In this example, we simulate a nitride-based blue-light emitting micro-LED (uLED) in Ansys Lumerical MultiphysicsTM with a semi-coupled workflow between the CHARGE and MQW (Multi-Quantum Well) solvers. We leverage several new features including 1. the support for higher order k.p method (6×6 and 8×8) in MQW solver, 2. support for wurzite crystal structures, and 3. a scripted solution for including material polarization effects in nitrides to simulate the uLED and calculate its band diagrams and spontaneous emission rates.
Overview
uLEDs have emerged as an excellent candidate for next generation displays due to their high self-emissive brightness, high integration density, and faster response times. Nitride-based blue uLEDs are crucial for realizing full-color uLEDs displays. However, non-radiative recombination mechanisms and polarization-induced quantum confined stark effect (QCSE) limit their efficiency. Numerical simulations can serve as a powerful tool to gain physical insights into these mechanisms and to determine the optimal device operating conditions. In this workflow, we use semi-coupled CHARGE and MQW solvers to simulate the uLED and demonstrate the effects of material polarization on its band diagram and spontaneous emission spectrum.
The uLED simulated in this example is based on an existing work [1]. The schematic of the uLED is shown above. The active region of the quantum well consists of an a single undoped \(\mathrm{In}_{0.2}\mathrm{Ga}_{0.8}\mathrm{N}\) quantum well of width 2 nm. It is surrounded by \(p\)-type \(\mathrm{Al}_{0.3}\mathrm{Ga}_{0.7}\mathrm{N}\) on one side and \(n\)-type \(\mathrm{In}_{0.02}\mathrm{Ga}_{0.98}\mathrm{N}\) on the other side.
Step 1: CHARGE Simulation:
In the first step, we simulate the uLED using CHARGE solver, which solves the Drift-Diffusion and Poisson equations self-consistently to return the carrier densities and the electric field distribution. We perform two simulations, the first simulation does not include the polarization effects while the second considers both spontaneous and strain-induced polarization. The material polarization effects manifest as surface charge densities, which are applied to the interfaces of the active region using the Surface Charge Density boundary condition. The values of surface charge concentration are pre-calculated by a scripted solution, more details on which can be found here: Material polarization effects in CHARGE simulation . Based on the selected voltage in the script, the field distribution and carrier densities are saved in Lumerical data files (.ldf).
Step 2: MQW Simulation
In this step, the active region of the uLED is simulated in the MQW solver by importing the data files created in the previous step. The MQW solver solves the Schrödinger equation in the quantum well by \(k.p\) method and returns the the electronic wave functions and sub-bands in conduction and valence bands. It also calculates the Fermi energy level and the occupation probability of each confined state. The occupation probabilities and the overlap between the conduction and valence band wave functions are used to determine the spontaneous emission rates in the uLED.
Run and Result
Instructions for running the model and discussion of key results
Step 1: Extract carrier density and electric field distribution from CHARGE simulation
- Open the project file [[GaNSQWLED_Piprek03ch9_v4_1D_polarized_QW.ldev]] and script file [[plot_CHARGE_and_export.lsf]].
- Set " polarization " variable to true and run the script file.
- Visualize current from the contact and record the value at highest voltage.
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Set variable " voltage_index " to highest index (32) and select script lines enclosed with " if(false) " statement and execute them. This step plots and saves the results in file [[charge_export_with_polarization.ldf]].
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Set " polarization " variable to false and run script.
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Visualize current from contact and find voltage index that gives similar current as with " polarization = true ".
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Set variable voltage_index to the number from the previous point and select script lines enclosed with " if(false) " statement.
- As an alternative the user can also use the highest index (32) to compare the effects of polarization at the same voltage value.
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This will plot and save results for that voltage index in file [[charge_export_without_polarization.ldf]].
Nitrides having wurzite crystal geometry exhibit spontaneous and strain-induced polarization due to their deviation from the ideal symmetric tetrahedral geometry. The total polarization is represented by the surface charge densities at the interfaces between the quantum well and barrier. These charges induce strong built-in electric fields that alter carrier densities and band diagrams in the active region. The electric fields in the quantum well without and with polarization for the same amount of current \((I\) are shown below):
As explained in the literature [1], without any polarization the electric field in the active region is positive, which causes the holes to gather on the \(n\)-side. However, polarization creates high negative electric fields in the active region, which drives the hole towards the \(p\)-side. This is also evident from the carrier densities extracted from the CHARGE simulation:
Step 2: Obtain the spontaneous emission rate of uLED using MQW solver
- Open the project file [[GaNSQWLED_Piprek03ch9_v4_1D_polarized_QW_MQW.ldev]] and script file [[save_mqw_inputs_from_charge_run_and_plot.lsf]].
- Run the script file. The script imports the results from CHARGE to set the input parameters of the MQW simulation. It runs two MQW simulations and plots spontaneous emission rate with and without the polarization effects.
In this step, the script imports the electric potential and charge density from the saved CHARGE results. We use the 6\(\times\)6 \(k.p\) method in MQW to solve Schrödinger equation in the quantum well. The conduction and valence band edges with and without the polarization effects at the same current \((I\) value are shown below:
The built-in electric fields due to polarization tilt the band diagram of the quantum well, this is referred to as the quantum-confined stark effect (QCSE). In this case, the tilting caused by polarization happens in the opposite direction in the conduction and the valence band. Due to the symmetry in the tilt, the net transition energy and therefore the emission peak wavelength remain unchanged. However, due to the lower number of available states without polarization, indicated by the shallower quantum wells, the emission spectrum is narrower as shown below:
Next, we compare the band diagrams and spontaneous emission spectrum for the same voltage value (3.1V). The effect of material polarization on the band diagrams is more dramatic compared to the previous (same current) case as shown below:
We see a large tilt in the band diagram when the polarization effects are considered. This causes reduction in the transition energy resulting in a 1 nm red-shift in the spontaneous emission spectrum.
We also see a drop in the magnitude of the emission when polarization effects are present. This can be attributed to the reduction in the carrier density in the active region.
Important model settings
Description of important objects and settings used in this model
Semi-coupled workflow
As we have previously mentioned, this example is a semi-coupled workflow between CHARGE and MQW, where we feed the CHARGE results into MQW for simulating the uLED. The advantages of this method over the fully-coupled approach is that it is easier to attain convergence in CHARGE and it is faster. The main drawback of the semi-coupled workflow is that it doesn't include feedback of the MQW results on the CHARGE transport, which can reduce the accuracy of results.
CHARGE parameters
Bandgap
We created the base materials of the alloys in the CHARGE material database based on the bandgap values in the reference [1]. The bowing parameters were also taken from the same reference. We interpolated the bandstructure parameters to include the strain effects in bandgap.
Mobility
The electron and hole mobility values of the base materials were taken from literature [1]. The value of Bowing parameter was set to 0 for all the alloys.
Doping
The \(\mathrm{In}_{0.2}\mathrm{Ga}_{0.8}\mathrm{N}\) quantum well is undoped. It is sandwiched between \(p\)-doped \(\mathrm{Al}_{0.3}\mathrm{Ga}_{0.7}\mathrm{N}\) with a constant doping concentration of \(10^{19}\) and \(n\)-doped \(\mathrm{In}_{0.02}\mathrm{Ga}_{0.98}\mathrm{N}\) with a doping concentration of \(10^{18}\). The \(p\)-doped \(\mathrm{Ga}\mathrm{N}\) has doping concentration of \(10^{20}\). The \(n\)-type \(\mathrm{Al}_{0.3}\mathrm{Ga}_{0.7}\mathrm{N}\) and \(n\)-type \(\mathrm{Ga}\mathrm{N}\) have the same doping concentration of \(3\times 10^{18}\).
Nitride polarization effect
The polarization effects are included using the Surface Charge Density boundary condition. The values of the concentration are calculated by a scripted solution. The calculation assumes that the polarization charges are partially screened by charge defects, such that only half of them contribute to the built-in fields. The screen factor can be selected by changing the variable " screen_factor " in [[build_polarizable_interfaces.lsf]] in Material polarization effects in CHARGE simulation . It is also assumed that the defect charges in the other bulk layers completely screen the polarization charges at the interfaces between the bulk semiconductor layers. As a result, the surface charge boundary condition is only applied to the interfaces between the quantum well and barriers.
MQW parameters
Strain
The lattice constants of the base materials of the quantum well: \(\mathrm{In}\mathrm{N}\), \(\mathrm{Ga}\mathrm{N}\), and \(\mathrm{Al}\mathrm{N}\) are 3.548\(\mathring{A}\), 3.189\(\mathring{A}\), and 3.112\(\mathring{A}\) respectively [1]. The lattice constant of the alloys were calculated from the base materials using the following equation:
$$ a(\mathrm{In}_x\mathrm{Ga}_{1-x}\mathrm{N}) = 3.548x+3.189(1-x) $$
$$ a(\mathrm{Al}_x\mathrm{Ga}_{1-x}\mathrm{N}) = 3.112x+3.189(1-x)$$
The strain is calculated using the equation: \(\displaystyle{\frac{a_0-a}{a}}\), where \(a_0\) is the lattice constant of the substrate. The substrate material is \(\mathrm{Ga}\mathrm{N}\) (\(a_0 = 3.189 \mathring{A})\) for all alloys in the quantum well.
Updating the model
Instructions for updating the model based on your device parameters
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Geometry
Users can change the thickness of any of the layers based on their requirements. However, it is important to note that changing the thickness of one or more layers might require shifting the other layers to ensure that the geometry is setup correctly. -
Materials
Several material properties like the bandgap, mobility, doping values have been taken from the literature [1]. The users can use different material properties based on other sources. If they use other nitride materials, they also need to include the corresponding surface charge density values for considering polarization effects, which is calculated by the scripted solution discussed and linked previously.
Taking the model further
- In the next stages, the model can include the calculation of spontaneous power from the spontaneous emission rate. Please contact Ansys Lumerical Customer Support for a scripted solution to convert MQW spontaneous emission result (1/m) to Watts.
- A fully-coupled, self-consistent workflow between CHARGE and MQW solver will be able to account the feedback from MQW solver in CHARGE for more accurate simulation of the uLED. The users can refer to our example on red micro-LED for understanding how a fully coupled simulation workflow is setup.
- In addition to the electrical simulation, the optical simulation of uLED using FDTD/STACK solver will allow users to calculate other figures of merit of the uLED including the external quantum efficiency. Please refer to our red micro-LED example fore more details.
Additional resource
Additional documentation, examples, and training material
Related publications
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J. Piprek, Semiconductor Optoelectronic Devices, Academic Press, 2003
See also
Related Ansys Innovation Courses