System and method for printing semiconductor patterns using an optimized illumination and reticle

A method for printing an integrated circuit pattern on a semiconductor wafer having a photoactive material thereon, the method comprising the steps of:

• providing a desired wafer feature pattern having at least one wafer feature element;
• deriving a merit function describing a relationship between an illumination source, a reticle, and an image, said source having at least one source parameter, said reticle having at least one diffractive feature, and said image having at least one image intensity;
• selecting at least one constraint in relation to said desired wafer feature pattern that said at least one image intensity must satisfy;
• selecting a combination of said at least one source parameter and said at least one diffractive feature so that said merit function is optimized in accordance with said at least one constraint;
• illuminating said reticle with illumination energy from said illumination source, so that said illumination energy is diffracted by said reticle and projected through a lens aperture to form said at least one image intensity on the wafer;
• exposing the photoactive material to said at least one image intensity;
• and
• developing said exposed photoactive material to form a printed feature,
• so that said printed feature conforms with said at least one wafer feature element of said desired wafer feature pattern in accordance with said at least one constraint, and wherein said at least one source parameter comprises a source direction having a source amplitude, wherein illumination from said source direction on said at least one diffractive feature produces at least one diffracted amplitude, and said step of selecting a combination further comprises
• selecting a plurality of source directions having diffracted orders overlapping in direction space in accordance with said desired wafer feature pattern;
• deriving a simplified function from said merit function;
• computing a diffracted amplitude corresponding to each of said plurality of source directions at selected source amplitudes and selecting a first optimized combination of computed diffracted amplitudes, source directions and source amplitudes so that said simplified function is globally optimized;
• selecting a final optimized combination of at least one source direction, at least one source amplitude and at least one diffracted amplitude so that said merit function is locally optimized using said first optimized combination as a starting solution, and so that said merit function is locally optimized in accordance with said at least one constraint;
• and
• forming said selected at least one diffractive feature so that said at least one selected diffracted amplitude is produced when said selected at least one diffractive feature is illuminated by said source from said selected at least one source direction.

A method for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form a desired image pattern on a wafer plane, the method comprising the steps of:

• providing a diffraction relationship for determining at least one diffracted amplitude diffracted by a reticle having at least one diffraction parameter when said reticle is exposed to illumination energy from an illumination source having at least one source parameter;
• providing a merit function for computing a merit value of the desired image pattern on the wafer plane as a function of variables including said at least one diffracted amplitude;
• selecting at least one constraint on at least one of said variables;
• determining an optimal value of said at least one diffracted amplitude so that said merit function attains a merit value that is optimized in accordance with said at least one constraint;
• and
• selecting a combination of at least one selected source parameter and at least one selected diffraction parameter to produce said optimal value of said at least one diffracted amplitude in accordance with said diffraction relationship.

A method for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form an image pattern on a wafer, the method comprising the steps of:

• providing a desired wafer feature pattern having at least one wafer feature element;
• deriving a merit function describing a relationship between an illumination source, a reticle, and the image pattern, said source having at least one source parameter, said reticle having at least one diffractive feature, and said image pattern having at least one image intensity;
• selecting at least one constraint in relation to said desired wafer feature pattern that said at least one image intensity must satisfy;
• and
• selecting a combination of said at least one source parameter and said at least one diffractive feature,
• so that said merit function is optimized in accordance with said at least one constraint, and wherein said at least one source parameter comprises a source direction having a source amplitude, wherein illumination from said source direction on said at least one diffractive feature produces at least one diffracted amplitude and said step of selecting a combination further comprises:
• selecting a plurality of source directions having diffracted orders overlapping in direction space in accordance with said desired wafer feature pattern;
• deriving a simplified function from said merit function;
• computing a computed diffracted amplitude corresponding to each of said plurality of source directions at selected source amplitudes and selecting a first optimized combination of computed diffracted amplitudes, source directions and source amplitudes so that said simplified function is globally optimized;
• selecting a final optimized combination of at least one source direction, at least one source amplitude and at least one diffracted amplitude so that said merit function is locally optimized using said first optimized combination as a starting solution, and so that said merit function is locally optimized in accordance with said at least one constraint;
• and
• forming said selected at least one diffractive feature so that said at least one selected diffracted amplitude is produced when said selected at least one diffractive feature is illuminated by said source from said selected at least one source direction.

A computer program product for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form a desired image, the computer program product comprising computer readable instructions for causing a computer to perform the method steps of:

• storing a desired image pattern on a wafer plane;
• storing a diffraction relationship for determining at least one diffracted amplitude diffracted by a reticle having at least one diffraction parameter when said reticle is exposed to illumination energy from an illumination source having at least one source parameter;
• storing a merit function for computing a merit value of an image pattern on the wafer plane as a function of variables including said at least one diffracted amplitude;
• storing at least one constraint on at least one of said variables;
• determining an optimal value of said at least one diffracted amplitude so that said merit function attains a merit value that is optimized in accordance with said at least one constraint;
• and
• selecting a combination of at least one selected source parameter and at least one selected diffraction parameter to produce said optimal value of said at least one diffracted amplitude in accordance with said diffraction relationship.

A computer program product for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form a desired image, the computer program product comprising computer readable instructions for causing a computer to perform a method having the steps of:

• storing a desired wafer pattern having at least one wafer feature element;
• storing a merit function describing a relationship between an illumination source, a reticle, and an image pattern, said source having at least one source parameter, said reticle having at least one diffractive feature, and said image pattern having at least one image intensity;
• storing at least one constraint in relation to said desired wafer feature pattern that said at least one image intensity must satisfy;
• and
• selecting a combination of said at least one source parameter and said at least one diffractive feature,
• so that said merit function is optimized in accordance with said at least one constraint, and wherein said at least one source parameter comprises a source direction having a source amplitude, wherein illumination from said source direction on said at least one diffractive feature produces at least one diffracted amplitude and said step of selecting a combination further comprises:
• storing a plurality of source directions having diffracted orders overlapping in direction space in accordance with said desired feature pattern;
• computing a simplified function derived from said merit function;
• computing a diffracted amplitude corresponding to each of said plurality of source directions at selected source amplitudes and selecting a first optimized combination of computed diffracted amplitudes, source directions and source amplitudes so that said simplified function is globally optimized;
• selecting a final optimized combination of at least one source direction, at least one source amplitude and at least one diffracted amplitude so that said merit function is locally optimized using said first optimized combination as a starting solution, and so that said merit function is locally optimized in accordance with said at least one constraint;
• and
• computing characteristics of said selected at least one diffractive feature so that said at least one selected diffracted amplitude is produced when said selected at least one diffractive feature is illuminated by said source from said selected at least one source direction.

A machine readable storage medium having stored therein a program of instructions executable by the machine to perform method steps for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form a desired image pattern on a wafer plane, said method steps comprising:

• storing a desired image pattern;
• storing a diffraction relationship for determining at least one diffracted amplitude diffracted by a reticle having at least one diffraction parameter when said reticle is exposed to illumination energy from an illumination source having at least one source parameter;
• storing a merit function for computing a merit value of an image pattern on the wafer plane as a function of variables including said at least one diffracted amplitude;
• storing at least one constraint on at least one of said variables;
• determining an optimal value of said at least one diffracted amplitude so that said merit function attains a merit value that is optimized in accordance with said at least one constraint;
• and
• selecting a combination of at least one selected source parameter and at least one selected diffraction parameter to produce said optimal value of said at least one diffracted amplitude in accordance with said diffraction relationship.

A machine readable storage medium having stored therein a program of instructions executable by the machine to perform method steps for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form a desired image, said method steps comprising:

• storing a desired wafer feature pattern having at least one wafer feature element;
• storing instructions for causing a computer to compute a merit function describing a relationship between an illumination source, a reticle, and an image pattern, said source having at least one source parameter, said reticle having at least one diffractive feature, and said image pattern having at least one image intensity;
• storing at least one constraint in relation to said desired feature pattern that said at least one image intensity must satisfy;
• and
• selecting a combination of said at least one source parameter and said at least one diffractive feature,
• so that said merit function is optimized in accordance with said at least one constraint, and wherein the step of selecting a combination further comprises approximating said diffractive feature using superimposed rectangular shapes.

A machine readable storage medium having stored therein a program of instructions executable by the machine to perform method steps for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form a desired image, said method steps comprising:

• storing a desired wafer feature pattern having at least one wafer feature element;
• storing instructions for causing a computer to compute a merit function describing a relationship between an illumination source, a reticle, and an image pattern, said source having at least one source parameter, said reticle having at least one diffractive feature, and said image pattern having at least one image intensity;
• storing at least one constraint in relation to said desired feature pattern that said at least one image intensity must satisfy;
• and
• selecting a combination of said at least one source parameter and said at least one diffractive feature,
• so that said merit function is optimized in accordance with said at least one constraint, and wherein said at least one source parameter comprises a source direction having a source amplitude, wherein illumination from said source direction on said at least one diffractive feature produces at least one diffracted amplitude and said step of selecting a combination further comprises:
• selecting a plurality of source directions having diffracted orders overlapping in direction space in accordance with said desired wafer feature pattern;
• deriving a simplified function from said merit function;
• computing a diffracted amplitude corresponding to each of said plurality of source directions at selected source amplitudes and selecting a first optimized combination of computed diffracted amplitudes, source directions and source amplitudes so that said simplified function is globally optimized;
• selecting a final optimized combination of at least one source direction, at least one source amplitude and at least one diffracted amplitude so that said merit function is locally optimized using said first optimized combination as a starting solution, and so that said merit function is locally optimized in accordance with said at least one constraint;
• and
• designing said selected at least one diffractive feature so that said selected at least one diffracted amplitude is produced when said selected at least one diffractive feature is illuminated by said source from said selected at least one source direction.

A machine readable storage medium having stored therein a program of instructions executable by the machine to perform method steps for selecting a combination of source illumination parameters and diffraction mask features for projecting energy through a lens aperture to form a desired image, said method steps comprising:

• storing a desired wafer feature pattern having at least one wafer feature element;
• storing instructions for causing a computer to compute a merit function describing a relationship between an illumination source, a reticle, and an image pattern, said source having at least one source parameter, said reticle having at least one diffractive feature, and said image pattern having at least one image intensity;
• storing at least one constraint in relation to said desired feature pattern that said at least one image intensity must satisfy;
• and
• selecting a combination of said at least one source parameter and said at least one diffractive feature,
• so that said merit function is optimized in accordance with said at least one constraint, and wherein the step of selecting a combination further comprises approximating said selected at least one diffractive feature using superimposed rectangular shapes.

A lithographic system for printing a desired wafer feature pattern on a semiconductor wafer including a photoactive material, the system comprising:

• an illumination source having at least one source parameter;
• a reticle having at least one diffraction parameter;
• and
• a lens;
• said illumination source, said reticle and said lens being arranged so that said illumination source illuminates said reticle so as to produce a plurality of diffracted amplitudes and said plurality of diffracted amplitudes are collected by said lens and projected to form a image on the semiconductor wafer and wherein
• said at least one source parameter and said at least one diffraction parameter are selected so that a merit function, expressed as a function of variables including said plurality of diffracted amplitudes, attains an optimal merit value and wherein said merit function is optimized in accordance with at least one constraint on at least one of said variables,
• so that exposing the photoactive material to said image and developing said exposed photoactive material forms a printed pattern that substantially conforms with the desired wafer feature pattern.