The diode model has certain dc currents for bottom and sidewall components. Exemplary here is the equation for the bottom part:

[\begin{array}{ll} {I_{D} = \begin{cases} {IS_{eff}\left( {e^{\frac{qV_{D}}{NkT}} - 1} \right) + V_{D} \cdot GMIN,} & {{if} V_{D} \geq - 3\frac{NkT}{q}} \ {- IS_{eff}\left\lbrack {1 + \left( \frac{3NkT}{qV_{D}e})^{3} \right.} \right\rbrack + V_{D} \cdot GMIN,} & {{if} - BV_{eff} < V_{D} < - 3\frac{NkT}{q}} \ {- IS_{eff}\left( e^{\frac{- q({BV_{eff} + V_{D}})}{NkT}} \right) + V_{D} \cdot GMIN,} & {{if} V_{D} \leq - BV_{eff}} \ \end{cases}} & \ \end{array}]

Two secondary effects are modelled if the appropriate parameters (see table Junction DC parameters) are given: Recombination current and bottom and sidewall tunnel current.

The breakdown region must be described with more depth since the breakdown is not modeled physically. As written before, the breakdown modeling is based on two model parameters: the `nominal breakdown voltage' bv and the current at the onset of breakdown ibv. For the diode model to be consistent, the current value cannot be arbitrarily chosen, since the reverse bias and breakdown regions must match. When the diode enters breakdown region from reverse bias, the current is calculated using the formula

1

if you look at the source code in file diotemp.c you will discover that the exponential relation is replaced with a first order Taylor series expansion.

:

[\begin{array}{ll} {I_{bdwn} = - IS_{eff}\left( {e^{\frac{- q{\lbrack font\ rm\ \lbrack char\ B\ mathalpha\rbrack\lbrack char\ V\ mathalpha\rbrack\rbrack}}{NkT}} - 1} \right)} & \ \end{array}]

The computed current is necessary to adjust the breakdown voltage making the two regions match. The algorithm is a little bit convoluted and only a brief description is given here:

if (IBV_{eff} < I_{bdwn}) then

(\begin{array}{ll} {IBV_{eff} = I_{bdwn}} & \ {BV_{eff} = {\lbrack font\ rm\ \lbrack char\ B\ mathalpha\rbrack\lbrack char\ V\ mathalpha\rbrack\rbrack}} & \ \end{array})

else

(\begin{array}{ll} {BV_{eff} = {\lbrack font\ rm\ \lbrack char\ B\ mathalpha\rbrack\lbrack char\ V\ mathalpha\rbrack\rbrack} - {\lbrack font\ rm\ \lbrack char\ N\ mathalpha\rbrack\rbrack}V_{t}\ln\left( \frac{IBV_{eff}}{I_{bdwn}} \right)} & \ \end{array})

Algorithm 7.1: Diode breakdown current calculation

Most real diodes shows a current increase that, at high current levels, does not follow the exponential relationship given above. This behavior is due to high level of carriers injected into the junction. High injection effects (as they are called) are modeled with ik and ikr.

[\begin{array}{ll} {I_{Deff} = \begin{cases} {\frac{I_{D}}{1 + \sqrt{\frac{I_{D}}{IK_{eff}}}},} & {{if} V_{D} \geq - 3\frac{NkT}{q}} \ {\frac{I_{D}}{1 + \sqrt{\frac{I_{D}}{IKR_{eff}}}},} & {otherwise.} \ \end{cases}} & \ \end{array}]

Diode capacitance is divided into two different terms:

• Depletion capacitance
• Diffusion capacitance

Depletion capacitance is composed by two different contributes, one associated to the bottom of the junction (bottom-wall depletion capacitance) and the other to the periphery (sidewall depletion capacitance). The basic equations are:

[C_{Diode} = C_{diffusion} + C_{depletion}]

Where the depletion capacitance is defined as:

[C_{depletion} = C_{depl_{bw}} + C_{depl_{sw}}]

The diffusion capacitance, due to the injected minority carriers, is modeled with the transit time** tt**:

[C_{diffusion} = {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\rbrack}\frac{\partial I_{Deff}}{\partial V_{D}}]

The depletion capacitance is more complex to model, since the function used to approximate it diverges when the diode voltage become greater than the junction built-in potential. To avoid function divergence, the capacitance function is approximated with a linear extrapolation for applied voltage greater than a fraction of the junction built-in potential.

[\begin{array}{llll} C_{depl_{bw}} & = & \begin{cases} {CJ_{eff}\left( 1 - \frac{V_{D}}{\lbrack font\ rm\ \lbrack char\ V\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack})^{- {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}}, \right.} & {{if} V_{D} < {\lbrack font\ rm\ \lbrack char\ F\ mathalpha\rbrack\lbrack char\ C\ mathalpha\rbrack\rbrack} \cdot {\lbrack font\ rm\ \lbrack char\ V\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}} \ {CJ_{eff}\frac{1 - {\lbrack font\ rm\ \lbrack char\ F\ mathalpha\rbrack\lbrack char\ C\ mathalpha\rbrack\rbrack}\left( {1 + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}I} \right) + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}\frac{V_{D}}{\lbrack font\ rm\ \lbrack char\ V\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}}{\left( 1 - {\lbrack font\ rm\ \lbrack char\ F\ mathalpha\rbrack\lbrack char\ C\ mathalpha\rbrack\rbrack})^{({1 + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}})} \right.},} & {{otherwise}.} \ \end{cases} & \ \end{array}]

[\begin{array}{ll} {C_{depl_{sw}} = \begin{cases} {CJP_{eff}\left( 1 - \frac{V_{D}}{\lbrack font\ rm\ \lbrack char\ P\ mathalpha\rbrack\lbrack char\ H\ mathalpha\rbrack\lbrack char\ P\ mathalpha\rbrack\rbrack})^{- {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ W\ mathalpha\rbrack\rbrack}}, \right.} & {if V_{D} < {\lbrack font\ rm\ \lbrack char\ F\ mathalpha\rbrack\lbrack char\ C\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\rbrack} \cdot {\lbrack font\ rm\ \lbrack char\ P\ mathalpha\rbrack\lbrack char\ H\ mathalpha\rbrack\lbrack char\ P\ mathalpha\rbrack\rbrack}} \ {CJP_{eff}\frac{1 - {\lbrack font\ rm\ \lbrack char\ F\ mathalpha\rbrack\lbrack char\ C\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\rbrack}\left( {1 + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ W\ mathalpha\rbrack\rbrack}} \right) + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ W\ mathalpha\rbrack\rbrack} \cdot \frac{V_{D}}{\lbrack font\ rm\ \lbrack char\ P\ mathalpha\rbrack\lbrack char\ H\ mathalpha\rbrack\lbrack char\ P\ mathalpha\rbrack\rbrack}}{\left( 1 - {\lbrack font\ rm\ \lbrack char\ F\ mathalpha\rbrack\lbrack char\ C\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\rbrack})^{({1 + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ W\ mathalpha\rbrack\rbrack}})} \right.},} & {{otherwise}.} \ \end{cases}} & \ \end{array}]