Tips & Tricks
2. Simulating Wide-Bandgap Semiconductors With Sentaurus Device

2.1 SiC Process and Device Simulation
2.2 AlGaN Process and Device Simulation
2.3 How can I improve convergence in simulations of wide-bandgap-based devices?
2.4 My simulation runs slowly. How can I speed it up?
2.5 Relevant Application Notes
2.6 References

Objectives

2.1 SiC Process and Device Simulation

You can simulate both structure formation and electrical device behavior relevant to SiC technology. Different SiC polytypes are supported such as 3C–SiC, 4H–SiC, and 6H–SiC.

For more information about SiC process simulation, see Section 15. Special Focus: SiC Process Simulation.

To learn how to simulate SiC devices with Sentaurus Device, see Section 15. Special Focus: 4H-SiC PiN Device Breakdown Simulation.

For other examples, see Section 2.5 Relevant Application Notes.

2.2 AlGaN Process and Device Simulation

TCAD Sentaurus provides relevant models to simulate the processing and electrical device behavior of AlGaN/GaN devices.

For more information about AlGaN process simulation, see Section 16. Special Focus: AlGaN Process Simulation.

To find out more about models and settings for AlGaN device simulation, see Section 16. Special Focus: Simulating AlGaN Devices With Sentaurus Device.

For other examples, see Section 2.5 Relevant Application Notes.

2.3 How can I improve convergence in simulations of wide-bandgap-based devices?

Simulations involving wide-bandgap materials are more prone to convergence problems due to the numeric challenges in performing floating-point operations with extremely large and extremely small numbers such as the concentrations of majority and minority carriers in wide-bandgap semiconductors.

2.3.1 Troubleshooting

If you experience convergence problems:

  1. Understand the physics of the device.
    Convergence problems are frequently caused by improper meshing of the structure. A good mesh needs to capture the physics well. For example, depletion regions and impact ionization generation must be captured well to prevent convergence issues.
  2. Start the debugging process by switching off all physical models. Then, switch them on again one-by-one to find out which model causes problems.
  3. See if boundary conditions (BCs) are contradictory.
    For example, an electrode touching a semiconductor and an insulator at a corner will apply an Ohmic BC (default) to nodes touching the semiconductor, and a gate-like BC to nodes touching the insulator. These different BCs will lead to abrupt variations in potential around the corner that can lead to convergence issues, especially if the Avalanche model is switched on. The simplest solution to this problem is to use a workfunction that leads to a flat band around the corner.
  4. Tighten up numeric settings (see Section 2.3.2 Numeric Settings).
  5. Sometimes, using more realistic physics can lead to better convergence (see Section 2.3.3 Realistic Physics).
  6. Use Sentaurus Device tools to find out which equation is responsible for problems and where it is in the device (see Section 2.3.4 Tools for Debugging Convergence Problems).

2.3.2 Numeric Settings

Sentaurus Device provides several switches that can improve convergence. Adjusting some of them, especially tightening up numeric accuracy in the global Math section, can help to improve the robustness of simulations of wide-bandgap-based devices. Most notably, using ExtendedPrecision, optionally combined with a larger number of precision Digits provides more accurate solutions of the linear system and tends to lead to better convergence.

In addition, it is often advantageous to smoothly switch the driving force from GradQuasiFermi to ElectricField for the computation of carrier velocity saturation in low density regions where numeric noise in the quasi-Fermi level would lead to a noisy computation of driving forces. The parameters RefDens_e|hGradQuasiFermi_ElectricField set the carrier density thresholds for the transition from one driving force to the other.

Similarly, RefDens_e|hGradQuasiFermi_Zero can be used to damp the driving force entering the HighFieldSaturation model such that it is essentially switched off in regions where densities are too low to contribute any significant conduction current. In analogy, RelTermMinDensity and RelTermMinDensityZero can be used to effectively reduce energy relaxation times in regions where carrier densities are too small.

Do not use RefDens_e|hGradQuasiFermi_ElectricField together with RefDens_e|hGradQuasiFermi_Zero. This might degrade convergence.

For a detailed discussion of Math settings for low density regions, see Section 9.6 Improving Convergence in Low-Density or Low-Current Regions.

For a Math section that lists the most important parameters used for numeric control in III–nitride simulations, see Section 16.6 AlGaN-Specific Numeric Parameters.

2.3.3 Realistic Physics

Sometimes, removing some numeric idealities can improve convergence. For example, switching on a small amount of optical generation helps to raise the concentration of minority carriers.

Often, generation values as low as 106 pairs/s-cm-3, which translate into a few carriers generated in years in micrometer-scale devices, are sufficient to make simulations of wide-bandgap semiconductors more robust:

Physics {
  ...
  Optics(OpticalGeneration(SetConstant(Value=1e6)))
}

In addition, ideal insulators can lead to the accumulation of minute quantities of carriers that are essentially isolated pools of carriers. For example, minority carriers will accumulate at insulator–semiconductor interfaces of MOSFETs and MISHFETs, or at internal barriers in heterostructure devices and lead to convergence problems with continuity equations.

Any numeric "tap" into these isolated pools of carriers leads to improved convergence. Switching on tunneling so that carriers connect to the next layer or to the "outside world" is a method used to improve convergence in these cases. Here is an example of how to switch on hole tunneling across an alumina barrier in a MISHFET:

Physics {
  ...
  hBarrierTunneling "NLM"
}

Math {
  ...
  Nonlocal "NLM" (Barrier(Region="Al2O3_Ins"))
}

2.3.4 Tools for Debugging Convergence Problems

Sentaurus Device provides the keywords CNormPrint and NewtonPlot, which constitute powerful tools to understand and resolve convergence issues.

CNormPrint prints, after each Newton iteration, one line for each equation being solved, with the name of the equation, the maximum update error, its corresponding coordinate, and the value of the solution variable at that location. Inspection of the output or log files typically indicates which equation is responsible for convergence problems and the location where errors are largest.

NewtonPlot plots TDR files with maps of errors and residuals for each equation, which is essentially the same information as CNormPrint, but in a more comprehensive and graphical way.

In both cases, the information is most useful after the Newton iteration that brought the solution closest to convergence, with often only one equation still struggling. In addition, you are typically interested in Newton plots only when the simulation is on the verge of failing to converge, that is, when the bias step is close to its minimum allowed by the MinStep keyword.

The following Math section excerpt demonstrates how to switch on these convergence-monitoring tools in such a way that Newton plots are created only for small bias steps and for the iteration that was closest to convergence:

Math {
  ...
  CNormPrint
  NewtonPlot (Error MinError Residual)
}

The generated NewtonPlot TDR files in this example are named n@node@_np_<iteration number>_min_des.tdr. The choice of file name is specified in the File section:

File {
  ...
  NewtonPlot= "n@node@_np_%d_%d_des.tdr"
}

The first C-format specifier (%d) is replaced by the bias step number and the second C-format specifier is replaced by min since you chose to plot only a file for the Newton iteration that is closest to convergence.

See Section 9. Nonlinear Newton Solver for further help on how to improve convergence.

2.4 My simulation runs slowly. How can I speed it up?

Devices based on wide-bandgap materials are usually used in power applications and are often large. As a consequence, mesh sizes also tend to be large and simulations take longer than simulations of devices for other applications.

The default linear solver SUPER is the most accurate and leads to the most robust simulations. Therefore, SUPER is typically the linear solver of choice when simulating wide-bandgap-based devices. However, significant progress has been made with the iterative solver ILS, which is significantly faster than SUPER. In addition, while SUPER can be used only for single-thread (single CPU core) simulations, ILS can be parallelized and can take advantage of modern multicore machines.

The ILS solver with default numeric parameters leads to simulations that are typically not robust enough. However, by tightening up some of its numeric parameters, you can run robust simulations of SiC- and GaN-based devices significantly faster than with the SUPER solver.

Typical Math sections are listed in Section 15.4 SiC-Specific Numeric Parameters and Section 16.6 AlGaN-Specific Numeric Parameters. However, depending on the specific application, other more relaxed settings might work faster.

To benefit from the multicore capability of the ILS solver, the number of parallel threads is set with NumberOfThreads:

Math {
  ...
  NumberOfThreads=4 * Simulation uses 4 threads (requires parallel license)
  ...
}

See Section 6.4 Linear Solvers for more details on ILS numeric parameters.

2.5 Relevant Application Notes

App. 1
Sentaurus Technology Template: Simulation of DC Characteristics of a GaN-Based HFET, available from ../Applications_Library/Hetero/HFET_GaN_DC.
App. 2
Optimization of GaN MISFET and DC Boost Converter Circuit, available from ../Applications_Library/Power/BoostConverter_GaN-SiC/BoostConverter_MixedMode.
App. 3
Simulation of Silicon Substrate Effect on AlGaN/GaN HFET Off-State Breakdown Voltage, available from ../Applications_Library/Power/HFET_GaN_BV.
App. 4
Simulation of Normally Off AlGaN/GaN HFET With P-Type GaN Gate and AlGaN Buffer, available from ../Applications_Library/Power/HFET_pGate_GaN.
App. 5
Process and Device Simulation of 4H-SiC NMOS Device Using TCAD Sentaurus, available from ../Applications_Library/Power/NMOS_SiC-4H.
App. 6
Simulation of 4H-SiC pIGBT With TCAD Sentaurus, available from ../Applications_Library/Power/pIGBT_SiC-4H.

2.6 References

Ref. 1
O. Ambacher et al., "Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures," Journal of Applied Physics, vol. 85, no. 6, pp. 3222–3233, 1999.

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