Resonant tunnelling into a size‐quantised metal film

Cottey, Alan

doi:10.1002/pssb.2220670224

Cited by 7 publications

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References 6 publications

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“…Unfortunately, he relegated the problem to a footnote, saying that it is simpler to consider the new kind of solution as a limiting case of the others than to treat it separately. Most correctly, Cottey has always treated separately the band edge states (BES) (23)(24)(25)(26) which are special cases of the IS. He studied almost exclusively symmetrical models, when he refined the theory of the quantum size effect (QSE) (25a-f, 26a, b ) , solving the one-dimensional Schrodinger equation for a periodic potential terminated by two infinite abrupt potential barriers.…”

Section: Introductionmentioning

confidence: 99%

From crystal orbitals to strange electronic states. I. Crystal orbitals by direct recursion (transfer matrix) method (DRM)

Biczó¹

1985

Can. J. Chem.

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). The history of Bloch's and Tamm's states is sketched. The present stage in the theory of the bounded infinite polymers and crystals and strange electronic states is outlined. To lay the foundations of the SCF LCAO bounded crystal orbital (BCO) method applicable for surface electronic problems, the direct recursion (transfer matrix) method (DRM) is formulated for perfect cyclic polymers and crystals. A simple combination of block-decomposition and matrix transpositions is applied to calculate U -' directly from the blocks of U, the similarity transformation bringing the recursion matrix T into its normal form. Several forms are given for the auxiliary and fundamental equation of the DRM. The crystal orbitals are derived by the DRM. Full matrix expression is presented for the resolvent (Green) matrix of perfect cyclic polymers, the unperturbed system in the SCF local-density approach of Ladik and Seel. The formulae of the charge-bond order matrix are derived both by the DRM and the indirect (Green matrix) recursion method (IRM).GEZA Blczo. Can. J . Chem. 63, 1992Chem. 63, (1985. On prCsente une revue de I'histoire des Ctats de Bloch et de Tamm. On prCsente 1'Ctat actuel de la thCorie relative aux polymeres infinis qui sont liCs et aux cristaux ainsi qu'aux Ctats Clectroniques particuliers. Dans le but d'Ctablir les bases de la mCthode LCAO-SCF des orbitales cristallines likes (BCO) pour des polymeres et des cristaux parfaits, on a dCveloppC une mCthode de rCcurrence directe (matrice de transfert) (DRM) qui serait applicable aux problemes de la structure Clectronique des surfaces. On utilise une combinaison simple de dCcompositions en blocs et de transpositions de matrices pour calculer U ' directement h partir des blocs de U; la transformation de similarit6 transforme la matrice de rCcurrence T e n sa forme normale. On prCsente plusieurs formes pour les Cquations auxiliaire et fondamentale de la DRM. Utilisant la DRM, on a dCduit les orbitales du cristal. On prCsente une expression pour la matrice complete de Green de polymkres cycliques parfaits, le systkme non perturb6 dans I'approche ii densit6 locale en champ auto-cohtrent de Ladik et Seel. Utilisant la DRM et la mCthode de recurrence indirecte (matrice de Green) (IRM), on a dCduit les formules de la matrice des charges et des ordres de liaison.[Traduit par le journal]

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Section: Introductionmentioning

confidence: 99%

From crystal orbitals to strange electronic states. I. Crystal orbitals by direct recursion (transfer matrix) method (DRM)

Biczó¹

1985

Can. J. Chem.

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Quantum size effect in SnTe observed by tunnel experiments

Altwein

Finkenrath

1975

Physica Status Solidi (b)

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In SnTe-Al,O,-A1 tunnel junctions with size quantization of the electron states in the SnTe electrode, oscillations of the 2nd derivative of the I ( U ) characteristics were observed a t 4K. From this it was possible to determine a series of points of theE(k) relation perpendicular t o the film plane in a range of 5100 meV around the Fermi energy. The results are in agreement with values calculated from band structure data. I n SnTe-Al,O,-Al-Tunneldioden mit Dickenquantisierung der Elektronenzustinde in der SnTe-Elektrode wurden bei 4 K Oszillationen in der zweiten Ableitung der I ( U ) -Kennlinien beobachtet. Daraus konnte der E(k)-Verlauf parallel zur Schichtnormale im Bereich von & 100 meV um die Fermi-Energie punktweise, in ubereinstimmung mit den Ergebnissen theoretischer Bandstrukturberechnungen, bestimmt werden.

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Band Theory of Size‐Quantised Electron States in Thin Crystalline Films

Cottey

1978

Physica Status Solidi (b)

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The discrete electron states in a thin film with an arbitrary three-dimensional periodic crystal potential are analysed. First the quantum size effect states of a symmetric film are found exactly for Dirichlet (y = 0) and Neumann (y' = 0) boundary conditions, and the interpolation between these extremes is studied. Then e surface scattering matrix formalism is set up in the general (unsymmetric) case. This treats the general situation when there may be M up-and M down-travelling Bloch waves with a given energy and surface-parallel component of crystal momentum modulo surface reciprocal lattice. The equations are solved in the general 1 x 1 and symmetric 2 X 2 cases.The QSE solutions approximate gently undulating parallel surfaces in k-space. Usually the separation of these surfaces is roughly uniform. An exception occurs in the 2 x 2 case near a band edge which is not a t the centre or edge of the Brillouin zone; the solutions are then in nearly degenerate pairs. The results agree with available experimental data.Die diskreten Elektronenzustiinde in dunnen Schichten mit beliebigem dreidimensionalem periodischem Kristallpotential werden analysiert. Zuerst werden die Quanten-Sizeeffektzustinde einer symmetrischen Schicht exakt fiir die Dirichletschen (y = 0) und Neumannschen (y' = 0) Grenzbedingungen gefunden und die Interpolation zwischen diesen Extrema untersucht. Dazu wird ein Oberfliichemtreumatrixformalismus fur den allgemeinen (unsymmetrischen) Fall eufgestellt. Dieser behandelt die allgemeine Situation, in der wandernde Blochwellen mit M-auf und M-ab und, gegebener Energie und einer zur Oberfliche parallelen Komponente des Kristallimpulses modulo des reziproken Oberflichengitters vorhanden sind. Die Gleichungen werden im allgemeinen 1 x 1-und symmetrischen 2 x 2-Fall gelost. Die QSE-Losungen passen sich befriedigend den gewellten parallelen Oberflichen im k-Raum an. Gewohnlich ist der Abstand dieser Flichen etwa gleichformig. Eine Ausnahme tritt im 2 x 2-Fall in der Niihe einer Bandkante a d , die nicht beim Zentrum oder Kante der Brillouinzone liegt; die Liisungen sind dann fast entartete Paare. Die Ergebnisse stimmen mit erreichbaren experimentellen Werten uberein.

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Resonant tunnelling into a size‐quantised metal film

Cited by 7 publications

References 6 publications

From crystal orbitals to strange electronic states. I. Crystal orbitals by direct recursion (transfer matrix) method (DRM)

From crystal orbitals to strange electronic states. I. Crystal orbitals by direct recursion (transfer matrix) method (DRM)

Quantum size effect in SnTe observed by tunnel experiments

Band Theory of Size‐Quantised Electron States in Thin Crystalline Films

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