Defect gap states on III–V semiconductor–oxide interfaces (invited)

Microelectronic Engineering 88 (2011) 1440–1443

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Defect gap states on III–V semiconductor–oxide interfaces (invited) J. Robertson ⇑, L. Lin Engineering Department, University of Cambridge, Cambridge CB2 1PZ, UK

a r t i c l e

i n f o

Article history: Available online 9 April 2011 Keywords: GaAs Oxide Calculation Interface states Passivation FET

a b s t r a c t Interfaces models of (1 0 0)GaAs and various high K oxides such as HfO2, Gd2O3 or Al2O3 are used to study the interfacial defects and mis-bonded sites which can introduce states into the semiconductor gap, and cause the Fermi level pinning observed in FETs. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction The continued scaling of complementary metal oxide semiconductor (CMOS) logic devices will require the use of high mobility channels such as GaAs and other III–V semiconductors [1–8]. However, their interfaces are more difficult to passivate than those of Si and they give rise to Fermi level pinning, so that their MOSFETs can have poorer than expected performance. This is a continuation of a 35-year old problem, the nature of the interface states of GaAs, the poor quality of its native oxide, and the problem of its passivation [4,9–11]. Until recently, the development of GaAs field effect transistors (FETs) was desirable. However, now it has become critical. A breakthrough was the use of epitaxial gadolinium gallium oxide as the gate oxide [12,13]. The technological application now requires the use of amorphous oxides such as those produced by atomic layer deposition (ALD) [14–16]. There have been a series of studies of the interfaces and growth of ALD oxides on GaAs [17–21]. There have been some theoretical studies of the surfaces of GaAs, bare, oxidized and with absorbates [22–25]. Recently, this has been extended to studies of the oxide interfaces [26–28]. Electronic structure calculations are a valuable means to find the nature of such defects, and to correlate with experimental results such as in situ X-ray photoemission spectroscopy (XPS) and capacitance–voltage (CV) measurements [17–21]. The nature of the gap states of GaAs has been widely debated [2,9,10]. The Fermi level on the (1 1 0) non-polar surface of GaAs is unpinned, there are no states in the gap. After addition of an oxide layer on (1 0 0)GaAs, the interface quality correlates with the photoluminescence intensity [13]. This is evidence that the ⇑ Corresponding author. Tel.: +44 1223 748331. E-mail address: [email protected] (J. Robertson). 0167-9317/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2011.03.134

interface gap states arise from defects, not from metal induced gap states [9,29,30]. Hence, we study the chemical origin of gap states due to defect bonding configurations. We note that defect states arise from differences in local bonding [31], it does not require long range order. We can use periodic supercell models to represent defects at interfaces of amorphous oxides. Furthermore, we know that HfO2 and Al2O3 can have low defect densities, so the defects arise from the interface, or from changes to the semiconductor subsurface bonding due to the addition of the oxide. 2. Preliminaries We first construct defect-free models of the (1 0 0)GaAs–oxide interface. These must obey electron counting rules to be insulating (no bands crossing the Fermi level) [29]. This was previously done for the (1 0 0)Si:SrTiO3 interface and then for Si:HfO2. The difficulty there was the junction of the covalent bonding of the Si to the ionic bonding of the oxide. Insulating interfaces are possible if they obey electron-counting rules to give a locally closed shell electronic structure [32–34]. The ionic bonding is not a problem per se. Fig. 1a shows the simplest (1 0 0)Si:HfO2 interface geometry [33,34]. (Note that the Si and HfO2 lattices are roughly lattice matched on (1 0 0) if the HfO2 lattice is rotated by 45° compared to the Si. Similarly, the GaAs and HfO2 are roughly matched with the same rotation [35]). The difficulty for (1 0 0)GaAs:HfO2 lattices interfaces is the socalled polarity problem [36–38]. Whereas each sp3 hybrid orbital possesses 1 electron which it contributes to each 2-electron bond in Si–Si or Si–O bonds, in GaAs each Ga hybrid orbital contributes 3/4 electron and each As hybrid orbital contributes 5/4 electron. For a (1 1 0) non-polar surface with an equal number of Ga and

J. Robertson, L. Lin / Microelectronic Engineering 88 (2011) 1440–1443

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other hand, a starting layer of a trivalent oxide such as Al2O3 or Gd2O3 is possible, and would be a good passivant, as is found experimentally. Fig. 1d and e shows some typical interfaces. We use Sc rather than Ga in the models for charge compensation, as Sc is a transition metal like Hf, and it is computationally cheaper to use than Gd with its f electrons. 3. Calculational method

Fig. 1. (a) Ideal insulating (1 0 0)Si:HfO2 interface for reference. (b) Abrupt (1 0 0)GaAs:HfO2 interface (metallic). (c) Insulating interface with OAs substitutions. (d) Insulating interface with GaHf substitutions. (e) Insulating, abrupt (1 0 0)GaAs:Gd2O3 interface, (f) Ga-terminated GaAs:Al2O3 interface, (g) Al-terminated GaAs:Al2O3 interface.

As hybrids, this is not a problem. However, for a polar surface such as (1 0 0)GaAs, which is either Ga or As terminated, this leaves the two hybrids on each surface atom either 1/2 electron short or in excess of the Si case, and it cannot easily form a closed shell. Pashley [38] has emphasized how this is the underlying cause of the complex reconstructions that occur on GaAs surfaces [39–41], not the As excess, but the difficulties caused by polarity. Many of these reconstructions have lateral As–As dimer bonds, such as that shown in Fig. 1b. Fig. 1b shows an interface of Ga-terminated GaAs and O-terminated HfO2. Its Fermi level lies in the valence band, due to the lack of the necessary 1/2 electron. A possible way to solve this problem and make an insulating interface is to use a 2  1 cells and substitute OAs sites at 50% of the sub-interfacial As layers to obtain the correct electron count (Fig. 1c). An alternative is to substitute 50% of the Hf atoms with GaHf, which again gives an insulating interface (Fig. 1d). This is confirmed by direct calculation, there are no gap states and Ef lies in the gap. These models are the basic insulating interface, into which we can add defects as desired. It is very interesting that we can construct interfaces of (1 0 0)GaAs with trivalent oxides like Gd2O3, Sc2O3 or Al2O3 without need for compensating sites to give an insulating interface, see Fig. 1e. In each layer, 2Ga + 2As has a similar charge as 2 Gd + 3 O. Fig. 1f and g shows similar insulating interfaces for Al2O3, either Ga terminated GaAs, or with a last layer of Al on the GaAs. Experimentally, the use of substitutional OGa of GaHf atoms is not so convenient because it is not in the top monolayer. On the

Supercells of the interfaces are constructed, with the various defects introduced. We choose cells with two interfaces and no vacuum layer. To introduce a As–As bond, the Al2O3 lattice is displaced by 1/4 a(1 0 0) at the As level. This converts these As sites from four to threefold. They can then be dimerized laterally. Similar displacements can be used to create Ga DBs or As DBs. Sometimes the nearby O sites must be shifted to terminate other defects. Then the number of compensating Sc to Hf atoms is varied to maintain the desired number occupancy of the defect level to 1 electron and to ensure that all other sites would be saturated. The supercells are relaxed by the plane wave pseudopotential code CASTEP [42]. The electron exchange–correlation energy is treated by the generalized gradient approximation. The supercell volume is constrained to be constant with 90° cell angles. On the other hand, we can constrain the x- or y-axis length to the ideal GaAs value if desired, to test the effect of mismatch strain. (1 0 0)GaAs and cubic HfO2 have 10% lattice mismatch, while GaAs and Gd2O3 have 4% mismatch. We note that Wang et al. [27] used cells with good lattice matching between GaAs and HfO2 layers by a slight rotation of their lattices, however this introduced extra defects in their starting structures, which is avoided if a simple ‘chemical’ match is used [26]. The size of the supercells needs consideration. The low conduction band effective mass of GaAs means that if the GaAs slab is too short, the band gap opens up due to quantum confinement. This can be helpful to correct the under-estimate of the band gap by the GGA method. Interestingly, the defects give rise to ‘deep’ or localized states which can be in the gap or resonant with the bands. As their states are drawn from many bands, they largely retain their energetic positions and order, as the band gap changes due to quantum confinement, the same effect is found when the band gap is corrected by other methods [43]. The key thing is that deep states will maintain their order with respect to each other. The band edges may not shift exactly the same as in the GGA to hybrid or the quantum confined cases, but this can be allowed for. Thus, it is preferable to use a large supercell of typically 15 GaAs layers, but a shorter one can also work. 4. Results and discussion Fig. 1c–g shows various insulating supercells, before the introduction of defects. Fig. 2a, c–g shows cells with various defects introduced. From chemical bonding arguments, we expect that As–As bonds, Ga–Ga bonds, Ga dangling bonds and As dangling bonds to be possible sources of defect gap states. On the other hand, the XPS work suggests that we also test As and Ga sites with different degrees of oxidation. We find that As–As dimer bonds give rise to a localized gap states in the upper gap (Fig. 3a). This is an antibonding (r⁄) state, as seen by the charge density map (Fig. 2b). The As dangling bond (DB) gives rise to a state just below the GaAs valence band top. The As site relaxes towards a more pyramidal geometry with bond angles closer to 97° which lowers the state out of the gap. The Ga dangling bond gives rise to an empty state which can lie either in the low GaAs conduction band (CB) or just in the top of the gap, depending on its geometry and occupancy.

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(a)

3

Ga in bulk GaAs As-As σ∗

As in bulk GaAs

PDOS

2 As-As

1 O in Al2O3 Al in Al2O3

0 -3

Energy (eV)

(b)

-2

-1

0 1 Energy (eV)

(c)

4

InAs

InP

O in Ga 1+

4

The Ga site relaxes towards a planar configuration when its DB is empty, and this relaxation raises the state into the CB, Fig. 3a. The shifts are large, and were tested on the (1 1 0) surface. We find that if the interface bonding allows the relaxation to occur, then there is no gap state, as do others [44,45]. On the other hand, if there is some constraint on how much this threefold Ga site can relax towards planar, or if the DB is singly occupied, then the DBs do give gap states. This may be why Komsa and Pasquarello [46] finds gap states. Wang et al. [27] proposes that the deeper gap state is due to As–As antibonds, while a state above this is due to Ga dangling bonds. We have also studied the chemical trends of these states, changing the III–V material from GaAs to InAs or InP, and aligning the resulting bands. Note that the valence bands of GaAs and InAs are aligned whereas the conduction band lowers from GaAs to InAs. We find that the As–As r⁄ state moves into the conduction band for InAs. The analogous P–P r⁄ state also lies in the conduction band in InP (Fig. 3b) because the P–P bond has a larger bonding–antibonding splitting. This is the same chemical trend as was found for like-atom bonds in the amorphous III–V semiconductors [47]. Xuan et al. [48] have observed that n-FETs based on (1 0 0)GaAs have poor mutual conductance, whereas those of InGaAs improve with increasing In content. InP n-FETs also have good mutual conductance values. This was related by Ye [49] to the proportionately

3

2 Ga DB 1.8 1.6 CB 1.4 As-As σ∗ 1.2 1 0.8 0.6 CNL 0.4 0.2 0 VB -0.2 GaAs

Ga 1+ PDOS

Fig. 2. (a) An As–As dimer bond at the GaAs:HfO2 interface. (b) Charge density of the r⁄ state. (c) Lateral Ga–Ga bond, (d and e) Ga, As dangling bond sites at interface. (f and g) Ga+ and As+ oxide configurations. (h) The reconstructed GaAs(1 1 1)A surface, with no As–As bonds.

2

2

O in As 1+ As 1+ 0 -3

-2

-1

0 1 Energy(eV)

2

3

4

Fig. 3. (a) Partial density of states (PDOS) of As atoms at a As–As bond. (b) Chemical trends of the energy levels of As–As r⁄ states, Ga dangling bonds and the charge neutrality level (CNL) for GaAs, InAs and InP. (c) Partial DOS at Ga and O sites of a Ga–O bond and As and O sites of a As–O bond, showing no gap states.

higher charge neutrality level in InGaAs which kept defects out of the gap. Our results suggest a better explanation in terms of defects. It suggests that n-FET performance correlates with whether interface states fall below the semiconductor conduction band edge or not. Additionally, Ga-rich interfaces appear to have better performance in one study [50]. The reconstructed b4  2(1 0 0)GaAs surface also possesses As– As dimers [39]. Why do these states lie outside the gap, whereas they lie inside the gap for the GaAs–oxide interfaces? The reason is that the surface As sites are threefold coordinated and p-bonded, whereas the As interface sites are fourfold coordinated and sp3 due to an extra bond to the oxide. This change in hybridization lowers the r⁄ state into the gap (Fig. 4).

J. Robertson, L. Lin / Microelectronic Engineering 88 (2011) 1440–1443

Ga

As

As-As pσ∗

p Ga sp3

As-As sp3 σ∗

p s

CB

As sp3

VB

s Fig. 4. Showing how change from threefold p-bonded to fourfold sp3 bonded As sites brings the As–As r⁄ state down into the band gap.

Xu et al. [51,52] found that FETs on the Ga-terminated A(1 1 1)GaAs face had good performance. This initial polar face has 25% Gas vacancies to make in non-polar, and crucially it has no As–As bonds [53,54] (Fig. 2h). These chemical trends suggest that As–As dimers are a likely cause of gap states. The AsGa antisite also contains As–As bonds and gives gap states [55]. This might be the source of midgap states seen in some CV data. Interestingly, we find that the nature of the gap states does not depend much on the nature of the covering oxide, whether it is HfO2 or Gd2O3 or Al2O3. This is consistent with the arguments about local chemistry. The in situ XPS spectra are a very useful source of data, because they give specific chemical information. However, they only give core level data, they do not give information on the gap states themselves, which comes better from CV data [56,57]. We must rely on indirect correlations for this. There is some evidence that the presence of As–As states in the As core level does correlate with worse CV plots, as discussed by Wang et al. [58]. There is also evidence of Ga suboxides correlating with worse CV characteristics. 5. Conclusion Defects at GaAs–oxide interfaces are calculated and correlated to FET performance. As–As antibonding states give rise to gap states. Ga dangling can also give gap states in some cases. References [1] R. Chau, B. Doyle, S. Datta, J. Kavalieros, K. Zhang, Nat. Mater. 6 (2007) 810. [2] H. Hasegawa et al., J. Vac. Sci. Technol., B 5 (1987) 1097. [3] M. Hong, J.R. Kwo, P. Tsai, Y. Chang, M.L. Huang, Jpn. J. Appl. Phys. 46 (2007) 3167. [4] K. Hudait, S. Datta, G. Dewey, R. Chau, Tech. Digest. IEDM, 2007, p. 23.5. [5] R.J.W. Hill, D.A.J. Moran, X. Li, H. Zhou, D. Macintyre, S. Thomas, A. Asenov, P. Zurcher, K. Rajagopalan, J. Abrokwah, R. Droopad, M. Passlack, I.G. Thayne, IEEE ED Lett. 28 (2007) 1080. [6] Y. Xuan, Y.Q. Wu, P. Ye, IEEE ED Lett. 29 (2008) 294. [7] T.D. Lin, H.C. Chiu, P. Chang, L.T. Tung, C.P. Chen, M. Hong, J. Kwo, W. Tsai, Y.C. Wang, Appl. Phys. Lett. 93 (2008) 033516. [8] M. Radosavljevic, B.C. Kung, S. Corcaran, G. Dewey, M.K. Kudait, J.M. Fastenau, J. Kavaleros, W.K. Liu, D. Lubyshev, M. Metz, K. Millard, N. Mukerjee, W. Rachmady, U. Shah, R. Chau, Tech. Digest. IEDM (IEEE), 2009, p. 13.1. [9] W. Monch, Phys. Rev. Lett. 58 (1987) 1260.

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