Tips & Tricks
3. Process Simulation of Stress Effects in Front-End-of-Line Structures

3.1 Advanced Calibration for Mechanics Simulations
3.2 Modeling Stress Induced by CESL and Epitaxial SiGe Layers in Sentaurus Process
3.3 Specifying NoBulkRelax for Accurate Viscoelastic Stress Analysis in Sentaurus Process
3.4 Lattice Mismatch Stress
3.5 Thermal Mismatch Stress
3.6 Intrinsic Stress
3.7 References

Objectives

3.1 Advanced Calibration for Mechanics Simulations

It is recommended to switch on AdvancedCalibration for mechanics simulations. The Advanced Calibration file (in section 2.15) includes a set of recommended mechanical parameters for the materials of the most common electronics as well as appropriate settings for mechanics simulations. These parameters are loaded automatically (see Section 6. Working With Advanced Calibration).

For more information, refer to the Advanced Calibration for Process Simulation User Guide.

3.2 Modeling Stress Induced by CESL and Epitaxial SiGe Layers in Sentaurus Process

To model the impact of built-in stress in a material upon its deposition, the normal stresses along all three axes with identical components must be specified. When the stress-rebalancing calculation is performed, the initial isotropic normal stress will change according to the particular geometry. For example, isotropic built-in stress in a very thin film will vanish in the normal direction to the surface; whereas, the lateral stress components will change and remain nonzero.

For accurate calculation of the stress introduced by amorphous stress sources such as a strained nitride contact etch stop layer (CESL), deposition must be split into several substeps. After each substep, stress rebalancing must be performed. When the number of substeps is large enough, the calculated stress values saturate to their correct levels. Practically, the number of substeps is in the range from 5 to 10, limited by the CPU time and the mesh size. One of the first descriptions of this approach was by Loiko et al. [Ref. 1]. See Section 3.6 Intrinsic Stress for the syntax using "fields" to introduce intrinsic stress at deposition steps.

From a physics perspective, this is caused by the interatomic bonds in amorphous material adjusting under the changing stress and geometry during deposition. This happens almost instantly, in a matter of picoseconds. Such adjustments of the interatomic bonds translate into local stress and should be updated after absorption of each atom for ultimate accuracy. However, for practical purposes, it is sufficient to do the updates in several substeps per deposition.

The requirement for the film thickness deposited per each substep is such that it is much less than the feature sizes of the surface on which it is being deposited. Considering that deposition typically makes the surfaces increasingly smooth during the deposition, it might be reasonable to start with smaller substeps and continue with increasing substeps until the entire film thickness is deposited.

For accurate calculation of the stress introduced by epitaxial films with lattice mismatch, a different approach is necessary. Specifically, stress rebalancing should be done only after depositing the entire film. To calculate the lattice mismatch stress, you can either:

For SiGe, you must switch off the lattice mismatch feature if you choose to use the intrinsic stress approach to avoid double-counting the effect by specifying:

pdbUnSetDoubleArray Silicon Germanium Conc.Strain

If multiple deposition steps are needed, you must switch off stress balance between these deposition steps. That is, add the following commands before the first SiGe deposition step:

pdbSet Mechanics EtchDepoRelax 0
pdbSet Mechanics StressHistory 0

After all SiGe deposition steps are completed, switch on the above two parameters by setting them to 1, and do a short diffusion to rebalance the stress.

From a physics perspective, this is caused by the entire epitaxial film having the same perfect crystal lattice as the substrate on which it is grown. Therefore, during the epitaxy, there are no irreversible adjustments of the interatomic bonds, which means that the final stress distribution is determined by the final shape of the epitaxial film (unless the stress is so high that dislocations are formed).

3.3 Specifying NoBulkRelax for Accurate Viscoelastic Stress Analysis in Sentaurus Process

Viscoelastic materials such as amorphous SiO2 exhibit viscous behavior by relaxing the deviatoric stress components. For accurate modeling of stress evolution in such materials, specify NoBulkRelax:

pdbSet mechanics NoBulkRelax 1

For example, stress in a narrow shallow trench isolation filled with a spin-on-glass oxide or flowable chemical vapor deposition(CVD) oxide can be quite different if NoBulkRelax is not switched on.

WARNING This parameter affects the oxidation shape, thickness, and stress inside the oxide. You must do a calibration accordingly. For LOCOS structures, this parameter changes the shape, especially when stress-dependent oxidation is switched on.

3.4 Lattice Mismatch Stress

To simulate lattice mismatch stress, two flags control the automatic updating of strain and lattice spacing:

pdbSet Silicon Mechanics UpdateStrain 1
pdbSet Mechanics LatticeHistory 1

These flags are switched on by default and should remain switched on for the calculation of the lattice mismatch stress.

To activate lattice mismatch stress, you also need to define the strain profile by specifying:

pdbSetDoubleArray Silicon <dopant_name> Conc.Strain {0 0 1 <n>}

Only the germanium strain profile is defined by default internally by:

pdbSetDoubleArray Silicon Germanium Conc.Strain {0 0 1 0.0425}

For other species such as carbon, you must set them yourself. The strain profile can be calculated approximately, based on the lattice constants of the materials. For example, the germanium strain profile can be calculated by:

(LGe – LSi)/LSi = (5.66 – 5.43)/5.43 = 0.042

The reference relaxed position is set to the bottom of the Si substrate by default. This works for the SiGe source/drain on a Si substrate. However, there are cases where you need to redefine the reference position such as for multiple-graded SiGe-strained layers. In those cases, you can set the top relaxed node coordinate accordingly by:

pdbSetDouble Silicon Mechanics TopRelaxedNodeCoord <n>

3.5 Thermal Mismatch Stress

By default internally, the coefficients of thermal expansion (CTEs) of the materials are recalculated relative to silicon when simulating thermal mismatch stress. This is due to the assumption that the substrate is very large compared to devices, so thermal expansion is dominated by the thick silicon substrate, and no thermal expansion stress or wafer bending occurs in the thick substrate.

For substrate materials other than silicon, you must tag it with the keyword substrate in the region command, so that the CTEs are calculated relative to the tagged substrate material instead. To overwrite the reference CTE by a user-specified value, use:

pdbSetDouble Mechanics RefThExpCoeff <n>

Relaxation of thermal mismatch stress is calculated when a temperature ramp is defined at diffusion by default in two dimensions. However, in three dimensions, the keyword stress.relax must be set in the diffuse command explicitly.

When automatic tracing of stress history is needed, ensure that you set:

pdbSet Mechanics StressHistory 1
pdbSet Mechanics EtchDepoRelax 1

With stress history switched off, the thermal mismatch stress is calculated only when a temp_ramp is defined in the diffuse command. In that case, remember to define the complete temperature ramp cycle. Otherwise, excess thermal mismatch stress might remain. For example, when a ramp-up from 25°C to 1000°C is simulated, at the following steps, there should be a ramp-down step to cycle the temperature back to 25°C. However, if stress history is switched on, Sentaurus Process will handle this automatically.

In 3D simulations, to speed up the simulation, you usually do not switch on stress history unless accurate stress history information is required.

3.6 Intrinsic Stress

Typically, intrinsic stress is applied using the stressdata command, which sets intrinsic stress for existing materials or regions, such as:

stressdata nitride sxxi=1e10 syyi=1e10 szzi=1e10   (unit is dyn/cm2)

Usually, a diffuse command follows a stressdata command, so that the intrinsic stress can rebalance due to the geometry. However, when using multiple steps for one deposition to rebalance stress after each sub-deposition step, the stressdata command is not a good choice. For this condition, in the deposit command, you can define stress in fields (unit is Pa), for example:

deposit nitride thickness=0.2<um> \
  fields= {StressELXX StressELYY StressELZZ} \
  values= {1e9 1e9 1e9} steps=5

Then, when stress is rebalanced after each substep, the intrinsic stress is applied accordingly.

3.7 References

Ref. 1
K. V. Loiko et al., "Multi-Layer Model for Stressor Film Deposition," in International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), Monterey, CA, USA, September 2006.

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