Multilayer film metrology using an effective media approximation
A metrology system includes a controller coupled to a detector to generate a detection signal based on the reflection of an illumination beam from a multilayer film stack. The multilayer film stack may include one or more zones with a repeating pattern of two or more materials. The controller may generate a model of reflection of the illumination beam by modeling the zones as thick films having zone thicknesses and effective permittivity values using an effective medium model relating the effective permittivity values of the zones to permittivity values and volume fractions of constituent materials. The controller may further determine values of the zone thicknesses and the volume fractions using a regression of the detection signal based on the effective medium model and further determine average thickness values of the constituent materials based on the number of films, the zone thicknesses, the volume fractions, and the effective permittivity values.
1. A metrology system comprising:
a controller communicatively coupled to a detector configured to generate a detection signal based on reflection of an illumination beam from a multilayer film stack, wherein the multilayer film stack includes one or more zones with two or more material compositions disposed in a repeating pattern, wherein a number of layers of each material composition within the one or more zones is known, the controller including one or more processors configured to execute program instructions causing the one or more processors to:
model reflection of the illumination beam by the multilayer film stack by modeling the one or more zones of repeating layers of the multilayer film stack as thick films having zone thicknesses and effective permittivity values using an effective medium model, wherein the effective medium model relates the effective permittivity values of the one or more zones to permittivity values of the two or more material compositions and volume fractions of the two or more material compositions within the one or more zones;
determine values of the zone thicknesses and the volume fractions using a regression of the detection signal based on the effective medium model; and
determine average thickness values of the two or more material compositions within the one or more zones based on the number of films having each of the two or more material compositions, the zone thicknesses, the volume fractions, and the effective permittivity values.
2. The metrology system of claim 1 , wherein the multilayer film stack further includes one or more non-repeating layers, wherein the one or more processors are further configured to execute program instructions causing the one or more processors to:
determine values of the thicknesses of the one or more non-repeating layers using the regression of the detection signal based on the effective medium model.
3. The metrology system of claim 2 , wherein the one or more non-repeating layers comprise:
at least one of a top layer, a bottom layer, or an intermediate layer between two zones of repeating layers.
4. The metrology system of claim 1 , wherein the effective medium approximation model comprises:
a uniaxial film model.
5. The metrology system of claim 4 , wherein the volume fractions comprise:
a first set of volume fractions associated with ordinary dispersion and a second set of volume fractions associated with extraordinary dispersion.
6. The metrology system of claim 1 , wherein the detection signal comprises:
at least one of a reflectometry, scatterometry, or ellipsometry detection signal.
7. The metrology system of claim 1 , wherein an illumination source of the illumination beam comprises:
a narrowband illumination source.
8. The metrology system of claim 1 , wherein an illumination source of the illumination beam comprises:
a broadband illumination source.
9. The metrology system of claim 1 , wherein the detector comprises:
a spectroscopic detector, wherein the detection signal comprises:
at least one of a spectroscopic reflectometry, or a spectroscopic ellipsometry detection signal.
10. The metrology system of claim 1 , wherein wavelengths of the illumination beam are at least an order of magnitude higher than thicknesses of the two or more repeating compositions.
11. The metrology system of claim 1 , wherein wavelengths of the illumination beam include at least one of ultraviolet, visible, or infrared wavelengths.
12. A metrology system comprising:
an illumination source configured to generate an illumination beam;
one or more illumination optical elements configured to direct the illumination beam to a multilayer film stack, wherein the multilayer film stack includes one or more zones with two or more material compositions disposed in a repeating pattern, wherein a number of layers of each material composition within the one or more zones is known;
one or more collection optical elements configured to capture reflected light from the multilayer film stack in response to the illumination beam;
a detector to generate a detection signal based on the light captured by the one or more collection optical elements; and
a controller communicatively coupled to the detector, the controller including one or more processors configured to execute program instructions causing the one or more processors to:
model reflection of the illumination beam by the multilayer film stack by modeling the one or more zones of repeating layers of the multilayer film stack as thick films having zone thicknesses and effective permittivity values using an effective medium model, wherein the effective medium model relates the effective permittivity values of the one or more zones to permittivity values of the two or more material compositions and volume fractions of the two or more material compositions within the one or more zones;
determining values of the zone thicknesses and the volume fractions using a regression of the detection signal based on the effective medium model; and
determine average thickness values of the two or more material compositions within the one or more zones based on the number of films having each of the two or more material compositions, the zone thicknesses, the volume fractions, and the effective permittivity values.
13. The metrology system of claim 12 , wherein the multilayer film stack further includes one or more non-repeating layers, wherein the one or more processors are further configured to execute program instructions causing the one or more processors to:
determine values of the thicknesses of the one or more non-repeating layers using the regression of the detection signal based on the effective medium model.
14. The metrology system of claim 13 , wherein the one or more non-repeating layers comprise:
at least one of a top layer, a bottom layer, or an intermediate layer between two zones of repeating layers.
15. The metrology system of claim 12 , wherein the effective medium approximation model comprises:
a uniaxial film model.
16. The metrology system of claim 15 , wherein the volume fractions comprise:
a first set of volume fractions associated with ordinary dispersion and a second set of volume fractions associated with extraordinary dispersion.
17. The metrology system of claim 12 , wherein the detection signal comprises:
at least one of a reflectometry, scatterometry, or ellipsometry detection signal.
18. The metrology system of claim 12 , wherein the illumination source comprises:
a narrowband illumination source.
19. The metrology system of claim 12 , wherein the illumination source comprises:
a broadband illumination source.
20. The metrology system of claim 12 , wherein the detector comprises:
a spectroscopic detector, wherein the detection signal comprises:
at least one of a spectroscopic reflectometry, or a spectroscopic ellipsometry detection signal.
21. The metrology system of claim 12 , wherein wavelengths of the illumination beam are at least an order of magnitude higher than thicknesses of the two or more repeating compositions.
22. The metrology system of claim 12 , wherein wavelengths of the illumination beam include at least one of ultraviolet, visible, or infrared wavelengths.
23. A method for determining layer thicknesses of a multilayer film comprising:
measuring light reflected from a multilayer film stack to generate a detection signal, wherein the multilayer film stack includes one or more zones with two or more material compositions disposed in a repeating pattern, wherein a number of layers of each material composition within the one or more zones is known;
modeling reflection of the light by the multilayer film stack by modeling the one or more zones of repeating layers of the multilayer film stack as thick films having zone thicknesses and effective permittivity values using an effective medium model, wherein the effective medium model relates the effective permittivity values of the one or more zones to permittivity values of the two or more material compositions and volume fractions of the two or more material compositions within the one or more zones;
determining values of the zone thicknesses and the volume fractions using a regression of the detection signal based on the effective medium model; and
determining average thickness values of the two or more material compositions within the one or more zones based on the number of films having each of the two or more material compositions, the zone thicknesses, the volume fractions, and the effective permittivity values.