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Concept# Surface integral

Summary

In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is, a function of position which returns a scalar as a value) over the surface, or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is called a surface as shown in the illustration.
Surface integrals have applications in physics, particularly with the theories of classical electromagnetism.
Surface integrals of scalar fields
Assume that f is a scalar, vector, or tensor field defined on a surface S.
To find an explicit formula for the surface integral of f over S, we need to parameterize S by defining a system of curvilinear coordinates on S, like the latitude and longitude on a sphere. Let such a parameterization be r(s, t), where (s, t) va

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Christophe Ballif, Loris Barraud, Priscille Marguerite Bôle Rothen, Stefaan De Wolf, Antoine Descoeudres

In silicon heterojunction solar cells, the passivation of the crystalline silicon wafer surfaces and fabrication of emitter and back surface field are all performed by intrinsic and doped amorphous silicon thin layers, usually deposited by plasma-enhanced chemical vapor deposition (PECVD). By using in-situ diagnostics during PECVD, it is found that the passivation quality of such layers directly relate to the plasma conditions, especially on the silane depletion fraction. Good interface passivation is indeed obtained from highly-depleted silane plasmas. Based upon this finding, layers deposited in a large-area very high frequency (40.68 MHz) PECVD reactor were optimized for heterojunction solar cells, yielding Voc’s up to 727 mV and aperture efficiencies up to 20.7% on 4 cm2 cells.

2011