Lecture 17 Diode and Transistor Theory

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Lecture 17Diode and Transistor Theory

• Diode theory
• MOSFET transistor theory
• Summary

• Michael L. Bushnell
• CAIP Center and WINLAB
• ECE Dept., Rutgers U., Piscataway, NJ

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Diode Modeling

• Model necessary semiconductor junction aspects in
  analog circuit models
• Breakdown voltage and output resistance depend on
  reverse-biased pn-junction depletion region
  properties
• Space charge region
• ND cm-3 n region doping (constant)
• NA cm-3 p region doping (constant)
• Built-in potential Y0 VT ln
• VT k T / q 0.026 V at 300o K

NA ND ni2
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Diode Model
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Depletion Region Widths

• Conservation of charge W1 NA W2 ND
• Poissons equation (in 1 dimension)

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Depletion Region Widths (contd)

• Linear e Integrate to get
• Let V 0 for x - W1
• At x 0, define V as V1
• Potential difference from x 0 to x W2 is V2
• Total junction voltage

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Depletion Region Properties

• p side penetration
• n side penetration
• Depletion Region Capacitance
• A junction cross-sectional area

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Depletion Region Properties

• Leading to
• Valid for reverse bias VR, and for forward bias,
  provided a small current flows.
• If VD is junction bias then

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pn Junction Depletion-layer Capacitance as f
(Bias Voltage VD)
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Avalanche Breakdown

• When reverse saturation current carriers get
  sufficient energy at ecrit they collide with
  silicon lattice atoms and create new
  electron-hole pairs -- Avalanche breakdown

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Avalanche Breakdown

• Reverse avalanche current near breakdown
• IRA M IR
• M (multiplication factor)
  , 3 n 6
• BV breakdown voltage
• Relevance Diodes operating at avalanche
  breakdown (Zener diodes) are commonly used as
  voltage references
• Zener breakdown different in heavily-doped
  junction, e becomes large enough to strip e--
  from valence bands tunneling
• Works only for BV lt 6 V

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Cross Section and Top View of n- Channel
MOS Transistor

• Depletion width under oxide
• f potential in depletion layer at Si SiO2
  interface
• Depletion region charge

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nMOS Cross Section With Positive VGS Applied

• Channel inverts when potential in Si reaches 2
  ff, ff 0.3 V

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MOSFET Transistor

• When inverted, with no substrate bias, depletion
  region contains fixed charge
• With substrate bias VSB
• Threshold voltage

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Large-Signal Behavior

• Induced channel charge
• nd saturation drift velocity
• W device width
• L channel length
• Voltage drop in channel along dy

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Large-Signal Behavior (continued)

• Substitute integrate
• Or
• When we enter saturation, drain end pinches off
  (like JFET)
• Finding ID by replacing VDS VGS Vt

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Summary

• Diode theory
• MOSFET transistor theory