Table 1 Sensitivity of the phase-sensitive imaging reflectometer.

This table compares the reconstructed values of different sample parameters by multiple metrology techniques. The “nominal value” column contains the design parameters. For phase-sensitive imaging reflectometry, the “Simultaneous” column shows the values simultaneously solved for using the genetic algorithm with the experimental data; only some of the sample parameters were solved for because of the limited number of data points. Were images at more angles available, we expect that we could simultaneously solve accurately for more of these parameters. The “single-parameter” column shows the sensitivity to these parameters in a single dimension, measured by how much the fit to the data worsens if an individual parameter is varied around the found solution. This column is a rough estimate of how low the confidence intervals could get with this dataset if we were solving for fewer parameters and were able to fix the rest using other metrology techniques. The error bars in the phase-sensitive imaging reflectometry columns are given at 1 SD, while the ranges reported for other techniques, when given, are more loosely defined reasonable ranges given to each measurement. For single-parameter confidence interval calculation, the dopant concentration versus depth was parameterized as the concatenation of an exponential spike at the surface and a Gaussian extending into the bulk (see the Supplementary Materials for complete table).

FeatureNominal valuePhase-sensitive imaging
reflectometry
SIMS*AFMEDS/HAADF
SimultaneousSingle-
parameter
confidence
interval
Layer thickness
[nm]
SiO2 on Si3N4 structure0–4(Set to 3)± 0.33.0–5.0
Si3N4 in structure50(Set to 50)Lower bound: 3041–45
Patterned SiO2
under structure
5(Set to 5)No sensitivity at
30-nm
wavelength
6.5–7.5
Structure height48.2 ± 0.2± 0.0245.0–45.848–51
SiO2 on higher-
doped substrate
0–42.7 ± 0.3± <0.052.0–4.0
SiO2 on lower-doped
substrate
0–42.0 ± 0.3± <0.052.0–4.0
Dopant-related etch
depth
6.09 ± 0.07± 0.027.8–8.05.5–7.5
Interface quality
[nm]
Average surface/
interface roughness
(Set to 0.5)Upper bound: 0.80.5–1.0
Surface roughness on
structures
(Set to 0.5)± 0.20.4–0.5
Surface roughness on
lower-doped substrate
(Set to 0.5)± 0.10.4–0.5
Surface roughness
on higher-doped
substrate
(Set to 0.5)± 0.30.4–0.5
DopantDepth-integrated
dose [atoms/cm2]
1.10 × 10150.75 × 1015 Upper
bound: 5.6 × 1015
Upper bound:
2.1 × 1015
1.05 × 10151.30 × 1015
Peak concentration
[atomic %]
(Shape set by
SIMS)
Upper bound: 9.33.83.1–4.1
Gaussian height
[atomic %]
(Shape set by
SIMS)
Upper bound: 3.21.10.8–1.8
Technique
summary
TopographyModel-basedDirectDirect
Composition informationModel-basedSpectroscopicSpectroscopic
Depth informationModel-basedDirectDirect
Transverse spatial resolutionNano-scale (10–100 nm)TOF/nano-SIMS:
≥ 100 nm
Nano-scale
(10–100 nm)
Atomic scale
(1–100 Å)
FOVMeso-to-micro (10–1000 μm)Meso (10 nm-
100 μm)
Atomic-to-nano
(1–1000 nm)
Sample preparationMinimalMinimalMinimalVersatile
challenging
DestructiveNon-destructiveDestructiveContract-basedDestructive

* The dopant measurements by SIMS were taken on an unpatterned sister wafer. The technique could have made similar measurements on layer thicknesses if there were wafers with the same fabrication steps as this sample, but with much bigger feature sizes (size depends on instrument).

† Variation in the SiO2 thicknesses between phase-sensitive imaging reflectometry (i.e., with phase and amplitude sensitivity) and EDS/HAADF is expected, because the sample had sufficient time to oxidize further between the two measurements. The sample was not prepared to perform surface roughness measurements.