edfas.org ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 24 NO . 4 36 rest overnight will produce additional profile changes that can be quantified by re-measuring the surface profile and comparing to the starting profile. Reheating, or annealing, the samplemay hasten the force redistribution by softening themountingwax andallowthe sample to come closer to its free state. If a significant time elapses between process steps, or the sample is annealed, a new surface profile should be taken that does not compensate for sample movement in terms of RST variation, but does allow ignoring the changes that have already takenplace. Thiswould suggest that a surface profile should be taken before each step in the thinning process. This may be best, but the time to take a full profile increases overall process time and it only reduces thickness variation without eliminating it. Measuring the profile before each step will not eliminate the need for thickness measurements to control RST variation but it will reduce the amount of RST variation measured and the difficulty of compensating for it. A mechanical profile measurement will need to be done whenever thickness correction is done. HOW SILICON THICKNESS IS MEASURED All silicon thickness measurement systems work on the same principle. Themeasurementmodel is the FabryPerot interferometer. It is necessary to understand how this model works to understand the various factors that can affect the validity of the thickness values generated. Figure 2 shows the basic operation of the Fabry-Perot interferometer. Whenever light passes through a change in refractive index, both a reflected and transmitted beam is created. The amount of the light reflected fromthe change is a function of the indices of refraction of both mediums as described by Fresnel’s equations. The incident light is reflected from the illuminated surface, but some amount of the incident light is transmitted through the silicon only to have some amount again reflected off the back surface. The light reflected from the back surface is again reflected off the front surface with some passing through. The light passing through will interfere with the incident light reflecting off the front surface. When the effective light path through the silicon is equal to an integer number times thewavelength of the incident light, the two light beams will add, enhancing the reflected intensity. When the path through the silicon is equal to an integer + 0.5 times the wavelength of the incident light, the reflected intensity will be reduced by the back surface reflection. The difference between the maximum and minimum reflected light is a function of the reflectivity of the front and back surfaces. If the front surface is not highly polished, the light entering the siliconwill be greatly reduced. The reflectivity of the backside, the active surface of the die, is a functionofwhat contacts the silicon. Areas covered with silica or nitride will be more reflective as there is a large difference in the refractive indices. Areas covered by polysilicon and areas with a high doping density gradient will reflect little light back to the incident surface. In active Fig. 2 The basis of optical thickness measurements. The reflected rays R0, R1, R2, and so on, interfere based on the wavelength of the incident light, the index of refraction of the material, and the thickness, l. Fig. 3 This hypothetical active structure demonstrates the problemwith reflectivity. Each color change produces a reflection toward the back surface of the die. The amount of reflected light is a function of the refractive indices of the materials at the interface. The highest reflection is from a metal-silicon interface, followed by a silicon-dielectric interface.
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