Transcript nanoHUB.org online simulations and more Example 1: Equilibrium PN-Junction Problem Statement: A pn-diode has NA=ND=1016 cm-3 doping and a length of 1 um of.

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Example 1: Equilibrium PN-Junction
Problem Statement:
A pn-diode has NA=ND=1016 cm-3 doping and a length of 1 um of both p and nregions. Calculate analytically and verify via simulations the values of the:
(a) Built-in voltage Vbi
(b) Total depletion region width W.
(c) Maximum electrical field at the metallurgical junction.
Analytically, the built-in voltage
is calculated using:
Vbi
 N A ND 
Vbi  VT ln 
  0.714V
2
n
 i 
One can also extract the
built-in voltage from the energy
band diagram using:
Vbi 
1
ECp  ECn   0.714V

q
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Example 1: Charge Density
W
Question1: What is the analytical value of the total depletion region width?
Answer1: The analytical value of the depletion region width is 0.432 um.
Question2: What is the extracted simulated value of the total depletion region width?
Answer2: The simulated value of the depletion region width is ~ 0.43 um.
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Example 1: Electric Field Profile
Emax
Question1: What is the analytical value of the peak electric field?
Answer1: The analytical value of the peak electric field is 33.14 kV/cm.
Question2: What is the extracted simulated value of the peak electric field?
Answer2: The simulated value of the peak electric field is 32 kV/cm.
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Example 2: PN-Junction Under Bias
Problem Statement:
A pn-diode has NA=ND=1016 cm-3 doping and a length of 1 um of both p and nregions. Simulate:
(a) Energy band profile under applied bias VA=0.6 V
(b) quasi-Fermi level variation with position
(c) electric field under bias
(d) forward IV-characteristic of the diode
The net built-in voltage is:
Vbi - VA = 0.714 -0.6 = 0.114 V
The value extracted from the
graph for the net built-in
voltage is 0.115 V.
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Example 2: Quasi-Fermi Level Variation
Question: Where is the variation of the quasi-Fermi levels significant?
Answer: The variation of the quasi-Fermi levels is significant in regions in which the
carrier concentration changes by orders of magnitude.
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Example 2: Electric Field Under Bias
Question1: Compare the equilibrium and non-equilibrium values of the field!
Answer1: The peak non-equilibrium field is lower.
Question2: Compare the equilibrium and nonequilibrium depletion region widths!
Answer2: The non-equilibrium depletion region with is smaller under forward bias.
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Example 2: Current Density
Question: How does the current vary with increasing the doping density of either
the p- or n-region, or both?
Answer: With increasing the doping density of either the p-side, or the n-side, or
both, the potential barrier for the minority carriers increases and the current
decreases.
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Example 3: Non-Symmetric
Junction
Problem Statement:
A pn-diode has NA=1016 cm-3 and ND=1018 cm-3 doping, and a length of 1 um of
both p and n-regions. Simulate:
(a) equilibrium energy band profile
(b) charge density, to see the extent of the depletion regions
(c) electric field profile to examine the contribution of the inversion charge
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Example 3: Charge Density
W
Question1: What is the analytical value of the total depletion region width?
Answer1: The analytical value of the depletion region width is 0.327 um.
Question2: What is the extracted simulated value of the total depletion region width?
Answer2: The extracted simulated value of the depletion region width is ~ 0.31 um.
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Example 3: Electric Field Profile
Inversion
charge
Depletion
charge
Question1: What is the analytical value of the peak electric field?
Answer1: The analytical value of the peak electric field is 50.2 kV/cm.
Question2: What is the extracted simulated value of the peak electric field?
Answer2: The simulated value of the peak electric field is 67.1 kV/cm.
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Example 4: Series Resistance
Problem statement:
In this exercise we will examine the series resistance effects under high bias
conditions. The p-side doping is NA=1016 cm-3 and the n-side doping is ND=1016
cm-3. The length of the p-side and the n-side region is taken to be 1 um. Plot
the following variables:
(a) Conduction band, valence band and the intrinsic level variation vs.
position for applied bias VANODE=1.2 V.
(b) Quasi-Fermi level variation.
(c) Forward IV-characteristics of a diode for applied bias between 0
and 1.2 V in 0.05 V increments. From the forward IV-characteristics under high bias conditions extract the series resistance.
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Example 4: Energy Band
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Example 4: Quasi-Fermi Level
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Example 4: Current Density
Series resistance
effect
Ideal characteristics
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Example 4: Current Density, Cont’d
The ideal diode current is
V1
 V1 
I  I 0 exp  
 VT 
V2
The non-ideal diode current is:
V=V2-V1=RID
=>
R= V/ID
 V2  RI 
I  I 0 exp 

V

T

From the equality of the
currents we have:
R
V2  V1 0.17

 0.18
I
0.67
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