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oxide interfaces
Microelectronic Engineering 88 (2011) 383–387
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Experimental and theoretical investigation of defects at (1 0 0) Si1 xGex/oxide interfaces M. Houssa a,⇑, G. Pourtois b, M. Meuris b, M.M. Heyns b,c, V.V. Afanas’ev a, A. Stesmans a a
Semiconductor Physics Laboratory, Department of Physics and Astronomy, University of Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium IMEC, 75 Kapeldreef, B-3001 Leuven, Belgium c Department of Metallurgy and Materials Engineering, University of Leuven, Belgium b
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Article history: Available online 7 September 2010 Keywords: Semiconductor/oxide interfaces MOS structures Defects ESR Electrical characterization First-principles modeling
a b s t r a c t The identification of a nontrigonal Ge dangling bond at SiO2/Si1 xGex/SiO2 heterostructures and its electrical activity are discussed, both from experimental and theoretical points of view. This dangling bond is observed from multifrequency electron-spin resonance experiments performed at 4.2 K, for typical Ge concentrations in the range 0.4 6 x 6 0.85. The electrical activity of this defect is revealed from capacitance–voltage characteristics measured at 300 and 77 K, and is found to behave like an acceptor defect. First-principles calculations of the electronic properties of this Ge dangling bond indicate that its energy level approaches the valence band edge of the Si1 xGex layer as the Ge content increases, confirming its acceptor-like nature. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction An important research effort is currently devoted to the investigation of high-mobility semiconductors for their potential applications in future high performance metal–oxide-semiconductor (MOS) devices [1–4]. In particular, the use of Ge and Ge-rich Si1 xGex alloys as channel materials is promising for the improvement of the electrical performances of these devices, due to their high electron and hole mobilities, which together with their lower processing temperatures (as compared to Si-devices), potentially enables their integration with high-j gate dielectrics. A major issue related to high-mobility semiconductors is the presence of a large density of defects at/near their interfaces with gate insulators, lying in the 1012–1013 defects/cm2 range [5–7], which hampers the electrical properties of MOS devices. In particular, Si1 xGex layers exhibit an increasing density of negative charges with increasing amount of Ge [8,9], suggesting the presence of acceptor-like defects, still not yet identified. As far as the Ge/oxide interface is concerned, recent progress has been achieved regarding the passivation of Ge by its thermal oxide [10–12], a key issue being to prevent the desorption of the GeO2 layer during its growth and the subsequent MOS transistor processing [13]. However, the fabrication of high-performance n-channel devices is still very challenging, especially with reduced equivalent oxide thickness [14], due to the reduced electron mobility achieved at ⇑ Corresponding author. Tel.: +32 16 32 72 91. E-mail address: [email protected] (M. Houssa). 0167-9317/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2010.09.001
Ge/oxide interface, pointing towards the possible presence of a high density of defects in the upper part of the Ge band-gap. In this paper, we review our recent experimental and theoretical findings regarding the characterization of defects at Si1 xGex/ oxide interfaces, emphasizing the identification of a specific interfacial Ge dangling bond and its electrical activity [15–17]. The paper is organized as follows. Experimental and theoretical details are given in Sections 2 and 3, respectively. Results are presented and discussed in Section 4, and conclusions are drawn in Section 5. 2. Experimental details The (1 0 0)Si1 xGex/oxide heterostructures investigated in this work were obtained through the condensation grown technique, which implies a three step process [8,9,18]. One first grows and epitaxial layer of Si0.73Ge0.27 layer on a SOI (silicon on insulator) substrate wafer. This is followed by the deposition of a very thin (6 nm) epi-Si layer which prevents any Ge oxidation at the early stage of the thermal condensation process. Subsequent application to multi-step dry oxidation/inert ambient annealing at temperatures ranging between 900 and 1150 °C results in the formation of Si/SiO2/Si1 xGex/SiO2 heterostructure with Ge-enriched Si1 xGex layers, with typical Ge fraction x in the range 0.45–0.93 [9]. The thermal budgets used during the growth of the heterostructure are lying well above the thermal stability of GeO2, such that SiO2 is the only oxide formed at the Si1 xGex interfaces. The identification of dangling bonds at the SiO2/(1 0 0)Si1 xGex/ SiO2 interfaces was achieved by performing first harmonic
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multifrequency (X, K and Q bands) electron-spin resonance (ESR) experiments at 4.2 K [15]. Field angular-dependent measurements were carried out for the applied magnetic field B rotating in the (0 1 1) plane of the sample. A co-mounted Si:P marker sample [g(4.2 K) = 1.99869] was used for the accurate g value and defect density determination purposes. The density of electrically active defects at the Si1 xGex/SiO2 interface was extracted from capacitance–voltage (C–V) measurements performed on MOS capacitors at 300 and 77 K [16]. The structures were formed by evaporating Au contacts on the top SiO2 layer (TOX) and the Si1 xGex layer was electrically connected to the bottom Si substrate using In Ga eutectic alloy. When the Si1 xGex layer is under accumulation, the measured capacitance corresponds to that of TOX, defined as CTOx. When the thin SiGe layer is fully depleted (typically between 10 and 20 V at 77 K), the capacitance decreases and present a typical threshold voltage VT which is used to extract the interface charge Qit as Qit = VTCTOx [16]. 3. Theoretical details First-principles calculations were performed on (1 0 0)Si1 xGex/ SiO2 slabs, using density functional theory (DFT) within the local density approximation (LDA) for the exchange–correlation functional [19]. We used a numerical atomic basis approximation as implemented in the SIESTA code [20], with localized atomic orbitals. The core electrons were implicitly treated by using norm-conserving pseudopotentials [21], including relativistic corrections, with the following electronic configuration of the elements: H 1s1, O (1s2) 2s2 2p4, Si (Ne) 3s2 3p2, and Ge (Ar 3d10) 4s2 4p2, where the core configurations are shown in parenthesis. Similarly to our recent works [22], a repulsive potential with a Gaussian shape, strongly localized on the nucleus, was included during the generation of the Si and Ge pseudopotentials to account for the correction of Darwin shifts [23]. This approach allows one to compute energy band gaps for Si and Ge which are in much better agreement with experimental values (especially for the case of Ge, since the calculated band gap using standard LDA is almost 0 eV), as further discussed below. Note that the pseudopotentials were carefully generated to avoid any artificial crossing of the symmetry points in the conduction band induced by the application of the additional potential [23], assuring that the minimum of the conduction band is located at the X point for Si and at the L point for Ge. The basis sets and pseudopotentials were first tested on bulk relaxed Si1 xGex structures, using a supercell with 8 atoms; computations performed on larger supercells (up to 64 atoms) gave typically the same results. A plane wave cutoff of 120 Ry and a (4 4 4) k point mesh were used for the computations, allowing convergence of the total energy of the systems below typically 10 meV. The atomic structure optimization was carried out by relaxing the forces on all the atoms until a 0.05 eV/Å force tolerance was reached, using a conjugate gradient method. 4. Results and discussion K-band ESR spectra of SiO2/Si1 xGex/SiO2 structures with varying Ge contents (x) are shown in Fig. 1(a), for the applied magnetic field B II n ([1 0 0] sample normal) [15]. For the range 0.54 6 x 6 0.73, a prominent signal is observed at gc = 2.0140 ± 0.0003 with peak-to-peak derivative width DBpp of about 23 G. Apart from a weak isotropic EX center signal at gc = 2.00246, corresponding to an SiO2 defect [24], no other interfering signal is observed, enabling reliable spectral analysis. Angular variation for B rotating in the (0 1 1) plane reveals an anisotropic signal splitting into three in a closely 1:2:1 intensity
Fig. 1. (a) First derivate-absorption K-band spectra of the Ge dangling bond signal observed for B II n ([1 0 0] interface normal] on SiO2/Si1 xGex/SiO2 heterostructures with different Ge fraction x. The signal at g = 1.99869 corresponds to the one from the co-mounted Si:P marker. (b) X-band ESR spectra measured for various angles of B with n on the sample with x = 0.7.
ratio (in sequence of gc), a shown in Fig. 1(b). Angular mapping resulted in the consistent three-branch g map shown in Fig. 2. Computer simulations of this g-map revealed a defect with C2v (monoclinic) symmetry and principal g-values g1 = 2.0338 ± 0.0003, g2 = 2.0386 ± 0.0006 and g3 = 2.0054 ± 0.0001, with the lowest value g3 direction 24 ± 2° off a <1 1 1> direction towards n in the (0 1 1) plane, i.e. 31 ± 2° off the [1 0 0] direction. Only three branches out of the seven expected for all equivalent defect orientations in a bulk (Si or Ge) diamond type crystal are observed, indicating the interfacial nature of the defect. Note the g-values of this specific defect are different from those of a Ge dangling bond recently observed at Ge/GeO2 interfaces, using electrically detected magnetic resonance [25]. This defect is tentatively attributed to a Ge dangling bond at the Si1 xGex/SiO2 interface, backbonded to Si and/or Ge atoms (the number of Si and Ge backbonds being still unknown), as sketched in Fig. 3. Very interestingly, the orientation of the Ge dangling orbital and the defect symmetry are very similar to those pertaining to the Si Pb1 defect present at (1 0 0)Si/SiO2 interfaces; the identified Ge dangling bond defect is thus labeled as Ge Pb1. Recent first-principles calculations of the g-tensors of Ge Pb1 defects at Si1 xGex surfaces within density functional theory [26] are in excellent agreement with the experimental values given above for the SiO2/Si1 xGex/SiO2 heterostructures, confirming the Pb1-like nature of this Ge interfacial defect. The capacitance–voltage curves of similar SiO2/Si1 xGex/SiO2 heterostructures present a shift of the threshold voltage VT towards
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Fig. 2. Angular g map of Ge Pb1 signals observed at different frequencies on a SiO2/ Si0.27Ge0.73/SiO2 structure for B rotating in the (0 1 1) plane. Data obtained at 8.9, 20.3 and 34 GHz are shown by stars, filled squares and open circles, respectively. The solid lines represent the fitting results for a monoclinic point symmetry defect in a diamond crystal. The dashed branches are not observed experimentally.
Fig. 4. (a) Charge density determined from the C–V curve shifts at 300 K (open circles) and 77 K (open squares) for the as-grown SiO2/Si1 xGex/SiO2 heterostructures as a function of the Ge fraction x. The data measured on the sample after H2 anneal at 500 °C during 30 min correspond to the triangles. (b) Density of Ge Pb1 defects extracted from ESR experiments. The vertical arrow indicates the effect of the passivating anneal in H2.
Fig. 3. Schematic illustration of a Ge Pb1 dangling bond at the Si1 xGex interface.
larger positive voltages with increasing Ge content (results not shown) [16], indicating the buildup of negative charges. Comparison between the 77 and 300 K C–V curves indicates that these defects are interface traps (so called Grey–Brown shift) [16], behaving like acceptor defects. The density of negative charges extracted from the C–V curves and the density of Ge Pb1 defects estimated from ESR experiments on samples with different Ge content are compared in Fig. 4(a) and (b), respectively. One clearly observes that both defect densities are very similar and present the same behavior as a function of the Ge content. The defects are observed for x P 0.4, present a maximum for x 0.7 and drops at larger Ge content, being not detected for x P 0.85. In addition, both defect densities appear to be much reduced after annealing the heterostructures in H2 at 500 °C during 30 min, as shown in Fig 4(a) and (b), demonstrating the efficient passivation of the Ge Pb1 dangling bond by hydrogen. Note that the electrical measurements sense (negatively) charged defects, while ESR only measures the neutral (paramagnetic) state of the Ge dangling bond. The agreement between the electrical and ESR data suggest that the defect occupancy changes from 300 to 4.2 K, being doubly occupied and negatively charged at 300 K and singly occupied and neutral at 4.2 K, as a result of the Fermi level shift with decreasing temperature, confirming that these defects are interface traps.
The dependence of the defect density with the Ge content is not completely understood. First of all, a certain fraction of Ge (about 40%) is required in the Si1 xGex layer for the defect to be observed. This indicates that the Ge dangling bond is backbonded to at least one Ge atom. On the other hand, the disappearance of the Ge Pb1 signal at high (85–90%) Ge concentration indicates that the presence of Si in the layer is necessary for the generation of this defect – Si atoms possibly enhancing the strain in the layer, the strain being most likely relaxed for large Ge concentrations. By comparing the electrical and ESR data, one can reasonably assume that the Ge Pb1 centers are acceptor-like defects, in contrast to Si dangling bonds at the (1 0 0)Si/SiO2 interface, which are known to be amphoteric defects [27]. To gain further insight, we performed a theoretical study of the electronic properties of (1 0 0)Si1 xGex/SiO2 structures, with a Ge dangling bond at the interface, using DFT, as further discussed below [17]. The calculated lattice parameter of the bulk relaxed Si1 xGex structures are shown in Fig. 5(a) as a function of the Si content. The calculated lattice parameter for bulk Ge and bulk Si is 5.58 and 5.37 Å, respectively; these values are typically 1% smaller than the experimental values. An almost linear decrease of the calculated lattice parameter with increasing Si content is observed, in very good agreement with experimental results reported on relaxed Si1 xGex alloys [28]; the latter experimental values are also shown in Fig. 5(a) for comparison. The evolution of the computed energy band gaps versus the Si content for the relaxed Si1 xGex structures is depicted in Fig. 5(b). The corresponding values computed for Ge (x = 1) and Si (x = 0) are 0.62 and 1.05 eV, respectively; the latter are typically
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Fig. 5. (a) Calculated lattice parameter of bulk relaxed Si1 xGex structures as a function of the Si content. The experimental data from Ref. [28] are also shown for comparison. Dashed lines are linear fits to the data. (b) Calculated energy band gap of bulk relaxed Si1 xGex structures vs. Si content. Dashed line and solid curve are linear and second-order polynomial fits to the calculated values, respectively. Experimental energy band gaps of relaxed Si1 xGex alloys measured at 4.2 K from Ref. [29] are shown for comparison. The dotted line corresponds to the simulated energy gap, shifted upward by 0.18 eV.
underestimated by about 10 to 15% with respect to the experimental ones obtained at 4.2 K. Most importantly, the dependence of the calculated energy gap on the Si content is very similar to what has been reported experimentally on relaxed Si1 xGex alloys [29], as shown in Fig. 5(b). Two distinct regimes can be observed: at low Si concentration (between 0% and 15%), the energy band gap increases linearly with the Si content. In this case, the minimum of the conduction band is located at the L point, characteristic of Ge. For higher Si concentration, a crossover in the conduction band minimum is observed from the L to X point, characteristic of Si-rich alloys [30]. Attendantly, the energy band gap of the Si1 xGex alloys increases with the Si content according to a second order-polynomial, consistent with the experimental results [29]. We point out that the use of the corrected pseudopotentials for Si and Ge leads to computed Si–O and Ge–O bond lengths of 1.62 and 1.78 Å in bulk SiO2 and GeO2 (a-quartz phases), respectively, which are typically 1% to 2% larger than experimental values. However, the computed energy gaps of bulk SiO2 (5.1 eV) and GeO2 (2.8 eV) are typically 40% smaller than experimental values, i.e. the presence of a repulsive potential centered on the Si and Ge nucleus does not improve the energy gap of their oxides.
We next investigate the electronic properties of the Ge dangling bonds at the (1 0 0)Si1 xGex/SiO2 interfaces. The modeled structure consists of 17 slabs of Si1 xGex layers (about 22.5 Å thick, whose bottom slab has been passivated by H atoms), a 3.2 Å thick SiGeOy (y < 2) transition region (where the Si or Ge atoms are in sub + 4 oxidation states), a 7.5 Å SiO2 layer (where the Si atoms are in + 4 oxidation state) and about 15 Å of vacuum, as illustrated in Fig. 6(a) for x 0.6. These slabs were generated from a reference Si/SiO2 interface model with SiO2 in tridymite form [31]. The fraction of Si or Ge atoms in sub + 4 oxidation states in the SiGeOy transition layer is consistent with X-ray photoemission spectroscopy data on Si/SiO2 [31] and Ge/GeO2 interfaces [32], respectively. It should be noted that the Si–O bond length decreases from the interface (1.67 Å) to the top surface (1.62 Å), in agreement with previously reported results on similar Si/SiO2 interface models [31]; this behavior is related to the reduced ionic charge on the Si atoms in lower oxidation states, resulting in a slight elongation of the Si–O bond. In addition, consistently with molecular dynamic simulations of Si1 xGex slabs [33], which predict the segregation of Ge at the surface, the concentration of Ge atoms at the Si1 xGex/ SiO2 interface lies typically between 75% and 100%. The lattice parameter of the Si1 xGex slab is fixed at the computed value for the corresponding bulk relaxed structure. A plane wave cutoff of 200 Ry and a (4 4 1) k point mesh are used for the computations. The artifacts due to the periodic cell-to-cell induced polarization on both the total energy and atomic forces are corrected by the implementation of a self-consistent dipole correction. A Ge dangling bond was generated at the (1 0 0)Si1 xGex/SiO2 interface by removing a bridging oxygen atom. Consistent with the proposed defect symmetry inferred from ESR experiments discussed above, the ‘‘constructed” Ge dangling bond resides on a strained dimer at the interface, as shown in Fig. 6(b). Depending on the Si concentration considered, the number of Si-backbonds varies between 1 (Ge-rich alloy) and 3 (Si-rich alloy). The calculated defect level associated to the neutral (unpaired) Ge dangling bond at the (1 0 0)Si1 xGex/SiO2 interface is shown in Fig. 7, as a function of the Si content; the position of the valence band (VB) and conduction band (CB) edges of the Si1 xGex slab are also shown, all the energies being relative to the valence band
Fig. 6. (a) Atomic configuration of the relaxed (1 0 0)Si1 xGex/SiO2 slab model (x 0.6). In (b), a bridging oxygen atom is removed at the interface, producing a Ge dangling bond residing on a Ge–Ge dimmer (Pb1-like Ge dangling bond), indicated by the dashed circle.
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the interfacial stress for Ge-rich layers (Ge being a softer material than Si), considering that the dangling bonds are formed to accommodate the stress present at the semiconductor/oxide interface. Finally, since ESR and electrical data indicate the possibility to reduce the density of these Ge dangling bonds by annealing the SiO2/Si1 xGex/SiO2 heterostructures in molecular hydrogen, we anticipate that their degrading effect on the electrical performances of MOS devices could be (at least partially) reduced by a proper hydrogen passivation. Acknowledgements Part of this work has been financially supported by the FWO (Fonds voor Wetenschappelijk Onderzoek) project G.0628.09. References Fig. 7. Calculated energy level of the Ge Pb1-like defect at the (1 0 0)Si1 xGex/SiO2 interface as a function of the Si content. The calculated valence band (VB) and conduction band (CB) edges are also shown; the valence band edge of the pure Ge slab (x = 1) is taken as reference (zero energy).
edge of the pure Ge slab; note that the energy band gap of the Si1 xGex slab is typically 0.2 eV higher than for the bulk structure, cf. Fig. 5(b), due to quantum confinement effects induced by the finite thickness of the Si1 xGex slabs used. Interestingly, the CB edge is almost independent of the Si content, while the VB edge decreases (relative to the pure Ge slab) with increasing Si content, reflecting the corresponding raise in the energy band gap of the Si1 xGex alloy, cf. Fig. 5(b). One also notices that the position of the defect level corresponding to the Ge dangling bond slightly increases with the Si content (by about 0.1 eV from Ge rich to Si-rich slabs). It thus appears that the dangling bond level approaches the VB edge of the Si1 xGex slab as the Si concentration decreases, mainly due to the narrowing of the energy band gap of the alloy. We point out that these results are consistent with recently reported first-principles calculations of the neutral Ge dangling bond level in bulk Ge, lying close (0.1 to 0.2 eV) to the VB edge [34]. From an electrical point of view, one can thus reasonably assume that the Pb1-like Ge dangling bond behaves as an acceptor-like defect at Ge-rich (1 0 0)Si1 xGex/SiO2 interfaces. Note that recent experimental results [35] indicate a larger shift of the VB edge with decreasing x (by about 0.5 eV from pure Ge to pure Si) than the one predicted from our simulations (about 0.3 eV), which may be related to residual compressive strain (of the order of 1%) in the Si1 xGex layer [35]. This larger shift of the VB edge would bring the neutral Ge dangling bond level even closer to the VB, or eventually within the valence band for a Ge content above 80%, further accentuating its acceptor-like character. 5. Conclusions A nontrigonal Ge dangling bond in SiO2/Si1 xGex/SiO2 heterostructures grown from the condensation technique has been revealed from ESR experiments, for Ge content 0.4 6 x 6 0.85. The orientation of the Ge dangling orbital indicate that this defect is similar to the Pb1 defect observed at (1 0 0)Si/SiO2 interfaces, and most likely corresponds to a dangling bond at a strained Ge dimer, backbonded to Si and Ge atoms. The electrical activity of this Ge dangling bond has been assessed by C–V measurements performed at 300 and 77 K, suggesting that this defect behaves like an acceptor. First-principles calculations of the electronic properties of this Ge dangling bond predict that its energy level approaches the valence band edge of the Si1 xGex layer as the Ge content increases, confirming its acceptor-like nature. The disappearance of this defect at large Ge concentration is not yet understood. A possible explanation would be the reduction of
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Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Experimental and theoretical investigation of defects at (1 0 0) Si1 xGex/oxide interfaces M. Houssa a,⇑, G. Pourtois b, M. Meuris b, M.M. Heyns b,c, V.V. Afanas’ev a, A. Stesmans a a
Semiconductor Physics Laboratory, Department of Physics and Astronomy, University of Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium IMEC, 75 Kapeldreef, B-3001 Leuven, Belgium c Department of Metallurgy and Materials Engineering, University of Leuven, Belgium b
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Article history: Available online 7 September 2010 Keywords: Semiconductor/oxide interfaces MOS structures Defects ESR Electrical characterization First-principles modeling
a b s t r a c t The identification of a nontrigonal Ge dangling bond at SiO2/Si1 xGex/SiO2 heterostructures and its electrical activity are discussed, both from experimental and theoretical points of view. This dangling bond is observed from multifrequency electron-spin resonance experiments performed at 4.2 K, for typical Ge concentrations in the range 0.4 6 x 6 0.85. The electrical activity of this defect is revealed from capacitance–voltage characteristics measured at 300 and 77 K, and is found to behave like an acceptor defect. First-principles calculations of the electronic properties of this Ge dangling bond indicate that its energy level approaches the valence band edge of the Si1 xGex layer as the Ge content increases, confirming its acceptor-like nature. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction An important research effort is currently devoted to the investigation of high-mobility semiconductors for their potential applications in future high performance metal–oxide-semiconductor (MOS) devices [1–4]. In particular, the use of Ge and Ge-rich Si1 xGex alloys as channel materials is promising for the improvement of the electrical performances of these devices, due to their high electron and hole mobilities, which together with their lower processing temperatures (as compared to Si-devices), potentially enables their integration with high-j gate dielectrics. A major issue related to high-mobility semiconductors is the presence of a large density of defects at/near their interfaces with gate insulators, lying in the 1012–1013 defects/cm2 range [5–7], which hampers the electrical properties of MOS devices. In particular, Si1 xGex layers exhibit an increasing density of negative charges with increasing amount of Ge [8,9], suggesting the presence of acceptor-like defects, still not yet identified. As far as the Ge/oxide interface is concerned, recent progress has been achieved regarding the passivation of Ge by its thermal oxide [10–12], a key issue being to prevent the desorption of the GeO2 layer during its growth and the subsequent MOS transistor processing [13]. However, the fabrication of high-performance n-channel devices is still very challenging, especially with reduced equivalent oxide thickness [14], due to the reduced electron mobility achieved at ⇑ Corresponding author. Tel.: +32 16 32 72 91. E-mail address: [email protected] (M. Houssa). 0167-9317/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2010.09.001
Ge/oxide interface, pointing towards the possible presence of a high density of defects in the upper part of the Ge band-gap. In this paper, we review our recent experimental and theoretical findings regarding the characterization of defects at Si1 xGex/ oxide interfaces, emphasizing the identification of a specific interfacial Ge dangling bond and its electrical activity [15–17]. The paper is organized as follows. Experimental and theoretical details are given in Sections 2 and 3, respectively. Results are presented and discussed in Section 4, and conclusions are drawn in Section 5. 2. Experimental details The (1 0 0)Si1 xGex/oxide heterostructures investigated in this work were obtained through the condensation grown technique, which implies a three step process [8,9,18]. One first grows and epitaxial layer of Si0.73Ge0.27 layer on a SOI (silicon on insulator) substrate wafer. This is followed by the deposition of a very thin (6 nm) epi-Si layer which prevents any Ge oxidation at the early stage of the thermal condensation process. Subsequent application to multi-step dry oxidation/inert ambient annealing at temperatures ranging between 900 and 1150 °C results in the formation of Si/SiO2/Si1 xGex/SiO2 heterostructure with Ge-enriched Si1 xGex layers, with typical Ge fraction x in the range 0.45–0.93 [9]. The thermal budgets used during the growth of the heterostructure are lying well above the thermal stability of GeO2, such that SiO2 is the only oxide formed at the Si1 xGex interfaces. The identification of dangling bonds at the SiO2/(1 0 0)Si1 xGex/ SiO2 interfaces was achieved by performing first harmonic
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multifrequency (X, K and Q bands) electron-spin resonance (ESR) experiments at 4.2 K [15]. Field angular-dependent measurements were carried out for the applied magnetic field B rotating in the (0 1 1) plane of the sample. A co-mounted Si:P marker sample [g(4.2 K) = 1.99869] was used for the accurate g value and defect density determination purposes. The density of electrically active defects at the Si1 xGex/SiO2 interface was extracted from capacitance–voltage (C–V) measurements performed on MOS capacitors at 300 and 77 K [16]. The structures were formed by evaporating Au contacts on the top SiO2 layer (TOX) and the Si1 xGex layer was electrically connected to the bottom Si substrate using In Ga eutectic alloy. When the Si1 xGex layer is under accumulation, the measured capacitance corresponds to that of TOX, defined as CTOx. When the thin SiGe layer is fully depleted (typically between 10 and 20 V at 77 K), the capacitance decreases and present a typical threshold voltage VT which is used to extract the interface charge Qit as Qit = VTCTOx [16]. 3. Theoretical details First-principles calculations were performed on (1 0 0)Si1 xGex/ SiO2 slabs, using density functional theory (DFT) within the local density approximation (LDA) for the exchange–correlation functional [19]. We used a numerical atomic basis approximation as implemented in the SIESTA code [20], with localized atomic orbitals. The core electrons were implicitly treated by using norm-conserving pseudopotentials [21], including relativistic corrections, with the following electronic configuration of the elements: H 1s1, O (1s2) 2s2 2p4, Si (Ne) 3s2 3p2, and Ge (Ar 3d10) 4s2 4p2, where the core configurations are shown in parenthesis. Similarly to our recent works [22], a repulsive potential with a Gaussian shape, strongly localized on the nucleus, was included during the generation of the Si and Ge pseudopotentials to account for the correction of Darwin shifts [23]. This approach allows one to compute energy band gaps for Si and Ge which are in much better agreement with experimental values (especially for the case of Ge, since the calculated band gap using standard LDA is almost 0 eV), as further discussed below. Note that the pseudopotentials were carefully generated to avoid any artificial crossing of the symmetry points in the conduction band induced by the application of the additional potential [23], assuring that the minimum of the conduction band is located at the X point for Si and at the L point for Ge. The basis sets and pseudopotentials were first tested on bulk relaxed Si1 xGex structures, using a supercell with 8 atoms; computations performed on larger supercells (up to 64 atoms) gave typically the same results. A plane wave cutoff of 120 Ry and a (4 4 4) k point mesh were used for the computations, allowing convergence of the total energy of the systems below typically 10 meV. The atomic structure optimization was carried out by relaxing the forces on all the atoms until a 0.05 eV/Å force tolerance was reached, using a conjugate gradient method. 4. Results and discussion K-band ESR spectra of SiO2/Si1 xGex/SiO2 structures with varying Ge contents (x) are shown in Fig. 1(a), for the applied magnetic field B II n ([1 0 0] sample normal) [15]. For the range 0.54 6 x 6 0.73, a prominent signal is observed at gc = 2.0140 ± 0.0003 with peak-to-peak derivative width DBpp of about 23 G. Apart from a weak isotropic EX center signal at gc = 2.00246, corresponding to an SiO2 defect [24], no other interfering signal is observed, enabling reliable spectral analysis. Angular variation for B rotating in the (0 1 1) plane reveals an anisotropic signal splitting into three in a closely 1:2:1 intensity
Fig. 1. (a) First derivate-absorption K-band spectra of the Ge dangling bond signal observed for B II n ([1 0 0] interface normal] on SiO2/Si1 xGex/SiO2 heterostructures with different Ge fraction x. The signal at g = 1.99869 corresponds to the one from the co-mounted Si:P marker. (b) X-band ESR spectra measured for various angles of B with n on the sample with x = 0.7.
ratio (in sequence of gc), a shown in Fig. 1(b). Angular mapping resulted in the consistent three-branch g map shown in Fig. 2. Computer simulations of this g-map revealed a defect with C2v (monoclinic) symmetry and principal g-values g1 = 2.0338 ± 0.0003, g2 = 2.0386 ± 0.0006 and g3 = 2.0054 ± 0.0001, with the lowest value g3 direction 24 ± 2° off a <1 1 1> direction towards n in the (0 1 1) plane, i.e. 31 ± 2° off the [1 0 0] direction. Only three branches out of the seven expected for all equivalent defect orientations in a bulk (Si or Ge) diamond type crystal are observed, indicating the interfacial nature of the defect. Note the g-values of this specific defect are different from those of a Ge dangling bond recently observed at Ge/GeO2 interfaces, using electrically detected magnetic resonance [25]. This defect is tentatively attributed to a Ge dangling bond at the Si1 xGex/SiO2 interface, backbonded to Si and/or Ge atoms (the number of Si and Ge backbonds being still unknown), as sketched in Fig. 3. Very interestingly, the orientation of the Ge dangling orbital and the defect symmetry are very similar to those pertaining to the Si Pb1 defect present at (1 0 0)Si/SiO2 interfaces; the identified Ge dangling bond defect is thus labeled as Ge Pb1. Recent first-principles calculations of the g-tensors of Ge Pb1 defects at Si1 xGex surfaces within density functional theory [26] are in excellent agreement with the experimental values given above for the SiO2/Si1 xGex/SiO2 heterostructures, confirming the Pb1-like nature of this Ge interfacial defect. The capacitance–voltage curves of similar SiO2/Si1 xGex/SiO2 heterostructures present a shift of the threshold voltage VT towards
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Fig. 2. Angular g map of Ge Pb1 signals observed at different frequencies on a SiO2/ Si0.27Ge0.73/SiO2 structure for B rotating in the (0 1 1) plane. Data obtained at 8.9, 20.3 and 34 GHz are shown by stars, filled squares and open circles, respectively. The solid lines represent the fitting results for a monoclinic point symmetry defect in a diamond crystal. The dashed branches are not observed experimentally.
Fig. 4. (a) Charge density determined from the C–V curve shifts at 300 K (open circles) and 77 K (open squares) for the as-grown SiO2/Si1 xGex/SiO2 heterostructures as a function of the Ge fraction x. The data measured on the sample after H2 anneal at 500 °C during 30 min correspond to the triangles. (b) Density of Ge Pb1 defects extracted from ESR experiments. The vertical arrow indicates the effect of the passivating anneal in H2.
Fig. 3. Schematic illustration of a Ge Pb1 dangling bond at the Si1 xGex interface.
larger positive voltages with increasing Ge content (results not shown) [16], indicating the buildup of negative charges. Comparison between the 77 and 300 K C–V curves indicates that these defects are interface traps (so called Grey–Brown shift) [16], behaving like acceptor defects. The density of negative charges extracted from the C–V curves and the density of Ge Pb1 defects estimated from ESR experiments on samples with different Ge content are compared in Fig. 4(a) and (b), respectively. One clearly observes that both defect densities are very similar and present the same behavior as a function of the Ge content. The defects are observed for x P 0.4, present a maximum for x 0.7 and drops at larger Ge content, being not detected for x P 0.85. In addition, both defect densities appear to be much reduced after annealing the heterostructures in H2 at 500 °C during 30 min, as shown in Fig 4(a) and (b), demonstrating the efficient passivation of the Ge Pb1 dangling bond by hydrogen. Note that the electrical measurements sense (negatively) charged defects, while ESR only measures the neutral (paramagnetic) state of the Ge dangling bond. The agreement between the electrical and ESR data suggest that the defect occupancy changes from 300 to 4.2 K, being doubly occupied and negatively charged at 300 K and singly occupied and neutral at 4.2 K, as a result of the Fermi level shift with decreasing temperature, confirming that these defects are interface traps.
The dependence of the defect density with the Ge content is not completely understood. First of all, a certain fraction of Ge (about 40%) is required in the Si1 xGex layer for the defect to be observed. This indicates that the Ge dangling bond is backbonded to at least one Ge atom. On the other hand, the disappearance of the Ge Pb1 signal at high (85–90%) Ge concentration indicates that the presence of Si in the layer is necessary for the generation of this defect – Si atoms possibly enhancing the strain in the layer, the strain being most likely relaxed for large Ge concentrations. By comparing the electrical and ESR data, one can reasonably assume that the Ge Pb1 centers are acceptor-like defects, in contrast to Si dangling bonds at the (1 0 0)Si/SiO2 interface, which are known to be amphoteric defects [27]. To gain further insight, we performed a theoretical study of the electronic properties of (1 0 0)Si1 xGex/SiO2 structures, with a Ge dangling bond at the interface, using DFT, as further discussed below [17]. The calculated lattice parameter of the bulk relaxed Si1 xGex structures are shown in Fig. 5(a) as a function of the Si content. The calculated lattice parameter for bulk Ge and bulk Si is 5.58 and 5.37 Å, respectively; these values are typically 1% smaller than the experimental values. An almost linear decrease of the calculated lattice parameter with increasing Si content is observed, in very good agreement with experimental results reported on relaxed Si1 xGex alloys [28]; the latter experimental values are also shown in Fig. 5(a) for comparison. The evolution of the computed energy band gaps versus the Si content for the relaxed Si1 xGex structures is depicted in Fig. 5(b). The corresponding values computed for Ge (x = 1) and Si (x = 0) are 0.62 and 1.05 eV, respectively; the latter are typically
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Fig. 5. (a) Calculated lattice parameter of bulk relaxed Si1 xGex structures as a function of the Si content. The experimental data from Ref. [28] are also shown for comparison. Dashed lines are linear fits to the data. (b) Calculated energy band gap of bulk relaxed Si1 xGex structures vs. Si content. Dashed line and solid curve are linear and second-order polynomial fits to the calculated values, respectively. Experimental energy band gaps of relaxed Si1 xGex alloys measured at 4.2 K from Ref. [29] are shown for comparison. The dotted line corresponds to the simulated energy gap, shifted upward by 0.18 eV.
underestimated by about 10 to 15% with respect to the experimental ones obtained at 4.2 K. Most importantly, the dependence of the calculated energy gap on the Si content is very similar to what has been reported experimentally on relaxed Si1 xGex alloys [29], as shown in Fig. 5(b). Two distinct regimes can be observed: at low Si concentration (between 0% and 15%), the energy band gap increases linearly with the Si content. In this case, the minimum of the conduction band is located at the L point, characteristic of Ge. For higher Si concentration, a crossover in the conduction band minimum is observed from the L to X point, characteristic of Si-rich alloys [30]. Attendantly, the energy band gap of the Si1 xGex alloys increases with the Si content according to a second order-polynomial, consistent with the experimental results [29]. We point out that the use of the corrected pseudopotentials for Si and Ge leads to computed Si–O and Ge–O bond lengths of 1.62 and 1.78 Å in bulk SiO2 and GeO2 (a-quartz phases), respectively, which are typically 1% to 2% larger than experimental values. However, the computed energy gaps of bulk SiO2 (5.1 eV) and GeO2 (2.8 eV) are typically 40% smaller than experimental values, i.e. the presence of a repulsive potential centered on the Si and Ge nucleus does not improve the energy gap of their oxides.
We next investigate the electronic properties of the Ge dangling bonds at the (1 0 0)Si1 xGex/SiO2 interfaces. The modeled structure consists of 17 slabs of Si1 xGex layers (about 22.5 Å thick, whose bottom slab has been passivated by H atoms), a 3.2 Å thick SiGeOy (y < 2) transition region (where the Si or Ge atoms are in sub + 4 oxidation states), a 7.5 Å SiO2 layer (where the Si atoms are in + 4 oxidation state) and about 15 Å of vacuum, as illustrated in Fig. 6(a) for x 0.6. These slabs were generated from a reference Si/SiO2 interface model with SiO2 in tridymite form [31]. The fraction of Si or Ge atoms in sub + 4 oxidation states in the SiGeOy transition layer is consistent with X-ray photoemission spectroscopy data on Si/SiO2 [31] and Ge/GeO2 interfaces [32], respectively. It should be noted that the Si–O bond length decreases from the interface (1.67 Å) to the top surface (1.62 Å), in agreement with previously reported results on similar Si/SiO2 interface models [31]; this behavior is related to the reduced ionic charge on the Si atoms in lower oxidation states, resulting in a slight elongation of the Si–O bond. In addition, consistently with molecular dynamic simulations of Si1 xGex slabs [33], which predict the segregation of Ge at the surface, the concentration of Ge atoms at the Si1 xGex/ SiO2 interface lies typically between 75% and 100%. The lattice parameter of the Si1 xGex slab is fixed at the computed value for the corresponding bulk relaxed structure. A plane wave cutoff of 200 Ry and a (4 4 1) k point mesh are used for the computations. The artifacts due to the periodic cell-to-cell induced polarization on both the total energy and atomic forces are corrected by the implementation of a self-consistent dipole correction. A Ge dangling bond was generated at the (1 0 0)Si1 xGex/SiO2 interface by removing a bridging oxygen atom. Consistent with the proposed defect symmetry inferred from ESR experiments discussed above, the ‘‘constructed” Ge dangling bond resides on a strained dimer at the interface, as shown in Fig. 6(b). Depending on the Si concentration considered, the number of Si-backbonds varies between 1 (Ge-rich alloy) and 3 (Si-rich alloy). The calculated defect level associated to the neutral (unpaired) Ge dangling bond at the (1 0 0)Si1 xGex/SiO2 interface is shown in Fig. 7, as a function of the Si content; the position of the valence band (VB) and conduction band (CB) edges of the Si1 xGex slab are also shown, all the energies being relative to the valence band
Fig. 6. (a) Atomic configuration of the relaxed (1 0 0)Si1 xGex/SiO2 slab model (x 0.6). In (b), a bridging oxygen atom is removed at the interface, producing a Ge dangling bond residing on a Ge–Ge dimmer (Pb1-like Ge dangling bond), indicated by the dashed circle.
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the interfacial stress for Ge-rich layers (Ge being a softer material than Si), considering that the dangling bonds are formed to accommodate the stress present at the semiconductor/oxide interface. Finally, since ESR and electrical data indicate the possibility to reduce the density of these Ge dangling bonds by annealing the SiO2/Si1 xGex/SiO2 heterostructures in molecular hydrogen, we anticipate that their degrading effect on the electrical performances of MOS devices could be (at least partially) reduced by a proper hydrogen passivation. Acknowledgements Part of this work has been financially supported by the FWO (Fonds voor Wetenschappelijk Onderzoek) project G.0628.09. References Fig. 7. Calculated energy level of the Ge Pb1-like defect at the (1 0 0)Si1 xGex/SiO2 interface as a function of the Si content. The calculated valence band (VB) and conduction band (CB) edges are also shown; the valence band edge of the pure Ge slab (x = 1) is taken as reference (zero energy).
edge of the pure Ge slab; note that the energy band gap of the Si1 xGex slab is typically 0.2 eV higher than for the bulk structure, cf. Fig. 5(b), due to quantum confinement effects induced by the finite thickness of the Si1 xGex slabs used. Interestingly, the CB edge is almost independent of the Si content, while the VB edge decreases (relative to the pure Ge slab) with increasing Si content, reflecting the corresponding raise in the energy band gap of the Si1 xGex alloy, cf. Fig. 5(b). One also notices that the position of the defect level corresponding to the Ge dangling bond slightly increases with the Si content (by about 0.1 eV from Ge rich to Si-rich slabs). It thus appears that the dangling bond level approaches the VB edge of the Si1 xGex slab as the Si concentration decreases, mainly due to the narrowing of the energy band gap of the alloy. We point out that these results are consistent with recently reported first-principles calculations of the neutral Ge dangling bond level in bulk Ge, lying close (0.1 to 0.2 eV) to the VB edge [34]. From an electrical point of view, one can thus reasonably assume that the Pb1-like Ge dangling bond behaves as an acceptor-like defect at Ge-rich (1 0 0)Si1 xGex/SiO2 interfaces. Note that recent experimental results [35] indicate a larger shift of the VB edge with decreasing x (by about 0.5 eV from pure Ge to pure Si) than the one predicted from our simulations (about 0.3 eV), which may be related to residual compressive strain (of the order of 1%) in the Si1 xGex layer [35]. This larger shift of the VB edge would bring the neutral Ge dangling bond level even closer to the VB, or eventually within the valence band for a Ge content above 80%, further accentuating its acceptor-like character. 5. Conclusions A nontrigonal Ge dangling bond in SiO2/Si1 xGex/SiO2 heterostructures grown from the condensation technique has been revealed from ESR experiments, for Ge content 0.4 6 x 6 0.85. The orientation of the Ge dangling orbital indicate that this defect is similar to the Pb1 defect observed at (1 0 0)Si/SiO2 interfaces, and most likely corresponds to a dangling bond at a strained Ge dimer, backbonded to Si and Ge atoms. The electrical activity of this Ge dangling bond has been assessed by C–V measurements performed at 300 and 77 K, suggesting that this defect behaves like an acceptor. First-principles calculations of the electronic properties of this Ge dangling bond predict that its energy level approaches the valence band edge of the Si1 xGex layer as the Ge content increases, confirming its acceptor-like nature. The disappearance of this defect at large Ge concentration is not yet understood. A possible explanation would be the reduction of
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