# Light-Emitting Diode

Model light-emitting diode as exponential diode and current sensor in series

Sensors

## Description

The Light-Emitting Diode block represents a light-emitting diode as an exponential diode in series with a current sensor. The optical power presented at the signal port W is equal to the product of the current flowing through the diode and the Optical power per unit current parameter value.

The exponential diode model provides the following relationship between the diode current I and the diode voltage V:

`$I=IS\cdot \left({e}^{\frac{qV}{Nk{T}_{m1}}}-1\right)$`
where:

• q is the elementary charge on an electron (1.602176e–19 Coulombs).

• k is the Boltzmann constant (1.3806503e–23 J/K).

• N is the emission coefficient.

• IS is the saturation current.

• Tm1 is the temperature at which the diode parameters are specified, as defined by the Measurement temperature parameter value.

When (qV / NkTm1) > 80, the block replaces ${e}^{\frac{qV}{Nk{T}_{m1}}}$ with (qV / NkTm1 – 79)e80, which matches the gradient of the diode current at (qV / NkTm1) = 80 and extrapolates linearly. When (qV / NkTm1) < –79, the block replaces ${e}^{\frac{qV}{Nk{T}_{m1}}}$ with (qV / NkTm1 + 80)e–79, which also matches the gradient and extrapolates linearly. Typical electrical circuits do not reach these extreme values. The block provides this linear extrapolation to help convergence when solving for the constraints during simulation.

When you select `Use parameters IS and N` for the Parameterization parameter, you specify the diode in terms of the Saturation current IS and Emission coefficient N parameters. When you select ```Use I-V curve data points``` for the Parameterization parameter, you specify two voltage and current measurement points on the diode I-V curve and the block derives the IS and N values. When you specify current and voltage measurements, the block calculates IS and N as follows:

• $\text{N}=\left(\left({V}_{1}-{V}_{2}\right)/{V}_{t}\right)/\left(\mathrm{log}\left({I}_{1}\right)-\mathrm{log}\left({I}_{2}\right)\right)$

• $\text{IS}=\left({I}_{1}/\left(\mathrm{exp}\left({V}_{1}/\left(\text{N}{V}_{t}\right)\right)-1\right)+{I}_{2}/\left(\mathrm{exp}\left({V}_{2}/\left(\text{N}{V}_{t}\right)\right)-1\right)\right)/2$

where:

• Vt = kTm1 / q.

• V1 and V2 are the values in the Voltages [V1 V2] vector.

• I1 and I2 are the values in the Currents [I1 I2] vector.

The exponential diode model provides the option to include a junction capacitance:

• When you select ```Fixed or zero junction capacitance``` for the Junction capacitance parameter, the capacitance is fixed.

• When you select ```Use parameters CJO, VJ, M & FC``` for the Junction capacitance parameter, the block uses the coefficients CJO, VJ, M, and FC to calculate a junction capacitance that depends on the junction voltage.

• When you select `Use C-V curve data points` for the Junction capacitance parameter, the block uses three capacitance values on the C-V capacitance curve to estimate CJO, VJ, and M and uses these values with the specified value of FC to calculate a junction capacitance that depends on the junction voltage. The block calculates CJO, VJ, and M as follows:

• $CJ0={C}_{1}{\left(\left({V}_{R2}-{V}_{R1}\right)/\left({V}_{R2}-{V}_{R1}{\left({C}_{2}/{C}_{1}\right)}^{-1/M}\right)\right)}^{M}$

• $VJ=-\left(-{V}_{R2}{\left({C}_{1}/{C}_{2}\right)}^{-1/M}+{V}_{R1}\right)/\left(1-{\left({C}_{1}/{C}_{2}\right)}^{-1/M}\right)$

• $M=\mathrm{log}\left({C}_{3}/{C}_{2}\right)/\mathrm{log}\left({V}_{R2}/{V}_{R3}\right)$

where:

• VR1, VR2, and VR3 are the values in the Reverse bias voltages [VR1 VR2 VR3] vector.

• C1, C2, and C3 are the values in the Corresponding capacitances [C1 C2 C3] vector.

It is not possible to estimate FC reliably from tabulated data, so you must specify its value using the Capacitance coefficient FC parameter. In the absence of suitable data for this parameter, use a typical value of 0.5.

The reverse bias voltages (defined as positive values) should satisfy VR3 > VR2 > VR1. This means that the capacitances should satisfy C1 > C2 > C3 as reverse bias widens the depletion region and hence reduces capacitance. Violating these inequalities results in an error. Voltages VR2 and VR3 should be well away from the Junction potential VJ. Voltage VR1 should be less than the Junction potential VJ, with a typical value for VR1 being 0.1 V.

The voltage-dependent junction is defined in terms of the capacitor charge storage Qj as:

• For V < FC·VJ:

`${Q}_{j}=CJ0\cdot \left(VJ/\left(M-1\right)\right)\cdot \left({\left(1-V/VJ\right)}^{1-M}-1\right)$`

• For VFC·VJ:

`${Q}_{j}=CJ0\cdot {F}_{1}+\left(CJ0/{F}_{2}\right)\cdot \left({F}_{3}\cdot \left(V-FC\cdot VJ\right)+0.5\left(M/VJ\right)\cdot \left({V}^{2}-{\left(FC\cdot VJ\right)}^{2}\right)\right)$`

where:

• ${F}_{1}=\left(VJ/\left(1-M\right)\right)\cdot \left(1-{\left(1-FC\right)}^{1-M}\right)\right)$

• ${F}_{2}={\left(1-FC\right)}^{1+M}\right)\right)$

• ${F}_{3}=1-FC\cdot \left(1+M\right)$

These equations are the same as used in [2], except that the temperature dependence of VJ and FC is not modeled. This model does not include the diffusion capacitance term that affects performance for high frequency switching applications.

The Light-Emitting Diode block contains several options for modeling the dependence of the diode current-voltage relationship on the temperature during simulation. Temperature dependence of the junction capacitance is not modeled, this being a much smaller effect. For details, see the Diode reference page.

### Thermal Port

The block has an optional thermal port, hidden by default. To expose the thermal port, right-click the block in your model, and then from the context menu select Simscape > Block choices > Show thermal port. This action displays the thermal port H on the block icon, and adds the Thermal Port tab to the block dialog box.

Use the thermal port to simulate the effects of generated heat and device temperature. For more information on using thermal ports and on the Thermal Port tab parameters, see Simulating Thermal Effects in Semiconductors.

### Variables

Use the Variables section of the block interface to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables (Simscape).

## Basic Assumptions and Limitations

The Light-Emitting Diode block has the following limitations:

• When you select `Use I-V curve data points` for the Parameterization parameter, choose a pair of voltages near the diode turn-on voltage. Typically this is in the range from 0.05 to 1 Volt. Using values outside of this region may lead to numerical issues and poor estimates for IS and N.

• You may need to use nonzero ohmic resistance and junction capacitance values to prevent numerical simulation issues, but the simulation may run faster with these values set to zero.

## Parameters

### Main

Optical power per unit current

The amount of optical power the light-emitting diode generates per unit of current flowing through the diode. The default value is `0.005` W/A.

Parameterization

Select one of the following methods for model parameterization:

• `Use I-V curve data points` — Specify measured data at two points on the diode I-V curve. This is the default method.

• `Use parameters IS and N` — Specify saturation current and emission coefficient.

Currents [I1 I2]

A vector of the current values at the two points on the diode I-V curve that the block uses to calculate IS and N. This parameter is only visible when you select ```Use I-V curve data points``` for the Parameterization parameter. The default value is `[ 0.0017 0.003 ]` A.

Voltages [V1 V2]

A vector of the voltage values at the two points on the diode I-V curve that the block uses to calculate IS and N. This parameter is only visible when you select ```Use I-V curve data points``` for the Parameterization parameter. The default value is `[ 0.9 1.05 ]` V.

Saturation current, IS

The magnitude of the current that the ideal diode equation approaches asymptotically for very large reverse bias levels. This parameter is only visible when you select ```Use parameters IS and N``` for the Parameterization parameter. The default value is `5e-5` A.

Emission coefficient, N

The diode emission coefficient or ideality factor. This parameter is only visible when you select ```Use parameters IS and N``` for the Parameterization parameter. The default value is `10`.

Ohmic resistance, RS

The series diode connection resistance. The default value is `0.1` Ω.

Measurement temperature

The temperature at which IS or the I-V curve was measured. The default value is `25` °C.

### Junction Capacitance

Junction capacitance

Select one of the following options for modeling the junction capacitance:

• `Fixed or zero junction capacitance` — Model the junction capacitance as a fixed value.

• `Use C-V curve data points` — Specify measured data at three points on the diode C-V curve.

• `Use parameters CJ0, VJ, M & FC` — Specify zero-bias junction capacitance, junction potential, grading coefficient, and forward-bias depletion capacitance coefficient.

Zero-bias junction capacitance, CJ0

The value of the capacitance placed in parallel with the exponential diode term. This parameter is only visible when you select ```Fixed or zero junction capacitance``` or ```Use parameters CJ0, VJ, M & FC``` for the Junction capacitance parameter. The default value is `20` pF.

Reverse bias voltages [VR1 VR2 VR3]

A vector of the reverse bias voltage values at the three points on the diode C-V curve that the block uses to calculate CJ0, VJ, and M. This parameter is only visible when you select `Use C-V curve data points` for the Junction capacitance parameter. The default value is ```[ 0.1 10 100 ]``` V.

Corresponding capacitances [C1 C2 C3]

A vector of the capacitance values at the three points on the diode C-V curve that the block uses to calculate CJ0, VJ, and M. This parameter is only visible when you select `Use C-V curve data points` for the Junction capacitance parameter. The default value is ```[ 15 10 2 ]``` pF.

Junction potential, VJ

The junction potential. This parameter is only visible when you select `Use parameters CJ0, VJ, M & FC` for the Junction capacitance parameter. The default value is `1` V.

The grading coefficient. This parameter is only visible when you select `Use parameters CJ0, VJ, M & FC` for the Junction capacitance parameter. The default value is `0.5`.

Capacitance coefficient, FC

Fitting coefficient that quantifies the decrease of the depletion capacitance with applied voltage. This parameter is only visible when you select `Use C-V curve data points` or ```Use parameters CJ0, VJ, M & FC``` for the Junction capacitance parameter. The default value is `0.5`.

### Temperature Dependence

Parameterization

Select one of the following methods for temperature dependence parameterization:

• ```None — Simulate at parameter measurement temperature``` — Temperature dependence is not modeled, or the model is simulated at the measurement temperature Tm1 (as specified by the Measurement temperature parameter on the Main tab). This is the default method.

• ```Use an I-V data point at second measurement temperature T2``` — If you select this option, you specify a second measurement temperature Tm2, and the current and voltage values at this temperature. The model uses these values, along with the parameter values at the first measurement temperature Tm1, to calculate the energy gap value.

• ```Specify saturation current at second measurement temperature T2``` — If you select this option, you specify a second measurement temperature Tm2, and saturation current value at this temperature. The model uses these values, along with the parameter values at the first measurement temperature Tm1, to calculate the energy gap value.

• `Specify the energy gap EG` — Specify the energy gap value directly.

Current I1 at second measurement temperature

Specify the diode current I1 value when the voltage is V1 at the second measurement temperature. This parameter is only visible when you select ```Use an I-V data point at second measurement temperature T2``` for the Parameterization parameter. The default value is `0.0034` A.

Voltage V1 at second measurement temperature

Specify the diode voltage V1 value when the current is I1 at the second measurement temperature. This parameter is only visible when you select ```Use an I-V data point at second measurement temperature T2``` for the Parameterization parameter. The default value is `1.05` V.

Saturation current, IS, at second measurement temperature

Specify the saturation current IS value at the second measurement temperature. This parameter is only visible when you select ```Specify saturation current at second measurement temperature T2``` for the Parameterization parameter. The default value is `1.8e-4` A.

Second measurement temperature

Specify the value for the second measurement temperature. This parameter is only visible when you select either``` Use an I-V data point at second measurement temperature T2``` or ```Specify saturation current at second measurement temperature T2``` for the Parameterization parameter. The default value is `125` °C.

Energy gap parameterization

This parameter is only visible when you select ```Specify the energy gap EG``` for the Parameterization parameter. It lets you select a value for the energy gap from a list of predetermined options, or specify a custom value:

• `Use nominal value for silicon (EG=1.11eV)` — This is the default.

• ```Use nominal value for 4H-SiC silicon carbide (EG=3.23eV)```

• ```Use nominal value for 6H-SiC silicon carbide (EG=3.00eV)```

• `Use nominal value for germanium (EG=0.67eV)`

• ```Use nominal value for gallium arsenide (EG=1.43eV)```

• `Use nominal value for selenium (EG=1.74eV)`

• ```Use nominal value for Schottky barrier diodes (EG=0.69eV)```

• `Specify a custom value` — If you select this option, the Energy gap, EG parameter appears in the dialog box, to let you specify a custom value for EG.

Energy gap, EG

Specify a custom value for the energy gap, EG. This parameter is only visible when you select ```Specify a custom value``` for the Energy gap parameterization parameter. The default value is `1.11` eV.

Saturation current temperature exponent parameterization

Select one of the following options to specify the saturation current temperature exponent value:

• ```Use nominal value for pn-junction diode (XTI=3)``` — This is the default.

• ```Use nominal value for Schottky barrier diode (XTI=2)```

• `Specify a custom value` — If you select this option, the Saturation current temperature exponent, XTI parameter appears in the dialog box, to let you specify a custom value for XTI.

Saturation current temperature exponent, XTI

Specify a custom value for the saturation current temperature exponent, XTI. This parameter is only visible when you select `Specify a custom value` for the Saturation current temperature exponent parameterization parameter. The default value is `3`.

Device simulation temperature

Specify the value for the temperature Ts, at which the device is to be simulated. The default value is `25` °C.

## Ports

The block has the following ports:

`W`

Optical output power

`+`

Electrical conserving port associated with the diode positive terminal

`-`

Electrical conserving port associated with the diode negative terminal

## References

[1] H. Ahmed and P.J. Spreadbury. Analogue and digital electronics for engineers. 2nd Edition, Cambridge University Press, 1984.

[2] G. Massobrio and P. Antognetti. Semiconductor Device Modeling with SPICE. 2nd Edition, McGraw-Hill, 1993.