Calculation of the diffusion induced stresses in silicon

When high concentrations of boron or phosphorus impurities are diffused into silicon single crystals, an elastic stress is suffered by the silicon lattice due to the mismatch sizes of the solute and solvent atoms. This diffusion induced stress is relieved by the generation and movement of dislocations. Moving dislocations cause the anomalous diffusion which in turn is related to the plastic deformation of the silicon crystal. Maximum stresses developed at the beginning of the process caused by boron and phosphorus are calculated and studied as a function of diffusion temperature. It is found that these stresses are sufficient to cause plastic flow. Attempts are made using well developed theories of plasticity in metals to calculate the range of phosphorus diffusion induced stresses necessary to cause plastic deformation in silicon crystals; they are found to be of the order 2.6 × 107 to 7.2 × 107 dyn/cm2. Durch Eindiffusion hoher Bor- oder Phosphorbeimischungskonzentrationen in Silizium-einkristalle wird das Siliziumgitter elastisch verspannt, da eine Fehlanpassung in der Grose der gelosten und der Wirtsgitteratome vorliegt. Diese diffusionsbedingte Spannung ist begleitet von der Erzeugung und Bewegung von Versetzungen. Wandernde Versetzungen verursachen die anomale Diffusion, die wiederum mit der plastischen Deformation des Siliziumgitters zusammenhangt. Die sich zu Beginn des Prozesses entwickelnden maximalen Spannungen werden berechnet und als Funktion der Diffusionstemperatur untersucht. Es wird gefunden, das diese Spannungen ausreichen, um plastisches Fliesen hervorzurufen. Unter Benutzung bekannter Theorien der Plastizitat in Metallen wird versucht, den durch Phosphordiffusion bedingten Bereich der Spannungen zu berechnen, der notig ist, um plastische Deformation in Siliziumkristallen zu erzeugen. Es ergibt sich, das dieser Bereich in der Grosenordnung von 2,6 × 107 bis 7,2 × 107 dyn/cm2 liegt.

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