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This example describes the simulation of a gallium arsenide PIN diode. We will look at the different mechanisms of recombination, including Auger and radiative recombination in GaAs and how they are influenced by the dopant distribution and the applied bias.


A project file is provided to assist with the application example. The project file contains the material properties, geometry, and simulation region required to run the example.




Associated files


See also





Open the GaAs_diode.ldev file in CHARGE. Notice that the diode is specified as follows:


The thickness of the active GaAs layer is 4um.

Aluminum is used for both the cathode and anode contacts, which are specified as ohmic contacts using the boundary conditions.  

By default, trap assisted recombination, Auger recombination and radiative recombination are turned on.

To define the space-charge regions in the GaAs, first, the background doping concentration of GaAs is set to represent a p-type epitaxial layer with a concentration of 1x1015 cm-3. This is accomplished by defining a region of constant doping that encompasses the entire geometry. Next, two diffusion doping regions are used to specify the n-type and p-type dopant concentrations under the cathode and anode respectively.


The doping concentration can be visualized as shown below. Click on the "mesh" button to mesh the simulation.  Once the meshing is done, right click on the CHARGE solver region and visualize "grid" where you can get an image plot of the net doping concentration N.  Alternatively, you can use the script below to interpolate the finite element mesh results onto a linear mesh for a 1D plot:



v_index=1; x =  -0.025e-6;   z = linspace(getnamed('gaas','z min'),getnamed('cathode','z min'),401);

doping = getresult('CHARGE','grid');

vtx = [doping.x, doping.z];   

N = abs(pinch(doping.N));  

N_src = interptri(doping.elements,vtx,N,x,z,0); 

plot(z*1e6,N_src,'depth (um)','doping (1/cm3)','doping', 'logplot');





Material Properties

For this example, GaAs and aluminum are used. Expand the Material Group in the Objects Tree.  Here you can view the materials used in the simulation. Two types of materials are used in this example:


Conductor (Aluminum for the anode and cathode contacts)

Semiconductor (GaAs for the bulk gaas)


The conductor is defined its work function. The semiconductor is defined using the more complex semiconductor model in CHARGE. In particular the "Recombination" tab of this material is of interest in this example.


For all parts of this example, the trap-assisted, radiative and Auger recombination models are enabled.


For descriptions of the bulk recombination processes as well as other semiconductor material models, please see Lumerical's knowledgebase entry on Semiconductors.




Steady-state simulation


In the GaAs_diode.ldev file, check the material properties for GaAs to make sure that all three recombination processes (radiative, Auger, and trap assisted) are enabled. Also verify that band to band tunneling and impact ionization are disabled. Set the electrical contact biases in the "Boundary Conditions" group according to the table below.



Voltage (volts)




0-0.4 in 5 steps


Run the simulation. Once the simulation is run, you will be able to right-click on the CHARGE object and visualize the "charge" dataset to look at n and p carrier profiles. Both n and p are smaller in the intrinsic section and larger in the n-type and p-type doped sections respectively.  To make your plot look similar to the plots below, go to the options of the visualizer window by clicking the chart settings button and select "square" from the axis scale options and also choose "log scale."   The square axis option changes the aspect ratio of the plot so it becomes a square for better visualization.




Similarly, you can visualize the recombination dataset also available within the CHARGE object.  All the recombination processes can be visualized independently. In this case, Rau refers to recombination due to the Auger model and Ropt refers to radiative recombination.  Again to recreate the plots below, choose "square" from the axis scale options in the properties of the visualizer.


Ropt at 0, 0.2, 0.4 volts





Rau at 0, 0.2, 0.4 volts



You will notice that both recombination rates increase rapidly with increasing bias, related to carrier injection into the intrinsic layer. At zero bias, the recombination rates are negligible, as expected from detailed balance.  


Auger recombination is more dominant outside of the intrinsic region since carrier concentration ( n , p) is lower in the intrinsic section and higher outside. When there are an excess of carriers (np >> ni2), Rau is related to the carrier concentration as follows:


$$R_{au} \approx \begin{cases} C_n n^2p, n >> p \\ C_p np^2, p >> n \end{cases} $$


Consequently, Auger recombination is largest near the edges of the intrinsic layer where the majority carrier density is large and an excess of carriers exists.


The radiative recombination Ropt is directly proportional to the excess carrier concentration: R α (np - ni2). Ropt is dominant within the intrinsic region where the excess carrier density (the np product) is largest due to the injection in forward bias.

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