The Devices: Semiconductor Fundamentals and Diodes

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The DevicesSemiconductor Fundamentals and Diodes

• References
• Semiconductor Device Fundamentals,
• R. F. Pierret, Addison-Wesley
• Digital Integrated Circuits A Design
  Perspective, J. Rabaey, Prentice Hall

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Semiconductor Fundamentals
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Silicon
Core of Si
Mostly empty
Ec
Shared valence electron
Ev
Mostly filled
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Electron and Hole
Carrier density n p ni
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Doping
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Junction Diode
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pn-Junction Diode

• p-type material is doped with acceptor impurities
  such as boron holes as majority carriers
• n-type material is created with donor impurities
  such as phosphorus or arsenic electrons
  are majority carriers
• Al contacts provides contact to p and n terminals
  
  

Al
A
B
sio2
p
n
Diode symbol
One-dimensional representation
Cross-section
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Energy Band Diagram
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Bringing p- and n-Materials Together

• Large concentration gradient at boundary
• Gradient causes electrons to diffuse from n to p
  and holes to diffuse from p to n
• p-type material is negatively charged with fixed
  acceptor ions in the vicinity of pn-boundary.
• n-type material is positively charged with fixed
  donor ions near the junction
• Electric field across the boundary directed from
  n to p-region
• Counteracts the diffusion of holes and electrons
  as it causes electrons to drift from p to n and
  holes to drift from n to p

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Redistribution of Charge
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Equilibrium
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Depletion Region
NA gt ND
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Built-In Potential
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Apply a Forward Bias VD

• Applied potential lowers the potential barriers
• Flow of mobile carriers across the junction
  increases as the diffusion current dominates the
  drift component
• Carriers traverse the depletion region and are
  injected in n- or p-regions where they become
  minority carriers
• Minority carriers diffuse through the region as a
  result of concentration gradient until they
  recombine with a majority carrier
• Current flow through the diode (exponential
  dependence on applied bias)

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Forward Bias
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Forward Bias
minority carrier concentration at equilibrium
value
Wn
Wp
Linear decay valid for short-base diode model
diffusion
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Linear Decay under Short-Base Diode Model

• Gradient in minority concentration causes
  diffusion current in neutral or bulk regions
• Diffusion current in n-region

Dp diffusion coefficient
AD junction area
q electron (hole) charge
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Law of the Junction

• Concentration at the edge of depletion region

• Concentration in the n-region under equilibrium
  condition

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Diode Current

• p-component of Diode current

• Diode current p-component n-component

• Saturation current

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Assumptions in the Analysis

• Short-base diode model widths of p and n-regions
  are smaller than a material constant called
  diffusion length Lp and Ln
• Long-base diode model minority carriers
  recombine with majority carriers in neutral
  region
• Minority carrier concentration drops
  exponentially
• In one diffusion length, the excess minority
  carrier concentration drops to 1/e ( 0.37) of
  its original value
• After a few diffusion lengths, virtually all
  injected carriers recombine minority carrier
  concentration reaches its thermal equilibrium
  value
• Resistance of neutral region is negligible
• Minority carrier concentration is much lower than
  majority concentration (low-injection condition)

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Reverse Bias

• Potential barrier is raised
• drift current becomes dominant current flows
  from n to p regions
• Therefore, the minority carriers in the neutral
  regions is small, drift current is small

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Reverse Bias
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Reverse Bias
-

Diffusion of minority carriers towards junction -
once they reach the junction they are swept
across the junction by electric field in the
depletion region
Actually larger than IS
due to thermal generation of hole-electron in
depletion region
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Diode Current
(a) On a linear scale
(b)On a logarithmic scale (forward bias)
Reverse bias VD ltlt 0, ID - IS
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Diode Model

ID

VD
VD

VDon
-
_
_
First order Diode Model
Ideal Diode Model
Fixed Vdon, typical value 0.7V
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Dynamic or Transient Behavior

• Determined by how fast the charges can be moved
  around
• Depletion region capacitance
• Forward bias reduces depletion-region
  width
• Reverse bias increases space charge and
  width of depletion-region

Depletion region charge
Depletion region width
Maximum electric field
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Depletion Region as Capacitance

• Space charge region (few mobile carriers) can be
  conceived as an insulator
• n and p regions are capacitor plates

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Equivalent Capacitance

• Generic expression for junction capacitance

m grading coefficient 1/2 for abrupt
junction 1/3 for linear or graded junction

• Junction capacitance is a small signal parameter
• Replace Cj by Ceq
• for a given voltage swing from Vhigh to Vlow, the
  same amount of charge is transferred as predicted
  by non-linear model

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Junction Capacitance
Cj(fF)
VD(V)
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Diffusion Capacitance

• Under forward bias, extra capacitance effect due
  to extra minority carrier charges stored at the
  boundaries of depletion region
• Excess charge directly related to current flowing
  through diode
• For n-region

Mean Transit Time
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Mean Transit Time and Diode Current

• Mean transit time is an important device
  parameter

For long-base diode

• Diode current (as a function of excess minority
  carrier charge)

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Diode Switching Time
Difficult to find solution !!
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Two Operation Intervals for Diode (Turn-Off)
Transient

• Initially reverse current I2 is used to remove
  excess minority carrier charge from neutral
  regions
• diode remains ON and the voltage over the diode
  is approximately constant
• linear drop in voltage requires exponential drop
  in current
• While building a reverse bias over diode, the
  space charge changes
• Cj dominates performance

In reality, both intervals overlap a little !
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Diode Switching Time
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Removal Of Excess Charge
Removes (add) excess carrier charge
Sustains normal diffusion current
Initial value of and
Turn-off time can be derived by solving for t
t1 for which QD evaluates to O
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Changing the space charge

• Once diode turns off, all source current flows
  through resistor
• Reverse bias extra space charge has to be
  provided (reverse bias current ignored)
• Assume VD (t t1) 0

90 is reached after 2.3 time constants Rsrc.Cj
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Turn-on transient

• Before it can be turned-on, space charge has to
  change first
• Solving for VD(t t3) 0 gives
• Excess minority charge exponentially reaches its
  final value

Takes for QD to reach 90 of final value
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Diode Model
RS

CD
VD
ID
_
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SPICE Parameters
First Order SPICE diode model parameters
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Secondary Effects

• Voltage drop in neutral region (resistance 1 to
  100 )
• Avalanche breakdown
• Reverse bias high implies magnitude Of electrical
  field across junction is high
• Carriers crossing depletion region reach high
  velocity
• High energy carriers on collision with immobile
  Si atom create electron-hole pairs
• These carriers in turn create more carriers
• Critical field ? 2?105V/cm for impurity
  concentrations of the order of 1016cm-3
• Saturation current approximately doubles every
  5-8ºC
• ICs rely heavily on reverse bias diodes
• increasing temperature causes leakage current to
  increase and decreases isolation quality

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Series Resistance
At higher current level, the effect of series
resistance kicks in Needs a larger applied
voltage to achieve the same level of current