Ideal Diode Equation
Topics of This Lecture
• Ideal Diode Equation
– Its origins
– Current versus Voltage (I-V) characteristics
– How to calculate the magnitude of the variables in
the equation using real data
– What the limitations of this equation are
– How it is used in PSpice simulations
P-N junctions
• The voltage developed
across a p-n junction
caused by
– the diffusion of electrons
from the n-side of the
junction into the p-side and
– the diffusion of holes from
the p-side of the junction
into the n-side
Built-in Voltage
kT  N D N A 

f 
ln 
2

q  ni 
Reminder
• Drift currents only flow when there is an
electric field present.
• Diffusion currents only flow when there is a
concentration difference for either the
electrons or holes (or both).
I ndrift  qA n nE
I pdrift  qA p pE
I
drift
 Aq  n n   p p E
I
diff
n
dn
 qADn n  qADn
dx
I
diff
p
I
diff
dp
  qAD p p   qAD p
dx
diff
diff
 I n  I p  qADnn  D p p 
I T  I diff  I drift
Symbol for Diode
Biasing a Diode
• When Va > 0V, the diode is forward biased
• When Va < 0V, the diode is reverse biased
When the applied voltage (Va) is zero
• The diode voltage and current are equal to zero
on average
– Any electron that diffuses through the depletion
region from the n-side to the p-side is
counterbalanced by an electron that drifts from the pside to the n-side
– Any hole that diffuses through the depletion region
from the p-side to the n-side is counterbalanced by an
hole that drifts from the n-side to the p-side
• So, at any one instant (well under a nanosecond), we may
measure a diode current. This current gives rise to one of
the sources of electronic noise.
Schematically
Modified from B. Van Zeghbroech, Principles of Semiconductor Devices
http://ece-www.colorado.edu/~bart/book/
Applied voltage is less than zero
• The energy barrier between the p-side and n-side
of the diode became larger.
– It becomes less favorable for diffusion currents to flow
– It become more favorable for drift currents to flow
• The diode current is non-zero
• The amount of current that flows across the p-n junction
depends on the number of electrons in the p-type material
and the number of holes in the n-type material
– Therefore, the more heavily doped the p-n junction is the smaller
the current will be that flows when the diode is reverse biased
Schematically
Modified from B. Van Zeghbroech, Principles of Semiconductor Devices
http://ece-www.colorado.edu/~bart/book/
Plot of I-V of Diode with Small
Negative Applied Voltage
Applied Voltage is greater than zero
• The energy barrier between the p-side and n-side of
the diode became smaller with increasing positive
applied voltage until there is no barrier left.
– It becomes less favorable for drift currents to flow
• There is no electric field left to force them to flow
– There is nothing to prevent the diffusion currents to flow
• The diode current is non-zero
• The amount of current that flows across the p-n junction depends
on the gradient of electrons (difference in the concentration)
between the n- and p-type material and the gradient of holes
between the p- and n-type material
– The point at which the barrier becomes zero (the flat-band condition)
depends on the value of the built-in voltage. The larger the built-in
voltage, the more applied voltage is needed to remove the barrier.
» It takes more applied voltage to get current to flow for a heavily
doped p-n junction
Schematically
Modified from B. Van Zeghbroech, Principles of Semiconductor Devices
http://ece-www.colorado.edu/~bart/book/
Plot of I-V of Diode with Small Positive
Applied Voltage
Ideal Diode Equation
• Empirical fit for both the negative and positive
I-V of a diode when the magnitude of the
applied voltage is reasonably small.

I D  I S  e

qVD
nkT

 1

Ideal Diode Equation
Where
ID and VD are the diode current and voltage, respectively
q is the charge on the electron
n is the ideality factor: n = 1 for indirect semiconductors (Si, Ge, etc.)
n = 2 for direct semiconductors (GaAs, InP, etc.)
k is Boltzmann’s constant
T is temperature in Kelvin
kT/q is also known as Vth, the thermal voltage. At 300K (room temperature),
kT/q = 25.9mV
Simplification
• When VD is negative
I D ~ I S
• When VD is positive
ID ~ ISe
qVD
nkT
To Find n and IS
• Using the curve tracer, collect the I-V of a
diode under small positive bias voltages
• Plot the I-V as a semi-log
– The y-intercept is equal to the natural log of the
reverse saturation current
– The slope of the line is proportional to 1/n
q
ln I D 
VD  ln I S
nkT
Example
Questions
• How does the I-V characteristic of a heavily
doped diode differ from that of a lightly doped
diode?
• Why does the I-V characteristics differ?
• For any diode, how does the I-V characteristic
change as temperature increases?
• For the same doping concentration, how does the
I-V characteristic of a wide bandgap (EG)
semiconductor compare to a narrow bandgap
semiconductor (say GaAs vs. Si)?
What the Ideal Diode Equation Doesn’t
Explain
• I-V characteristics under large forward and
reverse bias conditions
– Large current flow when at a large negative
voltage (Breakdown voltage, VBR)
– ‘Linear’ relationship between ID and VD at
reasonably large positive voltages (Va > f)
VBR or VZ
Slope = 1/RS
Slope = 1/rz
Von
Nonideal (but real) I-V Characteristic
• Need another model
– Modifications to Ideal Diode Equation are used in
PSpice
• We will see this in the list of parameters in the device
model
– We will use a different model
• It is called the Piecewise Model
PSpice
• Simplest diode model in PSpice uses only the
ideal diode equation
• More complex diode models in PSpice include:
– Parasitic resistances to account for the linear regions
– Breakdown voltage with current multipliers to map
the knee between Io and the current at breakdown
– Temperature dependences of various parameters
– Parasitic capacitances to account for the frequency
dependence
Capture versus Schematics
• It doesn’t matter to me which you use
– I find Schematics easier, but the lab encourages
the use of Capture
PSpice Schematics
Device Parameters
*** Power Diode ***
Type of Diode
.MODEL D1N4002-X D
Part Number
( IS=14.11E-9
Reverse Saturation Current
N=1.984
Ideality Factor
RS=33.89E-3
Forward Series Resistance
IKF=94.81
High-Level Injection Knee Current in Forward Bias
XTI=3
Temperature Dependence of Reverse Saturation Current
EG=1.110
Energy Bandgap of Si
CJO=51.17E-12
Junction Capacitance at Zero Applied Bias
M=.2762
Grading Coefficient Inversely Proportional to Zener Resistance
VJ=.3905
Turn-on Voltage
FC=.5
Coefficient Associated with Forward Bias Capacitance
ISR=100.0E-12
Reverse Saturation Current During Reverse Bias
NR=2
Ideality Factor During Reverse Bias
BV=100.1
Breakdown Voltage
IBV=10
Current at Breakdown Voltage
TT=4.761E-6 )
Transit Time of Carriers Across p-n Juntion
PSpice Capture
Editing Device Model
• The device parameters can be changed, but will only
be changes for the file that you are currently working
on.
– In Schematics, the changes only apply to the specific part
that you had highlighted when you made the changes.
– In Capture, the changes apply to all components in the file
that share the same part model.
– To simulate the Ideal Diode Equation, you can delete the
other parameters or set them to zero or a very large
number, depending on what would be appropriate to
remove their effect from the simulation
Important Points of This Lecture
• There are several different techniques that can
be used to determine the diode voltage and
current in a circuit
– Ideal diode equation
• Results are acceptable when voltages applied to diode
are comparable or smaller than the turn-on voltage and
more positive than about 75-90% of the breakdown
voltage
– Piecewise model
• Results are acceptable when voltage applied to the
diode are large in magnitude when comparable to the
turn-on voltage and the breakdown voltage.
• Embedded in the Ideal Diode Equation are
dependences on
– Temperature
– Doping concentration of p and n sides
– Semiconductor material
• Bandgap energy
• Direct vs. indirect bandgap
• PSpice diode model using Ideal Diode Eq.
– User can edit diode model
– Diode model can also be more complex to include
deviations from Ideal Diode Eq. such as frequency
dependence of operation