Home/Analysis Technologies/Thermal analysis/HEAT
Analysis Technologies | Thermal Analysis
A method that solves the heat conduction equation by the finite-element method to obtain the temperature distribution within a structure, and passes that temperature to optical analysis to evaluate thermo-optic effects.
Temperature field within a structure
Steady state, transient
Lumerical Multiphysics
What the method is
From heat sources and boundary conditions, obtain the temperature distribution within the structure. The subject is heat conduction in solids; fluids themselves are not solved. The material inputs are density, specific heat and thermal conductivity, plus electrical conductivity where electrical conduction is included. Both steady state and transient can be handled, so as well as the absolute temperature you can evaluate the time taken to reach steady state.
Coupling with electrical conduction happens inside the solution. There is a mode that solves heat conduction alone and an electro-thermal mode that includes electrical conduction; in the latter, Joule heating from the current enters the heat conduction equation as a source and heat and electrical conduction are solved self-consistently. That is the basic arrangement when self-heating has to be included for a high-current device.
What this method solves stops at the temperature field. The change in optical properties is evaluated by passing the temperature distribution to the optical analysis as temperature data, updating the refractive index through a temperature-dependent index model, and re-solving. The handover is one-way: optical results do not return to the temperature solution. In other words, the thermal and optical coupling is not self-consistent.
How it works
Heat conduction analysis is the problem of solving one partial differential equation for temperature. Heat capacity per unit volume times the rate of change of temperature, the inflow and outflow by conduction, and the heat source: the temperature distribution sought is the one that balances those three across the whole region.
Dividing the region into finite elements and representing temperature by values at mesh nodes turns the continuous problem into algebraic equations in a finite number of unknowns. The finer the elements the more precise the solution, and the greater the cost.
For steady state, the form with the time-derivative term dropped is solved. For transient, time is discretized too, and the time step is adjusted against a tolerance on the local truncation error. In either case the formulation presumes the timescale of interest is much longer than the relaxation time of the material.
Strengths of this method
Fixed temperature, heat flux, convection and radiation can be combined per surface, so the heat removal path can be represented close to the real assembly.
From one structural description you can obtain both the steady-state temperature distribution and the time variation of temperature during switching. The response time constant comes from this too.
Because heating from electrical conduction can be treated self-consistently as a source, self-heating is evaluated without relying on post-processing.
Where it fits
→ when you are designing a thermo-optic phase shifter driven by a heater
→ when you want to estimate the resonant wavelength shift from self-heating
→ when you want to evaluate thermal crosstalk between densely packed components
→ when you need the temperature time constant for switching
→ when you want the temperature rise from heating by optical absorption or current
You want to solve the flow: fluids themselves are not solved. A fluid only serves to provide a boundary condition, so where the flow field is the question, that is the territory of thermal-fluid analysis.
Carrier transport in semiconductors: where the current is set by carrier transport in a semiconductor, couple heat on the drift-diffusion side. The electrical treatment here goes as far as conduction in a conductor.
Optical response alone: if you only need optical response with no temperature change, electromagnetic or mode analysis is enough on its own.
Stress and deformation: evaluating mechanical stress and deformation is the territory of structural analysis tools.
Applications
Used for thermo-optic phase shifters and wavelength control of ring resonators.
Evaluate thermal crosstalk between densely packed components.
Estimate the drift in characteristics caused by self-heating.
Evaluate the temperature rise from optical absorption in devices such as metamaterial bolometers.
Inputs and outputs
INPUT
| Structure | The layer stack, with materials assigned per region |
|---|---|
| Material properties | Density, specific heat and thermal conductivity, plus electrical conductivity where electrical conduction is included |
| Heat sources | Uniform heat generation, or heat generation or charge data imported from another analysis |
| Boundary conditions | Fixed temperature, heat generation, heat flux, convection, radiation, adiabatic |
OUTPUT
| Temperature distribution | Temperature field within a structure |
|---|---|
| Heat flow | Heat flow from the power flow monitor |
| Transient response | The time variation of temperature and the time constant to reach steady state |
| Handover data | Temperature data passed to optical analysis, used together with a temperature-dependent index model |
How it works
Give density, specific heat and thermal conductivity. Solids and fluids are defined separately. Specify electrical conductivity too if electrical conduction is included.
Set the extent so that the heat sources and the heat removal path lie inside the analysis region. Leaving out the substrate or the assembly makes the temperature come out too high.
Choose steady state or transient, and whether to solve heat conduction alone or include electrical conduction. The mesh is set here too.
Give fixed temperature, heat generation, heat flux, convection, radiation and adiabatic conditions per surface, and place temperature and power flow monitors.
How you choose the boundary conditions decides the temperature distribution more than the amount of heat generated. Note also that the convection condition is intended for steady state. Step 04 is where most of your time should go.
Relationship to related methods
| Method | Relationship | Main targets | When to use which |
|---|---|---|---|
| HEAT (this method) | This method | Temperature distribution within a structure | Solves the heat conduction equation by the finite-element method for the temperature field and heat flow. It does not obtain the change in optical properties. |
| CHARGE | Coupling | Carrier transport in semiconductors | Where the current is set by carrier transport in a semiconductor, heat is coupled self-consistently on that side. |
| FDTD | Upstream | Optical absorption distribution | Receives the heat generation distribution obtained from absorption as a source. |
| FEEM | Downstream | Cross-sectional modes after a temperature change | The temperature obtained is passed across, and the change in effective index is obtained there through a temperature-dependent index model. |
| MQW | Downstream | Quantum well gain | The recipient when temperature is passed as a single scalar value. The temperature distribution within the well is not reflected. |
Supporting products
A commercial software environment providing heat conduction analysis. Electrical and quantum well analysis sit alongside it, and the handover of data to optical analysis happens there too. See here for licensing, system requirements and deployment.
FAQ
Related technical information
Photonic integrated circuit solutions →
Tell us the structure and the characteristics you want to evaluate, and we will propose the method and product that suit.