Home/Analysis Technologies/Semiconductor and electrical analysis/CHARGE
Analysis Technologies | Semiconductor and Electrical Analysis
A method that solves Poisson’s equation together with the electron and hole continuity equations to obtain the carrier distribution and current inside a semiconductor device.
Carrier transport in semiconductor devices
Steady state, transient, small-signal AC
Lumerical Multiphysics
What the method is
Poisson’s equation for the electrostatic potential, the continuity equations for electrons and holes, and the current density expressions made up of drift and diffusion are solved as a coupled set. Given the doping profile, material models, electrode potentials and, where needed, an optical generation rate, you obtain the carrier concentration distribution, potential, electric field and current.
There are three analysis types. Steady state gives the operating point, transient the time response, and small-signal AC the linear response around the operating point. From the same structural description you can cover DC characteristics, switching and bandwidth under consistent conditions.
Temperature can be handled in three ways: held constant, imported as a temperature distribution obtained elsewhere, or solved self-consistently together with heat conduction. For devices where self-heating affects operation, choose the third.
How it works
The drift-diffusion model is a semi-classical description that treats the semiconductor as a continuum. It combines Poisson’s equation for the electrostatic potential, the continuity equations for electrons and holes, and current density expressions writing the electron and hole flows as the sum of a drift term and a diffusion term. Because the three depend on one another, a solution satisfying all of them at once, a self-consistent solution, is found by iteration. Recombination and generation rates enter through the continuity equations.
The formulation was developed to handle numerically the regime where device scaling had made closed-form analytic models untenable. In procedure it is layered: discretize the governing equations, solve the resulting system of nonlinear algebraic equations by iteration, and solve a sparse linear problem inside that.
On the implementation side, the device is divided into an unstructured finite-element mesh and the solution is obtained at each mesh node. The published material does not state which discretization scheme is used for the continuity equations, so this page does not go into the discretization itself.
Strengths of this method
For scaled-down devices, closed-form analytic models do not hold. Solving the continuum transport equations numerically is the approach developed to handle that regime.
Steady state, transient and small-signal AC can all be solved from the same structural description, so operating point, switching and bandwidth can be compared on the same basis.
Trap-assisted recombination, Auger recombination, radiative recombination, stimulated emission, impact ionization and band-to-band tunneling can be enabled according to the problem.
Where it fits
→ when you need the depletion width and carrier distribution of a pn junction
→ when you need to evaluate the electrical characteristics of an electro-optic modulator
→ when you need dark current, responsivity and 3 dB bandwidth of a photodetector
→ when you want to estimate carrier collection efficiency and quantum efficiency in an image sensor
→ when you want to evaluate the responsivity and conversion efficiency of a solar cell
Optical response alone: if you want propagation or absorption of light itself, that is the territory of electromagnetic or mode analysis. Carrier transport analysis does not compute optical quantities.
Quantum well gain: the band structure and optical gain of an active layer where quantum confinement matters are handled by a method aimed at quantum wells.
Temperature distribution alone: if the heat generation is known and you only want the temperature distribution, heat conduction analysis on its own is enough.
A whole circuit or link: the performance of a circuit or link built from components is the territory of circuit-level analysis.
Applications
For a depletion-type phase shifter, obtain the change in carrier distribution against applied voltage.
Obtain dark current, responsivity and 3 dB bandwidth. The absorption distribution comes from electromagnetic analysis.
Carry the electrical characteristics of modulators and photodetectors into the design of the transmit and receive path.
Evaluate conversion efficiency and quantum efficiency from carrier collection efficiency.
Inputs and outputs
INPUT
| Structure | Device geometry, with materials assigned per region |
|---|---|
| Doping | The impurity concentration profile per region |
| Material models | Mobility, carrier lifetime, bandgap, effective mass, saturation velocity, recombination coefficients |
| Excitation | Electrode potential or sweep, optical generation rate, imported temperature or heat generation |
OUTPUT
| Carrier distribution | Electron and hole concentration, potential and electric field distributions |
|---|---|
| Electrical characteristics | Current, I-V characteristics, small-signal AC response |
| Band diagram | Band edge distributions from the band structure monitor |
| Handover data | Data files passing carrier distribution or heat generation to optical or heat conduction analysis |
How it works
Take the electrical and thermal properties of semiconductors and metals from the material database. Mobility, bandgap narrowing and recombination models are selected here too.
Give the impurity concentration profile per region. For optically driven devices, import the optical generation rate obtained from electromagnetic analysis.
Choose between steady state, transient and small-signal AC, and decide how temperature is handled. Place mesh constraints where current density or electric field changes rapidly.
Settle the electrode potentials and sweep steps and place the monitors. If it does not converge, revisit the step size, the mesh and the physical models you enabled.
The mesh at the junction and how the voltage is stepped decide whether it converges at all. Enabling high-field mobility models or impact ionization makes convergence harder. Step 03 is where most of your time should go.
Relationship to related methods
| Method | Relationship | Main targets | When to use which |
|---|---|---|---|
| CHARGE (this method) | This method | Carrier transport in semiconductors | Solves Poisson’s equation and the continuity equations self-consistently to obtain carrier distribution and current. |
| HEAT | Coupling | Temperature distribution within a structure | Can be coupled self-consistently with heat conduction. Electro-thermal analysis including self-heating is that combination. |
| FDTD | Upstream | Optical absorption distribution | The optical generation rate obtained from absorption is received here as an input. The handover is one-way. |
| MQW | Downstream | Quantum well band structure and gain | An active layer where quantum confinement matters is handled by a separate method. Carrier density and electric field are passed in a data file and the two are run in sequence. |
| FEEM | Downstream | Waveguide cross-sectional modes | Receives the index change converted from the carrier distribution as a material and obtains the change in effective index. |
Supporting products
A commercial software environment providing electrical analysis based on drift-diffusion. Heat conduction and quantum well analysis sit in the same environment, and handover of data to optical analysis happens there too. See here for licensing, system requirements and deployment.
FAQ
Related technical information
Tell us the device structure and the characteristics you want to evaluate, and we will propose the method and product that suit.