SPICE Diode

SPICE-compatible diode

Libraries:
Simscape / Electrical / Additional Components / SPICE Semiconductors

Description

The SPICE Diode block represents a SPICE-compatible diode.

SPICE, or Simulation Program with Integrated Circuit Emphasis, is a simulation tool for electronic circuits. You can convert some SPICE subcircuits into equivalent Simscape™ Electrical™ models using the Environment Parameters block and SPICE-compatible blocks from the Additional Components library. For more information, see subcircuit2ssc.

Equations

Variables for the SPICE Diode block equations include:

Variables that you define by specifying parameters for the SPICE Diode block. The visibility of some of the parameters depends on the value that you set for other parameters. For more information, see Parameters.
Geometry-adjusted variables, which depend on several values that you specify using parameters for the SPICE Diode block. For more information, see Geometry-Adjusted Variables.
Temperature, T, which is 300.15 K by default. You can use a different value by specifying parameters for the SPICE Diode block or by specifying parameters for both the SPICE Diode block and an Environment Parameters block. For more information, see Diode Temperature.
Temperature-dependent variables. For more information, see Temperature Dependence.
Minimal conductance, GMIN, which is 1e–12 1/Ohm by default. You can use a different value by specifying a parameter for an Environment Parameters block. For more information, see Minimal Conduction.
Thermal voltage, V_t. For more information, see Thermal Voltage.

Geometry-Adjusted Variables

Several variables in the equations for the SPICE diode model consider the geometry of the device that the block represents. These geometry-adjusted variables depend on variables that you define by specifying SPICE Diode block parameters. The geometry-adjusted variables depend on these variables:

AREA — Area of the device
SCALE — Number of parallel connected devices
The associated unadjusted variable

The table includes the geometry-adjusted variables and the defining equations.

Variable	Description	Equation
CJO_d	Geometry-adjusted zero-bias junction capacitance	$C J O_{d} = C J O * A R E A * S C A L E$
IBV_d	Geometry-adjusted reverse breakdown current	$I B V_{d} = I B V * A R E A * S C A L E$
IS_d	Geometry-adjusted saturation current	$I S_{d} = I S * A R E A * S C A L E$
RS_d	Geometry-adjusted series resistance	$R S_{d} = \frac{R S}{A R E A * S C A L E}$

Diode Temperature

You can use these options to define diode temperature, T:

Fixed temperature — The block uses a temperature that is independent from the circuit temperature when the Model temperature dependence using parameter in the Temperature settings of the Spice Diode block is set to Fixed temperature. For this model, the block sets T equal to TFIXED.
Device temperature — The block uses a temperature that depends on circuit temperature when the Model temperature dependence using parameter in the Temperature settings of the Spice Diode block is set to Device temperature. For this model, the block defines temperature as

$T = T_{C} + T O F F S E T$
Where:
- T_C is the circuit temperature.
  If there is no Environment Parameters block in the circuit, T_C is equal to 300.15 K.
  If there is an Environment Parameters block in the circuit, T_C is equal to the value that you specify for the Temperature parameter in the Spice settings of the Environment Parameters block. The default value for the Temperature parameter is 300.15 K.
- TOFFSET is the offset local circuit temperature.

Minimal Conduction

Minimal conductance, GMIN, has a default value of 1e–12 1/Ohm. To specify a different value:

If there is not an Environment Parameters block in the diode circuit, add one.
In the Spice settings of the Environment Parameters block, specify the desired GMIN value for the GMIN parameter.

Thermal Voltage

Thermal voltage, V_t, is defined by the equation

$V_{t} = N \frac{k * T}{q}$

Where:

N is the emission coefficient.
T is the diode temperature. For more information, see Diode Temperature.
k is the Boltzmann constant.
q is the elementary charge on an electron.

Current-Voltage Equations

These equations define the relationship between the diode current, I_d, and the diode voltage, V_d. As applicable, the model parameters are first adjusted for temperature. For more information, see Temperature Dependence.

$I_{d} = A R E A * (I_{f w d} - I_{r e v})$

$I_{f w d} = I_{n r m} * K_{i n j} + I_{r e c} * K_{g e n}$

$I_{r e v} = I_{r e v h} + I_{r e v l}$

$I_{n r m} = I_{S} e^{V_{d} / (N * V t) - 1}$

$I_{r e c} = I_{S R} e^{V_{d} / (N R * V t) - 1}$

$K_{i n j} = {(\frac{I K F}{I K F + I_{n r m}})}^{0.5}$

$K_{g e n} = {[{(\frac{1 - V_{d}}{V J})}^{2} + 0.005]}^{\frac{M}{2}}$

$I_{r e v h} = I B V * e^{- \frac{V_{d} + B V}{N B V * V t}}$

$I_{r e v l} = I B V L * e^{- \frac{V_{d} + B V}{N B V L * V t}}$

Where:

I_fwd is the forward current.
I_rev is the reverse current.
I_nrm is the normal current.
I_rec is the recombination current.
K_inj is the high-injection factor.
K_gen is the generation factor.
I_revh is the high-level breakdown current.
I_revl is the low-level breakdown current.
V_t is thermal voltage. For more information, see Thermal Voltage.
I_S is the saturation current.
I_SR is the recombination current.
IKF is the forward knee current.
VJ is the junction potential.
N is the emission coefficient.
NR is the reverse emission coefficient.
NBV is the reverse breakdown emission coefficient.
NBVL is the low-level reverse breakdown ideality factor.
M is the grading coefficient.
BV is the reverse breakdown voltage.
IBV is the reverse breakdown current.
IBVL is the low-level reverse breakdown knee current.

Junction Charge Model

The table shows the equations that define the relationship between the diode charge Q_d, and the diode voltage, V_d. As applicable, the model parameters are first adjusted for temperature. For more information, see Temperature Dependence.

V_d Range	Q_d Equation
$V_{d} < F C * V J$	$Q_{d} = T T * A R E A * I_{f w d} + C J O_{d} * V J * \frac{1 - {(1 - \frac{V_{d}}{V J})}^{1 - M}}{1 - M}$
$V_{d} \geq F C * V J$	$\begin{array}{l} Q_{d} = T T * A R E A * I_{f w d} + \\ C J O_{d} * (F 1 + \frac{F 3 * (V_{d} - F C * V J) + (\frac{M}{2 * V J}) * (V_{d}^{2} - {(F C * V J)}^{2})}{F 2}) \end{array}$

Where:

FC is the forward bias depletion capacitance coefficient.
VJ is the junction potential.
TT is the transit time.
CJO_d is the geometry-adjusted zero-bias junction capacitance. For more information, see Geometry-Adjusted Variables.
M is the grading coefficient.
$F 1 = V J * (1 - {(1 - F C)}^{(1 - M)}) / (1 - M)$
$F 2 = {(1 - F C)}^{(1 + M)}$
$F 3 = 1 - F C * (1 + M)$

Temperature Dependence

The relationship between the geometry-adjusted saturation current and the diode temperature is

$I S_{d} (T) = I S_{d} * {(T / T M E A S)}^{\frac{X T I}{N}} * e^{(\frac{T}{T M E A S} - 1) * \frac{E G}{N * V_{t}}}$

Where:

IS_d is the geometry-adjusted saturation current. For more information, see Geometry-Adjusted Variables.
T is the diode temperature. For more information, see Diode Temperature.
TMEAS is the parameter extraction temperature.
XTI is the saturation current temperature exponent.
N is the emission coefficient.
EG is the activation energy.
V_t is thermal voltage. For more information, see Thermal Voltage.

The relationship between the recombination current and the diode temperature is

$I S R (T) = I S R * {(\frac{T}{T M E A S})}^{\frac{X T I}{N R}} * e^{(\frac{T}{T M E A S} - 1) * \frac{E G}{N R * V_{t}}}$

Where:

ISR is the recombination current.
NR is the reverse emission coefficient.

The relationship between the forward knee current and the diode temperature is

$I K F (T) = I K F * [1 + T I K F * (T - T M E A S)]$

Where:

IKF is the forward knee current.
TIKF is the linear IKF temperature coefficient.

The relationship between the breakdown voltage and the diode temperature is

$B V (T) = B V * [1 + T B V 1 * (T - T M E A S) + T B V 2 * {(T - T M E A S)}^{2}]$

Where:

BV is the breakdown voltage.
TBV1 is the linear BV temperature coefficient.
TBV2 is the quadratic BV temperature coefficient.

The relationship between the ohmic resistance and the diode temperature is

$R S (T) = R S * [1 + T R S 1 * (T - T M E A S) + T R S 2 * {(T - T M E A S)}^{2}]$

Where:

RS is the ohmic resistance.
TRS1 is the linear RS temperature coefficient.
TRS2 is the quadratic RS temperature coefficient.

The relationship between the junction potential and the diode temperature is

$V J (T) = V J * (\frac{T}{T M E A S}) - 3 * V t * \ln (\frac{T}{T M E A S}) - (\frac{T}{T M E A S}) * E G_{T M E A S} + E G_{T}$

Where:

VJ is the junction potential.
EG_TMEAS is the activation energy for the temperature at which the diode parameters were measured. The defining equation is $E G_{T M E A S} = 1.16 e V - (7.02 e - 4 * T M E A S^{2}) / (T M E A S + 1108)$ .
EG_T is the activation energy for the diode temperature. The defining equation is $E G_{T} = 1.16 e V - (7.02 e - 4 * T^{2}) / (T + 1108)$ .

The relationship between the geometry-adjusted diode zero-bias junction capacitance and the diode temperature is

$C J O_{d} (T) = C J O_{d} * [1 + M * (400 e - 6 * (T - T M E A S) - \frac{V J (T) - V J}{V J})]$

Where:

CJO_d is the geometry-adjusted zero-bias junction capacitance. For more information, see Geometry-Adjusted Variables.
M is the grading coefficient.

Assumptions and Limitations

The block does not support noise analysis.
The block applies initial conditions across junction capacitors and not across the block ports.

Ports

Conserving

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+ — Positive voltage
electrical

Electrical conserving port associated with positive voltage.

- — Negative voltage
electrical

Electrical conserving port associated with negative voltage.

Parameters

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Main

Device area, AREA — Device area
`1.0` `m^2` (default) | positive scalar

Diode area. The value must be greater than 0.

Number of parallel devices, SCALE — Number of parallel devices
`1` (default) | positive scalar

Number of parallel diodes that the block represents. The value must be greater than 0.

Saturation current, IS — Saturation current
`1e-14` `A/m^2` (default) | nonnegative scalar

Magnitude of the current that the ideal diode equation approaches asymptotically for very large reverse bias levels. The value must be greater than or equal to 0.

High-injection knee current, IKF — High-injection knee current
`Inf` `A/m^2` (default) | scalar

Current value at which forward-beta high-current roll-off occurs. The value must be greater than or equal to 0.

Recombination current parameter, ISR — Recombination current
`0` `A/m^2` (default) | scalar

Magnitude of the current generated from the process of the recombination of electrons and holes inside the junction.

Emission coefficient, N — Emission coefficient
`1` (default) | positive scalar

Diode emission coefficient or ideality factor. The value must be greater than 0.

Emission coefficient for ISR, NR — Emission coefficient for ISR
`2` (default) | positive scalar

Diode emission coefficient for the recombination current. The value must be greater than 0.

Grading coefficient, M — Grading coefficient
`0.5` (default) | 0 < M < 0.9 | scalar

Grading coefficient, M. The value must be greater than 0 and less than 0.9.

Dependencies

This parameter is only visible when you select Yes for the Model junction capacitance parameter.

Junction potential, VJ — Junction potential
`1` `V` (default) | VJ > 0.01 | scalar

Junction potential, VJ. The value must be greater than 0.01 V.

Dependencies

This parameter is only visible when you select Yes for the Model junction capacitance parameter.

Ohmic resistance, RS — Series resistance
`0.01` `m^2*Ohm` (default) | nonnegative scalar

Series diode connection resistance. The value must be greater than or equal to 0.

Junction Capacitance

Model junction capacitance — Junction capacitance model
`No` (default) | `Yes`

Options for modeling the junction capacitance:

No — Do not include junction capacitance in the model.
Yes — Specify zero-bias junction capacitance, junction potential, grading coefficient, forward-bias depletion capacitance coefficient, and transit time.

Zero-bias junction capacitance, CJO — Zero-bias junction capacitance
`0` `F/m^2` (default) | nonnegative scalar

Value of the capacitance placed in parallel with the exponential diode term. The value must be greater than or equal to 0.

Dependencies

To enable this parameter, set Model junction capacitance to Yes.

Capacitance coefficient, FC — Capacitance coefficient
`0.5` (default) | 0 ≤ FC < 0.95 | scalar

Fitting coefficient,, FC, that quantifies the decrease of the depletion capacitance with applied voltage. The value must be greater than or equal to 0 and less than 0.95.

Dependencies

To enable this parameter, set Model junction capacitance to Yes.

Transit time, TT — Transit time
`0` `s` (default) | nonnegative scalar

Transit time, TT, of the carriers that cause diffusion capacitance. The value must be greater than or equal to 0.

Dependencies

To enable this parameter, set Model junction capacitance to Yes.

Specify initial condition — Initial condition model
`No` (default) | `Yes`

Options for specifying initial conditions:

No — Do not specify an initial condition for the model.
Yes — Specify the initial diode voltage.
Note
The SPICE Diode block applies the initial diode voltage across the junction capacitors and not across the ports.

Dependencies

To enable this parameter, set Model junction capacitance to Yes.

Initial condition voltage, V0 — Initial voltage
`0` `V` (default) | scalar

Diode voltage at the start of the simulation.

Note

The block applies the initial condition across the diode junction, so the initial condition is only effective when charge storage is included, that is, when one or both of the Zero-bias junction capacitance, CJO and Transit time, TT parameters are greater than zero.

Dependencies

To enable this parameter, set Model junction capacitance and Specify initial condition to Yes.

Reverse Breakdown

Model reverse breakdown — Reverse breakdown model
`No` (default) | `Yes`

Options for modeling reverse breakdown:

No — Do not model reverse breakdown.
Yes — Introduce a second exponential term to the diode I-V relationship, thereby modeling a rapid increase in conductance as the breakdown voltage is exceeded.

Reverse breakdown voltage, BV — Reverse breakdown threshold voltage
`Inf` `V` (default) | nonnegative scalar

If voltage drops below this value, the block models the rapid increase in conductance that occurs at diode breakdown. The value must be greater than or equal to 0.