Topography simulation method

• US 5,070,469 A
• Filed: 09/21/1989
• Issued: 12/03/1991
• Est. Priority Date: 11/29/1988
• Status: Expired due to Fees

• Current Assignee: Mitsubishi Denki Kabushiki Kaisha (Mitsubishi Electric Corporation)
• Original Assignee: Mitsubishi Denki Kabushiki Kaisha (Mitsubishi Electric Corporation)
• Inventors: Kunikiyo, Tatsuya, Fujinaga, Masato, Kotani, Norihiko
• Primary Examiner(s): CANGIALOSI, SALVATORE A
• Application Number:
  US07/410,627
• Time in Patent Office: 803 Days
• Field of Search: 364/578, 364/521, 364/522, 364/488-491, 371/27
• US Class Current: 703/2
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]
• CPC Class Codes: G06T 19/20 Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts
• CPC Class Codes: G06T 2219/2021 Shape modification
• CPC Class Codes: H01L 21/3083 characterised by their size, orientation, disposition, behaviour, shape, in horizontal or vertical plane

Abstract

A topography simulation method for simulating a surface topography of a material object material while a surface of material object is being processed, as by etching or a deposition, includes the steps of dividing a region to be analyzed, in a surface including the advancing direction of processing, into a plurality of regions in a grid in accordance with the surface topography of the material object by approximating the movement of the processed surface of the material object as the movement of an equi-concentration surface determined by the diffusion of particles, establishing diffusion coefficients for the respective regions on the basis of the surface processing velocity, calculating equi-concentration surfaces by the Diffusion equation, and assembling the obtained equi-concentration surfaces to produce a three-dimensional surface topography.

Claims

1. A method of predicting the three-dimensional shape of a surface of a workpiece on which a material is deposited by the transport of a material deposition species from a source to the surface of the workpiece in a deposition process comprising:

establishing a three-dimensional grid of points;

specifying an initial three-dimensional shape of a surface of a workpiece on which a material will be deposited at each point on the grid of points;

specifying the three-dimensional diffusion coefficient of the material deposition species that will be transported from a source to the surface of the workpiece;

specifying the initial concentration of the deposition species at the surface of the workpiece on which the material will be deposited;

specifying the time T during which the material will be deposited on the workpiece; and

successively solving the three-dimensional diffusion model equations for each of a plurality of time intervals representing deposition of the material on the workpiece beginning from the specified initial three-dimensional shape of the surface of the workpiece at the beginning of the first interval, the initial deposition species concentration, and the three-dimensional diffusion coefficient of the deposition species at each point on the grid of points to determine the shape of the surface of the workpiece on which the material is deposited at the end of each interval from the shape of the surface of the workpiece on which the material is deposited at the beginning of that interval until the total length of the time intervals reaches the specified time T, thereby producing the final shape of the deposited surface after the deposition process has continued for the time T.

2. A method of predicting the three-dimensional shape of a surface of a workpiece on which a material is deposited by the transport of a material deposition species from a source to the surface of the workpiece in a deposition process comprising:

establishing a three-dimensional grid of points;

specifying an initial three-dimensional shape of a surface of a workpiece on which a material will be deposited at each point on the grid of points;

specifying the initial concentration of the deposition species at the surface of the workpiece on which the material will be deposited;

specifying the time T during which the material will be deposited on the workpiece;

specifying a voltage difference between a region which is the source of the deposition species and the workpiece;

successively calculating the electric field intensity distribution between the region and the surface of the workpiece on which the material is deposited by solving the Poisson equation for each of a plurality of time intervals representing deposition of the material on the workpiece beginning from the specified initial three-dimensional shape of the surface of the workpiece at the beginning of the first interval and continuing until the total length of the time intervals reaches the specified time T;

successively calculating the three-dimensional diffusion constant of the deposition species between the source and the workpiece assuming the diffusion constant is proportional to the square of the electric field intensity; and

successively solving the three-dimensional diffusion model equations for each of the plurality of time intervals representing deposition of the material on the workpiece beginning from the specified initial three-dimensional shape of the surface of the workpiece at the beginning of the first interval, the initial deposition species concentration, and the three-dimensional diffusion coefficient of the deposition species at each point on the grid of points to determine the shape of the surface of the workpiece on which the material is deposited at the end of each interval from the shape of the surface of the workpiece on which the material is deposited at the beginning of that interval until the total length of the time intervals reaches the specified time T, thereby producing the final shape of the deposited surface after the deposition process has continued for the time T.