Multiscale Device Simulator

In this example we will see a very simple TiberCAD (v. 1.2) simulation:

1D calculation of Poisson and drift-diffusion for a bulk Silicon sample.

The following files should be in your working directory:
bulk.tib : TiberCAD input file
bulk.msh: mesh file

The mesh file can be obtained from the following GMSH geo file : bulk.geo

• Step 1 - Modeling the device »
• Step 2 - Meshing the device »
• Step 3 - TiberCAD Input file »
• Step 4 - Run TiberCAD »
• Output »

 

Step 1 - Modeling the device (up)

As a first step, we have to model the device. To do so, you can use DEVISE module of ISE-TCAD 9.5 software package or GMSH program.
Here we'll see in details the procedure for GMSH. (see also Getting started 1 )
There are two possible ways to use GMSH:

1. Interactive, using the graphical interface
2. Using a script file

In the following we'll see how to write a basic GMSH script (bulk.geo); for any details please refer to GMSH manual GMSH (http://geuz.org/gmsh/).

 

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N.B.: In a 1D simulation it is assumed that the geometrical model is restricted to the x axis.

In a 2D simulation it is assumed that the geometrical model is restricted to the xy-plane (z=0).

Any other geometrical orientation could give impredictable results

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In a GMSH script, several variables can be defined and given a value in this way:

these are valid GMSH variables: L is just the length of the Si sample; d is the value of a characteristic mesh length (see below).

• Definition of geometrical entities Points:

The first three expressions inside the braces on the right hand side give the three X, Y and Z coordinates of the point ; the last expression (d) sets the characteristic mesh length at that point, that is the ‘size’ of a mesh element, defined as the length of the segment for a line segment, the radius of the circumscribed circle for a triangle and the radius of the circumscribed sphere for a tetrahedron.
Thus, the smaller is the value of d, the greater is the mesh density close to that point. The size of the mesh elements will then be computed in GMSH by linearly interpolating these characteristic lengths in the whole mesh.

 

• Definition of a geometrical entity Line:

Line(1) = {1, 2};

The two expressions inside the braces on the right hand side give the identification numbers of the start and end points of the line.

• Definition of the physical entity Physical Line bulk ;:

The expression(s) inside the braces on the right hand side give the identification numbers of all the geometrical lines that need to be grouped inside the physical line.
In this way, in general, physical regions are created which associate together geometrical regions, and then the related mesh elements, which share some common physical properties. It's only these physical regions which can be referred to outside GMSH. In TiberCAD, this is done by associating one or more physical regions to a TiberCAD region through the keyword mesh_regions (see in the following).

• Definition of two physical entities Physical Point:

 

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N.B.: In general, in a nD simulation, (n-1)D physical regions (points in 1D, lines in 2D, surfaces in 3D) are used by TiberCAD to impose the required boundary conditions.
Each (n-1)D physical region defined in this way in GMSH will be associated in TiberCAD to a boundary condition region, through the keyword BC_reg_numb. Thus, in this case, Physical points Anode and Cathode will be associated respectively to two BC regions (see in the following).

 

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Step 2 - Meshing the device (up)

 

The .geo script file with the geometrical description can be run in GMSH, to display the modelled device and to mesh it through the GMSH graphical interface.
Alternatively, a non-interactive mode is also available in GMSH, without graphical user interface. For example, to mesh this 1D tutorial in non-interactive mode, just type:

gmsh bulk.geo -1 -o bulk.msh

where bulk.geo is the geometrical description of the device with GMSH syntax;
-1 means 1D mesh generation;

some command line options are:
-1 , -2, -3 to perform 1D, 2D or 3D mesh generation,
-o mesh_file.msh to specify the name of the mesh file to be generated

In this way, a .msh has been generated and is ready to be read in TiberCAD.

Step 3 - TiberCAD Input file (up)

 

Now we have to write down the TiberCAD input file (bulk.tib). For a detailed reference see the user guide (Input file) and Getting started 1

1. Description of Device Regions

First, we have to list all the TiberCAD Regions present in our Device: a TiberCAD Region is usually a section of the device featuring the same material and possibly the same doping.

 

The TiberCAD Region bulk is made of Silicon and n-doped with a concentration 1x10¹⁶ cm^-3 .

Through the keyword Region, one GMSH physical region (Physical Lines in 1D, Physical Surfaces in 2D, Physical Volumes in 3D) previously defined in the GMSH mesh (Step 1), can be associated to the present TiberCAD Region, in this way:

Region  GMSH_physical_region_name

In this case, the Physical Line bulk is associated to the TiberCAD Region bulk.

Alternatively, through the optional keyword mesh_regions , one or more GMSH physical regions can be associated to a single TiberCAD Region (see Tutorial 1).

 

2. Definition of Simulation

Now we define the Simulation driftdiffusion_1: it belongs to the class driftdiffusion

The TiberCAD simulation driftdiffusion_1  , belonging to the model driftdiffusion, will be applied to the whole device structure (physical_regions = all)

 

3. Definition of Boundary Conditions

The anode and cathode contacts of our 1D Si sample are defined as Boundary conditions regions (BC_Region anode, BC_Region cathode) in the following way:

Through the keyword BC_Region , one (n-1) -dimension GMSH physical region (Physical Point in 1D, Physical Line in 2D, Physical Surface in 3D) previously defined in the GMSH mesh (Step 1), can be associated to the present TiberCAD BC_Region, in this way:

In this case, the Physical Point anode is associated to the TiberCAD BC_Region anode and the Physical Point cathode is associated to theTiberCAD BC_Region cathode

Alternatively, through the optional keyword BC_reg_numb, one or more (n-1) -dimension GMSH physical regions previously defined in the GMSH mesh can be associated to a single TiberCAD BC_Region (see next Tutorials).

Both contacts are defined as ohmic, cathod is assigned a fixed voltage = 0.0, while anode voltage is given by the value of the variable Vb

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4. Definition of Simulation parameters

Vb is specified in the sweep block, in the Solver section

In this way, the simulation driftdiffusion_1 is performed for 10 ( steps = 10) values of the anode voltage (variable = Vb), between 0 and 1.

 

5. Definition of Execution parameters

 

In the Simulation section , we decide which simulations to perform and in which order; set solve = sweep, to execute the sweep which run driftdiffusion_1 simulation for the specified loop.

Output files with conduction and valence band profiles (plot = Ec,Ev..) and all the calculated values of the current at the contacts (ContactCurrents) (the IV characteristic) are generated.

 

Step 4 - Run TiberCAD (up)

Now we can run TiberCAD

• by double clicking on bulk.tib file (in Windows)
• or by command line in linux: tibercad bulk.tib

(see Quick Start guide)

 

Output (up)

The generated Output files are:

• driftdiffusion_materials.dat: material (mesh) regions, in this case just region 1
  
• driftdiffusion_nodal.dat: nodal quantities (here conduction and valence band)
  
• sweep_driftdiffusion_Vb.dat : integrated current at the two contacts for each sweep step

 

Attachment	Size
bulk.tib	1.16 KB
bulk.geo	181 bytes
bulk.msh	4.49 KB