Device Simulation

Lesson 6 covered predicting the structure a process sequence produces. This lesson covers the second half of a TCAD flow: given that structure, including its full three-dimensional doping profile, predict how it behaves electrically. Device simulation is what turns a simulated structure into the Id-Vg and Id-Vd curves that actually characterize a transistor, the curves device engineers compare against a technology's target specifications, and that a compact model (lesson 9) is ultimately fit to reproduce.

Reading time: about 8 minutes.

7.1 The drift-diffusion model

Lesson 2.3 introduced drift and diffusion as the two mechanisms carrying current through a semiconductor. The most widely used device simulation approach, the drift-diffusion model, solves a coupled set of equations built directly from those two mechanisms together with Poisson's equation (relating electric potential to the local charge density, including both mobile carriers and fixed dopant charge) across the entire simulated structure, self-consistently: carrier concentrations determine the charge density, which determines the electric field through Poisson's equation, which in turn determines the drift and diffusion currents, which determine how carrier concentrations evolve, solved iteratively until the whole system converges to a consistent solution at each bias condition.

Drift-diffusion is not the only device simulation approach, more detailed methods exist for effects it approximates (quantum confinement in a very thin nanosheet channel, or carrier transport so fast through a very short channel that the local drift-diffusion approximation itself starts to break down), but it remains the standard, most widely used workhorse for day-to-day device characterization across most of a technology's development, with more specialized, more computationally expensive models reserved for specific effects drift-diffusion is known not to capture well.

7.2 Meshing

A device simulator solves its equations numerically, not analytically, which means the continuous structure has to be broken into a finite set of discrete points, a mesh, at which the equations are actually solved. Mesh quality directly affects both simulation accuracy and runtime: too coarse a mesh in a region where fields or carrier concentrations change rapidly (for example, right at a p-n junction's depletion region, or inside a FinFET's thin fin) can miss that rapid variation entirely, giving an inaccurate result; too fine a mesh everywhere, including regions where nothing changes quickly, wastes computation time without improving accuracy where it is not needed. Practical device simulation meshes are therefore non-uniform, refined (denser) specifically in regions expected to need it, such as near junctions and channel surfaces, and coarser in regions like the bulk of a substrate far from any active structure, where the solution varies slowly.

7.3 Id-Vg and Id-Vd curves

The two standard measurements (both on real silicon and in simulation) that characterize a MOSFET are:

• Id-Vg: drain current plotted against gate voltage, at a fixed drain voltage, swept from below to above threshold. This curve directly shows threshold voltage (where the curve rises sharply, lesson 4.1), subthreshold swing (the slope of the curve on a logarithmic current axis, below threshold, lesson 4.4), and off-current (the drain current at zero or a small negative gate voltage, the device's nominally "off" leakage).
• Id-Vd: drain current plotted against drain voltage, at a fixed gate voltage (commonly repeated at several gate voltages, producing a family of curves), swept from zero up through the operating supply voltage. This curve shows the device's on-current (drain current at the full operating gate and drain voltage, the device's nominally "on" drive strength) and its saturation behavior, where drain current stops increasing much further as drain voltage keeps rising, because the channel pinches off near the drain.

Together, Id-Vg and Id-Vd give the three numbers (Vt, Ion, Ioff) a device team most directly compares against a technology node's target specifications, and that feed most directly into the compact model extraction covered in lesson 9.

These curves are also run at multiple temperatures and, for a technology with more than one threshold-voltage flavor (a standard cell library commonly offers several, trading speed against leakage), at multiple target threshold voltages, since both temperature and Vt flavor measurably shift subthreshold swing, on-current and off-current. A device simulation study therefore rarely produces just one Id-Vg/Id-Vd pair; it typically produces a matrix of curves across the temperature and Vt-flavor combinations the eventual PDK needs to characterize, each combination its own simulated Id-Vg and Id-Vd result.

7.4 Worked example: reading a simulated Id-Vg curve

7.5 Interview questions

What equations does a drift-diffusion device simulator solve together? The drift and diffusion current equations together with Poisson's equation relating electric potential to charge density, solved self-consistently across the structure for carrier concentrations, field and current at each bias point.

Why does mesh quality matter for device simulation? Too coarse a mesh in a rapidly varying region (like a junction or thin channel) can miss that variation and give an inaccurate result; too fine a mesh everywhere wastes computation without improving accuracy where the solution varies slowly.

What does an Id-Vg curve show, and what three quantities can be extracted from it? Drain current versus gate voltage at fixed drain voltage; it shows threshold voltage (where current rises sharply), subthreshold swing (the subthreshold region's slope on a log current axis), and off-current (current at the nominal off gate voltage).

What does an Id-Vd curve show that Id-Vg does not? On-current (drive strength at full operating voltage) and saturation behavior, where drain current levels off as drain voltage rises further because the channel pinches off near the drain.

Why might a device simulator use a more detailed model than drift-diffusion for some structures? Drift-diffusion approximates effects like quantum confinement in a very thin channel or transport too fast for a local drift-diffusion approximation to capture well; more detailed, more computationally expensive models are reserved for structures or effects where this approximation is known to be inaccurate.