On the distribution of eigenvectors of Toeplitz matrices with weakened requirements on the generating function

Abstract

We have grown by reduced pressure-chemical vapour deposition Si/Si 1−y C y /Si heterostructures for electrical purposes. The incorporation of substitutional carbon atoms into Si creates a carrier confinement in the channel region of metal oxide semiconductor (MOS) transistors. Indeed, tensile-strained Si 1−y C y layers present a type II band alignment with Si, with a conduction band offset of the order of 60 meV per atomic% of substitutional carbon atoms. For small SiH 6 flows, all the incoming carbon atoms are incorporated into substitutional sites. At 550 • C, when the SiCH 6 flow increases, the substitutional carbon concentration saturates at 1.44%. Meanwhile, the total carbon concentration C T still increases, following a simple law: C T /(1 − C T ) = (0.88-0.92)(F(SiCH 6 )/(F(SiH 4 )). This is a sign that a growing number of C atoms incorporates into interstitial sites. The hydrogenated chemistry adopted does not enable us to achieve selectivity over SiO 2 -masked wafers, but does not generate any adverse loading effect. We have integrated Si/Si 1−y C y /Si stacks (which have been shown to be stable versus conventional gate oxidations and electrical activation anneals) into the channel region of ultra-short gate length (40 nm) nMOS transistors. Secondary ion mass spectrometry profiling has shown that C atoms segregate from the Si 1−y C y layer into the Si cap and the SiO 2 gate, but also that they block the diffusion paths of B coming from the anti-punch through layer towards the gate, generating very retrograde doping profiles. The addition of C leads to a slight degradation of the electron mobility which seems to be linked to the presence of C atoms into interstitial sites. Finally, we have shown that using higher silane and methylsilane mass flows enables us to obtain higher substitutional C concentrations (max: 1.98%) in our Si 1−y C y layers, with a good resulting structural quality.(Some figures in this article are in colour only in the electronic version) High C content Si/Si 1−y C y heterostructures for n-type metal oxide semiconductor transistors

Robust and optimal multi-iterative techniques for IgA Galerkin linear systems

“…The statement above is quite vague but it can be made more precise, without using technicalities (see [10,42] for a rigorous analysis). If we are interested in the eigenvectors associated to eigenvalues in the interval [a, b], then we know that this subspace has dimension…”

Symbol approach in a signal-restoration problem involving block Toeplitz matrices

“…On the other hand the information on the domain where the minimum or the maximum is attained is important for the asymptotic eigenvector behavior (see the work in [21] for a global clustering study and the work in [3] for a single eigenvector asymptotic analysis): the eigenvectors related to the sub-cluster at (L + 1)/m are associated with the low frequencies for L even and with the high frequencies for L odd. The opposite behavior occurs for the eigenvectors related to the sub-cluster at L/m.…”

Improvement of Space-Invariant Image Deblurring by Preconditioned Landweber Iterations

“…The one-level equidistribution result has been further extended to L 1 generating functions in [40]; since the proof no longer uses (4.5), we cannot say that Lemma 4.3 holds if a ∈ L 1 , too. The result is probably true but is not of interest in image deblurring, where generating functions are related to the PSFs and hence they have a high degree of regularity.…”