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Ideal Diode Equation
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 larger than about 90% of the breakdown voltage
– Piecewise model• Results are acceptable when voltage applied to the diode are
large in magnitude when comparised to the turn-on voltage
• Embedded in the Ideal Diode Equation is 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
P-N junctions
• We already know that a voltage is 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
2ln
i
adbi n
NNqkTV
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).
)(
holesfor
electronsfor
)(
holesfor
electronsfor
pDnDqI
pqDI
nqDI
pnqI
qpI
qnI
pnDiff
pDiff
nDiff
pnDrift
pDrift
nDrift
When the applied voltage 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 electron 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
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
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
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 is also known as Vth, the thermal voltage. At 300K (room temperature),kT = 25.9meV
1nkT
qV
oD
D
eII
Simplification
• When VD is negative
• When VD is positive
nkTqV
oD
D
eII ~
oD II ~
To Find n and Io
• 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
oDD IVnkTqI 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 > Vbi)
Nonideal (but real) I-V Characteristic
• Need another model– Modifications to Ideal Diode Equation are used in
PSpice– We will use a different model 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