Solid-State Electronics 52 (2008) 1274–1279
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High-k-oxide/silicon interfaces characterized by capacitance frequency spectroscopy B. Raeissi a,*, J. Piscator a, O. Engström a, S. Hall b, O. Buiu b, M.C. Lemme c, H.D.B. Gottlob c, P.K. Hurley d, K. Cherkaoui d, H.J. Osten e a
Chalmers University of Technology, Department of Microtechnology and Nanoscience, SE-412 96 Göteborg, Sweden University of Liverpool, Brownlow Hill, Liverpool L69, 3GJ, UK c AMO GmbH, Otto Blumenthal–Strasse 25, 52074, Aachen, Germany d Tyndall National Institute, University College Cork, Lee Maltings, Prospect Row, Cork, Ireland e Institute of Electronic Materials and Devices, Leibniz University of Hannover, Appelstrasse 11A, D-30167 Hannover, Germany b
a r t i c l e
i n f o
Article history: Available online 15 May 2008 The review of this paper was arranged by Jurriaan Schmitz Keywords: MOS High-k HfO2 Gd2O3 Capacitance frequency spectroscopy Capture cross section
a b s t r a c t Electron capture into insulator/silicon interface states is investigated for high-k dielectrics of Gd2O3 prepared by molecular beam epitaxy (MBE) and atomic layer deposition (ALD), and for HfO2 prepared by reactive sputtering, by measuring the frequency dependence of Metal Oxide Semiconductor (MOS) capacitance. The capture cross sections are found to be thermally activated and to increase steeply with the energy depth of the interface electron states. The methodology adopted is considered useful for increasing the understanding of high-k-oxide/silicon interfaces. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The need for novel gate dielectric materials replacing present silicon dioxide based insulators in CMOS technology has become one of the most challenging requisites for a continuous development of electronics. Requirements for low leakage currents put strong demands on structural stability and charging characteristics in addition to limitations for the fundamental properties like dielectric constants and energy band offset values [1]. In order to limit gate tunneling currents while keeping a high enough capacitive coupling between the transistor gate and channel for devices of the ITRS 22 nm LSTP bulk node, it has been estimated that a product k DE 70 eV is needed. Here, k is the dielectric constant of the insulator and DE is the energy offset value between the conduction bands of silicon and gate insulator, respectively [2]. As Gd2O3 is found not too far from this value [2], this promotes the material to one of the interesting candidates for future gate dielectrics. In the present work, we have investigated the insulator/silicon interface state properties of Gd2O3/Si prepared by two different methods, molecular beam epitaxy (MBE) and atomic layer deposi* Corresponding author. Tel.: +46 31 772 1857; fax: +46 31 772 3622. E-mail address:
[email protected] (B. Raeissi). 0038-1101/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2008.04.005
tion (ALD). These results are compared with corresponding data from HfO2/Si prepared by reactive sputtering and, for further comparison also with thermally grown SiO2/Si structures. From capacitance versus voltage (C–V) measurements performed at different frequencies, we determine the size of cross sections for electron capture to interface states as a function of energy position in the silicon band gap. An interesting observation is that the energy dependence of the capture cross sections in all cases of the high-k materials resembles the corresponding feature for electron capture into SiO2/Si interface traps. In addition, from capacitance measurements performed at different temperatures, we find that the electron capture is thermally activated. As shown in a study of the influence on MOS capacitance by electron traffic at interface states [3], these properties are a consequence of the same underlying physical mechanism and depend on local vibronic properties of the interface defects [4–6]. This offers a novel methodology for characterizing interface states of insulator/semiconductor structures.
2. Theoretical background The thermal emission and capture processes taking place at a discrete electron state of an oxide/silicon interface as illustrated in Fig. 1 can be expressed by
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Nomenclature k DE t nT NT Nc ns vth en rn r0 q
dielectric constant of insulator the energy offset value between the conduction bands of silicon and gate insulator time concentration of captured electrons total concentration of interface states effective density of states in the silicon conduction band concentration of electrons in the semiconductor conduction band at the interface average thermal velocity of electrons in the semiconductor conduction band thermal emission rate of electrons from the interface state to the conduction band capture cross section for electrons at the interface state capture cross section at temperature equal to infinity electron charge
kB T f x Dl C Cox Cit Cs DGn DU
C¼
Boltzmann’s constant temperature Fermi–Dirac distribution angular frequency Fermi level position in relation to the conduction band edge total capacitance of MOS-structure oxide capacitance capacitance contribution from interface states capacitance contribution from the silicon depletion region under the oxide free energy position of the electron state in relation to the silicon conduction band activation energy for capture cross section
C ox ðC s þ C it Þ C ox þ C s þ C it
ð3Þ
where Cox is the oxide capacitance and Cs is the capacitance contribution from the silicon depletion region under the oxide. Both these quantities can be obtained by standard procedure [7]. According to Eq. (2), Cit depends on en and x. The former quantity is given by DGn ð4Þ en ¼ vth rn N c exp kB T where Nc is the effective density of states in the silicon conduction band, DGn is the free energy position of the electron state in relation to the silicon conduction band [4], kB is Boltzmann’s constant and T is absolute temperature. From measurements of the total capacitance, C, for different frequencies, x/2p, the capture cross sections and their temperature dependence can be obtained by fitting theoretical curves governed by Eqs. (2)–(4) and using the methodology described below.
Fig. 1. Energy band diagram of the insulator/silicon interface.
dnT ¼ en nT þ vth rn ðN T nT Þns dt
3. Model for charge carrier capture ð1Þ
where t is time, nT is the concentration of captured electrons, en is the thermal emission rate of electrons from the interface state to the conduction band, vth is the average thermal velocity of electrons in the semiconductor conduction band, rn is the capture cross section for electrons at the interface state, NT is the total concentration of interface states and ns is the concentration of electrons in the semiconductor conduction band at the interface. When measuring the differential capacitance of a MOS structure, the small signal voltage from the capacitance meter will influence the Fermi-level at the oxide/silicon interface to vary across a small energy interval such that the capacitance contribution, Cit, from interface states on this energy level can be determined. Solving Eq. (1) for small variations in ns, one finds [3] C it ¼ q2
NT en df pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 4e2n þ x2 dðDlÞ
ð2Þ
where x is the angular frequency of the AC signal from the capacitance meter, q is the electron charge, Dl is the Fermi level position in relation to the conduction band edge and f is the Fermi–Dirac distribution. The total capacitance of the MOS-structure is given by [7]
When extracting the values of the capture cross sections,rn, from Eq. (4), it is important to take into consideration their possible temperature dependence. This property is connected with the mechanism responsible for capturing the charge carrier from the conduction band. Two main relations have been observed in published experimental data. For pure electronic capture processes, without any influence of local phonon interactions, a temperature dependence on the form Tr, with 1 < r < 4, has been discovered as expected from a cascade mechanism [8] or from exciton processes [9]. In the second case, as a result of local phonon vibrational interactions, a temperature dependence governed by a Boltzmann factor exp (DU/kBT) has been observed. For a number of traps in III–V materials [10] and for irradiation induced interface states of SiO2/Si systems [5,6] it has been demonstrated that this latter mechanism determines electron capture. As a similar behavior will be demonstrated below for the interface electron states of the material combinations investigated in the present study, we give a description of the essential features of such phenomena. The total energy of a trap system in a semiconductor includes not only the electronic energy values but also energy contributions from its local atomic vibrational properties. Assuming for
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Fig. 2. Configurational coordinate diagram of a vibrating electron trap. Parabolas represent the oscillator potentials with minima positioned at the electronic energy levels. Transition of an electron between a trap level and the conduction band takes place at the crossing points 1 and 2 where the atomic positions coincide for empty traps and traps filled by an electron.
simplicity that the atomic bonding forces are proportional to the deviation from atomic equilibrium positions, the corresponding oscillator potentials follow a parabolic behavior as shown in Fig. 2. In order to take into account the many dimensional vibrational geometry determined by the semiconductor lattice, a reduced coordinate known as the configurational coordinate is used as an abscissa in this representation [11]. The ordinate axis in Fig. 2 represents the sum of electronic and atomic energies. Thus, the differences between the minima of the upper parabola and those of traps A and B represent the electronic energy positions of the traps in relation to the conduction band edge. In this scheme, the thermal emission of an electron from trap A to the conduction band is effected by increasing the vibrational energy along the parabola. This goes on until the system reaches the crossing point at position 1 with the parabola representing the empty trap A, whereupon the electron is transferred to the conduction band states. At this point, the oscillator turning points of the trap filled by an electron and of the empty trap, respectively, are identical, which allows the captured electron to leave. The empty trap A then thermalizes to its equilibrium point and gives off an energy corresponding to the value DU to the surrounding lattice as depicted in Fig. 2. Because the energy quantity DGn in Eq.(4) represents the difference between the conduction band edge and the Fermi-level position at the oxide/silicon interface, the thermal energy needed to emit an electron from the trap to the conduction band as obtained from a capacitance measurement is the sum DGn + DU. Correspondingly, in capturing and electron to trap A from the conduction band, the empty trap has to reach position 1 for the process to become possible. That requires thermal activation and furnishes the capture cross section value with a Boltzmann factor exp (DU/kBT). The quantity rn in Eq. (4), therefore, is expressed by DU rn ¼ r0 exp kB T
ð5Þ
The pre-exponential factor, r0, in this expression depends on a combination of matrix elements including electronic and atomic wave functions involved in the process. The mechanism revealing the temperature dependence given by Eq. (5) is known as multiphonon capture [10,11].
An electron captured into a trap system may be expected to take part in the atomic bonding which causes the relaxation of curvature in the oscillator potential and thus for a decrease in oscillator frequency when it is released to the conduction band. The bonding force can be argued to increase with the localization of the electron wave function which in turn is expected to increase for deeper energy positions [12]. Hence, a deeper electronic energy level will give rise to a higher curvature of the vibrational energy parabola as shown for trap B in Fig. 2. Moreover, as realized from the figure, this gives rise to a lower DU value determined by the crossing point at position 2. As a result, the capture cross section, rn, increases for increasing values of DGn. In the interpretation of our measured data below, we will assume a linear relation between DU and DGn . It is worth observing that changing the vibrational frequencies of the oscillator potentials in Fig. 2 also influences the density of atomic energy states. This change of available quantum states involves a change in entropy when an electron is released from the trap. As DGn is the distance between the conduction band edge and the Fermi-level it is to be considered as a free energy and thus a function of the entropy. Therefore, as earlier pointed out [13], the change in entropy with free energy position, which follows from a varying DU, influences the energy distribution of Dit when measured by capacitance methods. 4. Experimental details The first type of Gd2O3 layers were grown on silicon wafers by a modified MBE process [14] followed by the deposition of a protective layer of amorphous silicon in vacuo. NiSi electrodes were formed by full silicidation of sputtered nickel dots at 500 °C in an inert ambient as described in more detail in Ref. [15]. The second variant of Gd2O3 layers were prepared by ALD using Gd[N(SiMe2)]3 as a precursor. Carbon contamination during the deposition, assessed by Auger electron spectroscopy, was negligible. Deposition temperature varied between 175 and 275 °C and the number of cycles between 75 and 300. The samples with HfO2 were prepared by reactive sputtering. Immediately before loading the chamber, the wafers were treated in RCA standard clean followed by a dip in 2% HF. After deposition, the wafers were annealed at 800 °C to decrease oxide bulk charge. Aluminum electrodes were prepared by sputtering and photolithography. All oxides in this study were deposited on (1 0 0) oriented n– type silicon wafers of nominally 4–10 ohm cm resistivity. The gate contacts were circular with a diameter of 400 lm. In order to obtain samples with high concentrations of interface states all measurements were carried out before any forming gas or post metallization anneal. 5. Experimental results Fig. 3 shows results from C–V measurements on a NiSi/Gd2O3/Si structure where the oxide is prepared by MBE. While the upper part of the graphs in Fig. 3a at gate voltage larger than 0.8 V does not change with frequency, the peak at about 1.4 V for the 1 kHz curve has clear frequency dependence. From a plot of a theoretical ideal curve with accumulation capacitance equal to the measured one, the flat band capacitance can be determined which in turn can be used to establish a scale for DGn in relation to applied voltage. The peak in Fig. 3a indicates that the interface state distribution is concentrated to a limited energy range with a maximum concentration at about 0.2 eV from the conduction band edge. It is worth noting that the variation of the C–V curves for different frequencies, including also those for the samples presented below,
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Fig. 3. (a) Capacitance versus voltage for Gd2O3 sample prepared by MBE. (b) Capacitance versus frequency relation for DGn = 0.23 eV and rn = 3 1018 cm2, Dit = 4 1012 cm2 eV1. Points: Experimental. Curve: Theory.
Fig. 4. (a) Capacitance versus voltage for Gd2O3 sample prepared by ALD. (b) Capacitance versus frequency relation for DGn = 0.28 eV and rn = 2 1018 cm2 Dit = 3.2 1012 cm2 eV1. Points: Experimental. Curve: Theory.
is not a result of bulk oxide charge trapping during subsequent C–V sweeps. For a given voltage, the Fermi-level is at the same energy positions for all curves in the set. The movement of the graphs with frequency is a vertical shift, depending on the relation between en and x which gives a decrease of the capacitance when x approaches and overtakes en. The frequency dependence at 1.4 V, corresponding to DGn = 0.23 eV, is plotted in Fig. 3b. Here, a capture cross section of rn = 3 1018 cm2 has been fitted to make the theoretical curve shift along the frequency axis and coincide with the experimental data. The corresponding data for the NiSi/Gd2O3/Si samples prepared by ALD are shown in Fig. 4. These C–V characteristics have very different shapes compared with those of the MBE sample shown in Fig. 3a, which indicates that the energy distribution of interface states is smeared out across the upper part of the band gap or has a peak close to the conduction band edge. Frequency data are shown in Fig. 4b for the 0.2 V values in (a), where the theoretical curve is fitted for rn = 2 1018 cm2 at an energy level DGn = 0.28 eV. Using the method for fitting theoretical frequency spectra to experimental data as demonstrated in Figs. 3b and 4b at different energy positions in the silicon bandgap, the capture cross sections,
Fig. 5. Capture cross section versus interface state energy distance to conduction band. Dashed–dotted curve for SiO2 is taken from Ref. [16].
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rn, can be found as functions of DGn. Such relations are shown in Fig. 5 for the two types of Gd2O3 samples together with corresponding results for HfO2 samples prepared by reactive sputtering and investigated by the same method as demonstrated above. In all cases, a steep increase in capture cross sections is found with increasing depth into the band gap. For comparison, earlier published data [16] on capture cross sections for electron states at SiO2/Si interfaces are outlined in the diagram. One notices that in all cases, the energy dependence of the capture cross sections have a similar qualitative appearance. From Eq. (2), one expects a temperature dependence of Cit governed by the thermal emission rate as expressed by Eq. (4). Keeping the signal frequency from the capacitance meter constant at 1 kHz and varying the temperature for different voltage scans, C– V curves were measured for both Gd2O3 samples and the samples based on HfO2. An example from the Gd2O3 ALD samples is shown in Fig. 6a demonstrating that the total capacitance decreases with temperature in the steep part of the graph as expected from Eqs. (2)–(4). The temperature dependence for a voltage of 0.2 V is
plotted in Fig. 6b. When comparing these data with results from a theoretical treatment, one must take into consideration that the Fermi–level is temperature dependent and changes in the interval 0.18 < Dl < 0.28 eV when the temperature changes from 220 to 295 K. As the Fermi-level is used as a probe to select different DGn values, this means that different energy levels of the interface state distribution contribute to the interface state capacitance Cit. Therefore, the capture cross section rn varies accordingly during the measurement procedure. Assuming the same property for the Gd2O3/Si system, the dependence of rn on DGn as shown in Fig. 5, can be expressed by taking DU = 0.5–0.4 DGn. Using this relation in Eq. (5) together with the theory of Eqs. (1)–(4) gives the graph labeled Theory (1) in Fig. 6b. The second theoretical curve, Theory (2), in Fig. 6b was calculated by assuming that rn as a function of DGn still follows the room temperature data in Fig. 5, but without the temperature dependence given by Eq. (5). The accordance between Theory (1) and measured results strongly suggests that the capture mechanism is of the multiphonon type as described above in Section 3.
6. Discussion
Fig. 6. (a) Capacitance versus voltage for Gd2O3 sample prepared by ALD at different temperatures. (b) Capacitance versus temperature relation. Points: Experimental. Solid and dashed curves: Theory. For the curve labeled Theory (1) a multiphonon model was assumed for the capture mechanism. For Theory (2) it was assumed that the capture cross section follows the room temperature data in Fig. 5, but without the temperature dependence given by Eq. (5). Dit = 3.2 1012 cm2 eV1.
The combined features of exponential energy dependence and thermal activation of the capture cross sections found in this work may have a practical use in the characterization of interface states for different oxides. The Boltzmann factor in Eq. (5) is a mark for multiphonon capture [10,11]. Such processes occur as a result of local vibronic properties of the trap volume capturing the charge carrier. Beside this property, another characteristic feature of these systems is that optically determined energy positions may differ considerably from energy quantities found by methods based on thermal processes. Experimental data from optical and thermal measurements on irradiation induced electron states at SiO2/Si interface have earlier demonstrated the existence of this kind of trap system [5,6]. Recently also exponentially increasing capture cross sections have been demonstrated for HfO2/Si interfaces prepared by chemical vapor deposition [17]. The qualitative similarity of the energy dependence for capture cross sections of all three high-k materials and SiO2 indicates that the interface states in all cases have the same physical origin. For the Gd2O3 samples prepared by ALD and the HfO2 samples prepared by sputtering, TEM data show the existence of an SiOx interlayer. Recently, from studies of electron spin resonance (ESR), it was found that Al2O3, ZrO2 and HfO2, prepared by ALD on (1 0 0) silicon, after UV photo-dissociation and post-deposition heating gave rise to spectra typical for defect centra like EX, E’ and Pb, commonly present in SiO2 [18]. Similar agreement has been found between Pb0 density as measured by ESR and the density of interface states calculated from frequency dependent CV observed in HfO2/Si structures [19]. This may explain the similarity between the data from these samples and those of the SiO2/Si systems in Fig. 5. Therefore, in all cases here the Pb-center seems to be the most probable acting trapping system. More surprising is the resemblance also for the Gd2O3 samples prepared by MBE and especially their close similarity in capture cross section values as compared with the ALD samples. In this case no interlayer has been observed in TEM [15]. On the other hand, this does not exclude the existence of electron dangling bond orbitals at the Gd2O3/Si interface with properties similar to the Pb center. Due to its influence on channel mobility, threshold voltage control and reliability of the MOSFET, the high-k oxide/silicon interface plays a crucial role in future gate stack development. In the present paper, we have demonstrated how rarely investigated materials properties like energy and temperature dependence of capture cross sections can be investigated and connected. As these
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quantities are closely related with the microscopic properties of the transition region between the high-k oxide and the silicon crystal, they play a significant role for increased understanding of novel materials combinations of this kind. Acknowledgment The authors would like to acknowledge the Sixth European Framework programme through the PullNANO Project (IST– 026828), Swedish Foundation for Strategic Research (SSF) Project NEMO, EPSRC in UK, the Science Foundation Ireland (05/IN/1751) and the German Federal Ministry of Education and Research (BMBF) Project MEGA EPOS (13N9260) for financial support of this work. The ALD samples were supplied by Paul Chalker. References [1] Robertson J. High dielectric constant oxides. Eur Phys J Appl Phys 2004;28:265–91. [2] Engström O, Raeissi B, Hall S, Buiu O, Lemme MC, Gottlob HDB, et al. Navigation aids in the search for future high-k dielectrics: physical and electrical trends. Solid State Electron 2007;51:622–6. [3] Engström O, Raeissi B, Piscator J. Vibronic nature of hafnium oxide/silicon interface states investigated by capacitance frequency spectroscopy. J Appl Phys 2008;103. [4] Engström O, Grimmeiss HG. Vibronic states of silicon–silicon dioxide interface traps. Semicond Sci Technol 1989;4:1106–15. [5] Andersson MO, Engström O. Atomic relaxation of Si–SiO2 interface states measured by a photo-depopulation technique. Appl Surface Sci 1989;39:289–300.
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