# Metrology for Measuring Bumps in a Protection Layer Based on Phase Shifting Fringe Projection

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fringe Projection System and Sample Details

#### 2.1. System Setup

#### 2.2. System Design

#### 2.3. Reference Plane Identification and Rotation Center Calibration

#### 2.4. Sample Details

## 3. Theoretical Model of Fringe Projection Profilometry

#### 3.1. Basic Theoretical Model for Fringe Projection Profilometry

_{i}onto a sample surface. The diffracted light is collected over the angle θ

_{c}, and the sinusoidal grating pitch is d. The grating pitch d

_{i}projected along the telecentric lens onto the sample plane is given by

_{c}acquired on the CCD camera plane is given by

#### 3.2. Three-Step Phase-Shifting Technique

#### 3.3. Phase-Height Conversion

_{D}/dc is 1/3:

_{D}is the selected pixel row spacing (from center to center) within the camera ROI, which corresponds to one-third of a collecting fringe pitch. Thus, the three selected rows with equal spacing d

_{D}within ROI can simultaneously acquire three fringe images with 120° phase shifts. A fringe originally positioned at P

_{1}is displaced to P

_{2}when a curved profile is measured, as shown in Figure 4. To simplify the derivation, we considered the problem as one-dimensional, where the same result holds for both the x and y axes. The displacement caused by the shift in the fringe position can be given by

_{2}above the reference plane. This gives the modulation factor M(x):

#### 3.4. Bump Height Correction in Polymer Layers

## 4. Measurement Algorithm and System Calibration

## 5. Experimental Results and Discussion

#### 5.1. Measurement of Double Peripheral Solder Bumps

#### 5.2. Height Measurement of Bumps in a Polymer

#### 5.2.1. Reflectrometric Spectrum Model Fit

#### 5.2.2. Comparison of PL Measurement with Scanning White Light Interferometry

#### 5.2.3. Bump Height Correction for Polymer Layers

_{c}= 19.6°, d = 250 µm, m = 1.048×, and the conversion factor $\frac{d}{2\pi m}\frac{\mathrm{cos}{\theta}_{c}}{\mathrm{sin}({\theta}_{i}+{\theta}_{c})}$ has a constant value of 56.6. The phase modification terms $\Delta {\varphi}_{PL}$ and $\Delta {\varphi}_{ox}$ in Equations (20) and (21) are given by

#### 5.2.4. Comparison of 3D Measurement with Scanning Electron Microscopy

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Sample platform plane identification and rotation center calibration. The intersection of the two laser sources pointed toward the center of the circular motion rail indicates the best focus position for the sample plane.

**Figure 3.**Fringe projection geometry: projection angle θ

_{i}, viewing angle θ

_{c}, sinusoidal grating pitch d, and lens magnifications m and n of the projection and imaging modules, respectively.

**Figure 5.**(

**a**) UFI process uses a protective layer that is semitransparent and varies in thickness. This introduces a significant error in the bump height/coplanarity measurement. (

**b**) Spatial shift of fringes due to traveling around the PL layer.

**Figure 6.**(

**a**) Measurement of reference step heights with the fringe projection system. (

**b**) Comparison of fringe projection system measurement results with certified values (nominal step heights: 5, 15, 25, 35, 45, 55, 65, 75, and 85 µm).

**Figure 7.**Example measurement of a BGA sample: (

**a**) photograph of the BGA sample, (

**b**) I

_{_}{0}, (

**c**) I{2π/3}, and (

**d**) I{4π/3}.

**Figure 8.**Reconstruction of the 3D BGA sample: (

**a**) photograph of the scan area, (

**b**) wrapped phase map, (

**c**) 3D reconstructed topography.

**Figure 10.**(

**a**) Reflectance spectrum from PL measurement of the BGA sample. (

**b**) FT spectrum of OPD 1 and OPD 2 corresponding to the two distinct frequencies of oscillations, which are well separated.

**Figure 11.**(

**a**) Simulation model of the PI layer on the BGA sample; the silicon substrate has an insulating oxide layer above and a PI layer on top. The physical thicknesses of the PI and oxide are ${t}_{PI}$ and ${t}_{ox}$ respectively. (

**b**) Top: simulation interference spectrum of each pair of reflecting lights A, B, and C. Bottom: Fitting of the combined reflectance spectrum (A + B + C) with the experimental reflectance. The fitting results were ${t}_{PI}$ = 25.34 µm and ${t}_{ox}$ = 5.31 µm.

**Figure 12.**(

**a**) Scanning white light interferometer model for measuring the PI thickness. (

**b**) Experimental results showing the formation of interference fringes at the air–PI and oxide–Si substrate interfaces. The intensity corresponding to the PI–oxide interface was too weak to be sensed.

**Figure 13.**(

**a**,

**b**) Modified versions of Figure 5a,b, respectively, with an additional oxide layer between the PI and Si substrate based on the reflectance spectrum.

**Figure 14.**(

**a**) Unwrapped phase map of the 8 × 8 bump array for the polymer structure and the bump height map when corrected by PI for the oxide thickness influence. (

**b**) Corrected bump height map with average of 161.4 μm and coplanarity of 5.5%.

**Figure 15.**(

**a**) Cross-section SEM results for a Sn bump on PL: bump height of 163 µm, PL thickness of 25.1 µm (right side)–27.1 µm (left side), and oxide layer thickness of 5.95 µm. (

**b**) Schematic labeling the material in (

**a**).

Site | Nominal (μm) | Calibrated(μm) Stylus | Measured(μm) Fringe Projection | Discrepancy(μm) % |
---|---|---|---|---|

1 | 5 | 6.76 | 6.94 | −0.19 (2.75) |

2 | 15 | 16.92 | 16.36 | 0.57 (3.36) |

3 | 25 | 27.16 | 26.70 | 0.46 (1.69) |

4 | 35 | 37.01 | 36.92 | 0.09 (0.24) |

5 | 45 | 46.20 | 46.86 | −0.66 (1.42) |

6 | 55 | 55.69 | 55.95 | −0.26 (0.47) |

7 | 65 | 64.98 | 65.97 | −0.99 (1.52) |

8 | 75 | 74.39 | 74.86 | −0.47 (0.63) |

9 | 85 | 86.66 | 87.46 | −0.79 (0.92) |

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**MDPI and ACS Style**

Ku, Y.-S.; Chang, P.-Y.; Lee, H.-W.; Lo, C.-W.; Chen, Y.-C.; Cho, C.-H.
Metrology for Measuring Bumps in a Protection Layer Based on Phase Shifting Fringe Projection. *Appl. Sci.* **2022**, *12*, 898.
https://doi.org/10.3390/app12020898

**AMA Style**

Ku Y-S, Chang P-Y, Lee H-W, Lo C-W, Chen Y-C, Cho C-H.
Metrology for Measuring Bumps in a Protection Layer Based on Phase Shifting Fringe Projection. *Applied Sciences*. 2022; 12(2):898.
https://doi.org/10.3390/app12020898

**Chicago/Turabian Style**

Ku, Yi-Sha, Po-Yi Chang, Han-Wen Lee, Chun-Wei Lo, Yi-Chang Chen, and Chia-Hung Cho.
2022. "Metrology for Measuring Bumps in a Protection Layer Based on Phase Shifting Fringe Projection" *Applied Sciences* 12, no. 2: 898.
https://doi.org/10.3390/app12020898