A mesh can make a physically correct TCAD model appear wrong. An abrupt junction represented by too few elements may shift a predicted breakdown voltage; a coarse oxide interface can suppress the field peak that drives tunneling or reliability concerns. This TCAD meshing guide treats mesh design as part of the model definition, not as a final numerical setting applied after the structure and equations are chosen.<\/p>\n
The practical objective is not to create the finest possible grid. It is to place resolution where material properties, dopant concentration, potential, carrier density, temperature, or current density change on a short length scale. Everywhere else, unnecessary nodes consume memory and increase solve time without improving the engineering result.<\/p>\n
Before setting mesh lines or activating refinement, identify the quantity that will determine the design decision. A process simulation<\/a> may require accurate dopant contours after implantation, diffusion, oxidation, and annealing. A device simulation may instead depend on threshold voltage, channel current, junction leakage, peak electric field, or breakdown behavior. Thermal and spreading-resistance problems require resolution around heat sources, material boundaries, narrow current paths, and temperature gradients.<\/p>\n This distinction matters because a process mesh and a device mesh do not necessarily have the same requirements. During diffusion, the mesh must resolve steep concentration gradients near implanted layers and junctions. During electrical solution, the critical regions may move to the gate dielectric, channel, depletion boundary, drain-side high-field region, or contact edges. Remeshing between process and device stages is often more efficient than carrying a uniformly dense process grid into the electrical calculation.<\/p>\n Characteristic physical lengths provide a useful starting point. These can include junction depth, oxide thickness, channel length, depletion width, diffusion length, thermal penetration depth, and the radius of curvature at a contact or field plate. The smallest relevant feature is not always the smallest geometric feature. A thin passive layer may need limited resolution if it has little effect on the result, while a slightly wider depletion region may require close attention because it controls the electric field distribution.<\/p>\n A good initial mesh is deliberately nonuniform. Fine spacing belongs at semiconductor-oxide interfaces, heterojunctions, p-n junctions, narrow conductive paths, contact boundaries, corners, and regions with expected field crowding. Coarser spacing is appropriate in electrically quiet bulk regions, provided the transition into refined zones is gradual.<\/p>\n At a material interface, nodes should align with the interface rather than allowing elements to cut across it. Material parameters can change abruptly across silicon, oxide, metal, or compound semiconductor boundaries. If the interface is poorly represented, the discrete equations may blur a discontinuity that is central to the problem. This is particularly consequential for normal electric field, displacement continuity, thermal flux, and carrier transport near boundaries.<\/p>\n Junctions require comparable care. A doping profile can be smooth in a mathematical sense while still changing over a distance too short for a coarse mesh to capture. Resolve the region on both sides of the metallurgical junction, not simply the point where donor and acceptor concentrations cross. For reverse-biased devices, extend adequate refinement through the depletion region and toward the location of peak field. For forward conduction, check the regions where current crowding and quasi-Fermi potential gradients develop.<\/p>\n Corners deserve special treatment, but not unlimited refinement. Sharp geometric corners can create very high local fields in an idealized two-dimensional model. If the fabricated device has a rounded corner, represent that radius where practical. If the geometry must remain sharp, use local refinement and interpret singular or near-singular peaks cautiously. A single maximum field value at one corner is less useful than a mesh-converged field distribution over the physically meaningful region.<\/p>\n Small elements alone do not guarantee a reliable solution. Excessive aspect ratios, abrupt changes in neighboring element size, and poorly shaped triangles or quadrilaterals can degrade conditioning of the discretized equations. The symptoms are familiar: slow convergence, sensitivity to solver tolerances, oscillatory potential or carrier profiles, and results that move when a seemingly unrelated region is refined.<\/p>\n Use smooth mesh grading between fine and coarse regions. The permissible growth rate depends on the solver, equation set, and geometry, but a gradual transition is generally preferable to a single jump from nanometer-scale spacing to a much larger bulk element. In regions dominated by one-dimensional variation, elongated elements may be reasonable. Near curved interfaces, contacts, and multidirectional current flow, more balanced elements are usually safer.<\/p>\n For thermal analysis<\/a>, mesh quality should follow heat-flow paths rather than geometry alone. A fine grid directly beneath a localized heat source may be necessary, but the surrounding material must also be sufficiently resolved to carry the spreading heat flux. For a three-dimensional problem, refining only through the thickness while leaving lateral spacing coarse can underestimate lateral spreading resistance or distort the peak temperature location.<\/p>\n A disciplined workflow prevents mesh density from becoming an uncontrolled response to every convergence issue. Begin with a baseline mesh that resolves all interfaces and the expected active device regions. Solve the simplest relevant physical case first, such as equilibrium, a low-bias operating point, or steady-state heat flow. This establishes whether geometry, boundary conditions, and material assignments are correct before nonlinear effects are introduced.<\/p>\n Next, refine one region at a time according to the quantity of interest. If threshold voltage is the target, refine the gate dielectric, channel, and source\/drain junction regions before adding nodes elsewhere. If avalanche or breakdown is being studied, focus on the high-field junction curvature, depletion region, and dielectric boundaries. If thermal resistance is the result of interest, refine the heat source, interfaces with thermal conductivity contrast, and the volume through which heat spreads to the sink.<\/p>\n After each refinement, compare engineering outputs rather than only visual plots. Useful checks include terminal current, threshold voltage, peak field location, integrated charge, total power, maximum temperature, and extracted resistance. A mesh is approaching adequacy when these values change by less than the tolerance justified by the design decision. The tolerance should be tighter for model verification or publication-quality parameter extraction than for an early feasibility study.<\/p>\n A practical mesh-convergence record should identify the node count, minimum local spacing, refined regions, solver settings, and the resulting key metrics. This record makes later results defensible and helps distinguish physical changes from numerical ones. It also prevents a common mistake: comparing two simulations that differ in both physical assumptions and mesh resolution, then attributing the difference to only one cause.<\/p>\n Adaptive meshing can be valuable when gradients are not known in advance. Error estimators or solution-based criteria can add resolution where potential, carrier concentration, temperature, or dopant gradients become steep. This is particularly useful for complex junction geometries and three-dimensional heat-flow problems with localized sources.<\/p>\n Adaptivity is not a substitute for physical judgment. It may refine a numerical feature caused by an unsuitable boundary condition, an unrealistic sharp corner, or insufficient model calibration. Review where nodes are added and ask whether the region corresponds to a real mechanism. If a mesh repeatedly concentrates at a boundary far from the active device, the boundary placement or condition may need revision rather than more elements.<\/p>\n For large three-dimensional calculations, set a node budget before refinement begins. A million-node mesh can be appropriate for a detailed thermal, Poisson, diffusion, drift-current, or spreading-resistance problem, but only when the additional resolution changes the decision-relevant result. The right simulator is the one that matches the equation set and dimensionality of the problem, not a larger software bundle than the analysis requires.<\/p>\n Mesh convergence establishes that the numerical discretization is no longer dominating the result. It does not prove that the physical model is correct. Compare simulated junction depths, sheet resistance, capacitance, I-V curves, thermal resistance, or field profiles with measurement, established analytical limits, or trusted reference structures<\/a> whenever available.<\/p>\n Also check conservation. Terminal currents should balance within the expected numerical tolerance. Applied power should correspond to generated and removed heat in a steady-state thermal calculation. Potential and flux behavior at symmetry planes, insulating boundaries, and contacts should agree with the stated boundary conditions. These checks often reveal setup errors earlier than a denser mesh will.<\/p>\n The useful mesh is the smallest one that reproduces the physical quantity needed for the decision, with stable results under local refinement. Treat it as an engineering artifact worth documenting. That discipline produces simulations that are faster to run, easier to review, and more credible when their results guide a device or process choice.<\/p>\n","protected":false},"excerpt":{"rendered":" A TCAD meshing guide for choosing resolution, grading, and interfaces that preserve device physics while keeping semiconductor simulations efficient.<\/p>\n","protected":false},"author":0,"featured_media":48,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-47","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/posts\/47","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/comments?post=47"}],"version-history":[{"count":0,"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/posts\/47\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/media\/48"}],"wp:attachment":[{"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/media?parent=47"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/categories?post=47"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/siborg.ca\/blog\/wp-json\/wp\/v2\/tags?post=47"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Put Nodes Where Gradients and Interfaces Occur<\/h2>\n
Control Element Quality, Not Only Spacing<\/h2>\n
Build the Mesh in Controlled Passes<\/h2>\n
Use Adaptivity With Engineering Judgment<\/h2>\n
Validate Against More Than Convergence<\/h2>\n