2.4 Semiconductor Device Simulation

With the development of large scale integration in the late 1970's it became evident that the optimization of semiconductor manufacturing processes on a mere experimental basis is questionable. The numerical simulation of the fabrication process and the electrical characteristics of semiconductor devices offers a fast and inexpensive way to check device designs and processes. The tools for numerical simulation efforts can be separated into three categories (see Fig. 2.11): process simulation, device simulation, and circuit simulation. Process simulation is based on measurements such as doping profiles provided by SIMS (secondary ion mass spectroscopy), topography provided by TEM (transmission electron microscopy), the process recipe, and the lithography masks. Processes such as diffusion, oxidation, etching, lithography, and ion implantation are simulated. Device simulation uses the resulting device geometry and doping profile to reproduce and predict electrical data such as current-voltage (IV) curves, capacitance-voltage (CV) curves, or transfer frequencies. The output of device simulators can serve to calibrate compact models of circuit simulation programs. Integrated simulation packages can be used to perform these steps automatically. The abbreviation TCAD (technology computer-aided design) has been established to refer to process and device simulation approaches.

Figure 2.11: Hierarchy of process, device, and circuit simulation.

The simulation of semiconductor devices is either based on semi-classical or quantum-mechanical formulations. Based on fundamental equations -- the POISSON^2.3, BOLTZMANN^2.4, WIGNER^2.5, or SCHRÖDINGER^2.6 equation -- several models can be derived. They will be briefly described in the next sections.

Subsections

• 2.4.1 Hierarchy of Semiconductor Device Simulation Models
• 2.4.2 Classical Device Simulation
  • 2.4.2.1 The Drift-Diffusion Model
  • 2.4.2.2 The Energy-Transport Model
  • 2.4.2.3 Device Simulation
  
  
• 2.4.3 Quantum Device Simulation
  • 2.4.3.1 SCHRÖDINGER Equation and SCHRÖDINGER-POISSON Solvers
  • 2.4.3.2 WIGNER Equation and the Density-Gradient Model
  • 2.4.3.3 Quantum Device Simulation
  • 2.4.3.4 Non-Equilibrium GREEN's Function Device Simulation

A. Gehring: Simulation of Tunneling in Semiconductor Devices