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

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).

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 I D and V D 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 V th, the thermal voltage. At 300K (room temperature), kT = 25.9meV

Simplification When V D is negative When V D is positive

To Find n and I o 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

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 (E g ) 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, V BR ) – ‘Linear’ relationship between I D and V D at reasonably large positive voltages (V a > V bi )

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 I o 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