Post on 18-Dec-2015
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
2ln
i
ADf n
NN
q
kT
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
pndiffp
diffn
diff
ppdiffp
nndiffn
pndrift
pdriftp
ndriftn
III
pDnDqAIII
dx
dpqADpqADI
dx
dnqADnqADI
EpnAqI
pEqAI
nEqAI
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 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/
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.
Ideal Diode Equation
Where ID and VD are the diode current and voltage, respectivelyq 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 constantT 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
Simplification
• When VD is negative
• When VD is positive
nkT
qV
SD
D
eII ~
SD II ~
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
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
VonSlope = 1/rz
Slope = 1/RS
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