Etats électroniques des boîtes quantiques de semiconducteur : rôle de l'environnement et couplage dépendant du spin
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(49) \ ²´±[¬^ ¥«¢ 3:4 ¤± ¥«°¾¯e¢¤ª« (²[ ¬\Iª ´¢¾¯ ^ ¢¾¯. ∆ Ec =697 meV. Bande de conduction. Eg=533 meV Bande de valence. ∆ Ev =288 meV. GaAs. 3:4<L . InAs. gR&¯ uY¹}n¶uYCnpBrsrupqI_npesÔsË_xÔsÔnpyowxz@âoÄtenp_srs tCBĨs xzr oJ:s 4BÄsr¡tvs}upupnpups³seq\sjuYn¶uÄCOBrteup_s npsËx_=OsZsËB³_xzsÄt_qw_mysTxzsÄn¶q¶swu[ euYq¶oÄsImz_nsrqABÄxzFBr_qÖ_B ¸yxm_upnps ; x,y,z. . ªRh5R=OsÄs®xz ?>. ε β σ z0 . 3:4D; . ¯ ® ¯ΨS. J}; a J,4PJ 3;)4DI L?4DV. . ªRh5R=OsÄs®xz ?>. ε β σ z0 . ±jz_nsrqorsZBruYn¶Ot_q. . . . ¯ ® ¯ Ψ P±. J}V:; Y,s4 3;?4DY L?4PO. ±jOensrquYn¶O_q ¯ ® ¯ΨS. 3> J JC4DY Y,4PO L?4DV. . . ¯ ® ¯ Ψ P±. 3 OcL J:a,4DI Y,4DV L?4DL. ¯ ® ¯ΨD±. :L V?3 cV)453 >3 ?4PJ O,4 . ¯ ® ¯ΨD±. ?; 3Y :I?4PJ Y,4DV O,4D;. À± xznYxTR&¹}uYnpsrqsÄt9_sĸ_qUxz@âeOuÔtCB}muYzO_t_n&qsr q&§ Oort_esZBrs>uYn¶mOOt__q&n sruÔsrt9yxq&mh z_srun ysrxzq¡t_upenpsOe_q sA4 Br[O§ t_oÄt__sr,npBrOuYs Ot_srq¶su¨m_§ ¬^n¶t_²«qps¦q[mymxzOn¡_nYn[xm_srmq[OoÄn¶suBrxupÂnpOytexq¤qÖsru¤_s´myxz·x n nY"=OxzOmemnOn¶x u¦yxzz>_¸ynps xze3:u¦4DL esax_xzt__sw_s7=xzsÄtCBrswmO_n«sÄquYnpz_q R = 100. h = 15. . ². . . 3L.
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(53). Ê È x y x _ t _ s c p n Ä s x Y u O  s z x 8 r o s } Y u ¶ n O _ t q e s BÄOte_CBrupOt ñ_xzt__ses ÄB zt__CB}uYzt c srq¶u ExnYx }uYoÄn¶q¶oÄs2myxzn_t_sMm_xzn¶upsIznp_ u xzs Ëq &o}uYn¶s 4 . . S. ¯ ®¯ ® ¯iS ¯ ↑ ¯ ®¯ ® ¯iS ¯ ↓. orOuYnpxeuY¦qcu xsrO? s _> n¶_u ^gqÀmhsrsruc qIsr qc§ bs o}>?u4 xBÄupu qcxuporOOsÄt_n¶q¦q sb>e=OOq¶uYn srytvuIOemnpOs _3:n¦4DV sÄq¦4 VorsÄuY_xuYn¶q´q[o}_u sTxupq[xÔxyuYx t_R&_5sTGv__sÄs`qj=qpxzOtïsru tC_¦Brs qH^)R&o}ºèuYn¶sÄsq ±jz_nsrqo}u xupqRO_n¶_qIº . P. . . . Γ8. . . ¯. √1 ¯X 2¯ √1 ¯X 2. ®¯ ® + iY ¯ ↑ ®¯ ® − iY ¯ ↓. ±jz_nsrqo}u xupqRoÄOsrnpqIº q ¯ ®¯ ® 2¯ Z ¯↓ − q 3 ¯ ®¯ ® − 23 ¯Z ¯ ↑ +. −. ¯. ®¯ ® − iY ¯ ↑ ¯ ®¯ ® √1 ¯X + iY ¯ ↓ 6 √1 ¯X 6. ´ x _ t À q · R x p q e Y u
(54) Jt_O_qÀtesuYsÄt_enpOt_qjmyxzq BÄ:Rmeups_s¡·xR_xzt__s â_s R:RsÄtvujxzt_Oe·xznps s 4 uYBÄzsrtCuYxzBÄ s2z_¦npjsM[[m_oÄezqsÄynÖsQsrq¶RÔuRxJsZuY=OoÄorn¶sI·xsru xT§ ¬^t_y²¦xt_qR_orsIuYxzortvOu{¹ÄBÄn¶OsItïsruYq¶npuxznptïs uµ¶s}"uY=OorOs2nz_t³O_enpsIs ·3:xa4DV yxzyt_exËs2_oÄOz_oÄnpt_esrs:npr srJTq~s [ 4 ±m_Àxzen qBrm_On¶t_)qpBÕoZ¸eGvsÄ_qRsÄtvsÄt u_oÄt_t_Osr_OqÖs2te_O_s2qÖ·xTFRyxz upt_sÄ_nps2zt__q s]_aBÄzxwt__m_Cn¶B}q¶uYs¦OsÄt t 4 Br:RmeuYs¦esÄqÖoruYxuYq¡z_np_qqpsr_q BExzn xmzt_Oz_±À_n·xnpxznoZnp@â·orscx npupsrzqptCeu BÄxs
(55) uY
(56) s [¨§ srs}zt_uÀtHqp_sZxzs¾RT_qYz_x«mesImeuYnpsr_JnYsrx0µ¶qs B}m_I uYeo}zuu t uxupq xÈq¶_te5 =zxu tvxujups}u@O§ t8mx >lq\s u r xzmtes y=OOxznpnV uYxzsr_t s @âO3:,t 4 BruY Owtö¨§ OetM m_Rn¶oÄ: qpRsrtvsÄuptï s u . 1 2. J. Jz. z. Γ 6 Γ7. . Γ7. %. . . . Γ8 . 3V.
(57) ªR¬®I¢[²£ a§ °¤ª¦¢¤¥ M ¬ ¢9¢¤ I ª´¡ ¬\IªFw§ Iª«´¢. 3 4<;?4. OtCBrupzt_s7¡)BÕ¸. ¯ ®¯ ® ¯ ¯ q ¯ ®¯ ®iS ↑¯ ®¯ ® − 23 ¯Z ¯ ↑ + √16 ¯X + iY ¯ ↓ ¯ ®¯ ® √1 ¯X + iY ¯ ↑ 2 ¯ ¯ ®¯ ® ®¯ ® √1 ¯X + iY ¯ ↓ + √1 ¯Z ¯ ↑ 3 3 ¯ ®¯ ® ¯ ¯ q ¯ ®¯ ®iS ↓¯ ®¯ ® − 23 ¯Z ¯ ↓ − √16 ¯X − iY ¯ ↑ ¯ ®¯ ® √1 ¯X − iY ¯ ↓ 2 ¯ ¯ ®¯ ® ®¯ ® − √13 ¯X − iY ¯ ↑ + √13 ¯Z ¯ ↓. 3 4s . ¯ ® ¯J, mJ ¯1 ® ¯ ,↑ ¯23 1 ® ¯ , ¯ 23 32 ® ¯ , ¯ 21 12 ® ¯ , ¯ 12 2 ® ¯ ,↓ ¯ 32 1 ® ¯ ,− ¯ 23 23 ® ¯ ,− ¯ 21 21 ® ¯ ,− 2 2. ui u1 u3 u5 u7 u2 u4 u6 u8. O t,BruY@ñOxzt_uÖqÖnp_ows7@âoÄ¡npsrtC)BÕBĸswx_?sr>qR_=xzxzt_sÄ__srn¶q qm_n¶Om_n¶sÄ q_sr4 qRÊzxmteoÄznYxJu xuYsÄupeOnpt q e R:RsÄtïu³xzt_z_·xznpsuYu xzRsruÂes qYx m_n¶Jµ¶sBrupOt q¶_5=Jxztvu@§ xm>ls. Γ 6 Γ7 Γ8. J mJ z. z.
(58) . . ! ! # $ ! #. VsÄq¤bs >emornpsÄCt BrsÄq¾_|s BExznpx BrupoÄn¶qYxJuYztË_srq¤ 6upsÄq ñ (nYxzteSq Rqpq¶OtË¢¤s B}uYnpzt >F BrnpOHq BÄOcm ^ )¯ BExzt_M (_t_t_srt_v FBÄn¶OqSBrOmc^ ls}u B t_s{@âO_n¶t_q¶qpsrtvu¡myxzq_s«npsÄteqpsÄOt_sZR&srtvupquYnp¹rq æx_srq q¶_n¦sIsÄqRmzs upèssÄ}tïuYuYqAsrBÄV:eRUs7RBrsIOt ¨y§ tvteupssÄRnpesÄtï hu«__qpsrzqRtÂO 6upsÄ·xxq 4 BÄztvuYnpxztïuYs´tvupsÄn~=lsÄt_tesÄtïuMºyèsÄq¶u«xzOnpq¡upnp¹Äq eRUOtïBÄuYnpos¡Gv_ sA§ BÄ_ztTt_tyOxTta6uYnpx sÖBZBÄm_Onpn¶oZaBÄmqposÄReu sÄrtïuYu¾n¶ssrOq[l_uYFsÄRtvsÄTtexqp=OzsZt_Bqc_srsu¾t_xRËBÄ:eRnpsÄmeOqpsÄq¶qjuYswO>ltTmoÄ_n¶srq¾srtCBÄ sr6q uYsrhq BÄ4 xz¬^myyxTxIBÄorupuYo o R&xzOteoruYm [ xz_q¶OnpmluYOt ï± srt BrOt_qp_oÄnpxztïuÖet³mzupsÄtïuYsræ_s BrOt ytes RsÄtïuÖ_t_E @âOSn Rsyxzt_q orxsZBruYT n¶6OuYtÈs r L sr q¶u Oms 4 ±jO_n«et_swR s®6upsMsr u´§ ¬^mt_O²¦_q¦n¦me_sÄq«nps upr npJ Os _æq ·vx =xzsÄ_nR_ mR&uYsÄs®tï uY4 sÄaʧs xzhseuYB}n¶uYsÄE qI@[xzmeOuY_srnR_npsrq q teezt_u7s x =RUxzRsÄesÄtïnRu¾_¯g houYrsÄnpn sÄtïuY s(0-/º G r Vs _o}uYsrSn Rt_srR&tvs®u¤ m4 O¡_n[s}upuYs7s m=JzxzupsÄsrtï_uYnRsrm__n¶_sÄAs t_BÄOsrt tt yt_BÄs RR&srmetvupusMe_sÄsrq¾q«ors hsZs BrruYuYn¶q«O_t_sq BrOtvupnYxztvups __qSBreuYorqRyxzt_q·xTqpeuYs 4 . . . . . . . . ∆Ec = 697. ∆Ev = 288. . . ∆Ec = 413. &.
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(60) 2mno+,!" (x' h+W(w! X *)(/l+W ( h*)(/no+,i')m!"+W . (Z*? l#ng ! l*?( B B
(61) = B ~ax ~ay ~az Z@ HR u = ZB B 7@ CB ~a0i. . . . '. ± j O _ ¡ n w>lm_n¶FRsÄn·xweoZ@âOnHRÔxupzt&_t_5@âznSRs«è§ _t Änpq¶uYxzhq¶O_qÖ¨§ s ès}uÖ § _t_s rOtvupnYxztvuYs s BrOt_q¶_ornpOt_qI_t0n¶sÄm¹rnpszn¶uY¸eOt_OnHR&oa_o yt_cmyxzn¦uYn¶Oq Os }uYsr_npq Ä o ´ q z x È p q O _ s : 3 P 4 I 4 temOs}uYtË uY_s¤owmh@âOznH_R&n(o n¶sÄq¶=OupOsÄnjnj_xxzt_yq(O_s¤n¶_s RÔxmyt_xzs[zsÖor·q¶xz_q\5uY=JFGvxz_tvups
(62) s BÄsIJ«qÊuYm_npnpO¹rq[q _Otes rsÖup_sÄ_o ân¶Oq n ÕÔ¸yxJxuYt_OzsÄtwtïqpuÀ_èm_§ mOn¶zqpsroÄtvsu xJxzuYqpq¶Os t s}eujsÄ{q_s¾BrgOs t_UOBÄ_sÄsrtv_upn qR4 IqYxztMteswqR>l_m_5 n¶R&FRsrt_s¤qpsÄOet npqÊt_O,ñ=O srµ sÄqr > =Kxz^ Pusrs_npq _sÄt>ymxzzt_qYq(xztïs¤uMnpsrº m¹Änps¾t_ uYxzsÄt âOt }uYzt . . . . ²ij. . . ∈. 2. . . 3:4PI. Êx n¶sÄxuYOtÈsÄtïuYnpsUBrOtvupnYxztvuYsËsruM_oZ@âOnHRÔxJuYzt0eGnporqpsExoBÄn¶q¶uYxz t0srq¶uw_or__ups_srq 3iI. ~a0i − ~ai = ²ix~ax + ²iy~ay + ²iz~az. .
(63) \ ²´±[¬^ ¥«¢ 3:4 ¤± ¥«°¾¯e¢¤ª« (²[ ¬\Iª ´¢¾¯ ^ ¢¾¯ az. ay ax. >uY5@(oÄoRsÄtvuYxznps´_s2·xTq¶uYn¶CBrup_nps7urtCBb[^_sÄte_s. 3 4DI . 2εxz. z. ¦ow@âOnSR&xupOtÂe u ^gms R&ge_srq § oÄxzq¶uY5BÄ uYo´myxzn·xTz es \ g zsº 3:4PY . X. x. ²xz. . 3 4DY. r s ¶ q ¦ u · /BÄ:RmOqYxtvuYsM_s8BÄOtïuYnYxtvups7Gv_jn¶sÄm_n¶oÄq¶sÄtvupsT·xv@âOnSBrsaxzm_m_FGv_orsw_xzt_q«·x x _n¶sVB}uYsrq´Ot_ow@âOnSqpR&enRxup_OtetesMqRq¶__nH @ñx uBr^gsMm_s teu x nps¦mhzsrnp msrt__n¶5BÄsÄ_m_n¶xzoÄqpn¶srs]tv_upsËxË_t _B np¸ysZBrxzuYt_zOst RsÄtv4 u¦_saOteO_sÄen qpysrxztvt_uYq¦srtvsÄuq«__sÄq nps=B}xzuYn¶·Oxt_upq zt_q[ 觩xzsruteOsxzsÄOtïnpuYq{npsRGv_sÄsaq¤_sÄq«npsZ_Browup@âOOnSt_R&q xupsrOu teqR t_zsrupuoÄsÄq O sru z yO_n¶s npsÄ3 me4DnpY ow[ 4 VsIuYsrt_qpsr_nR_sr{q BÄOtïuYnYxtïuYsÄqmsÄeu«xzOnpqÖqps2_o Br: RmOqpsrnRsÄt _sr?> myxn¶uYs˺ xvBr:R&mzqYxztïuYs2¸c^g_npOq\u xupFGv_sº σij =. . σij. Cijkl ²kl. ~ai. ~aj. ²xx ²yy. x y. ²zz. z. x. y y. ²xy ²yz z x z. . ²xz. . v_Vnpsrm_nporqpsÄtïuYswetB ¸yxzteOsRsÄtïuR_sQ=OOCRs
(64) vx Br:R&mzqYxztïuYs2es7BrqpxzsZRsÄtïuIº. ²xx + ²yy + ²zz. G . . rs u Gv_Vnpsrm_nporqpsÄtïuYsrtvu¦sQBÄqpxzsZRsÄtïuÖuYo}uYnpxzOOtyx ys}u Gv_Vnpsrm_nporqpsÄtïuYswsQBÄqYxz sRsrtvuÖupnpzOtyxz 4 2²zz − ²xx − ²yy. ²xy ²yz. ²xx − ²yy ²xz. 3Y.
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