tailieunhanh - Wave Propagation 2010 Part 17

Tham khảo tài liệu 'wave propagation 2010 part 17', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 472 Wave Propagation .dnn i p t r Ĩ dt an e pan i p t 24 From Eq. 24 using the Hamiltonian in Eq. 23 and realizing the calculations we obtain the quantum kinetic equation for the confined electrons in a cylindrical quantum wire. Using the first-order tautology approximation method to solve this equation we obtain the expression of electron distribution function in cylindrical quantum wires nn p t n. rn - EN2IWXUJ Jk . ỀỈ X q n k l - X nn t p Nq 1 - nn p qNq n p q - n i p q - kn iỗ nn f. pNq - nn p q Nq 1 n 1 p q - n e p - q - kn iỗ nn f. p-q Nq 1 - nn f. pNq n l p - n p-q wq - kn iỗ nn f. p-qNq - nn t p Nq 1 25 n f. p - n p-q - Mq - kn i where Nq nn p is the time-independent component of the phonon electron distribution function Jk x is the Bessel function and the quantity Ỗ is infinitesimal and appears due to the assumption of an adiabatic interaction of the electromagnetic wave. Eq. 25 also can be considered a general expression of the electron distribution function in quantum wires. Calculations of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in a cylindrical quantum wire We consider a wire of GaAs with a circular cross section with a radius R and a length Lz embedded in AlAs. The carriers electrons are assumed to be confined by infinite potential barriers and to be free along the wire s axis Oz . It is noted that a cylindrical quantum wire with radius R 160 A has already been fabricated experimentally. In this case the total wave function of electrons in cylindrical coordinates r 0 z takes the form Zakhleniuk et al. 1996 n i p r 0 z -7Ue eipzZ n l. r r R 26 V 0 where V0 nR2Lz is the wire volume n 0 1 2 . is the azimuthal quantum number 1 2 3 . is the radial quantum number p 0 0 pz is the electron wave vector along the wire s z axis and pnp r is the wave function of electron moving in the x y plane and takes the form 1r n r Jn l Bn k Jn R 27 with Bn being the 6-th root of the n-th order Bessel function .