Spin diffusion of optically oriented electrons and photon entrainment in ...

Spin diffusion of optically oriented electrons and photon entrainment in n -gallium arsenide R. I. Dzhioev, B. P. Zakharchenya, V. L. Korenev, and M. N. Stepanova A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia

~Submitted May 22, 1997! Fiz. Tverd. Tela ~St. Petersburg! 39, 1975–1979 ~November 1997!

An experimental and theoretical study of spin transport in the n-GaAs semiconductor is reported. Transport of average electron spin from the photoexcited crystal surface is shown to be determined by the spin diffusion process. At the same time the transport of photoexcited carriers takes place primarily through photon entrainment, which transfers nonequilibrium carriers into the bulk of the semiconductor to distances considerably in excess of the electron spin diffusion length. A comparison of the experimental results with theory permits one to determine the average-spin diffusion length and electron-spin relaxation time. © 1997 American Institute of Physics. @S1063-7834~97!01111-8#

Investigation of spin transport in ferromagnet/ semiconductor hybrid systems has become a topical problem in recent years.1 A study of polarized electron tunneling from a ferromagnet into gallium arsenide was reported.2 The reverse problem of spin-dependent transport of optically oriented electrons from GaAs into a ferromagnet is also being investigated.3 The effect of stray fields in a demagnetized ferromagnetic film on electron spin polarization in a semiconductor was analyzed in the Ni/n-GaAs system.4 In the latter work, the interpretation of results depended critically on the relation between the domain size D in the film and the spin diffusion length L s of the semiconductor electrons. If D>L s , the electron spin undergoes effective relaxation in the domain magnetic fields. In the opposite case (D!L s ) the stray magnetic fields of the film decay rapidly near the surface, and there is no spin relaxation of the semiconductor electrons. In either of the above experiments one has to know the electron spin transport in the semiconductor, i.e. the effect of photon recycling, spin diffusion, and relaxation on the electron polarization. This work deals with an experimental and theoretical investigation of spin transport in the n-GaAs semiconductor ~spin transport in p-GaAs was considered in Ref. 5!. It is shown that the transport of average electron spin from a photoexcited crystal surface is dominated by spin diffusion. At the same time photoexcited carriers are transported primarily through photon entrainment, which transfers nonequilibrium carriers into the bulk of the semiconductor to distances considerably in excess of the electron-spin diffusion length. By comparing experiment with theory one can determine the average-spin diffusion length and the electron spin relaxation time. Electrons with spins oriented along the pump beam are produced in a semiconductor in interband absorption of circularly polarized light. If photoexcited carriers do not lose totally their spin orientation during their lifetime, photoluminescence will be partially circularly polarized. The degree of circular polarization of the photoluminescence in GaAs is determined by the projection s z of the average electron spin on the direction of the pump beam ~the z axis!,6 and in the case of uniform spin-density distribution in space r 5s z . 1765

Phys. Solid State 39 (11), November 1997

The optical orientation experiments were carried out on an n-type GaAs sample ~Si concentration 131015 cm23! grown along @001# by liquid-phase epitaxy ~layer thickness 35 mm! on a 400 mm-thick gallium arsenide substrate ~Si concentration 1018 cm23!. The sample was maintained in a liquid-helium cryostat and excited by a Kr1 laser (h n 51.65 eV, P55 mW, spot diameter d5300 m m!, with a photoelastic quartz modulator used to alternate the circular polarization sign at a frequency of 26.61 kHz. This permitted us to avoid the effect of polarization of the lattice nuclei on the optical electron orientation.6 The recombination radiation polarization was measured in reflection by a circular polarization analyzer ~a quarter-wave phase plate with a linear polarizer!. The desired regions of the luminescence band could be cut out with a double-grating spectrometer with a 16 A/mm dispersion. The electronic circuit performed synchronous counting of left- and right-hand circularly polarized photons ~N 2 and N 1 !. The degree of circular polarization was found as r 5(N 1 2N 2 )/(N 1 1N 2 ). We measured the dependence of r on magnetic field perpendicular to the exciting beam, as well as on the wavelength l of recombination radiation. Figure 1 presents spectra of luminescence I PL ~solid curve! and of the degree of circular polarization ~filled circles! obtained in zero magnetic field. If recombination occurred only close to the surface, r would remain constant throughout the spectral region covered. The noticeable decrease of r in the long-wavelength wing of the luminescence line indicates that the fraction of carriers recombining in the bulk of the crystal is fairly large. This becomes possible if one assumes the presence of photon entrainment which makes nonequilibrium carriers penetrate into the semiconductor bulk ~the diffusion length of nonequilibrium carriers in an n-type semiconductor is determined by the diffusion length of holes and is extremely short because of their low mobility!.7 It should be added that the luminescence magnetic depolarization curves have essentially different shape in the short- and long-wavelength wings of the line. Figure 2a shows the Hanle effect at the shortwavelength edge, and Fig. 2b, at the long-wavelength edge of the line. The curves in Figs. 2a and 2b are substantially

1063-7834/97/111765-04$10.00

© 1997 American Institute of Physics

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FIG. 1. Photoluminescence intensity I PL and degree of circular polarization r vs wavelength l. Filled circles—experimental values of r~l!, open circles—a plot of Eq. ~9!.

different in shape. The absolute measurement errors for r~l! ~filled circles in Fig. 1! and r (B) ~filled and open triangles in Fig. 2! do not exceed 0.06%. A theoretical analysis of electron spin diffusion in n-GaAs was made in Ref. 8 without inclusion of photon entrainment. It was shown that since the region involved in redistribution of excess carriers is dominated by the short hole-diffusion length, all of the photoluminescence ~PL! occurs near the semiconductor surface, and that the degree r of PL circular polarization is determined only by the electron spin density S~0! at the surface. In this case r should not depend on the wavelength l at which the radiation is detected. The shape of the radiation depolarization curve in transverse magnetic field B differs from a Lorentzian. This is a result of the fact that electrons lose their original orientation because of spin diffusion into the bulk of the semiconductor, while the spatial distribution of spin density is itself

dependent on magnetic field. As follows from our experiments ~see Figs. 1 and 2!, however, both r and the shape of the Hanle curve depend on the wavelength at which the radiation is detected. We are going to show here that adequate description of the spectral behavior of r (B50, l) and of the Hanle effect requires taking into account photon entrainment in GaAs. Indeed, while the photon recycling does not contribute to the spin density transport,9 it results in penetration of minority carriers into the bulk of the semiconductor. As a result, photoexcited holes, rather than being localized close to the semiconductor surface, are now distributed in depth on a characteristic length scale j, which is determined by the photon recycling efficiency. If this efficiency is low enough to be less than the electron-spin diffusion length, j !L s , the holes will concentrate close to the surface, and we come to the result obtained in Ref. 8. In the other opposite case, j @L s , the holes are distributed nearly uniformly throughout the layer where the electron spin density is nonzero. As a result, S, and, hence, r should now depend on the detection wavelength l because of the spectral dependence of the absorption coefficient a~l!. Indeed, a photon created in recombination of an electron and a hole at a distance z from the semiconductor surface escapes from the sample with a probability }exp@2a(l)z#.5 The process is dependent on the magnitude of L s a (l). If L s a (l)@1 ~the high-energy wing of the PL line!, one will detect the polarized light emitted from near the sample surface, and r }S (z50) ~the nearsurface region is determined by the absorption depth 1/a 0 ;1 m m of the pump light!. In this case one may again use the results obtained in Ref. 8. In the other limiting case, L s a (l)!1, PL is detected from distances up to a 21 (l) 21 from the surface, and r } a * a0 S(z)dz. This should result in a reduction of r in the low-energy part of the line, since the spin density in the bulk of the sample is lower than that at the surface. Besides, spin diffusion does not play any role in these conditions, and the Hanle curve takes on the conventional Lorentzian shape. Thus the existence of photon entrainment which redistributes uniformly the nonequilibrium carriers permits one to qualitatively explain the results of our experiments. Let us turn now to a more rigorous proof of the above statements. We shall consider a model by which photon entrainment redistributes the holes to distances j @L s , a (l) 21 . Then

r5

FIG. 2. Luminescence depolarization in a transverse magnetic field. l~Å!:a—8140, b—8190. Solid curves—theory. 1766


* `0 S ~ z ! p ~ z ! e 2 a z dz

n d * `0 p ~ z ! e 2 a z dz

~1!

,

where n d is the equilibrium electron density at donors, which are filled at low temperatures, and p(z)!n d is the concentration of nonequilibrium holes. Since the light spot diameter is substantially larger than all characteristic lengths @ j ,L s , a (l) 21 # , the spin distribution in the ~001! plane may be considered uniform, with all nonuniformities being due only to the spin dependence on the coordinate z. For j @L s , a (l) 21 we have p(z)5const, and Eq. ~1! simplifies to Dzhioev et al.

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r5

a * `0 S ~ z ! e 2 a z dz . nd

~2!

To calculate the r (B) dependence, one has to know the spatial distribution of the electron spin density and its magnetic field dependence. The spin density can be found from the diffusion equation D

] 2S S 1 v3S2 50, ]z2 ts

~3!

where D is the electron diffusion coefficient, t s is the electron spin relaxation time, v 5 m b gB/\ is the Larmor precession frequency of the electron spin, and g is the electron g factor. Equation ~3! was written under the assumption that the nonequilibrium-carrier lifetime t G 5n d /G ~G is the pair generation rate per unit volume! is large compared to t s ~the so-called weak pumping case8!. This assumption is valid for low light intensities, where the spin relaxes rapidly during the lifetime, and the radiation polarization is low. To find S( v ,z), Eq. ~3! has to be complemented by boundary conditions S~ v ,z→` ! 50,

2D

]S ]z

U

5G s sin .

~4!

z50

We have disregarded surface recombination, which is negligible at low temperatures.9 Here s in50.25 is the average electron spin at creation, and G s 5G/ a 0 is the pair generation rate per unit surface. Solving Eq. ~3! subject to conditions ~4! yields S~ v ,z ! 5sin

G sL s Re D

F

3exp 2

S

z Ls

1

A11i v t s A11i v t s

GD

~5!

,

where L s 5 AD t s is the spin diffusion length, i5 A21. Inserting Eq. ~5! into Eq. ~2!, we come to the final relation

r ~ B,l ! 50.25

G sL s Re n dD

S

a~ l !Ls

1

A11i v t s a ~ l ! L s 1 A11i v t s

D

. ~6!

Consider two limiting cases. At the high-energy wing of the line L s a (l)@1, so that the main contribution to polarized luminescence comes from electrons recombining at the sample surface, and Eq. ~6! assumes the form

r ~ B ! 50.25

G sL s Re n dD

520.25

G sL s n dD

S

1

A11i v t s

A

D

11 A11 v 2 t 2s 2 ~ 11 v 2 t 2s !

~7!

which coincides with the result obtained8 for the weakpumping conditions. In the other limiting case, L s a (l)!1 ~the low-energy wing!, Eq. ~6! yields

r ~ B ! 50.25 1767

ts a~ l !/a0 G st s a~ l ! . ~8! 2 50.25 n d 11 ~ v t s ! t G 11 ~ v t s ! 2


As follows from Eq. ~8!, in this case the Hanle effect is described by a Lorentzian curve. The factor t s / t G !1 accounts for electron depolarization in various spin relaxation processes during their lifetime t G . The factor a (l)/ a 0 ,1 appears because polarized electrons are created in the nearsurface region ' a 21 thick, but recombine through photon 0 recycling from a region of size a (l) 21 . a 21 0 , where they are polarized to a lesser degree than at the sample surface. Thus the spectral dependence of the luminescence polarization is dominated in this case by that of the absorption coefficient. Knowing the a~l! relation, one can derive the r c (l) dependence from Eq. ~6! and, conversely, one can determine the spectral dependence of the absorption coefficient in n-GaAs from the known r c (l) relation. Indeed, for B50 one finds from Eq. ~6!

r ~ B50,l ! 5s 0

S

D

a~ l !Ls , a ~ l ! L s 11

~9!

where s 0 50.25G s L s /n d D is the average electron spin near the GaAs surface. We recall that Eq. ~6! was derived under the assumption that j @ a (l) 21 , i.e. that holes are distributed over a length exceeding by far that of light absorption. When a~l! becomes small enough for this condition to fail, r in the low-energy wing of the line will be determined not by a 21 (l) but rather by the magnitude of j, in other words, it will no more be dependent on l. Let us turn now to a quantitative comparison of experimental results with the above theory. We consider first the spectral dependence r~l! in a zero magnetic field ~Fig. 1!. As already mentioned, if a~l! is known, one can calculate r~l! using Eq. ~9!. The open circles in Fig. 1 show the results of calculation using Eq. ~9! with the fitting parameters s 0 55.4% and L s 510 m m. The a~l! relation for T54.2 K was obtained using the results of Ref. 10 corrected for the temperature dependence of the GaAs gap width. The parameters s 0 and L s were chosen so as to fit the calculation to the experimental data on optical absorption ~filled circles! along both the horizontal and vertical axes. The agreement is seen to be quite good, with the exception of the long-wavelength portion of the spectrum (l.8215 Å). The discrepancy can be accounted for by the fact that the absorption coefficient in this region is small @ a (l),600 cm21 Ref. 10#, so that the condition j @ a 21 (l) fails, and Eqs. ~6! and ~9! are no longer valid. The degree of polarization r is determined in this case not by the light absorption depth a 21 (l) but rather by the hole penetration depth j ~since in the z. j region there are no nonequilibrium carriers!, and does not depend on l. This permits us to assess the size of this region j ; a 21 (l58225 Å);30 m m. Thus photon recycling distributes the holes practically uniformly over the thickness of the GaAs epitaxial layer ~35 mm!. Diffusion and photon recycling affect substantially the shape of the magnetic radiation depolarization curves as well. The results of the calculation are shown in Fig. 2 by solid lines. There were two fitting parameters, the spin relaxation time t s and the wavelength-dependent quantity a (l)L s . The problem can be simplified if we take into account that, in the high-energy wing of the line (l58140 Å) Dzhioev et al.

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a (l)L s @1, and the Hanle effect is described by a simpler expression ~7! containing only one parameter, the time t s . The solid line in Fig. 2a is drawn for t s 54.231028 s. When analyzing the Hanle effect at the wavelength l58190 Å ~Fig. 2b!, the parameter a (l)L s ;1, and one has to use Eq. ~6!. Since the time t s was determined above, one again has only one fitting parameter a (l58190 Å)L s . The curve in Fig. 2b was constructed for a (l58190 Å)L s 51.2. This value differs from the value of 1.7 determined for this parameter from Fig. 1 @a (l58190 Å)50.173104 cm21, Ref. 10, L s 510 m m#. The difference may be due to the fact that the absorption coefficient taken from published data10 may differ somewhat from that of the sample under study. Let us discuss now the mechanism of spin diffusion at low temperatures in weakly doped n-GaAs. The equilibrium electrons are localized at donors in this case. For n d 5231015 cm23, the overlap of electronic wave functions at adjacent donors is small ~n 1/3 d a'0.1, where a is the electron Bohr radius!, and the electron hopping diffusion among donors is essentially suppressed. Photoexcitation creates near the surface free carriers diffusing into the bulk of the semiconductor with an ambipolar diffusion coefficient determined by the small hole-diffusion coefficient. In other words, diffusion is small in this case as well. What then accounts for the electron spin diffusion in this case? In our opinion, this process is dominated by the photon entrainment, which distributes photoexcited electrons and holes uniformly throughout the epitaxial layer. In this case there are no diffusive fluxes of carriers in GaAs. Accordingly, there is no electric field and, thus, no ambipolar diffusion, which would slow down the faster electrons and accelerate the less mobile holes. Further, since photon entrainment does not transport the spin, the electron spin density is distributed nonuniformly. The electron spin diffusion is not connected in this case with diffusion of charged particle packets, and it should occur much faster than that under ambipolar diffusion. Indeed, in the case of photon entrainment there is no concentration gradient, and the electron flux Q e 5Q 1 e

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1 1Q 2 e 50. Here Q e 52D ] n 6 / ] z are fluxes of spin-up ~down! electrons. At the same time the electron spin density 2 flux Q s 5(Q 1 e 2Q e )/252D ] S/ ] z is not zero and is determined by the electron diffusion coefficient 2 2 D5L s / t s 524 cm /s, which exceeds substantially the ambipolar diffusion coefficient in n-GaAs. Thus the diffusive transport of the spin, as well as photon entrainment, affect significantly the spectral behavior of polarized luminescence and the Hanle effect in n-GaAs. Comparison of theory with experiment permits one to determine the main parameters characterizing spin transport in a semiconductor. The large spin diffusion length in n-GaAs can make this material promising for investigation of spin transport in multilayer ferromagnet/semiconductor structures.

The authors are grateful to K. V. Kavokin for fruitful discussions. Two of the authors, R.I.D. and V.L.K., express gratitude for the partial support of their work by the Russian Fund for Fundamental Research ~Grant 95-02-04161!. G. A. Prinz, Science 250, 1092 ~1990!; Phys. Today April ~1995!, p. 58. S. F. Alvarado, Phys. Rev. Lett. 75, 513 ~1995!. 3 M. W. J. Prins, R. Jansen, and H. van Kempen, Phys. Rev. B 53, 8105 ~1996!. 4 R. I. Dzhioev, B. P. Zakharchenya, and V. L. Korenev, Fiz. Tverd. Tela ~St. Petersburg! 37, 3510 ~1995! @Phys. Solid State 37, 1929 ~1995!#. 5 R. I. Dzhioev, B. P. Zakharchenya, R. R. Ichkitidze, K. V. Kavokin, and P. E. Pak, Fiz. Tverd. Tela ~St. Petersburg! 35, 2821 ~1993! @Phys. Solid State 35, 1396 ~1993!#. 6 F. Meier and B. Zakharchenya ~Eds.!, Optical Orientation, Vol. 8 of Modern Problems in Condensed Matter Sciences ~North-Holland, Amsterdam, 1984! @Russian trans., Mir, Moscow, 1989#. 7 Oldwig von Roos, J. Appl. Phys. 54, 1390 ~1983!. 8 M. I. D’yakonov and V. I. Perel’, Fiz. Tekh. Poluprovodn. 10, 350 ~1976! @Sov. Phys. Semicond. 10, 208 ~1976!#. 9 R. I. Dzhioev, B. P. Zakharchenya, K. V. Kavokin, and P. E. Pak, Fiz. Tverd. Tela ~St. Petersburg! 36, 2752 ~1994! @Phys. Solid State 36, 1501 ~1994!#. 10 M. D. Sturge, Phys. Rev. B 127, 768 ~1962!. 1 2

Translated by G. Skrebtsov

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