Optimized spin-injection efficiency and spin MOSFET operation based on low-barrier ferromagnet/insulator/n-Si tunnel contact
Yang Yang, Zhenhua Wu, Wen Yang, Jun Li, Songyan Chen, Cheng Li
aa r X i v : . [ c ond - m a t . m e s - h a ll ] M a y Applied Physics Express
Optimized spin-injection efficiency and spin MOSFET operation based on low-barrierferromagnet/insulator/n-Si tunnel contact
Yang Yang , Zhenhua Wu , Wen Yang , Jun Li ∗ , Songyan Chen , Cheng Li Department of Physics, Semiconductor Photonics Research Center, Xiamen University, Xiamen 361005, China KeyLaboratory of Microelectronic Devices and Integrated Technology, Instituteof Microelectronics, Chinese Academy of Sciences,100029 Beijing, China BeijingComputational Science Research Center, Beijing 100089, ChinaWe theoretically investigate the spin injection in different FM/I/n-Si tunnel contacts by using the lattice NEGF method. We find thatthe tunnel contacts with low barrier materials such as TiO and Ta O , have much lower resistances than the conventional barriermaterials, resulting in a wider and attainable optimum parameters window for improving the spin injection efficiency and MR ratio ofa vertical spin MOSFET. Additionally, we find the spin asymmetry coefficient of TiO tunnel contact has a negative value, while thatof Ta O contact can be tuned between positive and negative values, by changing the parameters. The spin degrees of freedom have caught the eyes of re-searchers due to they shed lights on the next-generation de-vices with novel charge-spin integrated functionalities. Re-alizing the spin-based electronics (spintronics) on silicon,i.e., the most prevailing material in semiconductor indus-try, has special significance because the established matureSi-technology could greatly facilitate the productions andmassive applications of spintronic devices. Fortunately, sil-icon is also considered as an ideal host for spintronics, asit exhibits long spin lifetime and di ff usion length. In thepast decade, milestone progresses have been achieved in Si-based spintronics. Room temperature electrical spin injec-tion in silicon through the ferromagnet / insulator / Si (FM / I / Si)tunnel contacts with Al O , SiO and crystalline MgO asbarriers were claimed to be observed. The spin polar-ized signals were detected by local three-terminal (3T),
3, 4) non-local-four-terminal (NL-4T) Hanle measurements, andthe spin transport in Si channel were demonstrated in spinmetal-oxide-semiconductor field-e ff ect transistor (spin MOS-FET).
6, 7)
Nevertheless, there remains challenges on obtainingclear and reliable signals, as well as understanding the spintransport process in the FM / I / Si tunnel contacts. The local 3THanle signals were under severely debates since they wererecently found to be dominated by the defect-states-assistedhopping, rather than the spin accumulation in silicon. Whilethe spin signals of NL-4T, spin MOSFETs were still veryweak,
6, 7) implying further optimizations of FM / I / Si contactsare required for their practical usages in spintronic devices.As pointed out by Fert et al., a noticeable spin signal by thespin injection from a ferromagnet into semiconductor can beobserved only if the contact resistance is engineered into anoptimum window: the contact resistance cannot be too lowto overcome the conductivity mismatch, nor be too high tokeep the electron dwell time shorter than the spin lifetime. Min et al. revealed that the resistances of conventional tun-nel contacts are orders of magnitude higher than the optimumvalue, due to the formation of Schottky barrier.
Therefore,controlling the contact resistance in a relatively low value isvery important for enhancing the spin signals. Graphene as alow resistance material has been demonstrated to be a good ∗ E-mail: [email protected] tunnel layer for the e ffi cient spin injection into silicon. It isstraightforward to expect other low barrier materials, such asTiO and Ta O , could also be used as the low resistance tun-nel barriers for improving the spin injection e ffi ciency. Theselow barrier materials have the advantage that they are compat-ible with the established Si-technology. Plus, the thicknessesof them can be adjusted, which o ff ers a freedom to tune thecontact resistance and also suppress the formation of param-agnetic silicide. However, the spin transport process in lowbarrier tunnel contact is much complicated, since both theSchottky barrier and the thermionic emission could take im-portant roles. Therefore, a unified model which takes accountof those e ff ects is necessary for studying the spin transport oflow barrier FM / I / Si tunnel contacts.In this paper, we present a theoretical investigation of thespin injection in di ff erent FM / I / n-Si tunnel contacts by thenon-equilibrium Green’s function (NEGF) method.
14, 15)
Thetransmission coe ffi cient of band profiles with various tun-nel and Schottky barrier are calculated by the lattice Green’sfunction. And the thermionic emission process is taken intoaccount by the temperature-dependent Fermi energy of n-Si and the Fermi-Dirac distributions. By using this method,the spin polarization (SP) of injected current, its parameters-dependence, and the magnetoresistance (MR) ratio of a verti-cal spin MOSFET are studied and discussed.The model of considered FM / I / n-Si tunnel contact issketched in Fig. 1(a). The contact region [ Z , Z ] is as-sumed to be located in between two semi-infinite leads. z ∈ [ Z , Z ) , [ Z , Z ] , ( Z , Z ], corresponds to the ferromagnet, in-sulator barrier, n-Si, respectively. Similar to the two currentmodel, the electrons with majority ( ↑ ) and minority ( ↓ ) spincan be viewed to flow in independent channels. In the contactregion, the Hamiltonian operator for each spin channel isˆ H σ C = − ~ ∂ z [ 1 m ∗ l ( z ) ∂∂ z ] + ~ k t m ∗ t ( z ) + U σ ( z ) , (1)where σ [ ∈ ( ↑ , ↓ )] is the index of spin, ~ is the reduced Planckconstant, k t is the transverse wave vector, and m ∗ t ( l ) ( z ) is thematerial-dependent transverse (longitudinal) electron e ff ec-tive mass. Here, we assume the electron e ff ective mass m ∗ F ( m ∗ I ) of ferromagnet (insulator) is isotropic, while the electron (a)(b) (c) J ( A / m ) T E (eV) V (V) A The contact region
FMSOIGateFM n-Si
FM/I/Sicontact t N tunneling E FM f m V A <0 Z Z Z Z W D Dm d T z n n c I D d I E CF c S E CS E FS E CF y S FM I n-Si thermionic emission
Fig. 1. (a) Schematic of the energy band profile of a FM / I / n-Si tunnelcontact under a reverse bias ( V A <
0) for the spin injection. The inset of (a)depicts the vertical spin MOSFET with a symmetric FM / I / n-Si / I / FMmultilayer structure. (b) and (c) The typical results of the averagedtransmission coe ffi cient T ( V A = . k t =
0) and the total currentdensity J ( d I = N D = × cm − and T =
300 K), respectively. e ff ective mass of n-Si is anisotropic, and m ∗ S t ( l ) is the trans-verse (longitudinal) electron e ff ective mass of n-Si. U σ ( z ) denotes the potential energy profile function for the σ spin channel, and consists of two parts U σ ( z ) = U σ CBO ( z ) + U S ( z ) . (2) U σ CBO ( z ) describes the profile of conduction band o ff set for σ spin, and is dependent on the conduction band bottom of fer-romagnet E σ CF , and the electron a ffi nity χ I ( χ S ) of insulatorbarrier (n-Si). Due to the exchange interaction, E ↑ ( ↓ ) CF is splitby the exchange splitting energy ∆ . U S ( z ) describes the spin-independent Schottky barrier energy profile, which is inducedby the charge accumulation nearby the FM / I and I / n-Si in-terfaces. Using the standard depletion layer approximation, U S ( z ) is determined by the work function of the ferromagnet φ m , the electron a ffi nity χ S of n-Si, the doping density N D , thethickness of the insulator barrier d I , the permittivity of insula-tor (n-Si) ǫ I ( ǫ S ), and the Fermi energy E FS of n-Si. For n-Sifrom nondegenerate to degenerate regime, E FS is dependenton the doping density N D and the temperature T , and can beobtained by numerically solving the charge-neutral conditionfunction. At thermal equilibrium, the ferromagnet’s Fermienergy E FM is equal to E FS . If the contact is under an appliedbias V A , then E FS = E FM + qV A , where q is the elementarycharge of electron. Note that for a reverse (forward) bias, i.e., V A < V A >
0) , the tunnel contact is in the spin injection(extraction) mode, respectively.By discretizing the contact region into an uniformly spaced1D grid with the spacing a , the Hamiltonian operator ˆ H σ C canbe transformed into a N × N tridiagonal matrix H σ C by themethod of finite di ff erences, where N is the total number ofgrid points. The retarded Green’s function in the lattice repre-sentation can be expressed as follow G σ C = [( E + i η ) I − H σ C − Σ σ L − Σ σ R ] − , (3) Table I.
Parameters of di ff erent insulator materials for the tunnel barriers.SiO Al O AlN (MgO) Ta O TiO χ I − χ S ( eV ) 3.1 2.8 1.6 (1.5) 0.3 0 m ∗ I ( m e ) 0.4 0.35 0.33 (0.35) 0.1 1.0 ǫ I ( ǫ ) 3.9 10 8.5 25 31 where E is the electron transmission energy, I is the identitymatrix and η is an infinitesimally small positive number. Thecoupling of the contact to the left (right) semi-infinite lead istaken into account by a N × N matrix of self-energy Σ σ L ( R ) Σ σ L ( R ) = ( Σ i j = − t i e ik σ L ( R ) a , for i = j = N ) Σ i j = , otherwise (4)where k σ L ( R ) = p m ∗ l ( z N + )[ E − E t ( z N + ) − U σ ( z N + )] / ~ is the longitudinal wave vector of a electron with σ spin in theleft (right) lead, E t ( z ) = ~ k t / [2 m ∗ t ( z )] k σ L ( R ) is the transversekinetic energy of electron, and t n = ~ / [2 m ∗ l ( z n ) a ] is thecoupling strength between the nearest grid points. In theabove expressions, z n denotes the coordinate of the n-th gridpoint. z and z N + are the coordinates of the first point in theleft and right leads, respectively. The transmission coe ffi cientof σ spin channel can be given by the NEGF formalism as T σ ( k t , E ) = T race [ Γ σ L G σ C Γ σ R G σ + C ] , (5)where Γ σ L ( R ) ≡ i [ Σ σ L ( R ) − Σ σ † L ( R ) ] is the broadening matrix. Thecurrent density of σ spin channel is then calculated by theLandauer formula J σ = − q π ~ Z ∞ Z ∞ T σ ( k t , E )[ f L ( E ) − f R ( E )] k t dk t dE , (6)where f L ( R ) ( E ) ≡ / [ e ( E − E FM ( FS ) ) / k B T +
1] is the Fermi-Diracdistribution functions in the left (right) lead and k B is theBoltzmann constant.For a contact with potential profile consisting of insulatorbarrier band o ff set and space-varying Schottky barrier, T σ and J σ can be calculated by Eq. (5) and Eq. (6). For the low tunnelbarriers, a portion of free electrons could be thermally exited[determined by f L ( R ) ( E )], even to obtain higher energies overthe barrier, so that T σ is close to 1. The transport of these elec-trons is not by tunnelling, but by the thermionic emission, andis automatically taken into account in this model. The typicalresults of the averaged transmission coe ffi cient of the two spinchannels, i.e., ¯ T ≡ ( T ↑ + T ↓ ) /
2, and the total electric currentdensity, i.e., J ≡ J ↑ + J ↓ , are displayed in Fig. 1(b) and (c).We can see the exponentially varying feature of ¯ T , and thecurrent rectifying e ff ect of Schottky contact are well repro-duced by our calculations. Note that, for contact in the spinextraction mode, though the calculated SP is found to be 25-60% smaller, the spin injection e ffi ciency is generally higherthan in the spin injection mode. Because for V A >
0, the de-pletion region is suppressed, and the contact resistance can belowered by orders of magnitude so that the spin depolariza-tion can be alleviated. In the following, we will focus on thetunnel contacts in spin extraction mode, e.g., for V A = + . m ∗ S t ( l ) = m e (at 300 K), ǫ s = ǫ and χ S = m e and ǫ is the free electron mass and the permittivity of vacuum, (a) (b) r m b () W * c)( (d)N cm D ( ) - N cm D ( ) - d (nm) I d (nm) I S P S P r m b () W * Fig. 2. (a)-(b) Dependence of r ∗ b and SP as a function of the dopingdensity N D of n-Si for FM / I / n-Si contact with di ff erent insulator barriers( d I = d I ( N D = × cm − ). V A = . T =
300 K is assumed in this figure. respectively. The ferromagnet material is chosen to be Fe, ofwhich the parameters are φ m = . m ∗ F = . m e and ∆ = . k ↑ ( ↓ ) F = − for the ↑ ( ↓ ) spin of Fe. Theparameters for di ff erent insulator barriers are listed in TABLEI. The e ff ective RA product r ∗ b of tunnel contact, and the spinasymmetry coe ffi cient (of contact resistance) γ is defined by r ↑ ( ↓ ) = r ∗ b [1 − ( + ) γ ] , (7)where r σ ≡ V A / J σ is the individual RA product for σ spin.If the electron travels beyond the ballistic regime, the spinaccumulation should be described by the spin drift-di ff usionmodel. Following Fert’s derivation, the SP of injected cur-rent in silicon can be given by Eq. (20) of Ref. 9.In Fig. 2(a) and (c), we show the calculation results of r ∗ b as a function of the doping density N D and the thickness ofbarrier d I . As expected, for a 1-nm-thick barrier, r ∗ b can be re-duced up to 5 orders by changing the barrier material fromSiO to TiO , i.e., decreasing the barrier height. While by in-creasing N D from 10 to 10 cm − , r ∗ b can only be adjustedby less than 3 orders. Though r ∗ b is very sensitively depen-dent on d I (except TiO with a 0 eV barrier height) [see inFig. 2(c)], the optimum value of r ∗ b ( ≈ − Ω · m ) for anoticeable MR requires an ultrathin layer with d I < . , Al O and AlN.Experimentally, there are considerable di ffi culties in fabricat-ing a sub-nanometer-thick layer with high qualities, i.e., withuniform and planar interfaces, very few defects and trapped-charges. Besides, the paramagnetic silicide, which is harmfulto the spin transport, can hardly be prevented from form-ing by such a thin layer ( d I < . and Ta O , could of-fer wider range of tunable thickness to balance the requiredresistances and the contact qualities.For SiO , Al O and AlN contacts with d I > N D and d I [seein Fig. 2(b) and (d)]. The reason is that r ∗ b of these contactsare much larger than the spin resistance r N ( ≡ ρ N l Ns f ) of n-Si, D T D T (a) (b) (c) (d)E (eV) E (eV)T (K) c -c I S (eV) g g P TE P TE g Fig. 3. (a) ∆ T as a function of the electron transmission energy E , fordi ff erent tunnel contacts ( V A = . d I = T =
300 K). (b) Thesame as (a), but for Ta O contact with di ff erent d I . The black dash-dot,dashed, and dash-dot-dot lines depict ∆ f F ( E ) at 150, 300 and 450 K,respectively. (c) γ as a function of temperature T for di ff erent tunnelcontacts. (d) P TE and γ as a function of the tunnel barrier height χ I − χ S ( m ∗ I = m e and ǫ I = ǫ ), at di ff erent temperatures. resulting in SP to be saturated at SP = γ ≈ Forlow barriers tunnel contacts, the behaviour of SP versus N D and d I are very di ff erent. We observe the SP of TiO contacthas a negative value, namely, the polarization direction of in-jected spins in silicon is opposite to that in ferromagnet. Thisis because the minority spin in ferromagnet has a smaller k ↓ F (than k ↑ F ), which better matches the relatively small evanes-cent wave vector ( ∝ √ χ I − χ S − E ) inside the TiO barrier,leading to a larger T ↓ than T ↑ . Thus for TiO contact, J ↓ islarger than J ↑ , and a negative γ (or SP) is produced. In con-trast, for conventional barriers, like SiO , Al O and AlN, themajority spin matches the the evanescent wave vector better,which makes T ↑ larger than T ↓ , and γ (or SP) be positive.To demonstrate this, in Fig. 3(a) we plot the di ff erence oftransmission coe ffi cient of the two spin channels, i.e, ∆ T ≡ T ↑ − T ↓ , as a function of the electron transmission energy E . The black dashed line of this figure denotes the di ff er-ence of the Fermi-Dirac distribution functions, i.e., ∆ f F ( E ) ≡ f R ( E ) − f L ( E ), which determines the contribution of an elec-tron with energy E to the current. From ∆ f F ( E ), we can seethe e ff ective energy range is 0 < E < .
16 eV. For E out ofthis range, the contribution ∆ f F ( E ) falls below 10 − . Becausein this range, ∆ T of TiO is negative, γ has a negative value.While for other barriers (with d I = ∆ T in this range arepositive, so γ of them are positive too. Interestingly, we findthe γ (or SP) for Ta O can be tuned from positive to nega-tive by decreasing d I , as exhibited in Fig. 2(d). The reason forthe sign change of γ can be illustrated in Fig. 3(b): the posi-tive (negative) region of ∆ T shrinks (expands) with decreas-ing d I . Besides, by changing the temperature, the broadeningof ∆ f F ( E ) can be varied, resulting in γ for Ta O be moresensitively dependent on the temperature, compared to otherbarriers [see in Fig. 3(c)]. For a 0.5-nm-thick Ta O contact, γ can even be tuned from positive to negative by increasingtemperature. While for TiO , the γ shows a non-monotonicdependence of temperature. The reason can be ascribed to the (a) (b) (c) (d) d (nm) I d (nm) I N c m D () - N c m D () - Fig. 4.
Calculated MR ratio of a vertical spin MOSFET with symmetricFM / I / n-Si / I / FM structure as a function of d I and N D . (a)-(d) the results ofspin MOSFETs with Al O , AlN, Ta O and TiO barriers, respectively. t N =
100 nm and T =
300 K is assumed in the calculations. impact of thermionic emission transport, which is prominentin the low barrier contact. In Fig. 3(d), we plot the propor-tion of thermionic emission, i.e., P TE , and γ as a function ofthe tunnel barrier height χ I − χ S . At 300 K, we can see thethermionic emission takes place only for χ I − χ S < / or increasing temperature,the proportion of thermionic emission increases. Also, we cansee a crossover of γ from negative to positive by increasing thebarrier height, which is consistent with the preceding discus-sions, i.e., a low barrier contact could have a negative γ .The vertical spin MOSFET can be modeled as a structureconsisting of a symmetric FM / I / n-Si / I / FM multilayer
12, 16) [see the inset of Fig 1(a)], of which the two terminal MR ratiocan be calculated according to the analytical equations of Fertand Ja ff r`es. In Fig. 4, we present the results of the MR ratioof vertical spin MOSFETs with a moderate channel length,i.e., t N =
100 nm. From panel (a) to (d), we can compare theoptimum parameters windows for the MR ratio of spin MOS-FETs with Al O , AlN, Ta O and TiO barriers. For conven-tional barriers, such as Al O , AlN, a MR ratio >
2% usuallyrequires a heavy doping with N D > cm − , and an ul-trathin barrier with d I <
12, 13)
In contrast,the magnitude of MR ratio and the optimum window is muchlarger for TiO . With N D = × cm − (nondegenerate n-Si) and d I = ≈
4% can be obtained by usingTiO . For Ta O , the MR ratio might be suppressed in certainregions, such as d I in the range of 0.5 ∼ γ occurring in this region. But amoderate value of MR ratio ≈
2% can still be obtained at arelatively large barrier thickness d I = . ff er improved performance ofSi-based spintronic devices.In summary, we investigate theoretically the spin injectionin the FM / I / n-Si tunnel contacts. We find that r ∗ b of contactswith low barriers, such as TiO and Ta O , are orders of mag-nitude smaller than that of the conventional tunnel contacts.Therefore, the maximum MR signal and optimum parameters window for TiO and Ta O contacts are larger than the con-ventional tunnel contacts. Interestingly, we also demonstratethe spin asymmetry coe ffi cient γ of TiO contact has a neg-ative value, and γ of Ta O contact can be tuned from neg-ative to positive by changing the thickness of tunnel barrierand temperature. The optimized spin signals and unique spinasymmetry properties of low barrier tunnel contacts can beutilized for developing e ffi cient spintronic devices. Acknowledgments
This work was supported by the Natural Science Founda-tion of Fujian Province of China (Grant No.2016J05163) andthe Fundamental Research Funds for the Central Universities(Grant No. 20720160019). Zhenhua Wu was supported by theMOST of China (Grant No.2016YFA0202300). Yang Yangand Cheng Li was supported by the National Basic ResearchProgram of China (Grant No. 2013CB632103).
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