Download Operation of a PN Junction

Drexel University
ECE-E302, Electronic Devices
PN Junction Diodes
Oct. 2013 BN ZW
Operation of a PN Junction
Objectives:

Investigate the DC current-voltage characteristics of the PN junction diode.

Experimentally verify theoretical model developed in lecture and extract ideality factor,
and reverse saturation current.

Produce a piece-wise linear model for the diode.

Compare closed form, piece-wise linear model, and PSPICE
simulations with
experiment.
Theory of Operation:
We can derive the diffusion current of holes from n-side to the p-side of a diode for
x ³ xn , where xn is the edge of the depletion region on the n-side, as:
éx - xù
éæ qVa ö ù
Dp
J p,diff = q
pn0 exp êç
ú
÷ -1ú ´ exp ê n
è
Lp
ë kT ø û
êë L p úû
Where Va is the applied bias. The hole diffusion current at the edge of depletion region (x n ) is:
éæ qV ö ù
D
J p,diff = q p pn0 exp êç a ÷ -1ú
Lp
ëè kT ø û
Similarly, electron diffusion current at the edge of depletion region (-x p ) is:
J n,diff = q
éæ qV ö ù
Dn
n p0 exp êç a ÷ -1ú
Ln
ëè kT ø û
Total current is the sum of these current and is independent of space, given b:
æ D
ö
Dp
é qV
ù
n
ç
J total = ç q n p0 + q
pn0 ÷÷ exp ê a -1ú
ë kT
û
Lp
è Ln
ø
æ D
ö
Dp
é qVa ù
n
ç
or I total = I 0 exp ê
-1ú, where I 0 = ç q n p0 + q
pn0 ÷÷ is the reverse saturation current.
ë kT
û
L
L
è n
ø
p
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Drexel University
ECE-E302, Electronic Devices
PN Junction Diodes
Oct. 2013 BN ZW
In practice an ideality factor n is phenomenologically added to the above closed-form description
in order to better model the diode I-V, resulting in:
é qV
ù
I d = I 0 exp ê a -1ú,
ë nkT û
(1)
Where Id is DC current through diode, and Vd is the voltage across the diode. Additionally:
lo= reverse saturation current
q = electron charge (1.6 x 10-19 C)
k = Boltzmann's constant (1.38 x 10-23 J/K)
T = absolute temperature in Kelvin degree
n = ideality factor, 1 ≤ n ≤ 2
For forward bias and voltages V greater than the turn-on voltage (0.2 V for germanium,
0.7 V for silicon, 1.2 V for GaAs), the “ 1 ” term in equation 1 can be ignored.
Equation (1) describes a nonlinear relation between the current Id and the voltage Vd of the diode,
and causes difficulty in analysis of electronic circuits. For example, consider the simplest circuit
we can construct as shown on the right. Assuming VDD =
1V and R = 500 Ω, we are asked to find ID, and VD.
Writing the loop equation, we have:
VDD = I d Rd +VD
(2)
And the diode equation is
é qV
ù
I d = I 0 exp ê d -1ú.
ë nkT û
Figure 1. A simple diode circuit.
These are two equations with two unknowns (Id, and Vd), which cannot be solved in closed form,
but can be solved numerically, or graphically. We can also produce a piece-wise linear model of
the diode for quick calculations. Finally we can use electronic circuit simulators such as PSPICE
in order to find Id and Vd.
Figure 2 shows the current-voltage relation of a diode as well as its approximation by a
piecewise linear model. The circuit components for the piecewise linear model are also shown.
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Drexel University
ECE-E302, Electronic Devices
PN Junction Diodes
Oct. 2013 BN ZW
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Drexel University
ECE-E302, Electronic Devices
PN Junction Diodes
Oct. 2013 BN ZW
Figure 2. left) Current-Voltage relation of a diode (black) according to Eq. (1) is approximated by a
piecewise linear model (blue). Middle) Piecewise linear model of diode. Right) Circuit elements of the
piecewise linear model.
Experiment:
Note: All of the work below should be done during the lab, not afterwards.

Set up the circuit of Figure 3, below.
V
V
A
DC Supply
500 
A
DC Supply
500 
Figure 3. Experimental set-ups for forward bias (left) and reverse bias (right)

Vary the DC power supply, and construct a table with measured Id vs Vd.

Use the curve tracer board and measure Id vs Vd.

From the measured data, determine the reverse saturation current I0 and ideality factor n.

From the measured data, determine piecewise linear circuit elements, namely, the turn-on
voltage V0 and the series resistance rD.
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Drexel University
ECE-E302, Electronic Devices
PN Junction Diodes
Oct. 2013 BN ZW

Simulate the circuit of Figure 1 in PSPICE, use parameters you have extracted above.
Note rD is RS in PSPICE.
Now assume the DC supply is 2V. Find Id and Vd from:
a) Closed form model of Equation 1,
b) Graphically from I-V you have generated. That is, plot (1) and (2) together. Use Matlab or
Excel.
c) Piecewise linear model of Figure 2.
d) PSPICE simulation
e) Measurement
Report:
Use ECE-E302 report template. Explain how you performed parameter extraction for closed
from, SPICE simulation, and piecewise linear model. Compare the modeling results with
measurements. Explain in what voltage or current range equation (1) adequately describes
diode behavior. Is the model valid for high injection regime (read your textbook to learn what
this means).
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