PN Junctions and Diodes

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PN Junctions and Diodes

• Introduction to semiconductor theory
• Part II
• Open diode, reverse, breakdown and forward biasing

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PN junction Concentrations
Anode
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Minority and majority carriers concentrations
x
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Its clear why we have diffusion currents, but
where are the drift currents coming from?...
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How is the drift current IS created?

• Many holes that are diffused from the p-type
  side into the n-type side recombine with
  electrons. Likewise, for diffused electrons.

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Depletion region is created

• The n side of the junction is full of ionized
  donor atoms. The p side has many ionized acceptor
  atoms. Depletion region has almost no free
  carriers.

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Electric Field is created across Depletion region
E

• The n side of the junction contains immobile
  positively ionized donor atoms. The p side has
  immobile negatively ionized acceptor atoms.
• Electric field E is created. Field is not
  constant.

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Constant total charge on each side. Charges are
equal and opposite.
Field is created by integrating the charge over
x. Maximum field intensity is at x0.
Junction potential is obtained by integrating E
over x
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Built-in Junction Potential

• Built-in junction potential

V0 depends both on the doping concentrations as
well as T. Typical value for V0 is 0.6 0.8 V
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Depletion Region Widths on each side

• There is charge equality between both sides of
  the depletion region

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Depletion Region Width

Where es is the electrical permittivity of Si
11.7e0 1.0410-12 F/cm Concentrations are in
per cm3. Results unit is m. Typical width
are 0.1 1 µm.
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Depletion Region example

• Let NA1017/cm3 and ND1016/cm3
• Let T300oK ? ni1.51010/cm3
• With these typical values, we obtain V0728mV.
• We then obtain Wdep0.32µm.
• Much of the depletion region will be on the n
  side of the junction (10001 widths ratio)

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Case 2 PN junction under reverse bias conditions
We shall analyze this case, assuming a forced
tiny reverse current
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Actual circuit is driven by a reversely connected
battery
V must be smaller than the breakdown voltage
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Observe electrons flowing in the external
circuit from the n type region to the p type
region
As electrons leave n region, holes leave p region
? Depletion region widens ? More charge
accumulates in depletion region
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Observe electrons flowing in the external
circuit from the n type region to the p type
region
? Barrier voltage increases from V0 to V0VR,
where VR is the external reverse voltage ?
Diffusion current ID decreases, whereas drift
current IS remains unchanged IS-IDI
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Depletion Region Width (VVR)
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Depletion Region Capacitance
Grading coefficient m depends on the
concentration profile
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Depletion Region Capacitance (Numerical Example)
For the typical values NA1017/cm3 and
ND1016/cm3 (T3000K), we obtain V00.728V ?
Cj00.32 fF/µm2 ? Cj0.41pF
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What is IS?

• Whenever VR is connected, there is an initial
  current that charges the depletion region
  capacitor to qjqNqNDxNA
• Steady state current is IS-IDIS as ID is very
  small

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Case 3 PN junction in the Breakdown Region
(VRltVZ)

• This time let us assume IgtIS
• As VR increases, depletion layers width
  increases, and ID goes all the way to 0
• There is no steady state as IgtIS
• Barrier voltage increases.

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Two Breakdown Mechanisms

• Zener Effect (VZlt5V)
• OR
• Avalanch Effect (VZgt7V)

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Zener Effect

• As VR increases, the field E increases to a point
  where it can break Si covalent bonds
• ? Hole/electron pairs are created to supplement
  the current in the reverse direction
• ? Junction voltage stops increasing

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Avalanch Effect

• As VR increases, speed of the minority carriers
  increases to a point where by collision these
  break Si covalent bonds
• ? (as in the Zener effect)
• Breakdown, in any effect, is not destructive, as
  long as the diodes power rating is not exceeded.

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Case 4 PN junction in forward-bias conditions

• I carries electrons into the n-region and holes
  into the p-region
• HOW??

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Forward biasing causes

• Depletion layer width decreases ? Barrier
  voltage decreases ? More holes from p-region
  cross over to the n-region (by diffusion), and
  more electrons from n-region cross over to
  p-region, by diffusion

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Forward-biased junction currents

• The total diffusion current ID increases
• At steady state ID-ISI

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V is the applied forward voltage. Pn(xn) result
above without proof
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Minority carriers profile

• Another result (exponential profile)
• pn(x)pn,0 (pn(xn)-pn,0)exp-(x-xn)/LP
• LP is the diffusion length. It depends on the
  steepness of the majority carriers profile

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Diffusion Length

• pn(x)pn,0 (pn(xn)-pn,0)exp-(x-xn)/LP
• Typical value LP between 1 and 100 nm
• The smaller LP, the faster injected holes
  recombine with majority electrons

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Recombination Time Constant

• Let tP denote the average time for injected
  minority holes recombination
• Typical values for tP 1 to 104 ns
• Result LP(DP tP )1/2

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Derivation of Diodes Steady State Holes Current
Formula
At steady state the current is constant
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Diodes Steady State Electrons and Total Current
Formulas
Similar to holes current
Total diodes forward-bias current
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Diodes Forward-Bias Total Current Formula
Replace pn,0 by ni2/ND and np,0 by ni2/NA
Where
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Diodes Saturation Current IS
IS is directly proportional to the junction area A
IS strongly depends on the temperature due to the
ni2 coefficient
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Numerical Example (Diode in Forward Bias)

• Let NA1017/cm3, ND1016/cm3, ni1.51010/cm3,
  LP5µm, LN10µm, A2500 (µm)2,
• DP (in n region) 10 cm2/Vs
• DN (in p region) 18 cm2/Vs
• Let I0.1mA
• Then IS210-15 A and V0.616 V