The following table contains the model parameters for the pn-junction diode model.
|Isr||recombination current parameter|
|Nr||emission coefficient for Isr|
|Cj0||zero-bias junction capacitance|
|Fc||forward-bias depletion capacitance coefficient|
|Bv||reverse breakdown voltage|
|Ibv||current at reverse breakdown voltage|
|Kf||flicker noise coefficient|
|Af||flicker noise exponent|
|Ffe||flicker noise frequency exponent|
|Xti||saturation current exponent|
|Tbv||Bv linear temperature coefficient|
|Trs||Rs linear temperature coefficient|
|Ttt1||Tt linear temperature coefficient|
|Ttt2||Tt quadratic temperature coefficient|
|Tm1||M linear temperature coefficient|
|Tm2||M quadratic temperature coefficient|
|Tnom||temperature at which parameters were extracted|
|Area||default area for diode|
The current equation of the diode and its derivative writes as follows:
The complete MNA matrix entries are:
The voltage dependent capacitance consists of a diffusion capacitance, a junction capacitance and an additional linear capacitance which is usually modeled by the following equations.
The S-parameters of the passive circuit shown in fig. 10.4 can be written as
The thermal noise generated by the series resistor is characterized by the following spectral density.
The shot noise and flicker noise generated by the DC current flow through the diode is characterized by the following spectral density.
Thus the noise current correlation matrix can be formed. This matrix can be easily converted to the noise wave correlation matrix representation using the formulas given in section 2.4.2 on page .
An ideal diode (pn- or schottky-diode) generates shot noise. Both types of current (field and diffusion) contribute independently to it. That is, even though the two currents flow in different directions ("minus" in dc current equation), they have to be added in the noise equation (current is proportional to noise power spectral density). Taking into account the dynamic conductance in parallel to the noise current source, the noise wave correlation matrix writes as follows.
Where is charge of an electron, the temperature voltage, the (dynamic) conductance of the diode and its junction capacitance.
To be very precise, the equation above only holds for diodes whose field and diffusion current dominate absolutely (diffusion limited diode), i.e. . Many diodes also generate a generation/recombination current ( ), which produces shot noise, too. But depending on where and how the charge carriers generate or recombine, their effective charge is somewhat smaller than . To take this into account, one needs a further factor . Several opinions exist according the value of . Some say 1 and 2/3 are common values, others say with and being bias dependent. Altogether it is:
Remark: Believing the diode equation is the whole truth, it is logical to define , because at the conductance of the diode must create thermal noise.
Some special diodes have additional current or noise components (tunnel diodes, avalanche diodes etc.). All these mechanisms are not taken into account in equation (10.21).
The parasitic ohmic resistance in a non-ideal diode, of course, creates thermal noise.
Noise current correlation matrix (for details on the parameters see above):
This section mathematically describes the dependencies of the diode characterictics on temperature. For a junction diode a typical value for is , for a Schottky barrier diode it is . The energy band gap at zero temperature is by default eV. For other materials than Si, eV (for a Schottky barrier diode), eV (for Ge) and eV (for GaAs) should be used.
with experimental values for Si given by
The following equations show the temperature dependencies of the diode parameters. The reference temperature in these equations denotes the nominal temperature specified by the diode model.
Some additionial temperature coefficients determine the temperature dependence of even more model parameters.
The area factor used in the diode model determines the number of equivalent parallel devices of the specified model. The diode model parameters affected by the factor are: