bias • Localized heating occurs • To reduce base resistances large interdigitated, comb like base and emitter contacts are used.

  39. Base Resistance • RB is the base spreading resistance and is variable with current • Reduction in base resistance corresponds to decreasing path length from base electrode to the effective region as current increases

  40. Drift BJT • Exponentially Doped Base • Close to diffused base region • Built-in Field  = (kT/q)(a/WB) (constant) • Assistance in transport of carriers across the base • Base transit time is reduced • Important for high frequency devices • Another approach is to use alloys to grade the base • What is a common material used for this?

  41. Heavy Doped Emitter • Bandgap Narrowing In degenerately doped emitter, impurity states broadened into bands (due to Pauli Exclusion Principle) and merged with conduction or valence band edge, resulting in an effective reduction of bandgap Eg = (3q2/16s)(q2NE/skT)1/2  NE1/2 When T, Eg  Eg = 22.5(NE/1018)1/2 [meV]

  42. Bandgap Narrowing • Increase in intrinsic carrier density, ni, due to decrease in Eg niE2 = NCNV exp(-(Eg-Eg)/kT) niE2 = ni2exp(Eg/kT) nB = ni2/NB pE = niE2/NE = (ni2/NE)exp(Eg/kT) Increase back injection Net effect is increased minority carrier concentration in the emitter.  ~ nE/pE ~ exp(-Eg/kT) NE  Eg   Reduction in current gain.

  43. Base Transit Time • Diffusion is dominant Excess base charge QB = 0WBqAEn(x)dx n(x) ~ x (linear) QB = qAEn(0)WB/2 • Since tB = QB/IC and n(0)  exp(qVBE/kT), IC = AJn|x=WB = (qADnni2/(NAWB)) exp(qVBE/kT) n(0) n(x) QB 0 WB

  44. Base Transit Time • Base Transit Time tB = QB/IC = WB2/(2Dn) For WB = 1m and Dn ~ 35cm2/s, tB = 143ps SincetB = WB/(n) = WB2/(nV), V ~ 50mV

  45. Base Transit Time • For a drift BJT, tB = WB2/(Dn), where  is between 2 and 4 • For an arbitrarily doped base, tB = (0WBp dx) (0WBn dx)/ [Dnni2exp(qVBE/kT)]

  46. Webster Effect • Reduction in base transport time because of non-uniform majority carrier concentration induced by carrier injection • Built in electric field develops in the base to create an opposing majority carrier drift current • Under high-level injection for npn BJT, tB  WB2/(4Dn) when n(0) >> NA So, tB(HL) = tB(LL)/2 Dn is effectively doubled (Webster Effect) • Ambipolar Transport!

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