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The fabrication of discrete and integrated circuit solid state devices requires semiconductor crystals with impurity concentrations as low as possible and crystals that contain very few imperfection. A number of laboratory techniques are available for growing high purity semiconductor crystal. The refining of silicon by the Czochralski Technology is the most common method of producing monocrystalline silicon large diameter monocrystalline silicon can be grown with the Czochralski technique. This method involves growing a single crystal ingot from the melt, using solidification on a seed crystal as depicted. Czochralski silicon can be grown with resistivity in the order of 1 to 2mO-cm. Which is sufficient for making of most IC’s; including low to medium power IC’s. Molten Si is held in a quartz crucible in graphite suspected, which is heated by a radio frequency induction coil. A small dislocation free crystal, known as a seed, is lowered to touch the melt and then gradually pulled out of the melt. The seed is rotated in the pulling stage, to get a cylindrical ingot. To suppress evaporation from the melt and prevent oxidation, argon gas is passed through the system. At first, when the crystal is withdrawn, its cross –sectional area increase. It then reaches a constant value determined by the temperature gradients, heat losses and the pull. As the melt solidifies on the crystals, heat of fusion is released and must be away through the crystal. While the rate of pull finds the rate at which latent heat is released. To obtain an ingot with a large cross-sectional area, the pull speed must be slow. The Czochralski technique is also used for growing Gallium; Gallium Arsenide through each case has its own particular requirements. The main drawback of the Czochralski technique is that the final silicon crystal inevitably contains oxygen impurities dissolved from the quartz crystal crucible.
The end of a pipe is inserted into water. A tuning fork is held over the pipe. If the pipe resonates at lengths of 15 cm and 35 cm, what is the frequency of the tuning for
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