Surface physics, Bravais lattice

Transcription

1 Surface physics, Bravais lattice 1. Structure of the solid surface characterized by the (Bravais) lattice + space + point group lattice describes also the symmetry of the solid material vector directions are given by the Miller indices {hkl} the most important surfaces are those having the highest atomic density in the direction of the surface and the longest distance between the atomic layers, cubic lattices {100} {110} {111}-surfaces these are also called low-index surfaces

2 BCC and FCC lattices, Miller indices The number of Bravais-lattices depends naturally strongly on the dimension Most commonly used symbols of the surface for cubic lattices (FCC and BCC) Note: chemistry of the fabrication of microsystems depends drastically on these surfaces

3 Relaxation The concept means how the distance d between the adjacent atomic layers changes in the vicinity of the surface Relaxation happens either outward (d increases) or inward (d is reduced) In Fe or Mo the change can be even -15% Reconstruction Relaxation and reconstruction 2D surface can restructure in a different way compared with the solid substrate It can also affect lower than the 1-2 atomic layers from the surface Also the symmetry of the surface can change under reconstruction, the unit cell is often larger than in the substrate as a result of minimization of free energy.

4 Reconstruction example of silicon Example of semiconductors concerning reconstruction (Si, Ge, GaAs etc..) the surface can reconstruct to rather different and complicated microstructure This is due to the covalent bonds (directed bonds) If the surface is cut (or etched) in some give direction, the covalent bonds point to empty space (so called dangling bonds) This means a lot of free energy which becomes minimized by restructuring so that the number o such dangling bonds becomes minimized A well-known such example is Si{111} surface which shows spontaneous long-range reordering (see figure)

5 Surface defects As in the solid substrate also the surface may contain various kinds of defects The lattice errors that have a longest range are dislocations and grain boundaries In the adsorbing layer the typical defects are impurities islands phase boundaries Secregation means that in composite materials (like CuNi) the concentration of some compound changes close to the surface (in this case Cu is more abundant on the surface than inside the substrate)

6 Surface tension ( ) γ n = dw da is the surface tension (pintajännitys) work done to create a given area of surface The integral of this equation gives the Gibb s free energy Ω s = daγ A ( n ) Total energy of the 3D lattice is Ω = pv + Ω s If T, V, µ are fixed the integral of Gibb s energy has a minimum.it also defines the geometrical structure of the phases (solid + gas) Surface tension is always minimized in the low-index planes => in thermodynamical equilibrum solid material creates low index surfaces, this however may be an extremely slow process.

7 Adsorption In case the interaction is strong between the adatoms and also between substrate and adatoms => adsorbed atoms create a solid lattice on the surface (different from substrate) so called lattice gas can be created by weak mutual adatom interaction + with low density of atoms => 2D lattice gas => atoms may occupy only some known lattice sites but the occupation is otherwise random In case the adatom-substrate interaction is weak + position independent (in the direction of the surface) => 2D gas or even liquid (Ex. nobel gas atom attached to the surface via the van der Waals interaction at high T). Noncommensurate lattice requires strong mutual interaction between adsorbed atoms + position independent interaction between substrate and adsorbed atoms > 2D lattice of adatoms that is not related to the structure of substrate, the lattice constant may not be any rational number of that of the substrate Islands occur, when the coverage of atoms is low.

8 Surface states of electrons means an electronic state where the wave function of an electron is localized close to the surface typical example is an adatom on the clean (silicon) surface surface states are also created on the clean (wafer) surface because the periodicity of the lattice is broken on the surface The Schrödinger equation may have a solution (surface wave) whose energy is inside the semiconductor gap of the bulk material Chemically one can say that on the surface the outward-oriented bonds are broken and the corresponding energy states are missing, this surface state is called a Shockley state and the corresponding bonds are dangling bonds An alternative surface state is a Tamm state, which means that the electronic affinity of a surface atom is remarkably different from the one of the substrate atom the result is again a localized electronic energy state In these electronic states, there also can occur a surface resonance, which means that the electronic wavefunction can extend over the whole crystal, but its amplitude is highly peaked at the surface

9 Example of various point groups

10 Plasmons and surface plasmons useful concepts e. g. in studying biological (MEMS) samples ε(r) describes the response of an electron system to the external field Vext ( ) ( q, ω) V q, ω = total potential = external potential/dielectric function ε q, ω ( ) Total potential V includes the so called shading effect of an external potential Plasmon corresponds to a situation in which the dielectric function gets the value zero => density oscillations of an electron system In the limit q 0 (large wavelenght) ε ω ( 0, ω) p = 2 ω p = 1 2 ω 4πne m 2,

11 Surface plasmon detection system

12 Ions in surface studies Sputtering techniques simple collision cascade of collisions thermal peak

13 Back-scattering geometries The energy distribution of backscattered ions measured. He, Ne, Ar kev best resolution when the masses of the primary beam atoms is close to that of the lattice atoms H, He MeV scattering cross section small, but scattering deep in the lattice

14 Rutherford backscattering scattering from Ni 2 Si scattering from Ni scattering from Si scattering from Ni 2 Si RBS causes electronic excitations: ionisation, electron-hole pairs and plasmons

15 SIMS and ATM SIMS (Secondary ion mass spectrometry) The surface is bombarded with nobel gas atoms. The mass spectrometer is needed to identify the ions that leave the surface => chemical analysis of the surface STM (Scanning tunneling microscope) A sharp needle is scanned above the surface and the current from the needle to the surface is measured The tunneling current depends exponentially on the lenght The needle moves using very accurate piezos (1 Å resolution) Typical values 0.01 V and 10-9 A