Example 1: Equilibrium PN-Junction

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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 n-regions. 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 voltageis calculated using:

2ln 0.714A D

bi Ti

N NV V V

n

One can also extract the built-in voltage from the energyband diagram using:

10.714bi Cp CnV E E V

q

Vbi

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Example 1: Charge Density

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.

W

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Example 1: Electric Field Profile

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.

Emax

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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 n-regions. 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 thegraph for the net built-involtage 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 eitherthe 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 currentdecreases.

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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

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.

W

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Example 3: Electric Field Profile

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.

InversionchargeDepletioncharge

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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

Ideal characteristics

Series resistanceeffect

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Example 4: Current Density, Cont’d

10 exp

T

VI I

V

V=V2-V1=RID

=>R= V/ID

The ideal diode current is

The non-ideal diode current is:

From the equality of thecurrents we have:

20 exp

T

V RII I

V

2 1 0.170.18

0.67

V VR

I

V1 V2

Example 1: Equilibrium PN-Junction

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