TEM-based phase retrieval of p–n junction wafers using the transport of intensity equation

Two cross-sectional specimens of pattered silicon wafers implanted with either arsenic or phosphor are investigated in the transmission electron microscope (TEM). Phase retrieval using the transport of intensity equation (TIE) is suggested as a means for nano-scale sensing of dopants in such p--n junction wafers. Improvements in TIE phase retrieval are proposed and implemented using a through-focus series of large numbers of images. Polynomial fitting to robustly estimate the required intensity defocus-derivative is shown to enhance data quality, resulting in phase maps that portray detail over a broad range of spatial-frequencies in a realistic manner.