, 1 K [ 8 ]. 2 3,. [9 ],,. 1,,,,.,,. h 5nm, l. 1 Fig. 1 Geometry Sketch of the four kinds of shaped quantum dot s R = 8nm, l = 1418nm., 015nm.

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1 CHIN ESE J OURNAL OF SEMICONDUCTORS Vol. 26 No. 12 Dec., ,2,g 1,2 1,2 3 (1, ) (2, ) (3, ) :..,,,,,. : ; ; ; PACC : 0365 ; 2110D ; 7280 E : O469 : A : (2005) [1 ].., Stranski2Krastanov ( S2K). S2K,, 1 3,. ( ),, [2 ] [3 ] [ 4 ] [5 ]. [5 ].,., [6 ] [7 ] [8 ].,,, Si/ Ge, InAs/ GaAs S2W Keat2 ing,,,.,,,.,,,. 3 ( :2003CB314901), ( :2003AA311070) g.,1976,,. net , Ζ 2005

2 , 1 K [ 8 ]. 2 3,. [9 ],,. 1,,,,.,,. h 5nm, l. 1 Fig. 1 Geometry Sketch of the four kinds of shaped quantum dot s R = 8nm, l = 1418nm., 015nm., : (1) = ad - as as = 0104, ad as,. (2), C11 = 150 GPa, C12 = C44 = 50 GPa. ( 001), (100) x, (001) z, y = 0., : x,.,, y = 0. xx, 2, zz, 3. 2,, xx, xx, xx. xx, xx. 3 zz :,,., zz,. zz,..,,, 5nm,, 15nm, 5nm, 25nm,. 4 xx, zz hh.,,,,.,,.,,.,

3 12 : xx (a) ; (b) ; (c) ; (d) Fig. 2 Contour plots of the xx strain component for the four kinds of shaped quantum dots ( a ) Lens shaped ; (b) Conical shaped ; (c) Cylindrical shaped ; (d) Pyramid shaped 3 zz (a) ; (b) ; (c) ; (d) Fig. 3 Contour plots of the zz strain component for the four kinds of shaped quantum dots ( a ) Lens shaped ; (b) Conical shaped ; (c) Cylindrical shaped ; (d) Pyramid shaped

4 ,. 1,.,,, 4 (a), ( b).,,,.,,,,. 4 xx, zz hh Fig. 4 xx, zz and hh strain distribution along the center axis path of each kind of quantum dots 5 (a) ; (b) ; (c) ; (d) Fig. 5 Strain distribution along the interface of the quantum dot and barrier material for different shaped quan2 tum dots (a) Lens shaped ; (b) Conical shaped ; (c) Cylindrical shaped ; (d) Pyramid shaped

5 12 : 2359.,,.,. 5.,, xx zz,,.,,,,,, 5 (a).,.,,,.,,, InAs/ GaAs, [9 ].,, xz xx zz,., 6 xz. 6 xz Fig. 6 xz shear strain distribution of the pyramid quantum dot 7., 7,.,.,,.,,.,,,..

6 xz (a) ; (b) ; (c) ; (d) Fig. 7 xz shear strain along the interface of the quantum dot and barrier material for different shaped quantum dots (a) Lens shaped ; (b) Conical shaped ; (c) Cylindrical shaped ; (d) Pyramid shaped 4.,.,.,.,,.,,,,. [ 1 ] Wang Z G. Controllable growt h of semiconductor nanometer structures.j Synt hetic Crystals,2002,31 (3) :208 (in Chinese) [..,2002, 31 (3) :208 ] [ 2 ] Noda S,Abe T, Tamura M. Mode assignment of excited states in self2assembled InAs/ GaAs quantum dots. Phys Rev B, 1998,58 (11) :7181 [ 3 ] Tadic M, Peeters F M,Janssens K L. Effect of isotropic ver2 sus anisotropic elasticity on the electronic structure of cylin2 drical InP/ In GaP self2assembled quantum dots. Phys Rev B, 2002,65 (1) :16533 [ 4 ] Gong Qian,Liang Jiben, Xu Bo,et al. The result s analysis of InAs quantum dot by the atom force microscope. Chinese Journal of Semiconductors,1999,20 (8) :622 (in Chinese) [,,,. InAs.,1999,20 (8) :622 ] [ 5 ] Chang Kai, Xia Jianbai. The effect s of electric field on t he e2 lectronic structure of a semiconductor quantum dot. J Appl Phys,1998,84 (3) :1454 [ 6 ] Yu Wenbin,Madhukar A. Molecular dynamics study of coher2 ent island energetics, stresses,and strains in highly strained epitaxy. Phys Rev Lett,1997,79 (5) :905 [ 7 ] Andreev A D,Downes J R,Faux D A,et al. Strain distribution in quantum dot s of arbitrary shape. Phys Rev B,1999,86 (1) : [ 8 ] Grundmann M, Stier O, Bimberg D. InAs/ GaAs pyramidal quantum dots : strain distribution, optical phonons and elec2 tronic structure. Phys Rev B,1995,52 (16) :11969 [ 9 ] Liu Yumin, Yu Zhongyuan, Yang Hongbo,et al. Elastic st rain field distribution of a self2organized growt h lensed2shaped quantum dot by finite element method. Chinese Journal of Semiconductors,2005,26 (7) :1317 A : :, InAs/ GaAs,, GaN/ AlN..,, :

7 12 : 2361 = xx yy zz xy yz zx = = xx yy zz xy yz xz 5 u/ 5 x 5v/ 5 y 5w/ 5z (5 u/ 5 y + 5v/ 5 x) / 2 (5v/ 5z + 5w/ 5 y) / 2 (5 u/ 5z + 5w/ 5 x) / 2 = D ( - 0 ) + 0 (A1) u, v, w x, y z.,. xx, yy, zz x, y z, xy, yz, zx x y, y z, z x, hy = xx + yy + zz. i, j ( i, j x, y, z). D : D = C11 C12 C C12 C11 C C12 C12 C C C C14 (A2),, U = 1 2 µ t ( - 0 ) d xd yd z (A3) (A1), (A3) 0 0.,, 0 = xx = yy = zz = ( adot - asub) / asub, adot, asub ( A3) : U = 1 2 µ [ C11 ( 2 xx + 2 yy + 2 zz ) + C12 ( xx yy + yy zz + zz zx x ) + 2 C44 ( 2 xy + 2 yz + 2 zx ) ( C11 / 2 + C12 ) ( xx + yy + zz ) ( C11 / 2 + C12 ) ]d xd yd z (A4), du d u( i, j, k) = du d v ( i, j, k) = du d w ( i, j, k) = 0 (A5) i, j, k x, y, z., 0,, 0., :,,. ( A4). (A5) ( ), ( A1).,. (A4),..,, 1,.

8 Influences of Differently Shaped Quantum Dots on Elastic Strain Field Distributions 3 Liu Yumin 1,2,g, Yu Zhongyuan 1,2, Yang Hongbo 1,2, and Huang Yongzhen 3 (1 S chool of Science, Bei j ing Universit y of Posts & Telecom munications, Bei j ing , China) (2 Key L aboratory of Minist ry of Education f or Optical Communication and L i ghtw ave Technologies, Bei j ing , China) (3 State Key L aboratory of Integrated Optoelectronics, Institute of Semiconductors, Chinese A cadem y of S ciences, B ei j ing , China) Abstract : Adopting the two2dimensional axis2symmetrical model,a systematic analysis of the elastic strain distribution of geo2 metrically differently shaped quantum dot s is conducted using the finite element method. The detailed result s for the elastic strain distribution of lens,cylinder,pyramid,and cone2shaped quantum dot s are given. These show that the shape of the quantum dot has obvious influences on both the normal and shear strain distributions,while not affecting the hydrostatic strain distribu2 tions. The hydrostatic strain distribution is almost the same in both the center axis and circumjacent path. The shear strain dis2 tributions are focused on the circumjacent path,and the extremas are located in the inflexion of the circumjacent path,while the other parts of the quantum dot,including the path along the center axis,have no shear strain. Key words : strain ; quantum dot ; self2organization ; low dimension material PACC : 0365 ; 2110D ; 7280 E Article ID : (2005) Project supported by the State Key Development Program for Basic Research of China ( No. 2003CB314901),the National High Technology Research and Development Program of China (No. 2003AA311070),and the Open Project of the State Key Laboratory on Integrated Optoelectronics g Liu Yumin male, was born in 1976,lecturer. His main research areas are nonlinear optics, semiconductor optoelectronics,and t he critical technology of high2speed optical communication. net Received 14 April 2005,revised manuscript received 31 August 2005 Ζ 2005 Chinese Institute of Electronics

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