Effect of partial ordering of a two-dimensional system of scatterers on the anisotropy of its kinetic coefficients N. S. Averkiev, A. M. Monakhov, and A. Yu. Shik A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia P. M. Koenraad COBRA Interuniversity Research Institute, Eindhoven University of Technology, the Netherlands ~Submitted March 3, 1998; accepted for publication April 3, 1998! Fiz. Tekh. Poluprovodn. 32, 1251–1253 ~October 1998! The effect of partial ordering of impurities ~correlated along one direction and uncorrelated along the other! on the kinetic coefficients is considered. It is shown that the geometry of the spatial impurity distribution by itself has no effect on the diffusion coefficient or conductivity for scattering by a spherically symmetric potential, and these coefficients remain the same as for an uncorrelated system of impurities. © 1998 American Institute of Physics. @S1063-7826~98!02210-8# The way that scattering by randomly located impurities and impurities that randomly occupy sites in a periodic lat- tice affect conductivity is now well understood. However, the d -doped layers that can now be grown on vicinal surfaces of semiconductors constitute a class of structures that differ from those considered previously, since they exhibit partial ordering of the scattering centers. 1 At the surface there is a periodic structure of monoatomic steps, and during doping impurities are deposited primarily on these steps, forming a system of parallel chains. Along such a chain the positions of impurities may be treated as completely uncorrelated. In this case, the chains themselves form a periodic lattice, whose period depends on the angle of misorientation of the surface relative to the principal crystal plane. In its geometry this system differs from any studied previously. Experimental studies show 2 that such layers have anisotropic electronic properties. In this paper we discuss how the geometry of the system of scatterers affects the anisotropy of the kinetic co- efficients. Consider the scattering of an electron localized in a d - layer and freely moving only in the plane of the layer. In this case, we can write the collision integral in the Boltzmann equation, which determines the correction f 1 to the equilib- rium distribution function f 0 , in the form I st ~ k! 5 E d 2 k8 2 p W~ k, k8 !@ f 1 ~ k8 ! 2 f 1 ~ k!# d ~ « k 2« k 8 ! , ~1! where W( k, k8 ) d ( « k 2« k 8 ) is the probability for the electron to make a transition from state k to state k8 as a result of elastic scattering. We are interested only in changes in the distribution function associated with spatial correlations in the impurity positions, and ignore the electron density near an impurity, which, in general, is needed to calculate kinetic coefficients. If we assume that the electron wave function in the plane of the layer is a plane wave, the probability W( k, k8) can be written in the form W~ q! 5 2 p \ U E dxdydz e iq x x e iq y y V ~ r! w 2 ~ z !U 2 , q5k2k8 , where w ( z ) is the quantum-well wave function along the direction z , and V ~ r! 5 ( j N v ~ r2R j ! is the impurity potential ~where R j is the coordinate of the j th impurity!. It is easy to show 3 that W~ q! 5 2 p \ u v ~ q! u 2 S ~ q! , where v ( q) is the Fourier transform of the effective two- dimensional impurity potential, which for a Coulomb poten- tial is v ~ q ! 5 2 p e 2 « q E exp~ 2q u z u ! w 2 ~ z ! dz , while S ( q), the so-called structure factor S ~ q! 5 U ( j N e i qR j U 2 , ~2! which contains all the information about the system geom- etry. Assuming that the positions of the impurities are en- tirely uncorrelated along a chain ~the x direction!, and that the chains themselves are positioned on a periodic lattice ~the y direction!, we obtain for the structure factor averaged over impurity positions ^ S ~ q! & 5N F 1 1 ~ 2 p ! 2 a n d ~ q x ! ( n d S q y 2 2 p a n D G , ~3! where N is the total number of impurities in the entire plane, and n is the average number of impurities per unit length of chain. The quantity ^ S ( q) & differs from the structure factor for completely uncorrelated impurities only at q x 50. Quali- SEMICONDUCTORS VOLUME 32, NUMBER 10 OCTOBER 1998 1116 1063-7826/98/32(10)/3/$15.00 © 1998 American Institute of Physics