Diode equations

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

pn

diff

p

diff

n

diff

pp

diff

p

nn

diff

n

pn

drift

p

drift

p

n

drift

n

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, 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/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

Von Slope = 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