High- K dielectrics for the gate stackJean-Pierre Locquet, Chiara Marchiori, Maryline Sousa, Jean Fompeyrine, and Jin Won Seo Citation: Journal of Applied Physics 100, 051610 (2006); doi: 10.1063/1.2336996 View online: http://dx.doi.org/10.1063/1.2336996 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/100/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Thermal stability and electrical properties of titanium-aluminum oxide ultrathin films as high- k gate dielectricmaterials J. Appl. Phys. 101, 034102 (2007); 10.1063/1.2432401 Leakage current and charge trapping behavior in Ti O 2 ∕ Si O 2 high- κ gate dielectric stack on 4 H Si Csubstrate J. Vac. Sci. Technol. B 25, 217 (2007); 10.1116/1.2433976 High- k and low- k nanocomposite gate dielectrics for low voltage organic thin film transistors Appl. Phys. Lett. 88, 243515 (2006); 10.1063/1.2213196 Low-frequency noise characteristics of HfSiON gate-dielectric metal-oxide-semiconductor-field-effect transistors Appl. Phys. Lett. 86, 082102 (2005); 10.1063/1.1866507 Al 2 O 3 / Si 3 N 4 stacked insulators for 0.1 μm gate metal–oxide–semiconductor transistors realized by high-density Si 3 N 4 buffer layers Appl. Phys. Lett. 82, 3931 (2003); 10.1063/1.1579850

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High-K dielectrics for the gate stackJean-Pierre Locquet,a� Chiara Marchiori, Maryline Sousa, and Jean FompeyrineIBM Research GmbH, Zurich Research Laboratory, 8803 Rüschlikon, Switzerland

Jin Won SeoInstitute Physics of Complex Matters, EPFL, 1015 Lausanne, Switzerland and Advanced Materialsand Metrology, MosBeam Foundation, PSE, 1015 Lausanne, Switzerland

�Received 4 January 2006; accepted 28 June 2006; published online 15 September 2006�

This article gives an overview of recent developments in the search for the next-generation dielectricfor the complementary metal-oxide semiconductor gate stack. After introducing the main quantitiesof interest, the paper concentrates on a figure of merit that connects two main properties of the gatestack, namely, the leakage current and the capacitance. This is done for single layers as well as forbilayers consisting of interfacial SiOx and a high-K dielectric. In the case of the bilayers, the impactof the interfacial layer SiOx is enormous, reducing the leakage current by an order of magnitude permonolayer. This extreme dependance makes a good correlation between the leakage and thestructural parameters nearly impossible. This is illustrated using numerical examples designed tohelp the reader evaluate the orders of magnitude involved. The origin of the interfacial layer istraced back by means of thermodynamic considerations. As the estimates put forward in theliterature do not correspond to the results observed, a detailed review is made, and additionalmechanisms are suggested. By using reasonable values for the Gibbs free energy of an interfacialsolid silicon oxide phase it is demonstrated how the reaction equilibria shift. Such an interface phasemay fundamentally change the stability criteria of oxides on Si. Furthermore, it can also provide amajor source of electronic defects that will affect the device performance. Finally, a second figureof merit is introduced that connects the capacitance with a strongly reduced carrier mobility, whichmight also be related to the same electronic defects. © 2006 American Institute of Physics.�DOI: 10.1063/1.2336996�

I. INTRODUCTION

The term high K used worldwide to refer to this field ofactivities is an unfortunate choice. In contrast to other“high’s” such as high temperature superconductivity, high Kis neither associated with a recent spectacular discovery oran exceptional material property. On the contrary, it refersmore to an “anything but” boundary condition on the dielec-tric constant of an insulator. A high-K material is an insulatorwith a dielectric constant ��� that is larger than that of silicondioxide ��=3.9�. There are two main areas in which the high-K dielectrics can be applied. In both cases, they are typicallyused in a parallel plate capacitor configuration, sandwichedeither between two metals or a metal and a semiconductor. Inthe former configuration, the dielectric is used to store chargein random-access memory �RAM� applications, whereas inthe latter case, the dielectric permits to modulate �or gate�the carrier concentration of an adjacent semiconductor in afield-effect transistor �FET�. While most of the articles in thisspecial issue on ferroelectrics are related to the former appli-cation, this paper focuses only on the latter use of high-Kdielectrics.

Historically, the use of insulators for this purpose goesback to the origins of the transistor itself. AlthoughLilienfeld1–3 and Heil4 attempted to realize solid-state de-vices around 1930, an observation of transistor action inn-type polycrystalline germanium �Ge� using a point-contact

configuration took place in 1947.5,6 However, the practicalsilicon �Si� metal-oxide semiconductor �MOS� transistorwith an oxidized Si gate was introduced much later. Thesilicon–silicon dioxide MOSFET was made in 1960 byKahgn and Attala7,8 and described in two patents.9,10 By1965, the field had progressed so much that Moore was ableto establish a famous trend, now called Moore’s law.11 Sincethen, the structural, chemical, and electric properties of asilicon dioxide gate dielectric have been improved tremen-dously in these past 45 years. Although the main focus wason using and optimizing silicon dioxide, many alternativehigh-K dielectrics have been explored over the years. A num-ber of early studies included aluminium oxide in a singlelayer12 as well as in bilayers with silicon dioxide.13–15 In thissense, high K is nearly as old as the Si–SiO2 MOSFETitself.

Besides having a sufficiently large �, there are severalother critical requirements a high-K dielectric must fulfillbefore it can replace SiO2. These are �i� thermodynamic sta-bility in contact with Si on one side of the dielectric and thegate metallization on the other side; �ii� kinetic stabilityagainst Si and the metal gate, in particular during high tem-perature processing and annealing; �iii� band offsets withSi�1 eV to assure low leakage currents; �iv� a passivated,low-defect-density interface with Si to ensure large carriermobility in the Si channel and good breakdown properties;and �v� a low defect density in the high-K dielectric itself toprevent flatband �VFB� and threshold �VT� voltage shifts anda�Electronic mail: loc@zurich.ibm.com

JOURNAL OF APPLIED PHYSICS 100, 051610 �2006�

0021-8979/2006/100�5�/051610/14/$23.00 © 2006 American Institute of Physics100, 051610-1

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instabilities. Several excellent reviews have already appearedsuch as the early one by Wilk et al.,16 the book High-K gatedielectrics edited by Houssa,17 and the recent review byRobertson.18 The reader is referred to these texts for a morecomplete overview.

II. CMOS PERFORMANCE: ITRS ROADMAP

For high-performance MOSFETs, the most significantparameter is the current between source and drain �Ids� thatthe transistor can drive. More current means that thetransistor—and all the parasitic capacitances and resistancesthat it is composed of—can be turned on faster. Two voltagesdetermine the response of the three-terminal device shown inFig. 1. First, the gate voltage �VG� charges the gate insulatorin the parallel plate capacitor configuration and induces anaccumulation or inversion of the charge carrier density in thesemiconductor QSi. A larger capacitance means more carriersin the semiconducting channel for the same applied voltage.The second voltage is the one applied between source anddrain �Vds�, which is responsible for driving the inducedcharges forward in the channel.

The capacitance of the gate insulator �Cox� in the parallelplate configuration depends on the area �A�, the insulatorthickness �tox�, and � of the insulator, Cox=��0A / tox with �0

the vacuum permittivity. For a channel width �W� and length�L� of 100 nm and a SiO2 tox of 1.5 nm, Cox=0.23 fF or, perunit area C /A=2.3 �F/cm2. This corresponds roughly to theone used for current 90 nm CMOS transistors. At VG=1 V,this leads to an induced carrier density of 1.4�1013 e / cm2.In practice, because silicon is a semiconductor with a bandgap of 1.1 eV, a threshold voltage �VT�—of the order of theband gap—must be overcome before carriers can be induced,and the carrier density is then proportional to Cox�VG−VT�.In the framework of high-K dielectrics, it is practical to com-pare the capacitive charge of an insulator with that of SiO2.For this, the concept of equivalent oxide thickness �EOT� isintroduced as follows: the EOT of a high-K insulator isequivalent to the SiO2 thickness that would yield the samecapacitance, i.e., tSiO2

= thigh K �3.9/�high K�.The second voltage Vds transports the induced charges.

The resulting current Ids depends on the geometry �W ,L� ofthe channel, the mobility ���, and the induced charge density�QSi=��0 / tox=C /A�, as well as on the applied voltages inEq. �1� derived from Sah,19

Ids = ���0

tox

W

L�VG − VT�Vds − 1/2Vds

2 . �1�

For convenience, this equation was written as a productof three different terms, which group together the parametersof the deposited materials �� ,� , tox�, the geometrical param-eters �W ,L�, and the power variables �VG ,VT�, respectively.Taking the same device dimensions as above and assumingVT=0 V, VG=0 V, Vds=1 V, and �=300 cm2/V s, we ob-tain the current through the transistor Ids=36�10−6 A.

The quantity typically quoted �for instance, in the Inter-national Technology Roadmap for Semiconductors20 �ITRS��is the saturation current Ids,sat normalized over the channelwidth W. Ids= Ids,sat when Vds= �VG−VT� and the power termin Eq. �1� becomes Vds

2 /2. For our example Ids,sat

=360 A/m. For high-performance logic, the expected evolu-tion of Ids,sat—and EOT—is shown in Fig. 2, suggesting thatmuch more current will be drawn from a single transistor inthe years to come. Simultaneously, the EOT must attain val-ues close to 0.5 nm. The parameters that can make this pos-sible are tox, �, and �, corresponding to three different sce-narios being pursued, namely, scaling, high K, and high �.Scaling has been the main driver for CMOS, but a tSiO2

be-low 1 nm exhibits too strong a tunneling current as demon-strated below. A high-K dielectric with �=4�SiO2

and tox

=2tSiO2would double Ids, but there are still many unsolved

issues as also described below. The third possibility to im-prove Ids is to increase � beyond the typical 300 cm2/V s, indevices that use strained Si, Ge, or III/V compounds. Forinstance, IBM’s recently announced 65 nm application-specific integrated circuit �ASIC� includes a form of strainedSi.21

III. LEAKAGE CURRENT OF SINGLE LAYERS

In this section, the leakage current through the gate in-sulator will be estimated. For very thin films, the leakagecurrent is essentially due to direct tunneling of holes or elec-trons from their respective bands across the band offset withthe insulator. For thicker films, other mechanisms such asFowler-Nordheim tunneling predominate. As will be derivedbelow, Fig. 6 shows that the tunneling current density �Jt� for

FIG. 1. The various elements composing a MOSFET, including the sub-strate �p-Si�, the sidewall trench insulation �STI�, the implanted source anddrain contact regions, as well as the gate contact with the dielectric abovethe channel region, indicated as a dotted line.

FIG. 2. The expected evolution of Ids,sat �left axis, solid squares� as well asthe equivalent SiO2 oxide thickness �right axis, solid circles� as a function ofthe year of introduction according to the ITRS Roadmap �Ref. 20�.

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SiO2 thicknesses �1.5 nm quickly becomes larger22 than100 A/cm2. Such a Jt leads to unacceptable heat dissipationand is the biggest factor in the thermal load of current mi-croprocessors. Theoretically, for a thin insulator with a bar-rier height � �eV� and an applied voltage across the oxide�Vox� smaller than � /q, Schuegraf and Hu23 approximated Jt

as

Jt =q3

8�h�

Vox2

tox2 exp�− 8��2m*��

3hq

tox

Vox

��1 − �1 −qVox

�3/2� , �2�

where q is the charge of an electron, h is Planck’s constant,and m* is the tunneling effective mass in the insulator. For a1.5 nm thick SiO2 film with �=4.05 eV, m*=0.22me, andA= �100 �m�2, we obtain Jt=−21.6 A/cm2 at Vox=1 V.

When a gate voltage VG is applied between the gatemetal and Si, only a part remains across the oxide Vox, whileother parts are related to the band bending � �eV� and thedifference in the work functions between the gate metal Wm

�eV� and the semiconductor WSi. WSi is a function of theelectron affinity �=4.05 eV�, the band gap �Eg=1.12 eV�,and the dopant versus intrinsic concentration �Na /Ni� whichdefines the position of the Fermi level and is the term be-tween parentheses in Eq. �3�,

VG =Wm

q− � + Eg/2 + kBT log�Na/Ni�

q + Vox +

�

q, �3�

where the first two terms correspond to the flatband voltageV�FB�.

In experiments, leakage currents are typically reported asa function of VG not Vox, which makes a comparison of vari-ous reported results tedious. To calculate Vox=Qox/Cox, oneuses Qox=−QSi �the charges on both sides of a capacitor havethe same magnitude but opposite polarity�, with QSi varyingas a function of �,

QSi = �2�SikBTNa��e−K + K − 1�

+Ni

2

Na2 �eK − K − 1�1/2

, �4�

where the sign indicates a positive sign when K is nega-tive, K=q� /kBT and �Si=11.7. The charge density on the Sisurface for p doping as a function of � is shown in Fig. 3 forthe three regions of interest, i.e., accumulation, depletion,and inversion. While in depletion, QSi does not change verymuch in a voltage region corresponding to Eg−0 eV���1.12 V; outside this region, QSi increases exponentiallyand consequently also Vox.

Next, both Vox��� and VG��� are calculated as a func-tion of � using Eq. �3�. Here we assume the same Na, A, andtSiO2

as above and Wm=4.05 eV for a poly-Si gate electrode.For �=0 eV, VG equals −1 V and corresponds to the flat-band voltage VFB. The results are plotted as a function of VG

in Fig. 4. The position of VFB is easily verified; it also cor-responds to Vox=0 V. In the depletion regime, � changes

linearly with VG whereas Vox remained almost constant. Inaccumulation and inversion, the opposite trend is observed,i.e., � is almost constant, while Vox varies linearly with VG.At the reference voltage VFB−1 V, Vox=−0.82 V and � /q=−0.18 V. Figure 4 also includes calculations for 3 nmSiO2. In this case, for the same applied VG, the magnitude ofVox is always larger than for thinner SiO2. The smaller Cox ofthe 3 nm SiO2 film leads to a larger voltage drop over theoxide.

With the above information, Jt�Vox����, Eq. �2� can nowbe calculated and plotted versus VG���. Note that this modelis only a simple approximation and not all the physics isappropriately taken into account. This was done for p- andn-Si using various SiO2 thicknesses and compared with theexperimental data.22 The parameters for both systems wereWm=4.05 eV, Na=4.7�1017/cm3, �=4.05 eV, and m*

=0.22me for p-Si, and Wm=5.17 eV, Nd=5.6�1017/cm3, �=3.45 eV, and m*=0.29me for n-Si. Good agreement be-

FIG. 3. Absolute values of the calculated charge on the Si surface as afunction of � using Eq. �4�. The flatband condition ��=0 eV� as well as theregions corresponding to accumulation, depletion, and inversion areindicated.

FIG. 4. The band bending �� /q� and Vox as a function of VG calculatedusing Eq. �3� for 1.5 and 3 nm SiO2. The flatband voltage VFB, the thresholdvoltage VT for inversion, as well as a reference voltage VFB−1 V are alsoindicated.

051610-3 Locquet et al. J. Appl. Phys. 100, 051610 �2006�

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tween the experimental data and the calculated curves is ob-served, see Fig. 5. In addition, the same parameters werethen used to calculate the expected behavior for 1.5 and2.0 nm thick SiO2 films. For the thinnest films, Jt can exceed1 A/cm2 substantially.

To compare Jt for different thicknesses and/or differentmaterials, it is useful to define a reference voltage. Hence,typically, 1 V is subtracted �added� to VFB in the case of p-Si �n-Si�. Such a comparison is made in Fig. 6, whereJt�VFB−1 V� is plotted versus the equivalent SiO2 thicknessfor SiO2 as well as for high-K materials.

The points representing SiO2 �solid squares� in this fig-ure of merit �FOM� shown in Fig. 6 correspond to the ex-perimental data22 shown in Fig. 5 extrapolated further, downto 0.5 nm thick SiO2. At the reference voltage VG= �VFB

−1 V�, a 1 nm SiO2 film has Jt=−2495 A/cm2. Next, theparameters of the barrier are gradually modified towardsthose of high-K dielectrics. First, only � was changed from3.9 to 20 and the lowest Jt is obtained �solid circles�. For

EOT=0.5 nm, this would represent an improvement in Jt ofmore than ten orders of magnitude. Unfortunately, a materialwith a large � also has smaller � and m* �Table I�. The effectis illustrated by the next two curves, where � is reducedfrom 4.05 to 1.4 eV �solid triangle up� and m* from 0.22 to0.14 �solid triangle down�. The latter curve is typical24 ofZrO2 or HfO2 based high-K materials. For EOT=0.5 nm, Jt

now improves only about three orders of magnitude com-pared with SiO2 and remains above 100 A/cm2.

As an example, a 3 nm HfO2-based film—with EOT=0.58 nm—has Jt=−73.2 A/cm2 at VG= �VFB−1 V�. Froman EOT viewpoint, for such a low EOT value, this is ordersof magnitude better than the result for SiO2. However, froma Jt only viewpoint, this is orders of magnitude worse thanSiO2, as a 3 nm SiO2 film has a Jt=−3.7�10−6 A/cm2.Overall, this FOM confirms that high-K materials may begood candidates to solve the large leakage issues with SiO2,at least for EOTs between 0.75 and 1.5 nm.

IV. MATERIAL SELECTION

There are many prospective insulating materials avail-able that could be used. Table I lists the main high-K candi-date materials with their � and Eg values as well as the con-duction �valence� band offset, CBO �VBO�.18 For each of thematerials listed, a relatively wide range of CBO and VBOvalues obtained using various methods has been reported.The tunneling barrier height � can be derived from the CBO�or VBO� by taking into account the energy difference be-tween the position of the Fermi level and the correspondingband.

The table also reveals that the CBO in general is muchsmaller than the VBO, which leads to highly asymmetricJt�VG� curves on p- and n-Si. Another consequence of thelow CBO is the appearance of other contributions25 to theleakage current. These include Schottky emission over thebarrier as well as Poole-Frenkel emission using the electri-cally active defects in the oxide. For both mechanisms, theconduction band of the high-K dielectric is populated bythermally emitted carriers, and the leakage may become lim-ited by the bulk resistance of the dielectric.25

FIG. 5. Experimental and calculated Jt�VG� for thin SiO2 films on p- andn-Si in accumulation, using poly-Si gate contacts. The vertical lines definethe reference voltages.

FIG. 6. Absolute values of the calculated Jt�VFB−1 V� vs EOT for variousoxide/Si systems discussed in the text. The top axis is the areal capacitancecorresponding to the EOT.

TABLE I. Main high-K materials with their parameters as tabulated byRobertson �Ref. 18�.

Material � Eg �eV� CBO �eV� VBO �eV�

SiO2 3.9 9.0 3.2 4.7Si3N4 7 5.3 2.4 1.8Al2O3 9 8.8 2.8 4.9La2O3 30 6.0 2.3 2.6Y2O3 15 6.0 2.3 2.6ZrO2 25 5.8 1.5 3.2Ta2O5 22 4.4 0.35 2.95HfO2 25 5.8 1.4 3.3HfSiO4 11 6.5 1.8 3.6TiO2 80 3.5 0 2.4a-LaAlO3 30 5.6 1.8 2.7SrTiO3 2000 3.2 0 2.1

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V. THERMODYNAMIC CONSIDERATIONS

Experimentally, these insulators must be deposited on Siwithout the occurrence of reactions that would induce theformation of other phases. The stability criteria for such bi-layers have two aspects: a thermodynamic and a kinetic one.If thermodynamic equilibrium conditions are assumed, thenthe tabulated Gibbs free energy Gf

0 of the different bulkphases26 can be used to estimate whether certain reactionswill take place. While there are a number of issues to usethermodynamic considerations for thin film problems �seediscussion below� they can be used as first-order estimates.Some very common reactions that can occur without thepresence of oxygen are, for instance,

MO2 + Si = M + SiO2, �5�

MO2 + 2Si = MSi + SiO2, �6�

2MO2 + Si = M + MSiO4, �7�

2MO2 + 2Si = MSi + MSiO4, �8�

where M represents a four-valent metal. The first reactioncorresponds to the decomposition of the metal oxide in favorof the formation of SiO2. The second reaction corresponds tothe decomposition of the metal oxide in favor of the forma-tion of a silicide phase and SiO2. Both cases have detrimen-tal effects by first decreasing the total capacitance owing tothe addition of a dielectric with �=3.9 in series with thehigh-K dielectric. On the other hand, the leakage is also in-creased because of the addition of a �mostly� conducting sil-icide. The last two reactions describe the formation of a sili-cate. In general silicates have a much lower dielectricconstant than the metal oxides that do not contain Si. Forinstance, in the case of Zr silicate, �=11. The impact ofsilicate formation is also detrimental to the total capacitance,but to a lesser extent than the formation of SiO2.

To illustrate how such thermodynamic estimates aremade, we take the Zr–Si–O system as an example as it is oneof the best tabulated systems �see Table II �Ref. 26�� and itsatisfies the equations above. The phase diagram contains 11phases, namely, the elements �Zr, O2, and Si�, the oxides�SiO2, SiO �gas�, ZrO2, and ZrSiO4�, and the silicides �SiZr,SiZr2, Si2Zr, and Si3Zr5�.

A. Formation of SiO2

With the data in this table, it is now possible to recon-struct a complete phase diagram and to estimate the likeli-hood of any reaction such as those in Eq. �5�,

ZrO2 + Si = Zr + SiO2 ��G1000 K0 = 177 kJ/mol� . �9�

As �G0= �GZr0 +GSiO2

0 �− �GZrO2

0 +GSi0 �=177 kJ/mol and is

positive, the left-hand side of the equation corresponds to thestable state. This indicates that once ZrO2 has been depositedon Si, it has little tendency to decompose into its constitu-ents. Another way of fulfilling the condition given by Eq. �5�is to look for those oxides that have a lower Gibbs freeenergy of formation for the oxide ��Gox

0 �. The thermody-namic reaction that describes the oxidation process is

M + O2 = MO2. �10�

From the same thermodynamic reference tables,26 it ispossible to calculate the �Gox

0 =GZrO2

0 − �GZr0 +GO2

0 � for theoxidation process. For the ZrO2 example at 1000 K, allquantities can be taken from Table II and �Gox

0

=−908 kJ/mol. This was also calculated as a function oftemperature for most of the high-K compounds listed inTable I and is shown in Fig. 7. To make a meaningful com-parison, all calculations were done for a reaction consuming1 mol of O2. For instance, for Y2O3, the reaction used was4/3 Y+O2=2/3 Y2O3. It is clear from these data that mostof the oxides in the list of high-K candidates �Table I� have alower �Gox

0 than SiO2, with the exception of Ta2O5. Therare-earth oxides, such as Y2O3 and La2O3, are the mostrobust, against oxidizing Si.

For the oxidation reaction �Eq. �10��, �Gox0 can be re-

lated to the equilibrium oxygen pressure PO2 �in Torr� using�Gox

0 =−RT ln �PO2/760 Torr� where R is 8.314 41J / �K mol� the universal gas constant and T is the tempera-ture �K�. For ZrO2 at 1000 K, PO2=2.8�10−45 Torr. Figure8 shows the temperature dependence of PO2 for the same listof compounds as in Table I. The graph can be interpreted asfollows: for PO2 values below the indicated data points, the

TABLE II. Phases in the Zr–O–Si system with their Gibbs free energy Gf0

for three different temperatures.

CompoundGf

0 �500 K��kJ/mol�

Gf0 �1000 K��kJ/mol�

Gf0 �1500 K�kJ/mol

O2�g� −104 −220 −346Si −10.6 −30.4 −56.9Zr −20.9 −52.4 −92.9SiO�g� −208 −328 −457SiO2 −934 −981 −1048ZrO2 −1126 −1181 −1256ZrSiO4 −2071 −2169 −2304SiZr −186 −237 −316SiZr2 −262 −346 −475Si2Zr −199 −266 −373Si3Zr5 −718 −938 −1276

FIG. 7. Calculated Gibbs energy of formation for the oxide as a function oftemperature according to Eq. �10�.

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oxide will not be stable and decompose, while for PO2 val-ues above the line, the oxide is stable. These predictionscannot be easily verified experimentally because such lowoxygen pressures cannot be attained. A good ultrahighvacuum system reaches a base pressure close to 10−10 Torr.Furthermore, to oxidize a ML/cm2 of a material in10−10 Torr O2—assuming oxidation and sticking coefficientsof unity—will require more than 104 s. For a pressure of10−45 Torr, this time will increase to about 1039 s. The equa-tion used to estimate the time scale will be reported in thenext section. These estimates demonstrate some limitationsof thermodynamic considerations for practical predictions re-garding the stability and the reactions of phases. However,they remain useful for comparing the relative stabilities ofthe different oxides.

In practical thin film deposition processes, PO2 is muchlarger than these estimates. In addition, there is only a shorttime window available for the oxidation to proceed. Thesekinetic considerations will be discussed in the next section.

B. Formation of silicides

The next condition that can be evaluated corresponds toEq. �6�, namely, the stability of the oxide against the forma-tion of metal silicides. There are four Zr silicides reported inTable II, but the one with the largest Si fraction will beconsidered first.

ZrO2 + 3Si = Si2Zr + SiO2 ��G1000 K0 = 24 kJ/mol� .

�11�

As �G0= �GSi2Zr0 +GSiO2

0 �− �GZrO2

0 +3GSi0 �=24 kJ/mol and is

positive, the left-hand side of the equation corresponds to thestable state. Also the reaction involving other Zr silicidesleads to a similar conclusion,

ZrO2 + 2Si = SiZr + SiO2 ��G1000 K0 = 23 kJ/mol� , �12�

2ZrO2 + 3Si = SiZr2 + 2SiO2 ��G1000 K0 = 143 kJ/mol� ,

�13�

5ZrO2 + 8Si = Si3Zr5 + 5SiO2 ��G1000 K0 = 302 kJ/mol� .

�14�

This indicates that once ZrO2 has been deposited on Si, it haslittle tendency to decompose into its constituents or to formsilicates as shown below,

2ZrO2 + Si = Zr + ZrSiO4 ��G1000 K0 = 171 kJ/mol� , �15�

2ZrO2 + 3Si = Si2Zr + ZrSiO4 ��G1000 K0 = 18 kJ/mol� .

�16�

Applying such an analysis to most oxides in the periodicsystem, Hubbard and Schlomm27 found that only a few ox-ides satisfy the above two equations. These are SrO, CaO,BaO, Al2O3, ZrO2, HfO2, Y2O3, and La2O3, as well as a fewother lanthanides. Other oxides such as Ta2O5, TiO2, and theperovskites including SrTiO3 and BaTiO3 were excludedowing to the occurrence of silicide formation.

However, even if silicides will appear �thermodynami-cally� when certain oxides are brought in contact with Si,there are still some possibilities to use such oxides as high-Kdielectrics. To illustrate this, Table III is compiled. It containssome of the phases in the Ti–Si–O system. These include theelements �Ti, O2, and Si�, the oxides �SiO�g�, SiO2, TiO,Ti2O3, and TiO2�, and the silicides �Si2Ti, SiTi, and Si3Ti5�.Additional phases in this table are SrO, BaO, and two solidSiO�S1� and SiO�S2� phases. Some phases were already re-ported in Table II. As before, the �G0 of various reactionscan be evaluated from the data in the table,

TiO2 + Si = Ti + SiO2 ��G1000 K0 = 32 kJ/mol� , �17�

TiO2 + 3Si = Si2Ti + SiO2 ��G1000 K0 = − 95 kJ/mol� ,

�18�

TiO2 + 2Si = SiTi + SiO2 ��G1000 K0 = − 97 kJ/mol� .

�19�

FIG. 8. Calculated equilibrium oxygen pressure PO2 as a function of tem-perature for various high-K compounds.

TABLE III. Phases in the Ti–O–Si system with their respective Gibbs freeenergy Gf

0 for three different temperatures. The O2, Si, SiO�g�, and SiO2

phases have already been listed in Table II. Some additional phases havebeen added and will be discussed in the text.

CompoundGf

0 �500 K��kJ/mol�

Gf0 �1000 K��kJ/mol�

Gf0 �1500 K��kJ/mol�

SiO�S1� −447.3 −488.3 −541.7SiO�S2� −540.0 −574.1 −623.9Ti −16.9 −44.6 −81.7TiO2 −973.3 −1028 −1102.1TiO −562.5 −601.3 −656.2Ti2O3 −1565.8 −1661.8 −1795.7SiTi −156.9 −204.4 −267.2Si2Ti −168.8 −233.0 −319.8Si3Ti5 −699.2 −902.4 −1167.5SrO −622.5 −672.8 −737.7SiSrO3 −1688 −1785 −1915BaO −591.5 −649.9 −723.1

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In contrast to the Zr–O–Si case, these calculations sug-gest that TiO2 in contact with Si will react and lead to theformation of Ti silicides. However, if a stable interface layercan be inserted between TiO2 and Si, then Ti-silicide forma-tion will be suppressed or at least delayed during an anneal-ing process. Such an interface layer could, for instance, bethe stable ZrO2 mentioned above and would allow us to takeadvantage of the higher dielectric constant of TiO2 �80�.Moreover, thin SiO2 or SiON layers ��1 nm� have alreadybeen used for this purpose.

The same logic has also been used to grow single-crystalperovskites such as SrTiO3 epitaxially on Si.28–31 In thiscase, an interface is engineered using a SrO and/or �Ba,Sr�Otemplate layer. Both SrO and BaO have a �Gox

0 that is muchlower than that of SiO2, so that the reaction in Eq. �5� doesnot occur. Accordingly, their equilibrium PO2 is also muchlower than that of SiO2 �Fig. 10�,

2SrO + Si = 2Sr + SiO2 ��G1000 K0 = 252 kJ/mol� . �20�

In addition, the formation of Sr silicate is not thermodynami-cally favored,

3SrO + Si = 2Sr + SrSiO3 ��G1000 K0 = 121 kJ/mol� .

�21�

Unfortunately, not enough thermodynamic data on the Srand Ba silicides are available to quantify the reactions inEqs. �6� and �8� for SrO and BaO. However, those groupsthat grew SrTiO3 on Si using a SrO/ �Ba,Sr�O buffer did notreport the appearance of thick Sr and/or Ba silicides28–30 norwas this predicted using numerical computations.31 In thosecases where such a buffer was not used, the formation of Tisilicides could not be avoided.32

C. Role of suboxides

Since the initial thermodynamic predictions regardingthe stability of ZrO2 and HfO2 were made, a number ofcontradicting results have appeared. These contradictionswere recently reviewed by Stemmer.33 In particular, severalgroups—including our own—simultaneously observed ZrO2

�or HfO2� as well as the presence of Zr or Hf silicide togetherwith SiO2 and/or Si suboxides, as illustrated in Fig. 9. Thisfigure shows the x-ray photoelectron spectroscopy �XPS�data as a function of binding energy of a 3 nm thick HfO2

film grown on Si �100� at 625 K. The Hf4f signature consistsof a doublet around 18 eV and a much weaker feature around14 eV. The former corresponds to Hf atoms in an oxide ma-trix �HfO2� whereas the latter corresponds to Hf atoms insilicide matrix �Hf silicides�. The inset shows the Si2p signa-ture with a large Si peak �99 eV� and a broad SiOx peak�102 eV�. The peak position of pure SiO2 is indicated by anarrow. The position of the SiOx peak in this figure suggests amajority of Si+2 and Si+3.

Hence, the reaction mechanisms described above do notprovide a correct picture of what happens. To account forthese discrepancies, Stemmer33 proposed reactions that in-clude gaseous species �such as SiO�g�� as well as the nons-toichiometry �such as ZrO2−x� of the oxides. In this subsec-

tion, we propose an additional mechanism based on theexistence of a solid Si suboxide SiO�S2� phase.

Most metallic species can form stable oxides with differ-ent oxidation states. A good example is Ti, where stablephases with oxidation state +II �TiO�, +III �Ti2O3�, and +IV�TiO2� exist. Additional phases with intermediate valencestates, such as Ti3O5 and TiO4O7, also exist and their ther-modynamic properties have been tabulated.26 From the val-ues in Table III, �Gox

0 of the Ti suboxides can be calculated,using the same procedure as demonstrated in the previoussubsections. These values were then used to estimate theequilibrium oxygen pressure in Fig. 10. As the Ti oxidationstate increases from +II to +IV, �Gox

0 at 1000 K for an oxi-dation process consuming 1 mol O2 decreases from−893 to −763 kJ/mol, whereas PO2 increases from 1.8�10−44 to 1.1�10−37 Torr. Clearly, to stabilize a Ti+IV

phase should require a higher O2 pressure than to stabilize aTi+II phase, in agreement with these estimates, as illustratedin Fig. 10.

Silicon can also have solid suboxide species, such asSi2O, SiO, and Si2O3. These can be synthesized as amor-phous thin films during the evaporation of Si under different

FIG. 9. Experimental XPS spectrum vs binding energy for a HfO2 filmgrown on Si. The Hf4f signature reveals HfO2 and Hf silicide. The Si2p

signature shown in the inset reveals a Si peak as well as a SiOx feature.

FIG. 10. Calculated equilibrium PO2 as a function of temperature for vari-ous high-K compounds, including suboxides.

051610-7 Locquet et al. J. Appl. Phys. 100, 051610 �2006�

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oxidizing conditions. Although the detailed structure of thesephases still is a topic of discussion,34,35 there is no doubt thatthe average Si valence in these films varies according to theirchemical formula. Upon heating above 1000 K, the filmshave a strong tendency to disproportionate into the phasesSiO2 and Si,34–36 which is one reason for the many contra-dictory results reported. The disproportionation reaction,which may take place on a nanometer scale, makes it diffi-cult to measure the thermodynamic properties of the puresuboxide phases over a large temperature window. Summa-rizing the recent literature, Hohl34 proposes a phase diagramthat includes SiO and Si2O3 as metastable phases that canexist up to 870 and 470 K, respectively. Two nearly identicalestimates for Gf

0 of SiO are available in the literature37,38 andare included in Table III as SiO�S1�. Note that these modelsstart from the premise that SiO is less stable than Si andSiO2, which is derived from the experimental disproportion-ation observation. The consequence of this premise is that,not surprisingly, the Gf

0�SiO� are estimated such that�G1000 K

0 of the following reaction must be positive,

SiO2 + Si = 2SiO�S1� ��G1000 K0 = 353 kJ/mol� . �22�

As a consequence the equilibrium oxygen pressure �Fig. 10�for this SiO�S1� phase is larger than that for SiO2, whichsuggest that upon oxidation first SiO2 forms before SiOforms. From an interface reaction point of view this does notmake sense.

Here we explore a different approach. While it is correctthat most of the thin film deposited SiO will decompose intoareas of Si and SiO2 upon annealing, the interface �3-4 ML�monolayer�� between the two phases always contains Sisuboxides, as shown, for instance, in Fig. 9. This may wellbe a different phase �S2� or structural arrangement than theSiO deposited originally. For instance, in the case of hightemperature �1200 °C� thermally grown SiO2 on Si, XPS hasshown that the interface actually contains all Si valencestates.39 The amount of suboxide phases present at such in-terfaces can be limited to 3-4 ML, but not eliminated, byhigh temperature annealing experiments.36 Whether this ispurely a consequence of steric hinderance that prevents asharp Si–SiO2 interface or a signature of a specific phasethat can only exist between Si and SiO2 cannot be resolved atthis point. As this SiO�S2� phase cannot be completely re-acted away despite the high temperature anneals, it poses adilemma. If this phase is described using the thermodynamicparameters for SiO�S1� mentioned above then, this SiO�S1�is not stable �see reaction in Eq. �22�� and should not exist inthe experimental data. As a consequence, it should also notplay a role in the thermodynamic considerations between Siand the high-K dielectrics.

However, since the 3-4 ML interface region cannot bereacted away, there is no point in ignoring it. For the purposeof this paper, we consider the interface phase a more stablephase than SiO�S1� and call it SiO�S2�. In that case, thereaction in Eq. �22� should therefore have the opposite sign.That is, whenever Si and SiO2 come in contact, this SiO�S2�phase is formed. In addition, we further speculate that thesame stable interphase may exist between Si and all high-Kdielectrics. Although thermodynamic considerations strictly

only apply to large systems, we nevertheless attempt to ex-tend the same line of reasoning to this interface phase.Clearly, its thermodynamic properties must be quite differentfrom those of the reported SiO�S1� phase.37,38 Since the goalis to describe a situation where SiO�S2� will be formed, dif-ferent values of Gf

0 must be provided.To illustrate this, we have—in a gedanken experiment—

created an average SiO�S2� solid suboxide and made an edu-cated guess about its thermodynamic parameters. This is adidactic example and hence neither the precise value of theGf

0 chosen, or the particular Si valence chosen plays a bigrole in demonstrating the argument. There are different waysto make such a guess. In this case, we have evaluated otherfour-valent metals that have a stable MO2 phase as well asknown stable suboxides. This limits the search to elementssuch as Ti, Sn, and Pb, Ti and Sn exhibit a very similarbehavior, whereas in the case of Pb the most stable oxide isPbO and not PbO2. It turns out that for the following discus-sion either the Ti–O or the Sn–O system would lead to nearlyidentical values of the estimated Gf

0�SiO��S2�. Hence, wehave used the Ti–O system as the model system. As ex-pected, TiO2 in contact with Ti will decompose into TiOaccording to

TiO2 + Ti = 2TiO ��G1000 K0 = − 130 kJ/mol� , �23�

which is the type of reaction we are looking for. As a startingpoint, Gf

0�SiO��S2� was estimated from Gf0�TiO�, adjusted

for the observed relative difference between Gf0�SiO2� and

Gf0�TiO2�. Hence Gf

0�SiO�= �1−x� Gf0�TiO� with x

= �Gf0�TiO2�−Gf

0�SiO2�� /Gf0�TiO2�. This procedure was used

to estimate the values of Gf0 SiO�S2� reported in Table III.

Not surprisingly, the estimated �Gox0 =−866 kJ/mol at

1000 K and the corresponding PO2 in Fig. 10 are not farfrom those of TiO.

To estimate the effect of this phase on the thermody-namic considerations developed above, the reactions in theZr–O–Si phase diagram will now be reevaluated against theappearance of this SiO�S2� phase. First, ZrO2 on Si will notdecompose into Zr and SiO as indicated by

ZrO2 + 2Si = Zr + 2SiO ��G1000 K0 = 41.3 kJ/mol� .

�24�

However, the next series of reactions show that the stabilityagainst silicide formation is completely lost,

ZrO2 + 4Si = Si2Zr + 2SiO ��G1000 K0 = − 112 kJ/mol� ,

�25�

ZrO2 + 3Si = SiZr + 2SiO ��G1000 K0 = − 113 kJ/mol� , �26�

2ZrO2 + 5Si = SiZr2 + 4SiO ��G1000 K0 = − 129 kJ/mol� ,

�27�

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5ZrO2 + 13Si = Si3Zr5 + 10SiO ��G1000 K0 = − 378 kJ/mol� .

�28�

Hence, as soon as ZrO2 comes in contact with Si, someSiO�S2� and Zr silicide will be formed at the interface. Com-pared with the case discussed in the previous subsections, itcosts much less energy to form this SiO phase than to formSiO2. Hence the equilibrium of the reaction shifts towardsthe right-hand side. Thermodynamically this may alreadysuffice to transform the entire ZrO2 film; kinetically, how-ever, the reaction depends on the availability of Si �throughdiffusion� for the reaction to proceed. Without Si diffusion,this reaction may remain limited to the interface region.

As the gedanken experiment was designed for this case,the �G1000 K

0 for the reaction of SiO2 in contact with Si lead-ing to the SiO�S2� phase can also be estimated according to

SiO2 + Si = 2SiO�S2� ��G1000 K0 = − 136 kJ/mol� .

�29�

These predictions are completely in agreement with theobservations in the literature33 and with our own measure-ments. Considering the local bonding configuration at the Siinterface, an abrupt transition from Si to SiO2 has never beenobserved using XPS. The same is true for an abrupt bondingconfiguration from Si to ZrO2 or HfO2. In general, the pres-ence of several ML of Si suboxide is observed at this inter-face, and silicides may also be observed, as seen in Fig. 9.This is frequently the case for high-K films grown under highvacuum conditions. One way to limit the interface reactionsis to prepare the films at low temperature and not to performany postgrowth annealing experiments. However, this is notcompatible with the standard industry procedures, which re-quire, for instance, an annealing in forming gas at �700 K.As mentioned above, another practical solution to avoid sil-icide formation is to use an interface layer, typically a0.5–1.0 nm thick SiO2 or SiON film. If such an SiO2 layer isinserted between Si and the high-K dielectric, then the for-mation of SiO�S2� and silicide can be avoided �or delayed� atthe SiO2/high-K interface. While this approach limits sili-cide formation, its impact on the capacity is detrimental, andit does not offer a solution for EOT below 0.5 nm.

At this point, the material recommendations of HubbardSchlomm,27 see previous subsection, can be reevaluatedagainst the thermodynamic parameters of this SiO�S2� phase.Virtually none of the materials suggested will pass the testwith the Gf

0�SiO��S2� chosen here. However, it should alsobe noted that for many relevant silicides, the thermodynamicproperties have not yet been reported and tabulated. In addi-tion, the somewhat arbitrarily chosen Gf

0 of this Si suboxidemay turn out to be not as negative as assumed in this gedan-ken experiment, and its values must be consistent with over-all thermodynamic properties in the Si–O phase diagram.Nevertheless, it is clear that this suggestion may have impli-cations regarding the search for high-K dielectrics that arestable in contract with Si. It may well turn out that no oxideis thermodynamically stable against Si suboxides.

D. Gaseous species

Up to now we have only considered the solid phases andsolid-state reactions. However, during both growth and an-nealing, the gaseous environment plays an important role. Toreview all the possible reactions with process gases wouldrequire an additional section. As we have already taken solidSiO into consideration, we will briefly explore the role of itsgaseous counterpart, SiO�g� in some reactions.

First, the vapor pressure of SiO�g� in equilibrium withthe solid SiO, Si, and SiO2 phases can be estimated from

SiO�S1� = SiO�g� ��G1000 K0 = 160 kJ/mol� , �30�

SiO�S2� = SiO�g� ��G1000 K0 = 246 kJ/mol� , �31�

SiO2 + Si = 2SiO�g� ��G1000 K0 = 355 kJ/mol� . �32�

In all three cases, the favorable side of the reaction is on theside of the solids. Nevertheless a SiO pressure �PSiO� inequilibrium with the solids can be derived using �G0

=−RT ln�PSiO/760 Torr�. For the three reactions, PSiO at1000 K is 3.3�10−6, 1.1�10−10, and 4.0�10−7 Torr, re-spectively, as illustrated in Fig. 11.

Next the decomposition of ZrO2 is explored in the fol-lowing reactions, where L stands for ZrO2+4Si,

ZrO2 + 2Si = Zr + 2SiO�g� ��G1000 K0 = 533 kJ/mol� , �33�

ZrO2 + 4Si = Si2Zr + 2SiO�g� ��G1000 K0 = 380 kJ/mol� ,

�34�

L = Si2Zr + SiO�g� + SiO�S1� ��G1000 K0 = 220 kJ/mol� ,

�35�

L = Si2Zr + SiO�g� + SiO�S2� ��G1000 K0 = 143 kJ/mol� .

�36�

For the last two reactions, a solid as well as gaseous SiOphase were considered as part of the reaction. These tworeactions may be in agreement with the simultaneous experi-

FIG. 11. Calculated equilibrium PSiO as a function of temperature for vari-ous reaction described in the text.

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mental observation of both Si suboxides and Zr silicides to-gether with ZrO2 on Si. As in the above case, �G remainspositive at 1000 K for these reactions, and the equilibriumPSiO are, respectively, 9.0�10−12, 8.9�10−8, 2.4�10−9,and 7.4�10−5 Torr.

Although the above equations suggest that ZrO2 will notdecompose, it should be pointed out that all of the aboveconsiderations used the tabulated Gf

0 values for standard tem-perature and pressure �760 Torr� �STP� conditions. However,besides the variation of Gf

0 as a function of temperature,which has already been illustrated in many graphs here, thereis also a pressure variation. For a solid the pressure depen-dence is negligible, whereas for 1 mol of an ideal gasGf

0�P�=Gf0�760 Torr�+RT ln�P /760 Torr�. For instance, for

P=10−9 Torr, Gf0�SiO� �g� at 1000 K will decrease from

−328 to −556 kJ/mol. This decrease in energy can be under-stood to result from the correspondingly larger volume thatone mol O2 at 10−9 Torr occupies. This will of course changethe energy balance of the above reactions, and �G will beless positive, or in other words, the SiO pressure in equilib-rium with the solids will increase. The pressure ratio�10−9 /760� corresponds to 12 orders of magnitude, and allthe equilibrium PSiO’s mentioned above will be increasedby this amount. In that case, PSiO at 1000 K of all of theabove reactions will exceed 760 Torr, the point above which�G becomes negative and the decomposition will proceed.Hence, it is clear that annealing under low-pressure condi-tions may provide an additional mechanism for oxide de-composition, that is complementary to previoussuggestions.33

E. Interface stability

To improve the usability of certain oxides that are notstable in contact with Si, we have seen that one method is touse an interface layer, typically 0.5–1 nm SiO2 or SiON. Inthis subsection the thermodynamic justification for such aprocess is provided. For instance, the stability of ZrO2 onSiO2 can be tested using the following reactions, where L�=ZrO2+4 SiO2. The solid-state reaction,

ZrO2 + SiO2 = ZrSiO4 ��G1000 K0 = − 6.5 kJ/mol� , �37�

has a slightly negative �G1000 K0 and hence a tendency to-

wards formation of the silicate. As the silicate has a lower ��11� than ZrO2, this may be detrimental to the EOT, whichdepends on the thickness ratio SiO2/ZrSiO4, but not neces-sarily to the leakage.

As there are no other solids in the Zr–Si–O system withequal or larger oxygen content, all other reactions with SiO2

must involve the generation of gaseous species. Considering,for instance, the decomposition reactions including solid SiO�S1 and S2�,

L� = Si2Zr + 2SiO�S1� + 4O2 ��G1000 K0 = 36.6 kJ/mol�

�38�

yields at positive �G1000 K0 , but already also a negative one

of −71.8 kJ/mol at 1100 K. For the SiO�S2� phase, �G0 isnegative already 200 K lower, and at 1000 K equal to−135 kJ/mol. This provides an additional mechanism to ex-

plain the simultaneous presence of ZrO2, Zr silicide, SiO2,and Si suboxides. These results show that there clearly is anincreased stability but that it may come at the price of silicateformation or be restricted to a limited temperature window.

In line with the ideas developed in the previous subsec-tions, the stability of ZrO2 against the solid SiO phases at theSi interface is also briefly explored. In particular, the pres-ence of SiO�S1� will enhance both the silicate formation aswell as Si precipitation and diffusion according to

L� = ZrSiO4 + Si ��G1000 K0 = − 41.9 kJ/mol� , �39�

where L� is ZrO2+2SiO�S1�.

F. Issues

While the focus of this paper is on high-K dielectrics,there is another area where these conclusions may also havean impact. The high-K dielectric needs a metallic top contact.Traditionally this has been done using heavily doped p or npolycrystalline silicon. However, it turned out that there arequite a number of issues at that contact. The above resultsagain suggest that this contact interface will not be stable andthat a silicide as well as SiO may be formed.

Finally, there are number of issues regarding the practi-cal validity of the thermodynamic considerations for this ap-plication that should be mentioned. First, in the thin filmconfiguration, materials are in contact with a specific surfaceorientation. In the case of complex oxide on Si, such a sur-face may include an element that either easily forms a sili-cide �for instance, the TiO2 surface of SrTiO3� or one thatdoes not easily form a silicide �for instance, the SrO surfaceof SrTiO3�. There can be a significant difference in stabilitybetween these two cases. Second, the thermodynamic quan-tities used here are derived from bulk samples under stan-dard conditions. However, it is often difficult to make com-pletely phase-pure material, which will affect the correctnessof the tabulated Gf

0 values. For instance, different values forthe Zr silicides have recently been proposed,40 which willshift the phase balances mentioned above.33 An additionalconcern is that the properties of thin films can vary consid-erably from bulk samples. Differences may be related tostrain and interface energies. In particular, for very thin films,a huge amount of strain as well as metastable phases caneasily be induced.

VI. KINETIC CONSIDERATIONS

In the previous section the thermodynamic stability ofoxides deposited on top of Si was considered in detail. How-ever, during the deposition step, the growing film fortunatelyis not under equilibrium conditions. The oxygen partial pres-sures used during oxide growth are many orders of magni-tude above those at which Si and SiO2 are in thermodynamicequilibrium. Hence, the entire Si wafer should become oxi-dized immediately. However, the speed at which this reactioncan proceed is limited by kinetic considerations.

One example of such considerations is to estimate themolecular incidence rate. The molecular incidence rate of agas species is the number of gas molecules that will impingeon 1 cm2/s. This is a function of the pressure P �Torr� and

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temperature T �K� as well as the mass M �a.u.� of the gasmolecules and is given by41

R = 3.513 � 1022P/�MT�1/2. �40�

For example, the incidence rate R of O2 at 300 K and 1 Torrequals 3.59�1020 O2 molecules/cm2 s. Assuming a stickingand oxidation coefficient of unity, that is, every impingingoxygen molecule will oxidize Si into SiO2, and consideringthe surface density of Si �001� atoms NSi=6.74�1014/cm2,the time to oxidize a Si �001� surface is 1.9�10−6 s. If thegoal is to prevent any Si oxidation, then either the Si surfacemust be protected or the evaporation rate of the metallicspecies �such as Zr� must be large enough to consume allimpinging O2 molecules. In this case, the Zr deposition rateshould exceed 1 ML per 1.9�10−6 s, which is clearly notpractical. These assumptions will only provide a lower limiton the oxidation time. When the sticking and oxidation co-efficient are smaller than unity, the time needed to oxidizethe surface will increase accordingly.

If the goal is to control the oxidation better than in theabove example, then different process conditions are needed,for instance, a reduction of the O2 pressure during growth. At10−6 Torr, the time needed to oxidize a Si surface into SiO2

is now increased to 1.9 s. Under such low-pressure condi-tions it then becomes feasible to control the oxidation stateof different materials. This is illustrated in Fig. 12, whichshows the total oxygen budget needed to oxidize differentmaterials. The oxygen budget is defined as the product ofpressure and exposure time. For the above example, consid-ering the oxidation of one Si ML, the required minimumoxygen budget is 1.9�10−6 Torr s. For simplicity, the latticeparameters of all materials in this plot were scaled to lead tothe same number of surface atoms as Si �001� �NSi=6.74�1014 /cm2�. Under these conditions, the amount of O2

needed to form a monolayer of HfO2, ZrO2, or SiO2 is thesame. In practice, such an assumption may work only for thefirst few monolayers, where epitaxy tends to keep the atomsaligned. However, for thicker films the lattice parameterswill differ considerably, and thus the values must be cor-rected accordingly.

In Fig. 12 the oxygen budgets for the different oxidationstates of Si and various other materials are estimated. Underlow-pressure conditions �10−6 Torr�, it is thus in principlesimple to tune the oxidation state from Si+I to Si+IV bychanging the exposure time by a factor of 4. For the subox-ides, each data series in the figure can correspond to a phaseseparation line. If an oxygen budget is chosen that falls be-tween two lines, then a mixture of two phases becomes pos-sible. For instance, in the case of HfO2, applying an oxygenbudget that exceeds the calculated one will allow excess oxy-gen in the reactor, which may lead to the formation of someSiO below the HfO2 film. Alternatively if not enough oxygenis provided to completely oxidize HfO2, then this may leadto Hf suboxides, a large density of oxygen vacancies, orpromote the formation of Hf silicides. The likelihood of anyof the above reactions can then again be determined by theabove thermodynamic considerations. But clearly the avail-ability of sufficient oxygen on the time scale at which thedeposition takes place is an essential kinetic parameter forthe successful growth of high-K dielectrics on Si.

The above figure provides a good first-order estimationof the O2 pressure needed. However, the oxidation coeffi-cients of different materials—and different oxidationstates—turn out to change considerably. For instance, theoxidation coefficient of Si at 600 K is below 10−3, whereasthose of Sr and Ba are close to 1. Hence in practice, a seriesof experiments is needed to accurately determine the oxygenbudget needed for each case.

Another good example of kinetic considerations is re-lated to diffusion. For instance, in the previous section, itwas shown that ZrO2 on Si is not stable against the formationof a Zr silicide and SiO. Yet, for this reaction to proceed, Simust be in contact with ZrO2. For a deposition process thatoccurs at sufficiently low temperature, Si diffusion can berestricted to the region near the interface. However, at highertemperature, this is not the case and as Si atoms diffuse intothe oxide, they will create a filamentary path containing SiOx

as well as Zr silicides.

VII. LEAKAGE CURRENT OF BILAYERS

As discussed above, for most high-K materials reportedto date, there is an interfacial SiOx or SiON ��1 nm� layer—intentionally or accidentally—present between the high-K di-electric and Si. Even if this layer is very thin, it is connectedin series with the dielectric and has a profound impact on theelectrical properties. For instance, if a 3 nm thick high-Klayer with �=20 �C /A=5.9�10−6 F/cm2� such as theHfO2-based oxides has a 1 nm thick SiO2 interfacial layerwith �=3.9 �C /A=3.45�10−6 F/cm2�, then the C /A of thetotal stack will drop to 2.18�10−6 F/cm2 or the EOT willincrease from 0.58 to about 1.6 nm. Even a 0.5 nm thickSiO2 layer will almost double the EOT to about 1.08 nm andhence cut the expected Ids in half �Eq. �1��.

The leakage current is also strongly affected. With twocapacitors in series �CSiO2

and Chigh K�, a part of VG will fallacross each capacitor. As the charge on each capacitor facewill be the same, Qox=−QSi, the voltage drops will beVSiO2

=−QSi /CSiO2and Vhigh K=−QSi /Chigh K, respectively,

FIG. 12. Calculated minimal oxygen budget as a function of thickness formaterials with different oxidation states.

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and determine Jt through each barrier. For capacitors in se-ries, the largest voltage drop falls across the smallest capaci-tor, in this case the SiO2 layer, as illustrated in Fig. 13. At thereference voltage VFB−1 V, VSiO2

=−0.52 V, Vhigh K

=−0.3 V, and Vtotal=−0.82 V, while � /q remains at−0.18 V as was the case for the single layers in Sec. III. Atthese voltages, Jt through each individual layer would be 900and 3.16 A/cm2.

To evaluate Jt of the bilayer, a simple first-order approxi-mation is to consider a thickness-averaged tunnel barrier,where �= ��SiO2

tSiO2+�high Kthigh K� / �tSiO2

+ thigh K�=2.06 eVand m*= �mSiO2

* tSiO2+mhigh K

* thigh K� / �tSiO2+ thigh K�=0.16. The

quantities are then used in Eq. �2� with Vox=VSiO2+Vhigh K

and tox= tSiO2+ thigh K. At VG=VFB−1 V, Jt drops by about

four orders of magnitude from −73.2 A/cm2 for a single3 nm HfO2-based film to −2.38�10−3 A/cm2 for the bi-layer.

The drastic changes to the EOT and Jt of these bilayerssubstantially alter the predictions of the previous FOM andnecessitate a modified version, see Fig. 14. Starting fromJt�VG� of single HfO2-based layers, with �=20, �=1.4 eV,and m*=0.14me �solid circles�, the SiO2 thickness is in-creased gradually from 0 to 1 nm in steps of 0.25 nm. Foreach monolayer of SiO2 added, Jt drops by about an order ofmagnitude, following a line more or less parallel to that ofsingle SiO2 layers �solid squares�. While Jt of a 3 nmHfO2-based layer with a 0.5 nm SiO2 interface decreases be-low 1 A/cm2, the EOT unfortunately is now larger than1 nm, which does not fulfill the long-term ITRS require-ments illustrated in Fig. 2. Of course, taken at constant EOTof 1 nm—which corresponds to the vertical line in Fig. 14—the leakage current density in such bilayers decreases as theSiO2 content decreases.

The above figure is derived from simple model calcula-tions only. For a precise correlation of these predictions withexperiment, a very accurate determination of the SiO2 inter-face thickness is required. Is that possible? Figure 15 showsa transmission electron microscope �TEM� cross section of a

3.4 nm thick HfO2 film with �1 nm SiO2. A precise thick-ness estimate is hampered because the diffraction contrastmust be sharp and not vary significantly over the area inves-tigated. Here both interfaces are not sharp—structurally orchemically—with a transition region from Si to SiO2 as wellas a transition region from SiO2 to HfO2. In addition, theTEM image contrast originates from a two-dimensional pro-jection of the sample, and the structural and/or chemicalvariation along the viewing direction can generate a verycomplex contrast which cannot be easily interpreted and maylead to blurring, even for sharp interfaces. In this particularcase, the SiO2 thickness cannot be determined to better than1.0±0.25 nm, which leaves an error bar of two orders ofmagnitude on Jt! The precision of other techniques such asspectroscopic ellipsometry and XPS is also not better andwith their limited spatial resolution of about 1 �m, they av-erage over the entire interface.

Several other complications make an accurate determi-nation difficult. First, the presence of charges �mobile andfixed� in the oxide or at the interface adds additional voltages

FIG. 13. The band bending �� /q�, the voltage over the corresponding ox-ides VSiO2 and VHfO2, as well as their total as a function of VG calculatedusing Eq. �3� for a bilayer consisting of 1.0 nm SiO2 and 3 nm HfO2.

FIG. 14. Calculated Jt�VFB−1 V� vs EOT for SiO2/HfO2-based bilayers,where the SiO2 thickness increases from 0 to 1 nm in steps of 0.25 nm. Thedotted line connects results from bilayers with identical HfO2 thickness�3 nm�. The vertical line corresponds to EOT=1 nm.

FIG. 15. TEM image of the 3.4 nm thick HfO2 film on Si �001� with�1.0 nm interfacial SiOx layer.

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over the gate �Eq. �3�� and, if not taken into account properly,changes the reference voltage �VG=VFB−1 V�, at which thedifferent samples are compared in Fig. 14. For the exampleof 3 nm HfO2, a fixed charge density Qf =5�102/cm2 willlead to an induced voltage QfA /Cox=0.135 V and an erroron Jt of at least a factor of 2. This amount of charge is farfrom insignificant and must be compared with QSi in Fig. 3.In that example the onset of inversion takes place for a sur-face charge of about 1012 q / cm2. Compared with the numberof Si �100� surface atoms, NSi=6.74�1014/cm2, this numberof defects corresponds to about 1% of the Si atoms. Such adefect concentration is quite common in high-K dielectrics.Many possible sources for defects have been discussed in theliterature, and we refer the reader to the reviews mentionedin the Introduction. However, in view of the thermodynamicconsiderations in Sec. V, the presence of the Si suboxidephase at the interface as well as the silicide may well be atthe origin of these defects.

A second error, similar to the previous one, can occurowing to variations in the metal work function �Wm� itselfand how it is modified by the presence of silicides at thehigh-K/metal-gate interface. Third, as discussed in detailabove, the precise nature of the interfacial SiO2 �SiOx� layeris not well known and can vary from sample to sample. Asmentioned, XPS results demonstrated that all Si valencestates are present at the interface between Si and SiO2.39 Theelectrical properties of these Si suboxides are not wellknown, except for the deposited SiO films. The presence ofsuch SiO phases—with an increased ��6 and a reducedEg�6 eV—will increase Jt, reduce EOT, and increase theuncertainty.

VIII. MOBILITY

There is a second essential FOM that is widely usedin the literature. It connects the high-field ��1 MV/cm� car-rier mobility with the EOT, as illustrated in Fig. 16. For thedata taken from Murto et al.,42 � is severely depressedat small EOT values compared with its “universal” value

�170 cm2/V s at 1.3 MV/cm� which corresponds to that of astandard SiO2/Si system. This is a very disappointing result,as the gain in Ids achieved by reducing EOT may be com-pletely lost through the � degradation. Although today thesituation might have improved somewhat thanks to extensivepostgrowth annealing treatments, the precise origin of thisphenomenon has not yet been elucidated.

There are two main models to explain the mobility deg-radation, namely, a scattering mechanism via remotephonons and Coulomb scattering with charged defects/roughness. The remote phonon scattering model, developedby Fischetti et al.,43 is based on the observation that all high-K dielectrics intrinsically have low energy phonons. Al-though “remote” from the carriers in the channel by at least1 nm, these lattice vibrations correspond to dipole displace-ments in the dielectric, which couple electrically to the car-riers. The second model44 is based on the observed excess oftrapped charges and/or interface states.42 Many experimentsconfirm the large number of charged defects in high-K di-electrics, observed, for instance, through the shift of VFB inIV and CV measurements. Most of these may be located nearthe SiOx /Si interface, the SiOx /high-K interface, or in thehigh-K dielectric itself. At this point, it seems likely that themobility degradation is due to a combination of these twomechanisms.

IX. CONCLUSION

We have “selectively” looked at the current state of theart in the field of high-K dielectrics for the gate stack. Twofigures of merit were presented that illustrate two major chal-lenges. On the one hand, the materials currently beingstudied—while improving Jt—do not yet provide a good so-lution for EOT down to 0.5 nm. To get there will requirematerials with higher � and/or higher �, while maintainingan interfacial SiOx thickness of less than 1 ML. Anotherpossibility may be to remove any Si–O bonds by creating a“metallic” silicide submonolayer—as occurs probably for the

FIG. 16. High-field mobility vs EOT for a broad rangeof materials showing a severely reduced mobility at lowEOT values. The legend specifies the surface treatment�O3, NH3�, the high-K material, and the gate metalused.

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3 Å EOT LaAlO3 on Si �Ref. 45�—but at the expense of amobility reduction related to an increased Coulomb scatter-ing.

As the phases, including interface phases, experimen-tally observed do not agree with the thermodynamic predic-tions, an in-depth review was provided that covers most rel-evant aspects. By introducing the solid SiO phases, eitherfrom literature values or by estimation, reactions that canexplain the observed results are proposed. Finally, the high-field � values at low EOT are also reported. These values areunacceptably low which seriously hampers the introductionof high-K dielectrics into CMOS devices.

ACKNOWLEDGMENTS

The authors gratefully acknowledge support from B.Mereu, A. Guiller, C. Rossel, D. Webb, H. Siegwart, D.Caimi, R. Germann, P. Staar, and A. Tapponier.

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