Abstract:
The ion beam induced charge (IBIC) technique is a scanning microscopy technique which uses finely focused MeV ion beams as probes to measure and image the transport properties of semiconductor materials and devices. Its success stems from the combination of three main factors: the first is strictly technical and lies in the availability of laboratories and expertise around the world to provide scanning MeV ion beams focused down to submicrometer spots. The second reason stems from the peculiarity of MeV ion interaction with matter, due to the ability to penetrate tens of micrometers with reduced scattering and to excite a high number of free carriers to produce a measurable charge pulse from each incident ion. Last, but not least, is the availability of a robust theoretical model able to extract from the measurements all the parameters for an exhaustive characterization of the semiconductor. This paper is focused on these two latter issues, which are examined by reviewing the current status of IBIC by a comprehensive survey of the theoretical model and remarkable examples of IBIC applications and of ancillary techniques to the study of advanced semiconductor materials and devices. 1. Introduction A charged particle with energy higher than 10？eV (i.e., charged particulate ionizing radiation) passing through a material deposits energy mainly through Coulomb interactions with the electrons within the absorber atoms [1–3]. If the primary charged particles are electrons, a large fraction of their energy can be lost in a single interaction, and their trajectories within the material are very tortuous because their mass is equal to that of the orbital electrons with which they are interacting. Also in the case of energetic (MeV) ions, most of their energy is lost in collisions with the atomic electrons; the interactions with the atomic nuclei occur much more rarely. Therefore, the ion undergoes a huge number of interactions and gradually loses its kinetic energy: the net effect is a gradual decrease of its velocity until the particle is stopped. The range of MeV light ions in matter is mainly determined by the electron stopping power (i.e., the average energy loss of the ion per unit path length) and depends on both the ion and target masses, atomic number, and ion velocity; for MeV light (H or He) ions, it extends to distances of the order of tens of micrometers (an exhaustive review of ion energy loss mechanisms in matter can be found in chapter 2 of [1]). Moreover, because of the high ion/electron mass ratio, the trajectories of MeV ions undergo few large

Abstract:
If M is a submanifold of a space form, the nullity distribution N of its second fundamental form is (when defined) the common kernel of its shape operators. In this paper we will give a local description of any submanifold of the Euclidean space by means of its nullity distribution. We will also show the following global result: if M is a complete, irreducible submanifold of the Euclidean space or the sphere then N is completely non integrable. This means that any two points in M can be joined by a curve everywhere perpendicular to N. We will finally show that this statement is false for a submanifold of the hyperbolic space.

Abstract:
For each submanifold of a stratified group, we find a number and a measure only depending on its tangent bundle, the grading and the fixed Riemannian metric. In two step stratified groups, we show that such number and measure coincide with the Hausdorff dimension and with the spherical Hausdorff measure of the submanifold with respect to the Carnot-Caratheodory distance, respectively. Our main technical tool is an intrinsic blow-up at points of maximum degree. We also show that the intrinsic tangent cone to the submanifold at these points is always a subgroup. Finally, by direct computations in the Engel group, we show how our results can be extended to higher step stratified groups, provided the submanifold is sufficiently regular.

Abstract:
We prove a height-estimate (distance from the tangent hyperplane) for $\Lambda$-minima of the perimeter in the sub-Riemannian Heisenberg group. The estimate is in terms of a power of the excess ($L^2$-mean oscillation of the normal) and its proof is based on a new coarea formula for rectifiable sets in the Heisenberg group.

Abstract:
We give a conceptual proof of the fact that if M is a complete submanifold of a space form, then the maximal integral manifolds of the nullity distribution of its second fundamental form through points of minimal index of nullity are complete.

Abstract:
In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter. In particular, given an isodiametric set, and up to negligible sets, we prove that its boundary is given by the graphs of two locally Lipschitz functions. Moreover, in the restricted class of rotationally invariant sets, we give a quite complete characterization of any compact (rotationally invariant) isodiametric set. More specifically, its Steiner symmetrization with respect to the Cn-plane is shown to coincide with the Euclidean convex hull of a CC-ball. At the same time, we also prove quite unexpected non-uniqueness results.

Abstract:
We study the class of transversal submanifolds. We characterize their blow-ups at transversal points and prove a negligibility theorem for their "generalized characteristic set", with respect to the Carnot-Carath\'eodory Hausdorff measure. This set is made by all points of non-maximal degree. Observing that C^1 submanifolds in Carnot groups are generically transversal, the previous results prove that the "intrinsic measure" of C^1 submanifolds is generically equivalent to their Carnot-Carath\'eodory Hausdorff measure. As a result, the restriction of this Hausdorff measure to the submanifold can be replaced by a more manageable integral formula, that should be seen as a "sub-Riemannian mass". Another consequence of these results is an explicit formula, only depending on the embedding of the submanifold, that computes the Carnot-Carath\'eodory Hausdorff dimension of C^1 transversal submanifolds.

Abstract:
In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.

Abstract:
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.