Quantitative Rheed Analysis of Biaxially-Textured Polycrystalline MgO Films on Amorphous Substrates Grown by Ion Beam-As
- PDF / 1,655,335 Bytes
- 7 Pages / 417.6 x 639 pts Page_size
- 98 Downloads / 201 Views
75 Mat. Res. Soc. Symp. Proc. Vol. 585 ©2000 Materials Research Society
pattern. The mathematically and numerically efficient, compact nature of our simulation method provides the potential for a real time, in situ, analysis of biaxial texture development in films as thin as 30 A during growth at conventional rates (i.e. - 1 A/s). This technique will enable us to probe the development of biaxial texture from the nucleation phase, through the grain growth, island coalescence, and bulk film growth stages, yielding insight into the mechanisms controlling biaxial texture development. Greater understanding of texturing mechanisms should lead to the ability to produced more highly aligned films, with the ultimate goal being the development of an IBAD process for synthesis of films, on amorphous substrates, whose microstructure approaches a single crystal. EXPERIMENT We employed the kinematic electron diffraction approximation for our RHEED simulation because it contains much of the important electron scattering physics and yields a
compact, analytic solution to the scattering probability. Equation (1) represents the kinematic electron scattering amplitude for an electron going from wave vector k to p in a crystal lattice
with a potential V(r), while Eq. (2) represents a single crystal potential, where G is the inverse lattice vector and R is the real lattice vector. We constructed the polycrystalline potential V(r), Eq. (3), as an aggregate of individual single crystalline grains, where each grain (g) is assigned a lateral dimension using an envelope function, Og(r-rg), a lattice slip displacement from neighboring grains, ag, and an orientation, Bg. Ak. p oc -iV(p-k)
Ikl= -is
-pl=
V(r)single crystal = 1R V(r)polycrystalline = Yg
d3r
v(r-R)
®g(r-rg) XG
(1)
e-i(p-k)r V(r)
= YXG VG eiGr VG
(2)
(3)
ei(BgG)(r-ag)
The orientation Bg is specified by a combination of rotation angles around the x-axis (wx), y-
axis (0y), and the z-axis (ý), Eq. (4). This polycrystalline potential construction has been
0oo] rool Fo00o1 r0-101 Bg-= L001J 0101 + 1100o 001 +CoxlOO-I +(oyOOO 0OJ _100J ,01
.
(4)
previously invoked by Hartman and Atwater6 , as well as by Litvinov et al. 7 . In order to create a compact and computationally efficient representation of the electron scattering probability into wave vector p, we made the following assumptions: each grain is the same size, the grain displacement factor ag is random, and the orientation distribution of the grain rotations around each axis can be represented by a gaussian with a full width at half maximum (FWHM) represented by Axo,, Aoy, and Aý for the x, y, and z axis rotations respectively. It is important to note that in all cases, the x axis is in the plane of the sample and oriented toward the incoming electron beam, while the z axis is perpendicular to the substrate face. Using the previously mentioned assumptions, we are able to integrate Eq. (3), instead of summing over individual grains, and produce an analytic solution for the kinematic scattering probability, sh
Data Loading...
