曾经的曾经3.Spin injection through the space-charge region Interfaces making up a semiconductor often develop a space-charge region—a region of local macroscopic charges.Typical examples are the Schottky contact and the depletion layer in p-n junctions.While phenomeno-logical models,such as the one introduced in Sec.II.C.1, capture a remarkable wealth of spin injection physics, they carry little information about spin-dependent pro-cesses right at the interfaces.Microscopic studies of spin-polarized transport and spin-resolved tunneling through space-charge regions are still limited in scope. The dif?culty lies in the need to consider self-consistently simultaneous charge accumulation and electric-?eld generation(through Poisson’s equation), both affecting transport.Non-self-consistent analyses of a Schottky-barrier spin injection were performed by Al-brecht and Smith(2002,2003)and Prins et al.(1995), while Osipov and Bratkovsky(2003)proposed an ef?-cient spin injection method using a?-doped Schottky contact.
Let us now consider spin injection through the deple-tion layer in magnetic p-n junctions(Fabian et al., 2002a;Zˇutic′et al.,2002,2003).The physics is based on drift and diffusion52limited by carrier recombination and spin relaxation,as described in more detail in Sec. IV.A.4.The transport equations are solved self-consistently with Poisson’s equation,taking full account of electric?eld due to accumulated charges.Additional examples of magnetic p-n junctions are discussed in Sec. IV.D.
The system is depicted in Fig.8.The p-n junction has a magnetic n region53with a net equilibrium electron spin P n0R,where R stands for the right(here n)region. Holes are assumed to be unpolarized.An important is-sue to be resolved is whether there will be spin accumu-
51The wave-vector component along the interface is con-served during scattering.
52Tunneling or?eld emission becomes important,for ex-ample,in thin Schottky barriers or in p-n junctions and het-erostructures at large reverse biases(Kohda et al.,2001; Johnston-Halperin et al.,2002;Van Dorpe,Liu,et al.,2003). 53Equilibrium magnetization can be a consequence of doping with magnetic impurities,yielding large carrier g factors,and applying magnetic?eld,or of using a ferromagnetic semicon-ductor(Ohno,1998;Pearton et al.,2003).
338Zˇutic′,Fabian,and Das Sarma:Spintronics:Fundamentals and applications Rev.Mod.Phys.,Vol.76,No.2,April2004
lation in the p region if a forward bias is applied to the
junction.In other words,will spin be injected across the depletion layer?Naively the answer is yes,since spin is carried by electrons,but the result shown in Fig.8sug-gests a more complicated answer.At small biases there is no spin injection.This is the normal limit of diode operation,in which the injected carrier density through the depletion region is still smaller than the equilibrium carrier density.Only with bias increasing to the high-injection limit (typically above 1V)is spin injected.The explanation for the absence of spin injection at small biases and for nondegenerate doping levels (Boltzmann statistics is applicable)is as follows.On the n side there are more spin-up than spin-down electrons,n ↑?n ↓.If 2q ?is the spin splitting of the conduction band,n ↑(?)/n ↑(??0)?exp(q ?/k B T ).Under a forward bias,electrons ?ow to the p region.The ?ow is limited by thermal activation over the barrier (given by the built-in electrostatic potential minus bias),which is,for the spin-up electrons,greater by q ?.For Boltzmann sta-tistics,the rate of transmission of spin-up electrons over the barrier is ?exp(?q ?/k B T ).Since current is propor-tional to both the carrier density and the transmission rate,the two exponential factors cancel out.Similarly for spin down.As a result,the spin-resolved current is unaffected by 2q ?and there is no spin current ?owing through the depletion layer.There is no spin accumula-tion.Spin injection appears only at large biases,where it is driven by electric drift leading to nonequilibrium spin population already in the n region (Fabian et al.,2002a;Z
ˇutic ′et al.,2002).In addition to spin injection,spin ex-traction has also been predicted in magnetic p -n junc-tions with a magnetic p region (Z
ˇutic ′et al.,2002).Under a large bias,spin is extracted (depleted)from the non-magnetic n region.
Electric ?eld in the bulk regions next to the space charge is important only at large biases.It affects not only spin density,but spin diffusion as well.That spin injection ef?ciency can increase in the presence of large electric ?elds due to an increase in the spin diffusion length (spin drag)was ?rst shown by Aronov and Pikus (1976)and was later revisited by other authors.54To be important,the electric ?eld needs to be very large,55more than 100V/cm at room temperature.While such large ?elds are usually present inside the space-charge regions,they exist in the adjacent bulk regions only at the high injection limit and affect transport and spin in-jection.In addition to electric drift,magnetic drift,in magnetically inhomogeneous semiconductors,can also enhance spin injection (Fabian et al.,2002a).
The following formula was obtained for spin injection at small biases (Fabian et al.,2002a):
P n L ?
P n 0L ?1??P n 0R ?2???P n R ?1?P n 0L P n 0R
?
1??P n 0R ?2??P n R ?P n 0L ?P n 0R
?
,(49)
where L (left)and R (right)label the edges of the space-charge (depletion)region of a p -n junction.Cor-respondingly,?P n
R
represents the nonequilibrium elec-tron polarization,evaluated at R ,arising from a spin
source.The case discussed in Fig.8is for P n 0L ??P n
R
?0.Then P n L
?0,in accord with the result of no spin injection.For a homogeneous equilibrium magnetiza-tion (P n 0L ?P n 0R ),?P n L ??P n R
;the nonequilibrium spin polarization is the same across the depletion layer.Equation (49)demonstrates that only nonequilibrium spin,already present in the bulk region,can be trans-ferred through the depletion layer at small biases (Z
ˇutic ′et al.,2001b;Fabian et al.,2002a).Spin injection of non-equilibrium spin is also very effective if it proceeds from
the p region (Z
ˇutic ′et al.,2001b),which is the case for a spin-polarized solar cell (Z
ˇutic ′et al.,2001a).The result-ing spin accumulation in the n region extends the spin diffusion range,leading to spin ampli?cation—increase of the spin population away from the spin source.These results were also con?rmed in the junctions with two differently doped n regions (Pershin and Privman,2003a,2003b).Note,however,that the term ‘‘spin polar-ization density’’used in Pershin and Privman (2003a,2003b)is actually the spin density s ?n ↑?n ↓,not the spin polarization P n .
54
See,for example,Margulis and Margulis (1994);Flensberg
et al.(2001);Z
ˇutic ′et al.(2001b);Fabian et al.(2002a);Yu and Flatte
′(2002a);Bratkovsky and Osipov (2003);Martin (2003);and Vignale and D’Amico (2003).55
The critical magnitude is obtained by piding a typical en-ergy,such as the thermal or Fermi energy,by q and by the spin diffusion length.At room temperature the thermal energy is 25meV ,while the spin diffusion length can be several
microns.
FIG.8.(Color in online edition)Spin injection through the
space-charge region of a magnetic p -n junction.The geometry is depicted in the inset,which shows a junction with a spin-split conduction band in the n region with spin-polarized electrons (solid circles)and unpolarized holes (empty circles).Under applied forward bias V the charge current ?ows to the right.The curves,labeled by V ,show the electron density polariza-tion pro?les P n (x )for the depicted geometry and GaAs ma-terials parameters.The equilibrium density polarization in the n region is about 0.5.At low bias (0.8V)there is no spin injection.Spin injection,manifested by the increase of P n in the p region,appears only at large biases (1.2and 1.5V),
where it is driven by electric drift (Z
ˇutic ′et al.,2002).Spin polarization of the current is discussed by Z ˇutic ′et al.(2001a)and Fabian et al.(2002a).Adapted from Z
ˇutic ′et al.,2002.339
Z
ˇutic ′,Fabian,and Das Sarma:Spintronics:Fundamentals and applications Rev.Mod.Phys.,Vol.76,No.2,April 2004
Theoretical understanding of spin injection has fo-cused largely on spin density while neglecting spin phase,which is important for some proposed spintronic applications.The problem of spin evolution in various transport modes (diffusion,tunneling,thermionic emis-sion)remains to be investigated.Particularly relevant is the question of whether spin phase is conserved during spin injection.Malajovich et al.(2001)showed,by studying spin evolution in transport through a n -GaAs/n -ZnSe heterostructure,that the phase can in-deed be preserved.
D.Experiments on spin injection 1.Johnson-Silsbee spin injection
The ?rst spin polarization of electrons by electrical spin injection (Johnson and Silsbee,1985)was demon-strated in a ‘‘bulk wire’’of aluminum on which an array of thin ?lm permalloy (Py)pads (with 70%nickel and 30%iron)was deposited spaced in multiples of 50?m,center to center (Johnson and Silsbee,1988d)to serve as spin injectors and detectors.In one detection scheme a single ferromagnetic pad was used as a spin injector while the distance to the spin detector was altered by selecting different Py pads to detect V s and through the spatial decay of this spin-coupled voltage infer L sN .56This procedure is illustrated in Fig.9,where the separa-tion between the spin injector and detector L x is vari-able.
Johnson and Silsbee (1985)point out that in the de-picted geometry there is no ?ow of the charge current for x ?0and that in the absence of nonequilibrium spins a voltage measurement between x ?L x and x ?b gives zero.Injected spin-polarized electrons will diffuse sym-metrically (at low current density the effect of electric
?elds can be neglected),and the measurement of voltage will give a spin-coupled signal V s related to the relative orientation of magnetizations in F1and F2.57The re-sults,corresponding to the polarizer-analyzer detection and the geometry of Fig.9,are given in Fig.10.An in-plane ?eld (B ?z ?),of a magnitude several times larger than a typical ?eld for magnetization reversal,B 0?100G,is applied to de?ne the direction of magnetiza-tion in the injector and detector.As the ?eld sweep is performed,from negative to positive values,at B 01there is a reversal of magnetization in one of the ferromag-netic ?lms accompanied by a sign change in the spin-coupled signal.As B z is further increased,at approxi-mately B 02,there is another reversal of magnetization,resulting in parallel orientation of F1and F2and a V s of magnitude similar to that for the previous parallel orien-tation when B z ?B 01.
