Download Ideal Diode Equation

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
kT  N d N a 
Vbi 
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 Drift  qn n  for electrons
I Drift  qp p  for holes
I Drift  q ( n n  p p )
I Diff  qDn n for electrons
I Diff   qD p p for holes
I Diff  q ( Dn n  D p p )
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 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
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.

I D  I o  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 is also known as Vth, the thermal voltage. At 300K (room temperature),
kT = 25.9meV
Simplification
• When VD is negative
I D ~ Io
• When VD is positive
I D ~ I oe
qVD
nkT
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
q
ln I D 
VD  ln I o
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 > 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