BJT Bipolar Junction Transistors and HBJT Heterojunction Bipolar Junction Transistors

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BJT Bipolar Junction Transistors and HBJT
Heterojunction Bipolar Junction Transistors

• ELEE4328 Fall 2009
• Week 13

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Bipolar Junction Transistor Beta

• The simple circuit model of a bipolar junction
  transistor is that of a current amplifier with
  current gain Beta ? Ic/Ib with base current Ib
  determined by a diode circuit (note ? Ic/Ie )
• base collector ? Ic/Ib
• Ib Ic
  Ie IcIb
• Vbe Ic ?Ib Ie
  IcIc/?(11/?)Ic
• Vce
  Ie((?1)/?)Ic
• Ie emitter Ic(?/(?1)Ie?Ie

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Bipolar Junction Transistor Beta

• By definition ? Ic/Ie has a value less than 1
  and from the previous slide ? ?/(? 1).
• Solving for ? in terms of ? gives ? ?/(1-?)
• Beta is in the range 20 lt ? lt 1000
• The corresponding alpha range is approximateley
  .05 lt ? lt0.999
• The beta and corresponding alpha are determined
  by ? the injection efficiency and B the base
  transport factor.

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Physical bipolar junction transistor layout in
one dimension

• The physical layout puts the base between the
  emitter and collector shown here for a npn
  transistor. The base is very narrow WB lt1 ?.
• Emitter Base Collector
• WEmitter WBase WCollector
• ND n type NA p type ND n type

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Injection Efficiency ?

• The base emitter diode has a emitter that is
  purposely doped much higher than the base (NDgtgtNA
  for a npn transistor) so that the current will be
  mostly electrons flowing into the base. The ratio
  of the eb diode electron current into the base
  divided by the total diode current flowing in the
  diode is the injection efficiency ? and is less
  than but close to 1. Note that the short diode
  equation is used.

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Injection efficiency Beta

• Assuming no recombination in the base beta will
  only depend on the injection efficiency.
• By definition the injection efficiency is the
  ratio of electron current into the base divided
  by total current that is ? Ic/Ie ?.
• From the equation for beta in terms of alpha we
  have then

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Base transport factor B

• The second factor that determines alpha and beta
  is the base transport factor that acounts for
  loss of current in the base due to recombination.
• For the npn transistor electrons flow from the eb
  diode to the collector depletion region by
  diffusion. The current density divided by the
  average charge gives the average velocity in
  crossing the base

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Base transport factor B 2

• Dividing the base width WB by the average
  velocity gives the base transit time
• An estimate of the fractional amount of
  recombination is given by the ratio of the
  transit time to lifetime and the base transport
  factor would be the amount remaining or 1 minus
  the fraction that recombines

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Base transport factor beta

• Assuming the diode injection efficeincy is 1 the
  beta will be determined by the base transport
  factor.
• In this case the base current is the
  recombination current which is 1-B and the
  collector current is the base transport factor
  times the emitter current or

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Beta using both injection efficiency and base
transport factor

• To take both injection efficiency and base
  transport factor into account alpha is just the
  product of the two
• Beta is found from the alpha as

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npn and pnp ? And B

• It is important to properly identify the
  constants in the equations for ? and B
• For the npn case done so far
• For the pnp bipolar junction transistor

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HBJT with graded composition eb diode

• For the graded composition eb heterojunction
  diode the injection effciency is modified by
  including the two ni of the eb diode.
• The HBJT is usually a AlxGa1-xAs wide band gap
  emitter with GaAs base and collector.
• The wideband gap allows NABase?NDEmitter
  decreasing base resistance while maintaining ?
  close to one.
• The graded composition effect on WB and the base
  transport factor except for NA increasing is
  usually neglected.

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Collector region

• For the npn transistor the electrons diffuse
  across the base and are swept away in the
  collector region by the reverse biased base
  collector pn junction.
• To make the base width independent of the
  collector voltage the base is doped a much higher
  density than the collector, that is for the npn
  transistor NAbasegtgtNdcollector .
• This also gives the collector base junction a
  high breakdown voltage in addition to minimizing
  base width collector voltage dependence.

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Collector Voltage Base Width Modulation

• As the collector junction in reverse bias voltage
  is increased it extends further into the base
  decreasing the effective base width, increasing
  the base transport factor, and increasing beta.
  This is called the Early effect.
• The increased beta results in a high collector
  current modeled by an Early voltage, the voltage
  all collector currents if extended to negative
  voltages would converge upon. The Early voltage
  is calculated from measured characteristics as

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Kirk effect or Base Pushout and High Current Beta
Decrease

• As the collector current increases the majority
  carrier concentration injected from the emitter
  (electrons for npn) exceeds the dopant
  concentration in the collector reducing the
  effective built in voltage of the base collector
  junction and decreasing the depletion region
  width. This results in an increased base width Wb
  and a decreased beta at high current.

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Recombination and Low current Beta Decrease

• At low currents emitter base recombination
  current due to defects in the base emitter
  junction decreases the injection efficiency and
  decreases beta.
• In III-V HBJT the Silicon Nitride Si3N4 is less
  effective that SiO2 in producing a stable surface
  resulting in high surface recombination in HBJTs
  and decreased beta at low currents.

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Gummel plot

• The decrease in beta at low and high currents is
  indicated by a Gummel plot that plots the log of
  collector and base current versus Vbe for a fixed
  Vce 1V or greater.
• Log Ic Ic
• Ib
• Vbe

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Gummel Poon Model for dopant varying with position

• The short diode current expression contains
  factors 1/(NDWE) and 1/(NAWB) for the npn.
• A charge density of the emitter QE (NDWE) and
  charge density of the base QB (NAWB) can be
  seen in the expressions.
• For dopant concentration variation with position
  the QE and QB referred to as Gummel numbers
  become

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Current crowding and base resistance

• Because there is a finite base resistance the
  base emitter junction is more forward biased
  close to the base contact and this is where the
  highest emitter to collector current flows.
• Concentrated collector current results in
  localized heating further concentrating the
  current at the base contact edge.
• The effect is reduced by increasing the edge of
  length of the emitter relative to its area, and
  using multiple emitters and or multiple base
  contacts forming an interdigitated base emitter.
• The emitter length (and gate length in HEMT and
  MOSFET) of a single emitter finger is kept to
  less than 75 microns due to phase shift
  transmission line effects along the emitter at
  high frequencies.

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Decreasing IC due to heating.

• For high frequency power transistors the DC bias
  point characteristic shows a decreasing collector
  current with increasing VCE.
• The Ic characteristic is given in terms of a
  thermo electric feedback coefficient ? (on the
  order of 1mV/degC)
• The temperature increase is given by
• Rth the thermal resistance can be calculated from
  h the die thickness h and thermal conductivity
  Kth
• The dynamic small signal characteristic does not
  follow static or low frequency decrease in
  collector current with increasing VCE
  characteristic (this would be a negative Rce) as
  thermal transients are on the order of 1/10 usec.

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Thermal Id current collapse

• There is an additional current collapse effect
  that can occur for multiple finger emitter
  designs where all the current is in a single
  emitter.
• An estimate of the current necessary for current
  collapse is given by (RE one emitter)

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Breakdown voltages

• For the npn BJT NDEmittergtgtNABasegtgtNDCollector
  and this results in a low EB diode breakdown
  (?7V) while NDCollector is made purposely low to
  get a high breakdown voltage (20 to 5000V).
• The high breakdown voltage is BVCBO collector
  base breakdown with emitter open.
• The breakdown voltage of the collector to emitter
  with base open BVCEO is much lower as holes
  generated in the collector region become a base
  current. The current is given by (n is a
  parameter)

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Ebers Moll model

• The Ebers Moll model models the transistor as two
  transistors one forward and one inverse.
• The inverse transistor generates an inverse
  characteristic for the BJT operated in inverse
  mode.

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Ebers Moll model 2

• In terms of the diodes and alphas the equations
  for the Ebers Moll model are
• From the ?, B it can be shown that

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Ebers Moll model 3

• IES is the emitter current with the base
  collector junction shorted and ICS is the
  collector current with the base emitter junction
  shorted.
• Model handles saturated forced beta condition

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Ebers Moll model 4

• In general the reverse beta is low and the
  reverse alpha is much smaller than 1.
• Inverse beta is significant for TTL and TTLS as
  the input high current IIH is the inverse beta
  current flowing into the emitter of the input
  transistor making it act as collector.
• It also gives correct results for saturation and
  forced beta conditions where the forced beta
  current assume both diodes conducting.