Measuring height difference in patterns on semiconductor wafers
An improved technique for determining height difference in patterns provided on semiconductor wafers uses real measurements (e.g., measurements from SEM images) and a height difference determination model. In one version of the model, a measurable variable of the model is expressed in terms of a function of a change in depth of shadow (i.e. relative brightness), wherein the depth of shadow depends on the height difference as well as width difference between two features on a semiconductor wafer. In another version of the model, the measurable variable is expressed in terms of a function of a change of a measured distance between two characteristic points on the real image of a periodic structure with respect to a change in a tilt angle of a scanning electron beam.
1. A computer-implemented method comprising:
obtaining a shadow model having a variable expressed as a function of height difference between features of a device at different locations on a semiconductor wafer, wherein the shadow model represents height-dependent shadowing associated with the features;
determining values of one or more parameters of the shadow model from measurement data obtained from images of the features; and
determining, by a computer processor, the height difference between the features using the determined values of the one or more parameters applied to the shadow model.
2. The method of claim 1 , further comprising:
determining coefficients of the one or more parameters of the shadow model by statistical analysis of the measurement data.
3. The method of claim 1 , further comprising:
using a scanning electron microscope (SEM) to obtain the images of the features; and
performing measurements on the images to obtain the measurement data.
4. The method of claim 1 , wherein the features of the device comprise a core trench and a gap trench.
5. The method of claim 4 , wherein the core trench and the gap trench are part of a periodic structure.
6. The method of claim 1 , wherein an additional parameter of the shadow model is a width difference between the features of the device at the different locations on the semiconductor wafer.
7. The method of claim 6 , wherein the variable of the shadow model is expressed as a function of a change in depth of shadow, wherein the change in depth of shadow depends on the height difference as well as width difference between the features of the device.
8. A system comprising:
a memory;
a processing device, operatively coupled with the memory, to:
obtain a shadow model having a variable expressed as a function of height difference between features of a device at different locations on a semiconductor wafer, wherein the shadow model represents height-dependent shadowing associated with the features;
determine values of one or more parameters of the shadow model from measurement data obtained from images of the features; and
determine the height difference between the features using the determined values of the one or more parameters applied to the shadow model.
9. The system of claim 8 , wherein the processing device is further to:
determine coefficients of the one or more parameters of the shadow model by statistical analysis of the measurement data.
10. The system of claim 8 , wherein the processing device is further to:
receive the images of the feature from a scanning electron microscope (SEM); and
perform measurements on the images to obtain the measurement data.
11. The system of claim 8 , wherein the features of the device comprise a core trench and a gap trench.
12. The system of claim 11 , wherein the core trench and the gap trench are part of a periodic structure.
13. The system of claim 8 , wherein an additional parameter of the shadow model is a width difference between the features of the device at the different locations on the semiconductor wafer.
14. The system of claim 13 , wherein the variable of the shadow model is expressed as a function of a change in depth of shadow, wherein the change in depth of shadow depends on the height difference as well as width difference between the features of the device.
15. A non-transitory computer readable medium comprising instructions that, when executed by a computer, cause the computer to perform operations comprising:
obtaining a shadow model having a variable expressed as a function of height difference between features of a device at different locations on a semiconductor wafer, wherein the shadow model represents height-dependent shadowing associated with the features;
determining values of one or more parameters of the shadow model from measurement data obtained from images of the features; and
determining, by a computer processor, the height difference between the features using the determined values of the one or more parameters applied to the shadow model.
16. The non-transitory computer readable medium of claim 15 , the operations further comprising:
determining coefficients of the one or more parameters of the shadow model by statistical analysis of the measurement data.
17. The non-transitory computer readable medium of claim 15 , wherein the features of the device comprise a core trench and a gap trench.
18. The non-transitory computer readable medium of claim 17 , wherein the core trench and the gap trench are part of a periodic structure.
19. The non-transitory computer readable medium of claim 15 , wherein an additional parameter of the shadow model is a width difference between the features of the device at the different locations on the semiconductor wafer.
20. The non-transitory computer readable medium of claim 19 , wherein the variable of the shadow model is expressed as a function of a change in depth of shadow, wherein the change in depth of shadow depends on the height difference as well as width difference between the features of the device.