Device Modeling IC-CAP

Semiconductor device modeling involves creating precise mathematical models that simulate the electrical behavior of semiconductor devices and circuits in response to various stimuli. A device model includes a set of equations with specific parameters or coefficients. Determining parameter values is a meticulous process that involves either direct extraction or optimization techniques to ensure the model equations closely fit the measured data.

Semiconductor device modeling forms the foundation of process design kits (PDKs), offering mathematical models that represent the behavior of the semiconductor devices, such as transistors, diodes, and capacitors, within the integrated circuits (ICs). As semiconductor device sizes shrink to the nanometer scale, device behavior becomes increasingly complicated as new physical phenomena occur. Accurate models enable design engineers to simulate and predict the behavior of devices before moving to costly physical prototyping.

Device modeling falls into the following categories:

• Physics-based models: Engineers recognize physics-based device models for their accuracy, as they rely on fundamental physical laws. One example is the 2D solution of Poisson's equation, which describes the electrical potential distribution in semiconductor devices.
• Empirical models: Derived by fitting equations to experimental data, these models prioritize practical predictability over theoretical foundations. For instance, the Curtice empirical model describes the I-V characteristics of metal-semiconductor field-effect transistors (MESFETs) and high-electron-mobility transistors (HEMTs).
• Semi-empirical models: These models combine physical principles with empirical data. For instance, Gummel-Poon is a semi-empirical model for bipolar junction transistors (BJTs).
• Table-based models: Table-based models, such as the HP Root FET model, interpolate measured data to simulate device behavior under different conditions.
• Artificial neural network (ANN) models: These models use artificial intelligence algorithms to learn from data and predict semiconductor device behavior. For instance, the DynaFET model applies neural networks to simulate the dynamic behavior and nonlinearities of field-effect transistors (FETs).

Modeling today’s industry-standard transistors is a complex and time-consuming process involving massive amounts of data. Extracting and verifying the quality of a Simulation Program with Integrated Circuit Emphasis (SPICE) model library can take weeks to months. As process technology advances, the model library needs continuous updates. Furthermore, the adoption of wide bandgap semiconductors relies on robust models for gallium nitride (GaN) devices to simulate highly nonlinear device behavior, including thermal and dynamic memory effects.

Semiconductor device modeling involves four basic steps to ensure accuracy and efficiency.

• Data measurement and analysis: This initial step measures the device’s physical and electrical properties, requiring extensive data collection. The procedure to select a typical die for measurements varies depending on the process development stage.
• Parameter extraction: This step involves extracting critical parameters such as DC, CV, S-parameters, and noise, which define the device's behavior under various conditions. The challenge for the modeling engineer is to implement a repeatable and robust procedure to extract the parameters of the model such that the mathematical model representation will match the measured data.
• Modeling: This step creates a mathematical model that accurately represents the device's behavior with the extracted parameters.
• Model validation: Validating the model ensures its reliability before it becomes available to users. Besides verifying the model's accuracy against measured data, modeling engineers must test its robustness by simulating it across multiple biases, geometry, and frequency conditions.