Probing hot-carrier transport and elastic scattering using ballistic-electron-emission microscopy

Theory of ballistic electron emission microscopy

“…By changing the semiconductor projected interface band structure, the experiment selects dierent regions in the 2D Brillouin zone (BZ), and the resulting changes observed in the BEEM current can be used to understand thek k distribution incoming from the metal side into the semiconductor. This point has been demonstrated by Schowalter and Lee [28], by performing experiments on Au ®lms A metalic ®lm, spatial resolution of %15 # A is deduced from experiment both for Au/Si(1 1 1) and Au/Si(1 0 0) ± not shown ± interfaces, indicating that transport is not simply ballistic (from [21]). …”

“…The logical hypothesis is that it must be a consequence of sharp electronic beams impinging on the interface, but it is not clear how this could happen within the ballistic electron scenario. An elegant experiment proving this particular point comes from Milliken et al [21]: a BEEM scan is performed on Au/Si, but part of the interface is covered with an insulating layer blocking the transmission of electrons. The growth properties of this layer are well known, and allow the design of two sharply de®ned regions.…”

Quantum-mechanical analysis of the elastic propagation of electrons in the Au/Si system: Application to ballistic-electron-emission microscopy

“…Two important and apparently irreconcilable results have been (i) the elegant demonstration of nanometric resolution (≈ 15Å) after propagation through films of as much as 100 − 150Å 4 , and (ii) the very similar results obtained for the interfaces with Si(111) and Si(100) 1,5,6 despite the strongly different k-space distribution of the projected Conduction Band Minima (CBM) available for injection of electrons into the semiconductor.…”

“…BEEM images of the step riser, when the tip crosses from above a part corresponding to the impenetrable SiO 2 to a part, where BEEM injection into the Si is possible, give a direct reflection of the size of the electron beam at the interface. The typical 15Å found are absolutely incompatible with the standard ballistic, free particle propagation used in the simple model and are difficult to justify even if parametrized electron-electron/electron-phonon interaction is taken into account 4,5 . On the other hand, we believe that the observed formation of narrowly focused Kossel-like lines as caused by the Au band structure may already explain the experimentally obtained nanometric resolution in the purely elastic limit.…”

“…Since this result was irreconcilable with the ballistic free electron theory, a variety of processes ranging from more isotropic tunnel distributions 4 over strong elastic electron-electron interaction 5 to k -violation at the non-epitactic interfaces 31 were proposed in an extensive debate in the literature. All these processes aimed at providing k -momentum to the current distribution to allow injection into the off-normal [111] ellipses, but ran into considerable trouble through the simultaneous, inherent loss of resolution 4 . On the other hand, the ring-like current pattern predicted by our band structure calculation is dominated by high k -momenta, (cf.…”