Amplification and Relaxation of Electron Spin Polarization in Semiconductor Devices

Transcription

1 Amplfcaton and Relaxaton of Electron Spn Polarzaton n Semconductor Devces Yury V. Pershn and Vladmr Prvman Center for Quantum Devce Technology, Clarkson Unversty, Potsdam, New York , USA

2 Spn Relaxaton of Conducton Electrons Due to Interacton wth Nuclear Spns Abstract: Relaxaton of conducton electron spns n semconductors owng to the hyperfne nteracton wth spn-½ nucle, n zero appled magnetc feld, s nvestgated. We calculate the electron spn relaxaton tme scales, n order to evaluate the mportance of ths relaxaton mechansm. Master equatons for the electron spn densty matrx are derved and solved. Polarzed nuclear spns can be used to polarze the electrons n spntronc devces. Man assumptons of the model: 1 The ntal densty matrx of the two-spn system s ρ t = ρe ρ. The evoluton equaton : Hδt Hδ t ρ t + δt = e ρ t e. The resultng electron densty matrx: ρ = tr ρ t + δt. σ I + 1 I I + I + 3 I + 4 Electrons move classcally and nteract wth nuclear spns located on electron trajectores. At each moment of tme an electron nteract wth only one nuclear spn or does not nteract at all. Change of electron spn state occurs only due to nteracton wth nuclear spns (zero external magnetc feld, spn-orbt couplng, etc..). Hamltonan of electron-nuclear spn nteracton: H = σ A( t) I. The constant of nteracton s selected n the form: A = A ( θ ( t + δ t ) θ ( t )). Low electron densty: back reacton of electron on nuclear spns s neglected. Evoluton of the electron densty matrx durng a sngle nteracton ( ) ( a ) ( ) 1 1 z sn 4 ( ) ( ) x ( ) 1 y ρ 1 00 = ρ00 cos a + 1+ P sn a + P Im ρ10 P Re ρ10 a 1 sn ( 4 ) z a x y e 1 ρ10 = ρ10 cos ( a) + P + ( P + P ) sn( a) ρ00 cos( a) ( ) ( ) ( ) e I Master equatons that connect the electron densty matrx elements before and after the nteracton.

3 Electron densty matrx after nteracton wth many nuclear spns We found that electron spn relaxes exponentally to the drecton of nuclear spn polarzaton. t t Longtudnal and transverse spn relaxaton tme: T =, T, = ln( cos( a )) ln cos( a ) cos ( a ) + sn ( a ) P Polarzed nuclear spns A δt where a =. a) b) Unpolarzed nuclear spns a) b) Reference: Yu. V. Pershn and V. Prvman, Nano Lett., 3, 695 (003). Evoluton of the electron spn densty matrx due to nteracton wth completely polarzed nuclear spns n a) (-z)-drecton. and b) (+x)-drecton. Intal electron spn polarzaton s n (+z)-drecton. a =0.01. Evoluton of the electron spn densty matrx elements caused by nteracton wth unpolarzed nuclear spns. Unpolarzed nuclear spns were modeled by zero polarzaton vector (dotted and dashed lnes), and by unt polarzaton vector drected randomly (nosy data lnes), wth a) a =0.01 and b) a =0.003.

4 Focusng of Spn Polarzaton n Semconductors by Inhomogeneous Dopng Abstract: We study the evoluton and dstrbuton of non-equlbrum electron spn polarzaton n n-type semconductors wthn the twocomponent drft-dffuson model n an appled electrc feld. Propagaton of spn-polarzed electrons through a boundary between two semconductor regons wth dfferent dopng levels (n/n + juncton) s consdered. We assume that nhomogeneous spn polarzaton s created locally and drven through the boundary by the electrc feld. We show that an ntally created narrow regon of spn polarzaton can be further compressed and amplfed near the boundary. Snce the boundary nvolves varaton of dopng but no real nterface between two semconductor materals, no sgnfcant spnpolarzaton loss s expected. The proposed mechansm wll be therefore useful n desgnng new spntronc devces. Physcal Model n ( ) e e = dv j ( ) + n ( ) n t ( ) τ sf j ( ) = σ ( ) E + ed n ( ) e dv E = N n εε 0 ( ) The equaton for electrc feld profle: ( ) + S ( )( r, t) The equaton for spn polarzaton densty: Two-component drft-dffuson model. Here: n= n +n s the electron densty; P = n n s the spn polarzaton densty; S descrbes the source of spn polarzaton. E e E e N j0 e + E E = + N x kt x ktεε 0 εε 0D εε 0 P ee e E P = D P + D P + D P + F t k T k T τ B Injecton of spn-polarzed electrons n a system wth two levels of dopng. B sf ( r, t)

5 Results: Electrc feld profle near the boundary, N /N 1 =5. Conclusons: Dynamcs of propagaton through the boundary of spn-polarzed electrons njected at τ=0, for N /N 1 =10. The blue curve denotes the electrc feld. The other curves show the dstrbuton of the spn polarzaton densty at dfferent tmes. Dstrbuton of the spn polarzaton densty created by a pont source located at x=-10. Spn accumulaton effect near the boundary becomes more pronounced wth ncreased N. Propagaton of spn-polarzed electrons through n/n + juncton studed wthn drft-dffuson model. Spatal dstrbuton of the electron spn polarzaton s calculated for dfferent dopng levels. We found that electron spn polarzaton can be enhanced at the boundary between two semconductors f electrons drft from low-doped to hgh-doped regon. Ths mechansm of electrons spn amplfcaton can be useful n desgnng new spntronc devces. Reference: Yu. V. Pershn and V. Prvman, Phys. Rev. Lett., 90, 5660 (003).

6 Spn Relaxaton of Electrons n DEG wth Antdot Lattce Abstract: We study the effect of Sna bllard lattce (perodc lattce of dsks n DEG) on electron spn relaxaton due to D yakonov-perel relaxaton mechansm. Usng a Monte Carlo smulaton scheme we show that n such system electron spn relaxaton can be effcently suppressed. We found that n a certan regme the electron spn relaxaton tme ncreases exponentally wth the dsk radus. If the radus to the lattce perod aspect rato s fxed, a power-law dependence of the electron spn relaxaton tme on the lattce perod s obtaned. Physcal model: r a Two-dmensonal lattce of antdots. Electron spn relaxaton s of D yakonov-perel type. Electron spn relaxaton tme s calculated usng a Monte Carlo algorthm wth the followng man assumptons: the spatal moton of electrons s consdered semclasscally; all electrons have the same velocty; scatterng s consdered to be elastc and sotropc; reflectng and dffusve boundary condtons are assumed; Electron spn relaxaton tme s calculated as a functon of a and r. An example of electron trajectory when antdots almost are tangent to each other.

7 Results Electron spn relaxaton tme as a functon of antdot radus for dfferent dstances between the antdots, ηl p =0.. The straght lnes are fttng functons. Conclusons: Relaxaton tme at fxed r/a as a functon of the dstance between antdotes. Relaxaton tme at fxed r as a functon of the dstance between antdotes. Electron spn relaxaton tme was calculated usng a Monte Carlo smulaton program. It was found that DP spn relaxaton mechansm could be suppressed by antdot lattce. Spn relaxaton tme ncreases exponentally wth ncrease of antdot radus r. Scalng of parameters leads to an unusual change of relaxaton tme. Dffusve scatterng on the dsks leads to an addtonal ncrease of electron spn relaxaton tme. Reference: Yu. V. Pershn and V. Prvman, preprnt.

8 Acknowledgments Ths research was supported by the Natonal Scence Foundaton, grants DMR and ECS , and by the Natonal Securty Agency and Advanced Research and Development Actvty under Army Research Offce contract DAAD