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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
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).
driftdiffT
pn
diff
p
diff
n
diff
pp
diff
p
nn
diff
n
pn
drift
p
drift
p
n
drift
n
III
pDnDqAIII
dx
dpqADpqADI
dx
dnqADnqADI
EpnAqI
pEqAI
nEqAI
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 p-side 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/
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/
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.
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
1nkT
qV
SD
D
eII
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
SDD IVnkT
qI lnln
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)
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
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
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
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