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