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The conventional spinorbit interaction due to the presence of an o-center impurity located in a spherical quantum dot of nite conning potential has been investigated. The dierent eective masses of dot and barrier are taken into consideration. The spinorbit interaction has been calculated in the excited state (2p). The variational method has been applied by using a new form of the trial wave function in addition to the conventional form that has been used in previous work. The new form has the advantage of satisfying the boundary conditions at the interface between dot and barrier in the case of dierent masses. It has been shown that the spinorbit interaction takes its highest value when the impurity is located in the vicinity of the position at which the radial electron probability takes its maximum value. The corresponding results of a central impurity has been investigated as the limiting case when the impurity radial coordinate tends to zero. The case of central impurity has been further explored by using the exact solution in the state (2p) of the radial Schrödinger equation in the presence of the impurity.

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The Design Rule Manual (DRM) is a critical component in the introduction and release of new technology nodes. It is the reference manual of definitive requirements, documented in detail, on all information regarding design rules and technology node design requirements. The DRM is a contract between the foundry and the designer. Designs must meet all documented requirements to be accepted for manufacture. The DRM’s critical role in process design enablement obligates it to a very high quality standard. The DRM must be accurate, reliable, and clear of ambiguity. Qualification of the DRM is crucial as design rules become extremely complex with advancing technology. DRM teams must ensure all descriptions and figures are correct and clear versus target requirements from the beginning of the technology development stage. The qualification process should cover all typical cases as well as corner and unexpected cases. Traditional methods of targeted pattern creation leave gaps in ensuring a high quality DRM. Those methods often miss complex scenarios leading to incomplete DRM documentation or descriptions with vague ambiguity. Ambiguity in the DRM leads to improper DRC rule coding, resulting in erroneous DRC checking. This paper presents a synthetic pattern/layout generation approach to high quality and high coverage DRM and DRC qualification. The generated patterns flow into a post-generation-analysis-fix step that helps discover and analyze issues while initial design rules and DRC code is being developed. Guided random generation of legal layout patterns produces simple and complex pattern configurations to challenge the accuracy and consistency between the original intention of the complex design rules and DRC rule deck. The post-generation-analysis-fix step helps identify locations of potential discrepancy. Flushing out these discrepancies and ambiguities drives enhancements to converge on robust DRM documentation and consistency between design rule intent and DRC run set implementation from early development throughout the life cycle of process node deployment.

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