First-principles evaluation of penetration energy of metal atom into Si substrate

Abstract

The difference in chemical potential between bulk metal and bulk Si was calculated for various metal atoms using the first-principles calculations. It was shown that such a difference is an adequate measure for the penetration energy of a metal atom from a metal/Si interface into a Si substrate and important in understanding the phenomena around metal/Si interfaces.

Defect Distribution and MIGS at Metal/Ge Interfaces; First-Principles Study

“…Using these values, for example, we can estimate the vacancy density in bulk layers as 10 10 cm -3 , which is in good agreement with recent experiments [4]. These formation energies in inner bulk layers mainly originate from the elastic energy loss produced by the insertion of foreign atoms in bulk crystal structure [5]. It is noted here that the formation energy decreases as the point defect approach the interface.…”

Acceleration of metal-atom diffusion in electric field at metal/insulator interfaces: First-principles study

“…1(a). [13][14][15][16] The slab is made of (3-4)-monolayer (3-4 ML) metal atoms and 16 ML α-quartz SiO 2 , where the back surface of SiO 2 is terminated by hydrogen (H) atoms and thus the unit cell has one diffusing metal atom, 36-48 metal layer atoms, and 64 Si, 120 O, and 8 H atoms. A vacuum of 20 Å thickness is inserted between adjusting slabs.…”

“…All atom positions are optimized to produce the interface structure except the 2 ML SiO 2 and H of the back surface; thus the metal layers are slightly strained. [13][14][15][16] The reliability of the present unit-cell size was checked by changing the film thickness perpendicular to the interface. In addition, to check the cell size (area) along the interface, we calculate the chemical potential energies of the metal atom when the metal atom is located deep in the present SiO 2 film, i.e., away from the interface, and in the 3×3×3 SiO 2 bulk and found that the energy difference between them is less than 0.2 eV for the atoms considered here, which is the typical magnitude of the calculation error in this work.…”

“…We consider the diffusion of a metal atom, which is originally located at the interface, into SiO 2 along the (001) direction and calculate adiabatic potentials for metal-atom diffusion as a function of the distance z of the metal atom from the interface, together with relaxing x-and ycoordinates of the diffusing atom and the positions of the other atoms. 15,17,18) To show the spatial distributions such as electron density, we also adopt this z-coordinate; namely, the interface is located at z = 0, the SiO 2 layers at z > 0, and the metal layers at z < 0. Electronic structures and diffusion potentials are calculated by the standard first-principles method in the density functional theory, using the Vienna ab initio simulation package (VASP) code, [19][20][21][22] where the Perdew-Burke-Ernzerhof exchange-correlation functional is employed in a generalized gradient approximation.…”

“…It is clearly seen that the electronic state of Ta decreases the hybridization with MIGS as the Ta atom leaves the interface. Since the hybridization of the Ta state with MIGS stabilizes the Ta atom, 15,16) the hybridization with MIGS is the origin of the transition region. This is the reason why the diffusion potentials of most of the metal atoms shown in Fig.…”