Error analysis in phase extraction in a 2D holographic imaging of semiconductor devices

Backside transient interferometric mapping method is a useful tool for ns-resolution imaging of transient changes in heat energy and free carrier concentration in semiconductor devices during high-energy electrical pulses. In this contribution we investigate the sources of errors in the extracted phase, which are specific to the spatial phase and reflectivity profile of the semiconductor device structure and to the used FFT extraction method. We show that the phase and reflectivity profile of the sample related to the structure of the top layers causes undulations in the phase, thus decreasing the phase extraction precision. To minimize the undulations, an optimal spectrum filter for the FFT method is proposed. In addition, the noise and fringe discontinuities are found to result in defects in the phase profile. In order to isolate these defects time efficiently, a pre-processing of the wrapped phase image is proposed. It effectively reduces the requirement for the unwrapping to a small region. The path independent method or the pixel-queue algorithm is then used for the unwrapping, which do not allow spreading of the defects. The findings are used to make a full-automated evaluation of the phase images.

[2]  R. Soref,et al.  Electrooptical effects in silicon , 1987 .

[3]  M. Takeda,et al.  Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry , 1982 .

[4]  Sergey Bychikhin,et al.  Quantitative internal thermal energy mapping of semiconductor devices under short current stress using backside laser interferometry , 2002 .

[5]  Seah Hock Soon,et al.  Smoothing filters in phase-shifting interferometry , 2003 .

[6]  D J Bone,et al.  Fourier fringe analysis: the two-dimensional phase unwrapping problem. , 1991, Applied optics.

[7]  Giovanni Breglio,et al.  Experimental detection of time dependent temperature maps in power bipolar transistors , 2000 .

[8]  E. A. Amerasekera,et al.  ESD in silicon integrated circuits , 1995 .

[9]  S. Holly,et al.  High-performance real-time heterodyne interferometry. , 1979, Applied optics.

[10]  C. Vest Holographic Interferometry , 1979 .

[11]  Michael Braun,et al.  Two-dimensional phase unwrapping using a minimum spanning tree algorithm , 1992, IEEE Trans. Image Process..

[12]  Hartmut Gruber,et al.  Holographic interferometric microscope for complete displacement determination , 1997 .

[13]  H. A. Vrooman QUAINT: Quantitative analyses of interferograms , 1991 .

[14]  Satoru Toyooka,et al.  A noise-immune method of phase unwrapping in speckle interferometry , 1997 .

[15]  M. Stecher,et al.  Interferometric temperature mapping during ESD stress and failure analysis of smart power technology ESD protection devices , 1999, Electrical Overstress/Electrostatic Discharge Symposium Proceedings. 1999 (IEEE Cat. No.99TH8396).

[16]  V. Dubec,et al.  Single-shot thermal energy mapping of semiconductor devices with the nanosecond resolution using holographic interferometry , 2002, IEEE Electron Device Letters.

[17]  B. J. Baliga,et al.  Modern Power Devices , 1987 .

[18]  Thomas Kreis,et al.  Digital holographic interference-phase measurement using the Fourier-transform method , 1986 .

[19]  Dionyz Pogany,et al.  Time-resolved analysis of self-heating in power VDMOSFETs using backside laserprobing , 1997 .

[20]  Pramod Rastogi Measurement of angular variations of 3D objects using holographic interferometry , 1994, Other Conferences.

[21]  Vernon,et al.  Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide. , 1994, Physical review. B, Condensed matter.

[22]  M. J. Huang,et al.  (Optics and Laser Technology, 34(6):457-464)Phase unwrapping based on a parallel noise-immune algorithm , 2002 .

[23]  D. H. Pontius,et al.  Second breakdown and damage in junction devices , 1973 .

[24]  Rihong Zhu,et al.  Processing technique for interference pattern with step using phase-shift interferometry , 2000, International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT).

[25]  D J Bone,et al.  Fringe-pattern analysis using a 2-D Fourier transform. , 1986, Applied optics.