Level-set method is a numerical simulation technique for interface tracking and shape modeling. In semiconductor process simulation, traditional algorithm implemented with solving classical physical/chemical partial differential equations are of relatively high complexity and are time-consuming, which significantly limits the performance of TCAD tools. Latest utilization of level set method has been proved to be accurate, numerically stable, as well as computationally efficient. This new strategy of simulating semiconductor fabrication processes such as deposition, etching, provides enhanced solutions for the semiconductor industry.
By solving the surface equation of multiple material regions, the level-set method is capable of describing geometric structure variations during semiconduction fabrication processes. Taking multi-material etching as an example, the structural change under user-specified processing conditions can be computed utilizing three-dimensional time-dependent level-set equations. The geometric variation rate depends on the local topographic information and the etching rate of the related material. The level-set equation can be expressed as:
where φ(x, y, z, t) = 0 corresponds to the surface equation, F represents the propagation expansion speed, →U (x, y, z, t) is the advection speed, and εκ describes the dependence of speed on curvature。In general, the numerical discretization method depends on the property of the Hamiltonian, as well as the targeted structure under concern. In the simplest case, one could implement first-order up-wind formalism, together with the well-known forward-Euler method for spatial and time discretization, respectively. While for complex process simulations, discretization methodology of higher orders may be necessary. For instance, ENO, or 5th-order WENO and third-order total variation diminishing Runge-Kutta (TVD-RK) methods should be considered, when numerical stability and accuracy requires further improvements.
Due to the increasing structural dimension of semiconductor process simulations, data structure and parallel algorithm are of significant importance throughout the entire simulation procedure. The level-set algorithm for multi-material etching has to be carefully designed, such that accuracy, efficiency and numerical stability can be satisfied simultaneously.
Two .bnd files with the initial (initial_struct.bnd) and the simulated 3D structure after the first etching step utilizing SEMulator3D (Silicon_etch_base.bnd) are provided, the competitors are requested to submit three .bnd files after each process simulation, together with the code and the descriptive algorithm documentation. The implementation should be carried out in C++, supporting multi-thread execution (optional), with CPU memory below 120G (max machine memory). Open source mathematical and geometrical libraries are permitted. The question consists of 3 cases with 3 simulated .bnd files for assessment. The algorithm can be implemented based on voxel data or surface mesh.
Detailed specification of the 3 cases are as follows:
1. Si etch:
Etching depth: 40 nm from the top side; Material parameters:
Polymer: etch ratio = 0.1, lateral ratio = 0.01;
SiO2_PECVD: etch ratio = 0.6, lateral ratio = 0.01;
Si_Amorph: etch ratio = 1, lateral ratio = 0.01;
2. Polymer etch:
Etching depth: 66 nm from the top side; Material parameters:
Si3N4_LPCVD: etch ratio = 0.3, lateral ratio = 0.01;
Polymer: etch ratio = 1, lateral ratio = 0.01;
SiO2_PECVD: etch ratio = 0.6, lateral ratio = 0.01;
3. Nitride etch:
Etching depth: 120 nm from the top side; Material parameters:
Si3N4_LPCVD: etch ratio = 1, lateral ratio = 0.01;
Polymer: etch ratio = 0.1, lateral ratio = 0.01;
SiO2_PECVD: etch ratio = 0.4, lateral ratio = 0.01;
SiO2_Thermal: etch ratio = 0.7, lateral ratio = 0.01;
Si_Amorph: etch ratio = 0.35, lateral ratio = 0.01;
Si_Xtal: etch ratio = 0.35, lateral ratio = 0.01.
The angular spread for visibility is 0.01 rad in all the three processes. The submitted result will be compared with result simulated obtained from Coventor SEMulator3D. Total simulation time of the tree processes should not exceed 1 day.