Supporting Information Ultrathin Hf0.5Zr0.5O2 Ferroelectric Films on Si
Supporting Information
Ultrathin Hf0.5Zr0.5O2 Ferroelectric Films on Si Anna Chernikova1, Maksim Kozodaev1, Andrei Markeev1, Dmitrii Negrov1, Maksim Spiridonov1, Sergei Zarubin1, Ohheum Bak2, Pratyush Buragohain2, Haidong Lu2, Elena Suvorova1,3,4, Alexei Gruverman2*, and Andrei Zenkevich1,5* 1
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700, Russia
2
Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588-0299,
USA 3
École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
4
A.V. Shubnikov Institute of Crystallography, Leninsky pr. 59, Moscow, 119333, Russia
5
NRNU “Moscow Engineering Physics Institute”, 115409 Moscow, Russia
* To whom correspondence should be addressed: [email protected], [email protected]
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1. Atomic Layer Deposition growth of TiN/Hf0.5Zr0.5O2 films on Si Hf0.5Zr0.5O2 films were deposited by thermal Atomic Layer Deposition (ALD) technique at T=240°C on HF-last n++-Si (ρ=0.005 Ohm⋅cm) wafers using Hf[N(CH3)(C2H5)]4 (TEMAH), Zr[N(CH3)(C2H5)]4 (TEMAZ) and H2O as precursors and N2 as carrier and purge gas. In order to obtain ultrathin Hf0.5Zr0.5O2 films described in this work, 15 ALD sypercycles, consisting of alternating TEMAH-H2O and TEMAZ-H2O cycles, was employed. The crystallization of the films was further achieved by the thermal ALD of TiN overlayer at T=400°C. ALD process of TiN was based on the TiCl4 and NH3 precursors. 1000 TiCl4-NH3 cycles were used to grow ~ 15 nm-thick TiN film.
2. Rutherford backscattering spectrometry (RBS) analysis RBS analysis of the Hf0.5Zr0.5O2/Si sample as grown by ALD was performed with He++ ions (E0=1.7 MeV, φ=0°, θ=160°). The experimental spectrum along with its modelling with the 2.5-nm-thick Hf0.5Zr0.5O2 layer is presented in Fig S1.
Figure S1. RBS spectrum of ultrathin alloyed Hf-Zr oxide film on Si as grown by ALD and its modeling with the 2.5-nm-thick Hf0.5Zr0.5O2layer.
3. Transmission electron microscopy analysis of Hf0.5Zr0.5O2 films The sample for the cross-sectional TEM was prepared with mechanical polishing followed by Ar+ ion milling (with E=5 keV reduced to 0.5 keV for final polishing at 2° to the sample surface) at room temperature. Plan-view TEM samples were prepared by chemical
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etching of the Si substrate in HF:HNO3 solution after chemical plasma etching of the top TiN electrode with SF6. The composition and the thickness of as grown Hf0.5Zr0.5O2 film and an interfacial SiOx layer were evaluated using the cross-sectional transmission electron microscopy (TEM) analysis performed with FEI Tecnai Osiris microscope equipped with X-ray energy dispersive spectrometer (EDS, Bruker Quantax). The distribution of elements and the thickness of the layers in the cross-section were measured using a Quantax EDS (Bruker) and Esprit software in scanning bright-field (BF) STEM and HAADF STEM modes in a FEI Tecnai Osiris microscope (200 kV X-FEG field emission gun, X-ray detector (Super-X) with 4ൈ30 mm2 windowless SDD diodes and 0.9sr collection angle at 22° take-off angle) (Fig S2).
Figure S2. STEM HAADF image of (a) TiN/Hf0.5Zr0.5O2/Si sample cross-section and (b) the corresponding EDS map obtained by the superimposition of the individual elemental maps (see Fig. S3).
The EDS map of the TiN/Hf0.5Zr0.5O2/Si sample cross-section in Fig S2 was obtained by the superimposition of the individual elemental maps (Fig S3). The distribution of elements and thicknesses of layers in the cross-section were measured using a Quantax EDS (Bruker) and Esprit software in scanning bright-field (BF) STEM and HAADF STEM modes in a FEI Tecnai Osiris microscope (200 kV X-FEG field emission gun, X-ray detector (Super-X) with 4ൈ30 mm2 windowless SDD diodes and 0.9sr collection angle at 22° take-off angle). The phase composition of crystalline grains in plan-view samples was studied by conventional bright-field transmission electron microscopy (BF/TEM), high-resolution S-3
transmission electron microscopy (HRTEM) and electron diffraction with a FEI Tecnai Osiris microscope (200 kV X-FEG field emission gun, 1.2 mm spherical aberration, 1.2 mm chromatic aberration, 0.24 nm resolution at Scherzer defocus and 0.14 nm information limit). The HRTEM study was done on the edge (about 100 nm wide) of Hf0.5Zr0.5O2 films without TiN and Si. For the modeling of HRTEM image in Fig. 2, the best fit between the experimental and the simulated HRTEM images was achieved at defocus of 69 nm and film thickness of 3.0–3.3 nm oriented along the [-110] direction relatively to the electron beam with the slight tilt of about 0.5°.
Figure S3. EDS maps for Zr, Hf, Si, Ti and O taken from the cross-section of the TiN/Hf0.5Zr0.5O2/Si sample. TEM/HRTEM images and SAED patterns were recorded on a 4kൈ2.6k Gatan Orius CCD camera with large field of view in Osiris. Images were processed with the Gatan Digital Micrograph 3.11.0 software (Gatan, Inc., Pleasanton, CA, USA), including Fourier Transform (FT) and spatial filtering. The HRTEM cross-section image of the sample is shown in Fig S4.
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Figure S4. HRTEM cross-section image of TiN/Hf0.5Zr0.5O2/Si sample. SAED patterns were obtained from Hf0.5Zr0.5O2film and Si substrate in the plan-view sample for the best calibration of SAED patterns and precise phase interpretation with accuracy about 0.5 %. Fig S5 shows ring SAED pattern obtained on the 150-nm edge of the film. The following monoclinic, orthorhombic, tetragonal, cubic ZrO2, HfO2, ZrHfO2 phases from the Karlsruhe Data Base (2015) were considered for the simulation and comparison: #9993, 18190,23402, 23928, 26488, 27023, 41012, 41572, 42986, 51051, 56696, 66781, 66784, 67004, 68589, 68781, 68782, 70014, 70015, 72955, 72956, 76019, 77713, 77714, 77716, 79914, 83682, 88316, 92095, 93028, 93031, 93123, 173, 960, 180936, 185123, 248448, 248449, 647697, 655671, 658755 (for ZrO2), 27313, 53033, 53034, 57385, 60902, 79913, 83863, 87456, 173965, 173966,174039, 174040, 638740, 638741, 638742 (for HfO2), 171370 (Zr0.994Hf0.006O1.968), and 171371 (Zr0.994Hf0.006O2). The best fit is observed for monoclinic P121/c (a=0.515, b=0.521, c=0.531 nm, β=99.23°)1 and orthorombic Pbc21 (a=0.507, b=0.526, c=0.508 nm)2 phases of ZrO2. We note that phase diagrams of HfO2 and ZrO2 are very similar and the lattice parameters of the corresponding phases are the same within ~0.5%, for which reason we use the parameters of the binary oxides to analyze the structural properties of the alloyed Hf0.5Zr0.5O2.
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Figure S5. (a) SAED patterns with superimposed simulated rings for monoclinic (red) and orthorhombic (green) phases- the ring labelled “111 orth” can be attributed to the orthorhombic phase only; (b) and (c) simulated ring diffraction patterns for the orthorhombic and monoclinic phases, respectively.
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4. Piezoresponse Force Microscopy testing PFM imaging and hysteresis loop measurements were carried out by means of a commercial AFM system (MFP-3D, Asylum Research) using Pt-coated conductive AFM tips (PPP-EFM, Nanosensors). Resonance-enhanced PFM mode3 was used in both cases, with the ac drive frequency being kept close to the tip-sample contact resonance at about 350 kHz and an ac amplitude of 0.3 V. Scan rate was 1 Hz for domain writing (poling bias ±3V was applied to the tip) and for PFM imaging. PFM hysteresis loops were measured in the pulse mode, where stepup dc pulses were applied to induce polarization switching (pulse duration 12.5 ms), and the PFM signal was measured at the pulse off period (12.5 ms), within 5 s of a total measurement cycle. 5. X-ray photoelectron spectroscopy analysis X-ray photoelectron spectroscopy (XPS) analysis was performed using ThetaProbe spectrometer with the AlKα monochromatized X-ray source (Thermo Fischer Scientific) coupled with the ALD reactor.
Figure S6. Hf4f core-level spectrum wrt. the valence band maximum (VBM) taken on a thick Hf0.5Zr0.5O2 film on Si.
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Figure S7. Reflection Electron Energy Loss Spectroscopy (REELS) spectrum taken in situ on as grown Hf0.5Zr0.5O2 film. The derived band gap Eg = 5.0 eV.
6. Modeling of the electric field distribution across the TiN/Hf0.5Zr0.5O2/Si stacks Here, we describe the results of the modeling of the potential distribution and subsequent voltage drops across TiN/Hf0.5Zr0.5O2/SiOx/Si metal-oxide-semiconductor stack and implications on the actual coercive voltage in ultrathin Hf0.5Zr0.5O2layer and the observed line broadening in Si2p XPS spectra. In particular, PFM measurements reveal that as grown Hf0.5Zr0.5O2 films exhibit the nominal coercive voltage Vc ≈ ±2 V, which is unrealistic considering the film thickness ~2.5 nm and the breakdown electric field for this alloyed oxide. However, this can be explained by the fact that only fraction of the applied voltage drops in the ferroelectric film, while most of it drops in the screening region of the (highly doped) Si substrates well as in the interfacial SiO2 layer. To assess the distribution of the voltage across the stack under investigation we have built a screening model, which takes electrostatics, carrier drift and diffusion into account. Firstly, both as grown film, an interfacial SiOx layer and Si substrate are assumed homogenous, in which case the problem is reduced to strictly one-dimensional. Secondly, carrier transport inside dielectrics is assumed negligible, so only electrostatics is modeled. The system of equations, which governs charge and potential distributions in silicon substrate is: S-8
ρ = e( p − n + N d ) εε0∆V = −ρ J n = µ n ∇Vn + µn k BT∇n J p = µ p ∇Vp + µ p k BT∇p ∇J n = 0 ∇J p = 0
Inside the dielectric layers, it reduces to the Laplace equation:
εε0∆V = 0 Different solution domains are joined with boundary conditions. On the SiO2-Si boundary we have V← = V→ Jn = 0 Jp = 0 where V← is the boundary voltage in silicon, while V→ is in SiO2. On SiO2-ferroelectric boundary we have
ε FE ∇V→ − ε SiO ∇V← = ρ pol 2
where ρ pol is the boundary charge in ferroelectric film, ε SiO2 and ε FE are permittivities of SiO2 and ferroelectric, respectively, while ∇V← and ∇V→ are electric fields on respective boundaries. Technically, the analysis was performed by casting the problem to its weak form and considering only piecewise-linear functions as a solution subspace. Equations were then solved, using Newton method, with Jacobian matrix calculated directly by linearizing the weak formulation. The results of these calculations are shown in Fig S8. The voltage drop across the ferroelectric film is at least two times smaller than the applied voltage. The apparent non-
S-9
linearity is caused by the charge screening process in semiconducting substrate. The drop is smaller, when it is caused by electrons, but in situation with reversed polarity, space charge region is formed by holes and due to their lower mobility the drop is much more significant. This can also explain the observed asymmetry in the switching behavior. The potential distribution across the stack comprising ferroelectric 2.5-nm-thick Hf0.5Zr0.5O2 film at the particular applied voltage V=2.3 V is shown in Fig S9. The presence of polarization charge on the ferroelectric boundaries causes additional shift in the potential, which varies depending on the polarization state of the film. It can be seen that the main part (~75%) of the voltage drops in the n+-Si (ne=1019 cm-3) substrate in this case, while only ~15% of the voltage is applied directly to the ferroelectric Hf0.5Zr0.5O2 film.
Figure S8. Relationship between the voltage applied to the MOS stack and the potential drop across ferroelectric Hf0.5Zr0.5O2 film. Zero is shifted due to presence of remnant polarization.
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Figure S9. A distribution of the applied voltage across the MOS stack (dashed lines denote boundaries between Si, SiO2 and Hf0.5Zr0.5O2 film). The Fermi level in Si is assumed to be at 0 V.
To compare calculations with experimental XPS results, the reference Si2p line was convoluted with potential distribution using the formula: ∞ x I (ε ) = ∫ I ref (ε − V ( x)) exp − dx , 0 λ
where I ref is a reference spectrum, V ( x) is a potential distribution in the substrate and λ is the electron mean free path. The result for the film, spontaneously polarized upwards, is shown in Fig S10. The deviation in the left part of the peak can be caused by presence of oppositely polarized domains in the ferroelectric film. The performed modeling combined with the simulated broadening of the Si2p core-level peak upon crystallization of Hf0.5Zr0.5O2 film provides an insight regarding the reason for the seemingly high values of coercive voltages observed in PFM measurements.
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Figure S10. The observed broadening of Si2p core level XPS peak taken from the adjacent Si substrate beneath SiOx interlayer and ferroelectric Hf0.5Zr0.5O2 film as simulated by the band bending in Si to the presence of the screening charges.
7. Pulsed switching testing Polarization switching kinetics has been measured by measuring the transient current signals generated by a series of voltage pulses applied across a ferroelectric capacitor using a technique called PUND (Positive Up Negative Down). The pulse train was generated using an Agilent 33220A generator and the associated current through a series resistor (50 Ohm input impedance) was measured with a Tektronix TDS3014B oscilloscope. A typical voltage pulse train and current signals are shown Fig S11. An input pulse train consists of alternating pairs of unipolar pulses (positive and negative). The transient current Is due to the application of the first pulse in the pair of unipolar pulses consists of the polarization switching current Ips associated with transition from the negative polarization state to a fully saturated positive polarization state plus the loading (non-switching) current Ins due to dielectric charging. The transient current due to the second pulse in the pair of unipolar pulses is only due to dielectric charging, i.e. only Ins is detected during the second pulse application. The polarization switching current Ips can be found as a difference between current signals generated by the first and second unipolar pulses. The
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current peaks at the terminating edge of a voltage pulse correspond to dielectric discharging. The same analysis is performed for switching under negative voltage pulses.
Figure S11. A typical PUND voltage pulse train used for the pulsed switching testing and associated transient currents measured in the TiN/Hf0.5Zr0.5O2/Si stacks.
References 1. Smith, D. K. Jr., Newkirk, H. W., «The crystal structure of baddeleyite and its relation to the Polymorphism of ZrO2» Acta Cryst.1965, 18, 983-991. 2. Kisi, E. H., Howard C. J., Hill, R.J. «Crystal structure of orthorhombic zirconia in partially stabilized zirconia» J. Am. Ceram. Soc., 1989, 72, 1757-1760. 3. https://www.asylumresearch.com/Applications/PFMAppNote/PFMAppNote.shtml , 2015.
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Ultrathin Hf0.5Zr0.5O2 Ferroelectric Films on Si Anna Chernikova1, Maksim Kozodaev1, Andrei Markeev1, Dmitrii Negrov1, Maksim Spiridonov1, Sergei Zarubin1, Ohheum Bak2, Pratyush Buragohain2, Haidong Lu2, Elena Suvorova1,3,4, Alexei Gruverman2*, and Andrei Zenkevich1,5* 1
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700, Russia
2
Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588-0299,
USA 3
École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
4
A.V. Shubnikov Institute of Crystallography, Leninsky pr. 59, Moscow, 119333, Russia
5
NRNU “Moscow Engineering Physics Institute”, 115409 Moscow, Russia
* To whom correspondence should be addressed: [email protected], [email protected]
S-1
1. Atomic Layer Deposition growth of TiN/Hf0.5Zr0.5O2 films on Si Hf0.5Zr0.5O2 films were deposited by thermal Atomic Layer Deposition (ALD) technique at T=240°C on HF-last n++-Si (ρ=0.005 Ohm⋅cm) wafers using Hf[N(CH3)(C2H5)]4 (TEMAH), Zr[N(CH3)(C2H5)]4 (TEMAZ) and H2O as precursors and N2 as carrier and purge gas. In order to obtain ultrathin Hf0.5Zr0.5O2 films described in this work, 15 ALD sypercycles, consisting of alternating TEMAH-H2O and TEMAZ-H2O cycles, was employed. The crystallization of the films was further achieved by the thermal ALD of TiN overlayer at T=400°C. ALD process of TiN was based on the TiCl4 and NH3 precursors. 1000 TiCl4-NH3 cycles were used to grow ~ 15 nm-thick TiN film.
2. Rutherford backscattering spectrometry (RBS) analysis RBS analysis of the Hf0.5Zr0.5O2/Si sample as grown by ALD was performed with He++ ions (E0=1.7 MeV, φ=0°, θ=160°). The experimental spectrum along with its modelling with the 2.5-nm-thick Hf0.5Zr0.5O2 layer is presented in Fig S1.
Figure S1. RBS spectrum of ultrathin alloyed Hf-Zr oxide film on Si as grown by ALD and its modeling with the 2.5-nm-thick Hf0.5Zr0.5O2layer.
3. Transmission electron microscopy analysis of Hf0.5Zr0.5O2 films The sample for the cross-sectional TEM was prepared with mechanical polishing followed by Ar+ ion milling (with E=5 keV reduced to 0.5 keV for final polishing at 2° to the sample surface) at room temperature. Plan-view TEM samples were prepared by chemical
S-2
etching of the Si substrate in HF:HNO3 solution after chemical plasma etching of the top TiN electrode with SF6. The composition and the thickness of as grown Hf0.5Zr0.5O2 film and an interfacial SiOx layer were evaluated using the cross-sectional transmission electron microscopy (TEM) analysis performed with FEI Tecnai Osiris microscope equipped with X-ray energy dispersive spectrometer (EDS, Bruker Quantax). The distribution of elements and the thickness of the layers in the cross-section were measured using a Quantax EDS (Bruker) and Esprit software in scanning bright-field (BF) STEM and HAADF STEM modes in a FEI Tecnai Osiris microscope (200 kV X-FEG field emission gun, X-ray detector (Super-X) with 4ൈ30 mm2 windowless SDD diodes and 0.9sr collection angle at 22° take-off angle) (Fig S2).
Figure S2. STEM HAADF image of (a) TiN/Hf0.5Zr0.5O2/Si sample cross-section and (b) the corresponding EDS map obtained by the superimposition of the individual elemental maps (see Fig. S3).
The EDS map of the TiN/Hf0.5Zr0.5O2/Si sample cross-section in Fig S2 was obtained by the superimposition of the individual elemental maps (Fig S3). The distribution of elements and thicknesses of layers in the cross-section were measured using a Quantax EDS (Bruker) and Esprit software in scanning bright-field (BF) STEM and HAADF STEM modes in a FEI Tecnai Osiris microscope (200 kV X-FEG field emission gun, X-ray detector (Super-X) with 4ൈ30 mm2 windowless SDD diodes and 0.9sr collection angle at 22° take-off angle). The phase composition of crystalline grains in plan-view samples was studied by conventional bright-field transmission electron microscopy (BF/TEM), high-resolution S-3
transmission electron microscopy (HRTEM) and electron diffraction with a FEI Tecnai Osiris microscope (200 kV X-FEG field emission gun, 1.2 mm spherical aberration, 1.2 mm chromatic aberration, 0.24 nm resolution at Scherzer defocus and 0.14 nm information limit). The HRTEM study was done on the edge (about 100 nm wide) of Hf0.5Zr0.5O2 films without TiN and Si. For the modeling of HRTEM image in Fig. 2, the best fit between the experimental and the simulated HRTEM images was achieved at defocus of 69 nm and film thickness of 3.0–3.3 nm oriented along the [-110] direction relatively to the electron beam with the slight tilt of about 0.5°.
Figure S3. EDS maps for Zr, Hf, Si, Ti and O taken from the cross-section of the TiN/Hf0.5Zr0.5O2/Si sample. TEM/HRTEM images and SAED patterns were recorded on a 4kൈ2.6k Gatan Orius CCD camera with large field of view in Osiris. Images were processed with the Gatan Digital Micrograph 3.11.0 software (Gatan, Inc., Pleasanton, CA, USA), including Fourier Transform (FT) and spatial filtering. The HRTEM cross-section image of the sample is shown in Fig S4.
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Figure S4. HRTEM cross-section image of TiN/Hf0.5Zr0.5O2/Si sample. SAED patterns were obtained from Hf0.5Zr0.5O2film and Si substrate in the plan-view sample for the best calibration of SAED patterns and precise phase interpretation with accuracy about 0.5 %. Fig S5 shows ring SAED pattern obtained on the 150-nm edge of the film. The following monoclinic, orthorhombic, tetragonal, cubic ZrO2, HfO2, ZrHfO2 phases from the Karlsruhe Data Base (2015) were considered for the simulation and comparison: #9993, 18190,23402, 23928, 26488, 27023, 41012, 41572, 42986, 51051, 56696, 66781, 66784, 67004, 68589, 68781, 68782, 70014, 70015, 72955, 72956, 76019, 77713, 77714, 77716, 79914, 83682, 88316, 92095, 93028, 93031, 93123, 173, 960, 180936, 185123, 248448, 248449, 647697, 655671, 658755 (for ZrO2), 27313, 53033, 53034, 57385, 60902, 79913, 83863, 87456, 173965, 173966,174039, 174040, 638740, 638741, 638742 (for HfO2), 171370 (Zr0.994Hf0.006O1.968), and 171371 (Zr0.994Hf0.006O2). The best fit is observed for monoclinic P121/c (a=0.515, b=0.521, c=0.531 nm, β=99.23°)1 and orthorombic Pbc21 (a=0.507, b=0.526, c=0.508 nm)2 phases of ZrO2. We note that phase diagrams of HfO2 and ZrO2 are very similar and the lattice parameters of the corresponding phases are the same within ~0.5%, for which reason we use the parameters of the binary oxides to analyze the structural properties of the alloyed Hf0.5Zr0.5O2.
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Figure S5. (a) SAED patterns with superimposed simulated rings for monoclinic (red) and orthorhombic (green) phases- the ring labelled “111 orth” can be attributed to the orthorhombic phase only; (b) and (c) simulated ring diffraction patterns for the orthorhombic and monoclinic phases, respectively.
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4. Piezoresponse Force Microscopy testing PFM imaging and hysteresis loop measurements were carried out by means of a commercial AFM system (MFP-3D, Asylum Research) using Pt-coated conductive AFM tips (PPP-EFM, Nanosensors). Resonance-enhanced PFM mode3 was used in both cases, with the ac drive frequency being kept close to the tip-sample contact resonance at about 350 kHz and an ac amplitude of 0.3 V. Scan rate was 1 Hz for domain writing (poling bias ±3V was applied to the tip) and for PFM imaging. PFM hysteresis loops were measured in the pulse mode, where stepup dc pulses were applied to induce polarization switching (pulse duration 12.5 ms), and the PFM signal was measured at the pulse off period (12.5 ms), within 5 s of a total measurement cycle. 5. X-ray photoelectron spectroscopy analysis X-ray photoelectron spectroscopy (XPS) analysis was performed using ThetaProbe spectrometer with the AlKα monochromatized X-ray source (Thermo Fischer Scientific) coupled with the ALD reactor.
Figure S6. Hf4f core-level spectrum wrt. the valence band maximum (VBM) taken on a thick Hf0.5Zr0.5O2 film on Si.
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Figure S7. Reflection Electron Energy Loss Spectroscopy (REELS) spectrum taken in situ on as grown Hf0.5Zr0.5O2 film. The derived band gap Eg = 5.0 eV.
6. Modeling of the electric field distribution across the TiN/Hf0.5Zr0.5O2/Si stacks Here, we describe the results of the modeling of the potential distribution and subsequent voltage drops across TiN/Hf0.5Zr0.5O2/SiOx/Si metal-oxide-semiconductor stack and implications on the actual coercive voltage in ultrathin Hf0.5Zr0.5O2layer and the observed line broadening in Si2p XPS spectra. In particular, PFM measurements reveal that as grown Hf0.5Zr0.5O2 films exhibit the nominal coercive voltage Vc ≈ ±2 V, which is unrealistic considering the film thickness ~2.5 nm and the breakdown electric field for this alloyed oxide. However, this can be explained by the fact that only fraction of the applied voltage drops in the ferroelectric film, while most of it drops in the screening region of the (highly doped) Si substrates well as in the interfacial SiO2 layer. To assess the distribution of the voltage across the stack under investigation we have built a screening model, which takes electrostatics, carrier drift and diffusion into account. Firstly, both as grown film, an interfacial SiOx layer and Si substrate are assumed homogenous, in which case the problem is reduced to strictly one-dimensional. Secondly, carrier transport inside dielectrics is assumed negligible, so only electrostatics is modeled. The system of equations, which governs charge and potential distributions in silicon substrate is: S-8
ρ = e( p − n + N d ) εε0∆V = −ρ J n = µ n ∇Vn + µn k BT∇n J p = µ p ∇Vp + µ p k BT∇p ∇J n = 0 ∇J p = 0
Inside the dielectric layers, it reduces to the Laplace equation:
εε0∆V = 0 Different solution domains are joined with boundary conditions. On the SiO2-Si boundary we have V← = V→ Jn = 0 Jp = 0 where V← is the boundary voltage in silicon, while V→ is in SiO2. On SiO2-ferroelectric boundary we have
ε FE ∇V→ − ε SiO ∇V← = ρ pol 2
where ρ pol is the boundary charge in ferroelectric film, ε SiO2 and ε FE are permittivities of SiO2 and ferroelectric, respectively, while ∇V← and ∇V→ are electric fields on respective boundaries. Technically, the analysis was performed by casting the problem to its weak form and considering only piecewise-linear functions as a solution subspace. Equations were then solved, using Newton method, with Jacobian matrix calculated directly by linearizing the weak formulation. The results of these calculations are shown in Fig S8. The voltage drop across the ferroelectric film is at least two times smaller than the applied voltage. The apparent non-
S-9
linearity is caused by the charge screening process in semiconducting substrate. The drop is smaller, when it is caused by electrons, but in situation with reversed polarity, space charge region is formed by holes and due to their lower mobility the drop is much more significant. This can also explain the observed asymmetry in the switching behavior. The potential distribution across the stack comprising ferroelectric 2.5-nm-thick Hf0.5Zr0.5O2 film at the particular applied voltage V=2.3 V is shown in Fig S9. The presence of polarization charge on the ferroelectric boundaries causes additional shift in the potential, which varies depending on the polarization state of the film. It can be seen that the main part (~75%) of the voltage drops in the n+-Si (ne=1019 cm-3) substrate in this case, while only ~15% of the voltage is applied directly to the ferroelectric Hf0.5Zr0.5O2 film.
Figure S8. Relationship between the voltage applied to the MOS stack and the potential drop across ferroelectric Hf0.5Zr0.5O2 film. Zero is shifted due to presence of remnant polarization.
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Figure S9. A distribution of the applied voltage across the MOS stack (dashed lines denote boundaries between Si, SiO2 and Hf0.5Zr0.5O2 film). The Fermi level in Si is assumed to be at 0 V.
To compare calculations with experimental XPS results, the reference Si2p line was convoluted with potential distribution using the formula: ∞ x I (ε ) = ∫ I ref (ε − V ( x)) exp − dx , 0 λ
where I ref is a reference spectrum, V ( x) is a potential distribution in the substrate and λ is the electron mean free path. The result for the film, spontaneously polarized upwards, is shown in Fig S10. The deviation in the left part of the peak can be caused by presence of oppositely polarized domains in the ferroelectric film. The performed modeling combined with the simulated broadening of the Si2p core-level peak upon crystallization of Hf0.5Zr0.5O2 film provides an insight regarding the reason for the seemingly high values of coercive voltages observed in PFM measurements.
S-11
Figure S10. The observed broadening of Si2p core level XPS peak taken from the adjacent Si substrate beneath SiOx interlayer and ferroelectric Hf0.5Zr0.5O2 film as simulated by the band bending in Si to the presence of the screening charges.
7. Pulsed switching testing Polarization switching kinetics has been measured by measuring the transient current signals generated by a series of voltage pulses applied across a ferroelectric capacitor using a technique called PUND (Positive Up Negative Down). The pulse train was generated using an Agilent 33220A generator and the associated current through a series resistor (50 Ohm input impedance) was measured with a Tektronix TDS3014B oscilloscope. A typical voltage pulse train and current signals are shown Fig S11. An input pulse train consists of alternating pairs of unipolar pulses (positive and negative). The transient current Is due to the application of the first pulse in the pair of unipolar pulses consists of the polarization switching current Ips associated with transition from the negative polarization state to a fully saturated positive polarization state plus the loading (non-switching) current Ins due to dielectric charging. The transient current due to the second pulse in the pair of unipolar pulses is only due to dielectric charging, i.e. only Ins is detected during the second pulse application. The polarization switching current Ips can be found as a difference between current signals generated by the first and second unipolar pulses. The
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current peaks at the terminating edge of a voltage pulse correspond to dielectric discharging. The same analysis is performed for switching under negative voltage pulses.
Figure S11. A typical PUND voltage pulse train used for the pulsed switching testing and associated transient currents measured in the TiN/Hf0.5Zr0.5O2/Si stacks.
References 1. Smith, D. K. Jr., Newkirk, H. W., «The crystal structure of baddeleyite and its relation to the Polymorphism of ZrO2» Acta Cryst.1965, 18, 983-991. 2. Kisi, E. H., Howard C. J., Hill, R.J. «Crystal structure of orthorhombic zirconia in partially stabilized zirconia» J. Am. Ceram. Soc., 1989, 72, 1757-1760. 3. https://www.asylumresearch.com/Applications/PFMAppNote/PFMAppNote.shtml , 2015.
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