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2-6                                                              MEMS: Design and Fabrication


             the release of stored strain energy caused by such things as doping or mechanical deformation (wafer
             warpage), grain growth will increase linearly with increasing annealing time. To minimize the energy
             associated with grain boundaries, the gains tend to grow in a way that minimizes the grain boundary area.
             This driving force is inversely proportional to the radius of curvature of the grain boundary, and the
             growth rate is proportional to the square root of the annealing time. Heavy P-doping causes significant
             grain growth at temperatures as low as 900°C because P increases grain boundary mobility. If other impu-
             rities are incorporated in the gain boundaries, they may retard grain growth, which then results in the
             growth rate’s being proportional to the cube root of the annealing time.
               Thermal oxidation of polysilicon is carried out in a manner essentially identical to that of single-crystal
             Si. The  oxidation  rate of undoped polysilicon is  typically between  that  of (100)- and (111)-oriented
             single-crystal Si. Heavily P-doped polysilicon oxidizes at a rate significantly higher than undoped polysili-
             con. However, this impurity-enhanced oxidation effect is smaller in polysilicon than in single-crystal Si.
             The effect is most noticeable at lower oxidation temperatures ( 1000°C). Like single-crystal Si, oxidation
             of polysilicon can be modeled by using process simulation software. For first-order estimates, however,
             the oxidation rate of (100) Si can be used to estimate the oxidation rate of polysilicon.
               The resistivity of polysilicon can be modified by impurity doping using the methods developed for single-
             crystal doping. Polysilicon doping can be achieved during deposition (called in situ doping) or after film
             deposition either by diffusion or ion implantation. In situ doping is achieved by adding reaction gases
             such as diborane (B H ) and phosphine (PH ) to the Si-containing source gas. The addition of dopants
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             during the deposition process not only affects the conductivity of the as-deposited films, but also affects
             the deposition rate. Relative to the deposition of undoped polysilicon, the addition of P reduces the dep-
             osition rate, while the addition of B increases the deposition rate. In situ doping can be used to produce
             conductive films with uniform doping profiles through the film thickness without the need for high-
             temperature steps commonly associated with diffusion or ion implantation. Nonuniform doping through
             the thickness of a polysilicon film can lead to microstructural variations in the thickness direction that can
             result in stress gradients in the films and subsequent bending of released structural components. In addi-
             tion, minimizing the maximum required temperature and duration of high-temperature processing steps
             is important for the fabrication of micromechanical components on wafers that contain temperature-
             sensitive layers.
               The primary disadvantage of in situ doping is the complexity of the deposition process. The control of
             film thickness, deposition rate, and deposition uniformity is more complicated than the process used to
             deposit undoped polysilicon films, in part because a second gas with a different set of temperature- and
             pressure-related reaction parameters is included. Additionally, the cleanliness standards of the reactor are
             more demanding for the doped furnace. Therefore, many MEMS fabrication facilities use diffusion-based
             doping processes. Diffusion is an effective method for doping polysilicon films, especially for very heavy
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             doping (e.g., resistivities of 10 Ω-cm) of thick ( 2µm) films. However, diffusion is a high-temperature
             process, typically from 900 to 1000°C. Therefore, fabrication processes that require long diffusion times
             to achieve uniform doping at significant depths may not be compatible with pre-MEMS, complementary
             metal-oxide-semiconductor (CMOS) integration schemes. Like in situ doping, diffusion processes must
             be performed properly to ensure that the dopant distribution through the film thickness is uniform, so
             that dopant-related variations in the mechanical properties through the film thickness are minimized. As
             will be discussed below, the use of doped oxide sacrificial layers relaxes some of the concerns associated
             with doping the film uniformly by diffusion because the sacrificial doped SiO can also be used as a dif-
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             fusion source. Phosphorous, which is the most commonly used dopant in polysilicon MEMS, diffuses sig-
             nificantly faster in polysilicon than in single-crystal Si, due primarily to enhanced diffusion rates along
             grain  boundaries. The  diffusivity  in  polysilicon  thin  films  (i.e., small  equiaxed  grains)  is  about
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             1   10 cm /s.
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               Ion implantation is also used to dope polysilicon films. The implantation energy is typically adjusted
             so that the peak of the concentration profile is near the midpoint of the film. When necessary, several
             implant steps are performed at various energies in order to distribute the dopant uniformly through the
             thickness  of the  film. A  high-temperature  anneal  step  is  usually  required  to  electrically  activate  the



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