Computer simulation method of silicon oxidation

A method of fabricating a semiconductor device including simulating silicon oxidation to determine a time-dependent shape change of a Si region and a SiO2 region connected to said Si region in an oxidation process, said simulating silicon oxidation being computer-implemented and comprising the steps of:

• (a) configuring nodes on a simulation region including a Si region and a SiO2 region;
• said SiO2 region connected to said Si region to form a Si/SiO2 interface;
• (b) solving a diffusion equation of said oxidant at said individual nodes in said SiO2 region to calculate a surface concentration of said oxidant at said Si/SiO2 interface, resulting in a first value of said surface concentration of said oxidant at each of said nodes in a present time step;
• (c) adjusting said first value of said surface concentration of said oxidant at each of said nodes in said SiO2 region to generate a second value of said surface concentration of said oxidant at each of said nodes in said SiO2 region in said present time step;
• (d) calculating a thickness increase of said SiO2 region using said second value of said surface concentration of said oxidant at each of said nodes in said SiO2 region in said present time step;
• (e) calculating a new position of said Si/SiO2 interface in said present time step using said thickness increase of said SiO2 region obtained in said step (d);
• and
• (f) calculating shape deformations of said Si region and said SiO2 region using said new position of said Si/SiO2 interface obtained in said step (e):
• wherein said steps (a) to (f) are repeated from a first time step to a last time step at intervals of a time increment,
• wherein in said step (c) of adjusting said first value of said surface concentration of said oxidant in said present time step, said second value of said surface concentration of said oxidant is set as zero with respect to one of said nodes where said thickness increase of said SiO2 region obtained in said step (d) has a value equal to or less than a specific small value and at the same time, said first value of said surface concentration of said oxidant is stored for a next time step,
• wherein said stored first value of said surface concentration of said oxidant is added to a first value of said surface concentration of said oxidant obtained in said next time step, thereby producing a second value of said surface concentration of said oxidant in said next time step, said second value of said surface concentration of said oxidant thus produced being used in the following step (d) of calculating said thickness increase of said SiO2 region in said next time step, and
• wherein in said step (c) of adjusting said first value of said surface concentration of said oxidant in said present time step, said second value of said surface concentration of said oxidant is set as said first value of said surface concentration of said oxidant with respect to one of said nodes where said thickness increase of said SiO2 region obtained in said step (d) has a value greater than said specific small value.

A method of fabricating a semiconductor device including simulating silicon oxidation to determine a time-dependent shape change of a Si region and a SiO2region connected to said Si region in an oxidation process, said simulating silicon oxidation comprising:

• (a) configuring nodes on a simulation region including a Si region and a SiO2 region;
• said SiO2 region connected to said Si region to form a Si/SiO2 interface;
• (b) solving a diffusion equation of said oxidant at said individual nodes in said SiO2 region to calculate a surface concentration of said oxidant at said Si/SiO2 interface, resulting in a first value of said surface concentration of said oxidant at each of said nodes in a present time;
• (c) adjusting said first value of said surface concentration of said oxidant at each of said nodes in said SiO2 region to generate a second value of said surface concentration of said oxidant at each of said nodes in said SiO2 region in said present time;
• (d) calculating a thickness increase of said SiO2 region using said second value of said surface concentration of said oxidant at each of said nodes in said SiO2 region in said present time;
• (e) calculating a new position of said Si/SiO2 interface in said present time using said thickness increase of said SiO2 region obtained in said calculating the thickness increase of said SiO2 region;
• and
• (f) calculating shape deformations of said Si region and said SiO2 region using said new position of said Si/SiO2 interface obtained in said calculating a new position of said Si/SiO2 interface,
• wherein said steps (a) to (f) are repeated from a first time to a last time at intervals of a time increment,
• wherein said adjusting said first value of said surface concentration of said oxidant in said present time, said second value of said surface concentration of said oxidant is set as zero with respect to one of said nodes where said thickness increase of said SiO2 region obtained during said calculating a thickness increase of said SiO2 region has a value equal to or less than a specific small value and at the same time, said first value of said surface concentration of said oxidant is stored for a next time,
• wherein said stored first value of said surface concentration of said oxidant is added to a first value of said surface concentration of said oxidant obtained in said next time, thereby producing a second value of said surface concentration of said oxidant in said next time, said second value of said surface concentration of said oxidant thus produced being used in the following said calculating said thickness increase of said SiO2 region in said next time, and
• wherein in said adjusting said first value of said surface concentration of said oxidant in said present time, said second value of said surface concentration of said oxidant is set as said first value of said surface concentration of said oxidant with respect to one of said nodes where said thickness increase of said SiO2 region obtained during said calculating said thickness increase of said SiO2 region has a value greater than said specific small value.