Depth resolution theory

Each analytical technique discus.sed in this chapter has its own advantages and disadvantages, arising from both the physical processes involved and technical requirements. The theory behind each of the techniques would in it.self fill a book, whereas the present purpose was to set out briefly the depth profiling approach as it related to each. The theories of sputtering and of depth resolution have al.so been the subject of many publications. Individual applications (corrosion, semiconductors, catalysis, organic materials, etc.) will be described separately in this volume. 

Bradley, R.M., Cirlin, E. (1996) Theory of improved resolution in depth profiling with sample rotation. Applied Physics Letters, 68,3722-3724. 

Gourlay extended the slender body theory of Tuck with the unsteady slender body theory. This improvement allows one to consider a ship moving in a non-uniform depth since the coordinate system is now earth-flxed, whereas it is ship-fixed for classic numerical methods. The ID system still uses vertical cross-sections and decomposition into an inner and outer expansion. The pressure integration is only made on the ship length based on the ship section B(x) at each x along the hull. Resolution of the ID equation is made with the finite difference method. Comparison with experimental results for soft squat situations h/T > 4) showed good agreement with numerical results. No tests were made for hard squat conditions (i.e., shallow depths) where flow around the ship is affected. 

The consensus of opinion is that the most suitable frequency is about 300 MHz, which has a penetration depth of about 7 cm in systems of high relative permittivity. Theory suggests that the signal-to-noise ratio and resolution of EMRI are very much worse than they are for MRI. However, the high point sensitivity of EMRI compared with MRI provides advantages for probe experiments and thus EMRI... 

These terms represent a bulk effect, a classical surface potential effect, and a surface field effect, respectively. Selection rules are stated through which these various contributions to the net photocurrent can be resolved. A complete theoretical description of photoemission, therefore, will enable resolution of each of these components as functions of the angles and j8), the available light intensity with depth, and the substrate epitaxy. This theory is discussed in detail in Ref. 51 note also Chapters 4 and 6 in this book. 

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