Using Junction Diode Equations

Equation Variable Definitions shows the diode equation variable definition.

Table 15-4: Equation Variable Definitions

Variable

Definition

cd

total diode capacitance

f

frequency

gd

diode conductance

id

diode DC current

id1

current without high level injection

ind

diode equivalent noise current

inrs

series resistor equivalent noise current

vd

voltage across the diode

Equation Quantity Definition shows the equation quantity definition:

Table 15-5: Equation Quantity Definition

Quantity

Definition

tox

3.453143e-11 F/m

k

1.38062e-23 (Boltzmann's constant)

q

1.60212e-19 (electron charge)

t

temperature in °Kelvin

Δ t

t - tnom

tnom

nominal temperature of parameter measurements in °Kelvin

vt(t)

k · t/q: thermal voltage

vt(tnom)

k · tnom/q: thermal voltage

Using Junction DC Equations

The basic diode is modeled in three regions:

For a forward bias diode, the anode is more positive than the cathode. The diode is turned on and conducts above 0.6 volts. Set the model parameter RS to limit conduction current. As the forward bias voltage increases past 0.6 volts, the limiting resistor prevents the value of the diode current from becoming too high and the solution from converging.

Forward Bias: vd > -10 · vt


 

For reverse bias, the anode (node1) is more negative than the cathode. The diode is turned off, and conducts a small leakage current.

Reverse Bias: BVeff < vd < -10 · vt

 

For breakdown, the parameter BV (VB) is set, inducing reverse breakdown or avalanche. This effect is seen in Zener diodes and occurs when the anode-cathode voltage is less than BV. Model this action by measuring the voltage (BV) and the current (IBV) at the reverse knee or onset of avalanche.


NOTE: BV is always described as a positive number.
Breakdown: vd < - BVeff

 

The BV parameter is adjusted as follows to obtain BVeff:

 

If IBVeff > ibreak, then,

 

Otherwise,

 

Most diodes do not behave as ideal diodes. The parameters IK and IKR are called high-level injection parameters. They tend to limit the exponential current increase.


NOTE: The exponential equation is used in both the forward and reverse regions.

Forward Bias

 

Reverse Bias

 

where id1 is

For vd >= -BVeff:

 

Otherwise:

 

You can estimate the reverse saturation current IS, emission coefficient N, and model parameter RS from DC measurements of the forward biased diode characteristics. You can determine N from the slope of the diode characteristic in the ideal region. In most cases, the emission coefficient is the value of unit, but is closer to 2 for MOS diodes.

In practice, at higher levels of bias, the diode current deviates from the ideal exponential characteristic. This deviation is due to the presence of ohmic resistance in the diode as well as high-level injection effects. The deviation of the actual diode voltage from the ideal exponential characteristic at a specific current determines the value of RS. In practice, RS is estimated at several values of id and averaged, since the value of RS depends upon diode current.

Using Diode Capacitance Equations

The diode capacitance is modeled by cd in Equivalent Circuit, Diode Transient Analysis. The capacitance, cd, is a combination of diffusion capacitance, (cdiff), depletion capacitance, (cdep), metal, (cmetal), and poly capacitances, (cpoly).

 

Using Diffusion Capacitance Equations

The transit time (TT) models the diffusion capacitance, caused by injected minority carriers. In practice, TT is estimated from pulsed time-delay measurements.

 

Using Depletion Capacitance Equations

The depletion capacitance is modeled by junction bottom and junction periphery capacitances. The formula for both bottom area and periphery capacitances is similar, except each has its own model parameters. There are two equations for forward bias junction capacitance that are selected using .OPTIONS DCAP.

DCAP=1

The junction bottom area capacitance formula is:

vd < FC · PB

 

 

 

The junction periphery capacitance formula is:

vd < FCS · PHP

 

 

 

then,

 

DCAP=2 (default)

The total depletion capacitance formula is:

vd < 0

 

 

 

DCAP=3

Limits peak depletion capacitance to FC · CGDeff or FC · CGSeff, with proper fall-off when forward bias exceeds PB (FC > 1).

Metal and Poly Capacitance Equations (LEVEL=3 Only)

To determine the metal and poly capacitances, use the equations:


 

Using Noise Equations

Equivalent Circuit, Diode AC Noise Analysis shows the noise model for a diode. An independent current source, inrs, in parallel with the resistor models the thermal noise generated by a resistor. To determine the value of inrs, use the equation:

 

The unit of inrs is Amp/(Hz) 1/2 .

The shot and flicker noise of the diode are modeled by the current source ind, which is defined by:

 

Temperature Compensation Equations

This section describes the temperature compensation equations.

Energy Gap Temperature Equations

Use the following equations to determine energy gap for temperature compensation.

TLEV=0 or 1


 

TLEV=2


 

Leakage Current Temperature Equations


 

TLEV=0 or 1

 

TLEV=2

 

Breakdown Voltage Temperature Equations

TLEV=0

 

TLEV=1 or 2

 

Transit Time Temperature Equations

 

Contact Potential Temperature Equations

TLEVC=0


 

TLEVC=1 or 2


 

TLEVC=3


 

where TLEV=0 or 1

 

 

and TLEV=2

 

 

Junction Capacitance Temperature Equations

TLEVC=0


 

TLEVC=1


 

TLEVC=2

 


NOTE: In the above equation MJ is not MJ(t).

 

TLEVC=3

 

 

Grading Coefficient Temperature Equation

 

Resistance Temperature Equations

 

Star-Hspice Manual - Release 2001.2 - June 2001