B ych kov{ R ash b a E ect an d g -Facto r T u n in g in Mo d u lation Do p ed Si G e Qu antu m W ells

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1 Vol. 105 (2004) ACT A PHY SIC A POLON IC A A No. 6 P ro ceedi n gs of t h e XXX I I I I nt ern at io na l Sch ool of Sem i cond uc t in g Co m p ou n ds, Ja szo wi ec B ych kov{ R ash b a E ect an d g -Facto r T u n in g in Mo d u lation Do p ed Si G e Qu antu m W ells H. M al issa a, W. Ja nt sc h a, M. M uhl ber ger a, F. Scha f f le r a, Z. Wi l a mo ws k i b, M. Dr a xl er c and P. Ba uer c a I nst it ut fur H albleiter - und Festkorperphysik, Johannes Kepl er Uni versit at 4040 Li nz, Austri a b Insti tute of Physi cs, Polish Aca dem y of Sciences al. Lotni k w 32/ 46, W arsaw, Poland c Insti tut f ur Exp erim entalphysik, Johannes Kepl er Uni versi tat 4040 Li nz, Austri a W e investi gate the spin resonan ce of electrons in one-sided mod ulatio n dop ed Si 1 À x Ge x ( x = 0{ 10%)) quantum w ells deùned by Si 0 : 7 5 Ge 0 : 25 barriers. In such structures, the Bych ko v{ Rashba e ect induces an e ective magnetic Ùeld in the quantum well layer w hich causes anisotropy of both the g- factor and the spin coherence time. Ev aluation of the Rashba coe cient as a function of x yields a monotonic increase. F or x = 5% the shif t in the resonance Ùeld exceeds the ESR linew idth already, demonstrating the p ossibili ty to use this e ect for g -factor tuning to select indivi du al spins in an ensemble. PACS numb ers: Fg, {d 1. I nt rod uct io n Am ong the cri teri a for spi ntro nics and quantum computi ng are (i ) the possibility to mani pul ate indi vi dually addressable spins in a large ensemble and (i i) a spi n coherence ti me tha t exceedsthe mani pul ati on ti m e by orders of m agnitude [1]. Lo w di mensional structures bui lt from Si 1 x Ge x appear as possibl e candi dates for such ta sks. It has been shown tha t the spin coherence ti m e in Si quantum wells deùned by SiGe barri ers is of the order of 1{ 3 sec [2{ 4], three orders of m agni tude longer tha n in I I I{ V compounds [5], a consequence of the m uch smaller (585)

2 586 H. Malissa et al. spi n{ orbi t intera cti on (SOI) in Si [6]. Exp erimenta lly, the spin lifeti mes have been determ i ned both by standard electron- spin- resonance (ES R) exp eri ments and by spi n-echo exp eriments. The latter demonstra te directl y a possibl e and very preci se wa y of spi n m anipula ti on: in thi s m etho d, spins are rota ted by an angle of = 2 or, depending on the chosen microwave pul se length, and decoherence pro cesses can be observed di rectl y by looki ng at the echo am plitude [6]. In these experi m ents, a reasonabl e com prom ise between pul se am pli tude and pul se wi dth i m plies a pulse l ength of about 10 ns. The rati o of coherence ti m e to m anipula ti on ti me thus is onl y of the order of 100 wherea s have been postul ated [1]. We have shown earl ier, however, tha t spin relaxati on in Si quantum wel ls is governed by the Bychko v{ R ashba e ect [2] whi ch resul ts from one-sided m odul ati on dopi ng and the resulti ng loss in m irro r sym metry. Thi s e ect has been shown to a ect the linewi dth (and thus the tra nsverse spin relaxati on ti m e), the g-factor and the longitudi nal spi n relaxa ti on ti m e vi a the D ' yakonov{ Perel' m echani sm [7]. W e have shown tha t a spin coherence ti m e of 25 ñ sec can be exp ected for high m obilit y sampl es,if the asym metry can be rem oved whi ch leaves us wi th the intri nsic El liott{ Yafet spin relaxa ti on [3, 8, 9]. For quantum dots made of II I{ V com pounds the spin coherence ti m ehas been shown to increa sesti ll further so tha t it app ears possibl e to ful Ùl the cri teri on of a rati o of for quantum dots in SiGe structures. The other cri teri on m enti oned i s the possibi l ity to select indi vi dual spin wi thi n an ensemble for mani pula ti on. W e proposed earlier to make use of the dependence of the g-factor on the alloy concentra ti on in an Si 1 À x Ge x alloy [4]. Appl yi ng an electri c Ùeld perpendicul ar to the sampl e surface wi thi n a structure tha t exhi bi ts a gradient of x i n growth di recti on z wi l l shift the wa vefuncti on in z di recti on [10] and as a consequence the -f actor can be \ tuned " into or out of resonance when a m icrowave Ùeld of suita ble frequency is appl ied. W e have al ready demonstra ted tha t the shift i n resonance exceeds the l i newi dth al ready for %. In thi s paper we inv estigate the e ect of Ge in the channel in m ore deta il on sam ples wi th a still higher m obilit y and we demonstra te tha t, like for pure Si channels, the Bychko v{ R ashba Ùeld is also the m ost essential contri buti on for both spi n rel axa ti on and the g-factor. W e eval uate the Bychko v{ R ashba coe cient and we observe an increase in it wi th increasing from 0 to 10%. Thi s i ncrease appears surpri sing at Ùrst gl ance since the barri er height decreases (the Ge concentra ti on in the barri er rem ains almost constant in our sam pl e series) and theref ore we appro ach rather the case of bul k m ateri al wi th a Ùeld gradient. A possibl e concl usion from tha t wi ll be tha t the higher SOI in Ge-alloyed Si or an addi ti onal -gradi ent wi thi n the well is responsible for thi s e ect. Sampl es were grown by m olecul ar beam epita xy on 3 m thi ck, step-graded and ful ly relaxed Si 1 y Ge y bu ers (nom inally 0 25) on to p of a (100) Si

3 Bychkov{ Rashba E e ct and g-factor T uni ng substra te. The quantum wel l consi sts of Si 1 À x Ge x (0 ç x ç 0 : 1), it has a thi ckness of 12 nm and thus it is pseudom orphi c and strained. The strain causesa splitti ng of the  2 conducti on band m inima in such a way tha t only the ellipsoids wi th thei r main axi s oriented perpendicul ar to the sam ple surface ( m 0 ) are popul ated. On top of thi s a spacer ( : 0 25, nm ) and an Sb doped layer ( nm, [Sb] = cm 3 ) are grown, followed by another bu er (the sam e ) and a 10 nm Si cap. Al tho ugh the Ge concentra ti on is well repro duci bl e wi thi n one run, it is di cul t to predeùne vi a the growth parameters i n our MBE system. The experi m enta l determ inati on of and by X-ray techni ques and secondary i on mass spectroscopy (SIMS) poses al so some pro blems. Theref ore we used l ow- energy R utherf ord backscatteri ng (500 kev He) to i nv estigate the compositi on of our relati vel y com plex layer sequence [11]. Results are given in the T able. T ABLE

4 588 H. Mal issa et al. W e investi gate the conducti on electron spin resonance in modulati on doped SiGe quantum wel l s i n a standard X- band spectrom eter (Bruker El exsys E 580) wi th a TE1 02 cavi ty. Typi cal spectra are given in Fi g. 1. In the upp er half of the diagram, spectra are shown f or perpendicul ar m agneti c Ùeld, i n the l ower half for in-pl ane Ùeld for the three sampl es wi th a nom inal x of 0, 0.05, and 0.1, respectively. The spectra exhi bi t asym m etry appro achi ng rather a D ysonian shape whi ch has been expl ained in term s of electri c di pole contri buti ons [3]. It is clearl y seen tha t the resonance Ùeld shifts to wards higher Ùeld (l ower g-factor) wi th increasing x and at the sam e ti m e the linewi dth increases. 3. In t er pr et at io n an d d iscu ssio n W e have earlier shown in a deta iled inv estigati on of the inûuence of the electro n density and the m omentum relaxa ti on ti me on the ani sotro py of the g-factor and the ESR linewi dth and also on the longitudi nal spin relaxati on of hi gh m obility Si quantum wel ls tha t these quanti ti es can be expl ained consi stentl y in term s of the Bychko v{ Rashba Ùeld, H B R, whi ch results from the one-sided m odul ati on doping of our sam ples [3, 12]. In the present situa ti on, the cycl otro n frequency is in the range! c 1 and thus H BR can be trea ted as a small perturba ti on and we obta in for the g-factor [2] cos (1) where i s the stati c resonance Ùeld, i ts i ncl i nati on angl e wi th respect to the surface norm al, the unp erturb ed - factor of SiGe, the 2D electron density and stands for the R ashba coe cient whi ch characteri zes the SO intera cti on resulti ng from bi -linear term s in the -vecto r and the spi n in the Ha milto nian. For the linewi dth for in-pl ane Ùeld ori enta ti on we obta in [2, 13] (2) Both quanti ti es can be eval uated from the spectra shown i n Fi g. 1. The R ashba coe cient can be eval uated thus from the - factor anisotro py and i ndependentl y from the linewi dth. R esults are given in Fi g. 2 as a functi on of alloy compositi on. From Fi g. 1 we see tha t for 5% of Ge in the quantum well the shi ft in the resonance Ùeld exceeds the l i newi dth al ready by a factor of 5 for i n- plane ori enta ti on and by roughly a factor 3 for perpendicul ar Ùeld. Thi s shows tha t the resonances are clearl y separated at an even l ower Ge concentra ti on. Thi s i s im porta nt because the spi n coherence ti me wi ll be longer for lower.

5 Bychkov{R ashba E e ct and g-factor T uni ng Fig. 2. BR parameter as a function of Ge concentration, calculated from g -factor anisotropy (solid circles) and from linew idth (solid squares). the triangle represents the BR parameter for a pure Si quantum w ell obtained earlier (see Ref. [2]). W e concl ude thus tha t the use of di erent compositi ons of SiGe alloy can be a useful to ol for the engineering of spintro nic structures where it is importa nt to have a possibility for selecti ve spi n mani pul ati on by g-factor tuni ng. Our eval uati on of the BR Ùeld i n SiGe QW shows tha t, i n spi te of the exp ectati on based on the fact tha t tha t the height of the barri er decreases, the BR parameter in alloyed QW ' s is bi gger tha n in a pure Si QW. Thi s observati on leads to the concl usion tha t either (i) the spin{ obi t param eter i n the quantum wel l or (i i) a gradient of the Ge concentra ti on wi t hi n the QW can be an im porta nt source of the BR e ect. The data show tha t thi s contri buti on can be even more importa nt tha n an e ecti ve electri c Ùeld in the QW and the asym metry of the QW interf aces. Such a concept woul d also expl ain the puzzl ing e ect observed in pure Si QW s where the BR param eter i s al most i ndependent of the electron concentra ti on. The l atter should screen the electri c Ùeld and thus m odify the penetrati on of the electron wa ve functi on into the barri er. W ork supp orted by the Fond zur Forderung der W issenschaftl ichen Forschung, Austri a, OeAD and Gm e, both Vi enna, and in Poland under the grant PB Z-KBN 044/ P03/ R ef er en ces [1] D.P. Di V incenzo, F or tschr. Ph ys. 48, 771 (2000). [2] Z. Wilamow ski, W. Jantsch, H. Malissa, U. R ossler, Ph ys. Rev. B 66, (2002). [3] Z. Wilamo w ski, W. Jantsch, Ph ys. Rev. B 6 9, (2004).

6 590 H. Mal issa et al. [4] W. Jantsch, Z. Wilamow ski, N. Sandersfeld, M. M uhlb erger, F. Scha er, Ph ysi ca E 1 3, 504 (2002). [5] B. Beschoten, E. Johnston- H alp eri n, D. K. Y oung, M. Poggio, J.E. Grimaldi, S. K eller, S.P. DenBaars, U.K. Mishra, E. L. H u, D. D. A wschalom, Ph ys. R ev. B 63, (2001). [6] Z. Wilamow ski, W. Jantsch, N. Sandersf eld, M. M uhlb erger, F. Scha er, S. Lyon, Ph ysi ca E 16, 111 (2003). [7] M. D 'yakono v, V. Perel', Sov. Ph ys. JE TP 38, 177 (1973). [8] R. Elliot, Ph ys. R ev. 96, 266 (1954). [9] Y. Y afet, Soli d State Ph ys. 14, 1 (1963). [10] R. V ri j en, E. Yablono vitch, K. W ang, H.W. Jiang, A. Balandin, V. Roychow dhury, T. Mor, D. P. DiV incenzo, Ph ys. Rev. A (2000). [11] M. Draxler, M. M uhlb erger, P. Bauer, in preparation. [12] Y. Bychko v, E. Rashba, 6039 (1984). [13] Z. Wilamo w ski, W. Jantsch, 439 (2002).

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