High-K dielectrics for the gate stack

JOURNAL OF APPLIED PHYSICS 100, 051610 共2006兲

High-K dielectrics for the gate stack Jean-Pierre Locquet,a兲 Chiara Marchiori, Maryline Sousa, and Jean Fompeyrine IBM Research GmbH, Zurich Research Laboratory, 8803 Rüschlikon, Switzerland

Jin Won Seo Institute Physics of Complex Matters, EPFL, 1015 Lausanne, Switzerland and Advanced Materials and Metrology, MosBeam Foundation, PSE, 1015 Lausanne, Switzerland

共Received 4 January 2006; accepted 28 June 2006; published online 15 September 2006兲 This article gives an overview of recent developments in the search for the next-generation dielectric for the complementary metal-oxide semiconductor gate stack. After introducing the main quantities of interest, the paper concentrates on a figure of merit that connects two main properties of the gate stack, namely, the leakage current and the capacitance. This is done for single layers as well as for bilayers consisting of interfacial SiOx and a high-K dielectric. In the case of the bilayers, the impact of the interfacial layer SiOx is enormous, reducing the leakage current by an order of magnitude per monolayer. This extreme dependance makes a good correlation between the leakage and the structural parameters nearly impossible. This is illustrated using numerical examples designed to help the reader evaluate the orders of magnitude involved. The origin of the interfacial layer is traced back by means of thermodynamic considerations. As the estimates put forward in the literature do not correspond to the results observed, a detailed review is made, and additional mechanisms are suggested. By using reasonable values for the Gibbs free energy of an interfacial solid silicon oxide phase it is demonstrated how the reaction equilibria shift. Such an interface phase may fundamentally change the stability criteria of oxides on Si. Furthermore, it can also provide a major source of electronic defects that will affect the device performance. Finally, a second figure of merit is introduced that connects the capacitance with a strongly reduced carrier mobility, which might also be related to the same electronic defects. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2336996兴 I. INTRODUCTION

The term high K used worldwide to refer to this field of activities is an unfortunate choice. In contrast to other “high’s” such as high temperature superconductivity, high K is neither associated with a recent spectacular discovery or an exceptional material property. On the contrary, it refers more to an “anything but” boundary condition on the dielectric constant of an insulator. A high-K material is an insulator with a dielectric constant 共⑀兲 that is larger than that of silicon dioxide 共⑀ = 3.9兲. There are two main areas in which the highK dielectrics can be applied. In both cases, they are typically used in a parallel plate capacitor configuration, sandwiched either between two metals or a metal and a semiconductor. In the former configuration, the dielectric is used to store charge in random-access memory 共RAM兲 applications, whereas in the latter case, the dielectric permits to modulate 共or gate兲 the carrier concentration of an adjacent semiconductor in a field-effect transistor 共FET兲. While most of the articles in this special issue on ferroelectrics are related to the former application, this paper focuses only on the latter use of high-K dielectrics. Historically, the use of insulators for this purpose goes back to the origins of the transistor itself. Although Lilienfeld1–3 and Heil4 attempted to realize solid-state devices around 1930, an observation of transistor action in n-type polycrystalline germanium 共Ge兲 using a point-contact a兲

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0021-8979/2006/100共5兲/051610/14/$23.00

configuration took place in 1947.5,6 However, the practical silicon 共Si兲 metal-oxide semiconductor 共MOS兲 transistor with an oxidized Si gate was introduced much later. The silicon–silicon dioxide MOSFET was made in 1960 by Kahgn and Attala7,8 and described in two patents.9,10 By 1965, the field had progressed so much that Moore was able to establish a famous trend, now called Moore’s law.11 Since then, the structural, chemical, and electric properties of a silicon dioxide gate dielectric have been improved tremendously in these past 45 years. Although the main focus was on using and optimizing silicon dioxide, many alternative high-K dielectrics have been explored over the years. A number of early studies included aluminium oxide in a single layer12 as well as in bilayers with silicon dioxide.13–15 In this sense, high K is nearly as old as the Si– SiO2 MOSFET itself. Besides having a sufficiently large ⑀, there are several other critical requirements a high-K dielectric must fulfill before it can replace SiO2. These are 共i兲 thermodynamic stability in contact with Si on one side of the dielectric and the gate metallization on the other side; 共ii兲 kinetic stability against Si and the metal gate, in particular during high temperature processing and annealing; 共iii兲 band offsets with Si艌 1 eV to assure low leakage currents; 共iv兲 a passivated, low-defect-density interface with Si to ensure large carrier mobility in the Si channel and good breakdown properties; and 共v兲 a low defect density in the high-K dielectric itself to prevent flatband 共VFB兲 and threshold 共VT兲 voltage shifts and

100, 051610-1

© 2006 American Institute of Physics

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FIG. 1. The various elements composing a MOSFET, including the substrate 共p-Si兲, the sidewall trench insulation 共STI兲, the implanted source and drain contact regions, as well as the gate contact with the dielectric above the channel region, indicated as a dotted line.

instabilities. Several excellent reviews have already appeared such as the early one by Wilk et al.,16 the book High-K gate dielectrics edited by Houssa,17 and the recent review by Robertson.18 The reader is referred to these texts for a more complete overview. II. CMOS PERFORMANCE: ITRS ROADMAP

For high-performance MOSFETs, the most significant parameter is the current between source and drain 共Ids兲 that the transistor can drive. More current means that the transistor—and all the parasitic capacitances and resistances that it is composed of—can be turned on faster. Two voltages determine the response of the three-terminal device shown in Fig. 1. First, the gate voltage 共VG兲 charges the gate insulator in the parallel plate capacitor configuration and induces an accumulation or inversion of the charge carrier density in the semiconductor QSi. A larger capacitance means more carriers in the semiconducting channel for the same applied voltage. The second voltage is the one applied between source and drain 共Vds兲, which is responsible for driving the induced charges forward in the channel. The capacitance of the gate insulator 共Cox兲 in the parallel plate configuration depends on the area 共A兲, the insulator thickness 共tox兲, and ⑀ of the insulator, Cox = ⑀⑀0A / tox with ⑀0 the vacuum permittivity. For a channel width 共W兲 and length 共L兲 of 100 nm and a SiO2 tox of 1.5 nm, Cox = 0.23 fF or, per unit area C / A = 2.3 ␮F / cm2. This corresponds roughly to the one 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 band gap of 1.1 eV, a threshold voltage 共VT兲—of the order of the band gap—must be overcome before carriers can be induced, and the carrier density is then proportional to Cox共VG − VT兲. In the framework of high-K dielectrics, it is practical to compare the capacitive charge of an insulator with that of SiO2. For this, the concept of equivalent oxide thickness 共EOT兲 is introduced as follows: the EOT of a high-K insulator is equivalent to the SiO2 thickness that would yield the same capacitance, i.e., tSiO2 = thigh K 共3.9/ ⑀high K兲. The second voltage Vds transports the induced charges. The resulting current Ids depends on the geometry 共W , L兲 of the channel, the mobility 共␮兲, and the induced charge density 共QSi = ⑀⑀0 / tox = C / A兲, as well as on the applied voltages in Eq. 共1兲 derived from Sah,19

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

Ids = ␮

⑀⑀0 W 2 共VG − VT兲Vds − 1/2Vds . tox L

共1兲

For convenience, this equation was written as a product of three different terms, which group together the parameters of the deposited materials 共␮ , ⑀ , tox兲, the geometrical parameters 共W , L兲, and the power variables 共VG , VT兲, respectively. Taking the same device dimensions as above and assuming VT = 0 V, VG = 0 V, Vds = 1 V, and ␮ = 300 cm2 / V s, we obtain the current through the transistor Ids = 36⫻ 10−6 A. The quantity typically quoted 关for instance, in the International Technology Roadmap for Semiconductors20 共ITRS兲兴 is the saturation current Ids,sat normalized over the channel width W. Ids = Ids,sat when Vds = 共VG − VT兲 and the power term 2 / 2. For our example Ids,sat in Eq. 共1兲 becomes Vds = 360 A / m. For high-performance logic, the expected evolution of Ids,sat—and EOT—is shown in Fig. 2, suggesting that much more current will be drawn from a single transistor in the years to come. Simultaneously, the EOT must attain values close to 0.5 nm. The parameters that can make this possible are tox, ⑀, and ␮, corresponding to three different scenarios being pursued, namely, scaling, high K, and high ␮. Scaling has been the main driver for CMOS, but a tSiO2 below 1 nm exhibits too strong a tunneling current as demonstrated below. A high-K dielectric with ⑀ = 4⑀SiO2 and tox = 2tSiO2 would double Ids, but there are still many unsolved issues as also described below. The third possibility to improve Ids is to increase ␮ beyond the typical 300 cm2 / V s, in devices that use strained Si, Ge, or III/V compounds. For instance, IBM’s recently announced 65 nm applicationspecific integrated circuit 共ASIC兲 includes a form of strained Si.21 III. LEAKAGE CURRENT OF SINGLE LAYERS

In this section, the leakage current through the gate insulator will be estimated. For very thin films, the leakage current is essentially due to direct tunneling of holes or electrons from their respective bands across the band offset with the insulator. For thicker films, other mechanisms such as Fowler-Nordheim tunneling predominate. As will be derived below, Fig. 6 shows that the tunneling current density 共Jt兲 for

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SiO2 thicknesses 艋1.5 nm quickly becomes larger22 than 100 A / cm2. Such a Jt leads to unacceptable heat dissipation and is the biggest factor in the thermal load of current microprocessors. Theoretically, for a thin insulator with a barrier height ␾ 共eV兲 and an applied voltage across the oxide 共Vox兲 smaller than ␾ / q, Schuegraf and Hu23 approximated Jt as Jt =

再

2 − 8␲冑2m*␾␾ tox q3 Vox exp 2 Vox 8␲h␾ tox 3hq

冋 冉

⫻ 1− 1−

qVox ␾

冊 册冎 3/2

共2兲

,

where q is the charge of an electron, h is Planck’s constant, and m* is the tunneling effective mass in the insulator. For a 1.5 nm thick SiO2 film with ␾ = 4.05 eV, m* = 0.22me, and A = 共100 ␮m兲2, we obtain Jt = −21.6 A / cm2 at Vox = 1 V. When a gate voltage VG is applied between the gate metal and Si, only a part remains across the oxide Vox, while other parts are related to the band bending ⌿ 共eV兲 and the difference in the work functions between the gate metal Wm 共eV兲 and the semiconductor WSi. WSi is a function of the electron affinity 共␹ = 4.05 eV兲, the band gap 共Eg = 1.12 eV兲, and the dopant versus intrinsic concentration 共Na / Ni兲 which defines the position of the Fermi level and is the term between parentheses in Eq. 共3兲, VG =

冋

册

␹ + Eg/2 + kBT log共Na/Ni兲 Wm ⌿ − + Vox + , 共3兲 q q q

where the first two terms correspond to the flatband voltage V共FB兲. In experiments, leakage currents are typically reported as a function of VG not Vox, which makes a comparison of various reported results tedious. To calculate Vox = Qox / Cox, one uses Qox = −QSi 共the charges on both sides of a capacitor have the same magnitude but opposite polarity兲, with QSi varying as a function of ⌿,

冋

FIG. 3. Absolute values of the calculated charge on the Si surface as a function of ⌿ using Eq. 共4兲. The flatband condition 共⌿ = 0 eV兲 as well as the regions corresponding to accumulation, depletion, and inversion are indicated.

linearly with VG whereas Vox remained almost constant. In accumulation 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 nm SiO2. In this case, for the same applied VG, the magnitude of Vox is always larger than for thinner SiO2. The smaller Cox of the 3 nm SiO2 film leads to a larger voltage drop over the oxide. With the above information, Jt关Vox共⌿兲兴, Eq. 共2兲 can now be calculated and plotted versus VG共⌿兲. Note that this model is only a simple approximation and not all the physics is appropriately taken into account. This was done for p- and n-Si using various SiO2 thicknesses and compared with the experimental data.22 The parameters for both systems were Wm = 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-

QSi = ⫿ 冑2⑀SikBTNa 共e−K + K − 1兲 +

N2i

共e N2a

K

− K − 1兲

册

1/2

,

共4兲

where the ⫿ sign indicates a positive sign when K is negative, K = q⌿ / kBT and ⑀Si = 11.7. The charge density on the Si surface for p doping as a function of ⌿ is shown in Fig. 3 for the three regions of interest, i.e., accumulation, depletion, and inversion. While in depletion, QSi does not change very much in a voltage region corresponding to Eg − 0 eV艋 ⌿ 艋 1.12 V; outside this region, QSi increases exponentially and consequently also Vox. Next, both Vox共⌿兲 and VG共⌿兲 are calculated as a function of ⌿ using Eq. 共3兲. Here we assume the same Na, A, and tSiO2 as above and Wm = 4.05 eV for a poly-Si gate electrode. For ⌿ = 0 eV, VG equals −1 V and corresponds to the flatband voltage VFB. The results are plotted as a function of VG in Fig. 4. The position of VFB is easily verified; it also corresponds to Vox = 0 V. In the depletion regime, ⌿ changes

FIG. 4. The band bending 共⌿ / q兲 and Vox as a function of VG calculated using Eq. 共3兲 for 1.5 and 3 nm SiO2. The flatband voltage VFB, the threshold voltage VT for inversion, as well as a reference voltage VFB − 1 V are also indicated.

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TABLE I. Main high-K materials with their parameters as tabulated by Robertson 共Ref. 18兲.

FIG. 5. Experimental and calculated Jt共VG兲 for thin SiO2 films on p- and n-Si in accumulation, using poly-Si gate contacts. The vertical lines define the reference voltages.

tween the experimental data and the calculated curves is observed, see Fig. 5. In addition, the same parameters were then used to calculate the expected behavior for 1.5 and 2.0 nm thick SiO2 films. For the thinnest films, Jt can exceed 1 A / cm2 substantially. To compare Jt for different thicknesses and/or different materials, it is useful to define a reference voltage. Hence, typically, 1 V is subtracted 共added兲 to VFB in the case of p -Si 共n-Si兲. Such a comparison is made in Fig. 6, where Jt共VFB − 1 V兲 is plotted versus the equivalent SiO2 thickness for SiO2 as well as for high-K materials. The points representing SiO2 共solid squares兲 in this figure of merit 共FOM兲 shown in Fig. 6 correspond to the experimental data22 shown in Fig. 5 extrapolated further, down to 0.5 nm thick SiO2. At the reference voltage VG = 共VFB − 1 V兲, a 1 nm SiO2 film has Jt = −2495 A / cm2. Next, the parameters of the barrier are gradually modified towards those of high-K dielectrics. First, only ⑀ was changed from 3.9 to 20 and the lowest Jt is obtained 共solid circles兲. For

FIG. 6. Absolute values of the calculated Jt共VFB − 1 V兲 vs EOT for various oxide/Si systems discussed in the text. The top axis is the areal capacitance corresponding to the EOT.

Material

⑀

Eg 共eV兲

CBO 共eV兲

VBO 共eV兲

SiO2 Si3N4 Al2O3 La2O3 Y 2O 3 ZrO2 Ta2O5 HfO2 HfSiO4 TiO2 a-LaAlO3 SrTiO3

3.9 7 9 30 15 25 22 25 11 80 30 2000

9.0 5.3 8.8 6.0 6.0 5.8 4.4 5.8 6.5 3.5 5.6 3.2

3.2 2.4 2.8 2.3 2.3 1.5 0.35 1.4 1.8 0 1.8 0

4.7 1.8 4.9 2.6 2.6 3.2 2.95 3.3 3.6 2.4 2.7 2.1

EOT= 0.5 nm, this would represent an improvement in Jt of more than ten orders of magnitude. Unfortunately, a material with a large ⑀ also has smaller ␾ and m* 共Table I兲. The effect is illustrated by the next two curves, where ␾ is reduced from 4.05 to 1.4 eV 共solid triangle up兲 and m* from 0.22 to 0.14 共solid triangle down兲. The latter curve is typical24 of ZrO2 or HfO2 based high-K materials. For EOT= 0.5 nm, Jt now improves only about three orders of magnitude compared 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 = 共VFB − 1 V兲. From an EOT viewpoint, for such a low EOT value, this is orders of magnitude better than the result for SiO2. However, from a Jt only viewpoint, this is orders of magnitude worse than SiO2, as a 3 nm SiO2 film has a Jt = −3.7⫻ 10−6 A / cm2. Overall, this FOM confirms that high-K materials may be good 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 available that could be used. Table I lists the main high-K candidate materials with their ⑀ and Eg values as well as the conduction 共valence兲 band offset, CBO 共VBO兲.18 For each of the materials listed, a relatively wide range of CBO and VBO values obtained using various methods has been reported. The tunneling barrier height ␾ can be derived from the CBO 共or VBO兲 by taking into account the energy difference between the position of the Fermi level and the corresponding band. The table also reveals that the CBO in general is much smaller than the VBO, which leads to highly asymmetric Jt共VG兲 curves on p- and n-Si. Another consequence of the low CBO is the appearance of other contributions25 to the leakage current. These include Schottky emission over the barrier as well as Poole-Frenkel emission using the electrically active defects in the oxide. For both mechanisms, the conduction band of the high-K dielectric is populated by thermally emitted carriers, and the leakage may become limited by the bulk resistance of the dielectric.25

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TABLE II. Phases in the Zr–O–Si system with their Gibbs free energy G0f for three different temperatures.

V. THERMODYNAMIC CONSIDERATIONS

Experimentally, these insulators must be deposited on Si without the occurrence of reactions that would induce the formation of other phases. The stability criteria for such bilayers have two aspects: a thermodynamic and a kinetic one. If thermodynamic equilibrium conditions are assumed, then the tabulated Gibbs free energy G0f of the different bulk phases26 can be used to estimate whether certain reactions will take place. While there are a number of issues to use thermodynamic considerations for thin film problems 共see discussion below兲 they can be used as first-order estimates. Some very common reactions that can occur without the presence of oxygen are, for instance, MO2 + Si = M + SiO2 ,

共5兲

MO2 + 2Si = MSi + SiO2 ,

共6兲

2MO2 + Si = M + MSiO4 ,

共7兲

2MO2 + 2Si = MSi + MSiO4 ,

共8兲

where M represents a four-valent metal. The first reaction corresponds to the decomposition of the metal oxide in favor of the formation of SiO2. The second reaction corresponds to the decomposition of the metal oxide in favor of the formation of a silicide phase and SiO2. Both cases have detrimental effects by first decreasing the total capacitance owing to the addition of a dielectric with ⑀ = 3.9 in series with the high-K dielectric. On the other hand, the leakage is also increased because of the addition of a 共mostly兲 conducting silicide. The last two reactions describe the formation of a silicate. In general silicates have a much lower dielectric constant than the metal oxides that do not contain Si. For instance, in the case of Zr silicate, ⑀ = 11. The impact of silicate formation is also detrimental to the total capacitance, but to a lesser extent than the formation of SiO2. To illustrate how such thermodynamic estimates are made, we take the Zr–Si–O system as an example as it is one of the best tabulated systems 关see Table II 共Ref. 26兲兴 and it satisfies the equations above. The phase diagram contains 11 phases, namely, the elements 共Zr, O2, and Si兲, the oxides 关SiO2, SiO 共gas兲, ZrO2, and ZrSiO4兴, and the silicides 共SiZr, SiZr2, Si2Zr, and Si3Zr5兲.

Compound

G0f 共500 K兲 共kJ/mol兲

G0f 共1000 K兲 共kJ/mol兲

G0f 共1500 K兲 kJ/mol

O2共g兲 Si Zr SiO共g兲 SiO2 ZrO2 ZrSiO4 SiZr SiZr2 Si2Zr Si3Zr5

−104 −10.6 −20.9 −208 −934 −1126 −2071 −186 −262 −199 −718

−220 −30.4 −52.4 −328 −981 −1181 −2169 −237 −346 −266 −938

−346 −56.9 −92.9 −457 −1048 −1256 −2304 −316 −475 −373 −1276

M + O2 = MO2 .

共10兲

From the same thermodynamic reference tables,26 it is 0 0 0 0 = GZrO − 共GZr + GO 兲 for the possible to calculate the ⌬Gox 2 2 oxidation process. For the ZrO2 example at 1000 K, all 0 quantities can be taken from Table II and ⌬Gox = −908 kJ/ mol. This was also calculated as a function of temperature for most of the high-K compounds listed in Table I and is shown in Fig. 7. To make a meaningful comparison, all calculations were done for a reaction consuming 1 mol of O2. For instance, for Y2O3, the reaction used was 4 / 3 Y + O2 = 2 / 3 Y2O3. It is clear from these data that most of the oxides in the list of high-K candidates 共Table I兲 have a 0 than SiO2, with the exception of Ta2O5. The lower ⌬Gox rare-earth oxides, such as Y2O3 and La2O3, are the most robust, against oxidizing Si. 0 can be reFor the oxidation reaction 关Eq. 共10兲兴, ⌬Gox lated to the equilibrium oxygen pressure PO2 共in Torr兲 using 0 = −RT ln 关PO2 / 760 Torr兴 where R is 8.314 41 ⌬Gox J / 共K mol兲 the universal gas constant and T is the temperature 共K兲. For ZrO2 at 1000 K, PO2 = 2.8⫻ 10−45 Torr. Figure 8 shows the temperature dependence of PO2 for the same list of compounds as in Table I. The graph can be interpreted as follows: for PO2 values below the indicated data points, the

A. Formation of SiO2

With the data in this table, it is now possible to reconstruct a complete phase diagram and to estimate the likelihood of any reaction such as those in Eq. 共5兲, ZrO2 + Si = Zr + SiO2

0 共⌬G1000

K

= 177 kJ/mol兲.

共9兲

0 0 0 0 + GSiO 兲 − 共GZrO + GSi 兲 = 177 kJ/ mol and is As ⌬G0 = 共GZr 2 2 positive, the left-hand side of the equation corresponds to the stable state. This indicates that once ZrO2 has been deposited on Si, it has little tendency to decompose into its constituents. Another way of fulfilling the condition given by Eq. 共5兲 is to look for those oxides that have a lower Gibbs free 0 兲. The thermodyenergy of formation for the oxide 共⌬Gox namic reaction that describes the oxidation process is

FIG. 7. Calculated Gibbs energy of formation for the oxide as a function of temperature according to Eq. 共10兲.

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TABLE III. Phases in the Ti–O–Si system with their respective Gibbs free energy G0f for three different temperatures. The O2, Si, SiO共g兲, and SiO2 phases have already been listed in Table II. Some additional phases have been added and will be discussed in the text.

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

oxide will not be stable and decompose, while for PO2 values above the line, the oxide is stable. These predictions cannot be easily verified experimentally because such low oxygen pressures cannot be attained. A good ultrahigh vacuum system reaches a base pressure close to 10−10 Torr. Furthermore, to oxidize a ML/ cm2 of a material in 10−10 Torr O2—assuming oxidation and sticking coefficients of unity—will require more than 104 s. For a pressure of 10−45 Torr, this time will increase to about 1039 s. The equation used to estimate the time scale will be reported in the next section. These estimates demonstrate some limitations of thermodynamic considerations for practical predictions regarding the stability and the reactions of phases. However, they remain useful for comparing the relative stabilities of the different oxides. In practical thin film deposition processes, PO2 is much larger than these estimates. In addition, there is only a short time window available for the oxidation to proceed. These kinetic considerations will be discussed in the next section.

B. Formation of silicides

The next condition that can be evaluated corresponds to Eq. 共6兲, namely, the stability of the oxide against the formation of metal silicides. There are four Zr silicides reported in Table II, but the one with the largest Si fraction will be considered first. ZrO2 + 3Si = Si2Zr + SiO2

0 共⌬G1000

K

= 24 kJ/mol兲. 共11兲

0 0 0 0 ⌬G0 = 共GSi + GSiO 兲 − 共GZrO + 3GSi 兲 = 24 2Zr 2 2

As kJ/ mol and is positive, the left-hand side of the equation corresponds to the stable state. Also the reaction involving other Zr silicides leads to a similar conclusion, ZrO2 + 2Si = SiZr + SiO2

0 共⌬G1000 K

2ZrO2 + 3Si = SiZr2 + 2SiO2

= 23 kJ/mol兲,

0 共⌬G1000

K

Compound

G0f 共500 K兲 共kJ/mol兲

G0f 共1000 K兲 共kJ/mol兲

G0f 共1500 K兲 共kJ/mol兲

SiO共S1兲 SiO共S2兲 Ti TiO2 TiO Ti2O3 SiTi Si2Ti Si3Ti5 SrO SiSrO3 BaO

−447.3 −540.0 −16.9 −973.3 −562.5 −1565.8 −156.9 −168.8 −699.2 −622.5 −1688 −591.5

−488.3 −574.1 −44.6 −1028 −601.3 −1661.8 −204.4 −233.0 −902.4 −672.8 −1785 −649.9

−541.7 −623.9 −81.7 −1102.1 −656.2 −1795.7 −267.2 −319.8 −1167.5 −737.7 −1915 −723.1

5ZrO2 + 8Si = Si3Zr5 + 5SiO2

0 共⌬G1000

共14兲 This indicates that once ZrO2 has been deposited on Si, it has little tendency to decompose into its constituents or to form silicates as shown below, 2ZrO2 + Si = Zr + ZrSiO4

0 共⌬G1000

2ZrO2 + 3Si = Si2Zr + ZrSiO4

K

= 171 kJ/mol兲,

0 共⌬G1000

K

= 18 kJ/mol兲.

Applying such an analysis to most oxides in the periodic system, Hubbard and Schlomm27 found that only a few oxides satisfy the above two equations. These are SrO, CaO, BaO, Al2O3, ZrO2, HfO2, Y2O3, and La2O3, as well as a few other lanthanides. Other oxides such as Ta2O5, TiO2, and the perovskites including SrTiO3 and BaTiO3 were excluded owing to the occurrence of silicide formation. However, even if silicides will appear 共thermodynamically兲 when certain oxides are brought in contact with Si, there are still some possibilities to use such oxides as high-K dielectrics. To illustrate this, Table III is compiled. It contains some of the phases in the Ti–Si–O system. These include the elements 共Ti, O2, and Si兲, the oxides 关SiO共g兲, SiO2, TiO, Ti2O3, and TiO2兴, and the silicides 共Si2Ti, SiTi, and Si3Ti5兲. Additional phases in this table are SrO, BaO, and two solid SiO共S1兲 and SiO共S2兲 phases. Some phases were already reported in Table II. As before, the ⌬G0 of various reactions can be evaluated from the data in the table, TiO2 + Si = Ti + SiO2

0 共⌬G1000

TiO2 + 3Si = Si2Ti + SiO2

K

= 32 kJ/mol兲,

0 共⌬G1000

K

共17兲

= − 95 kJ/mol兲, 共18兲

TiO2 + 2Si = SiTi + SiO2 共13兲

共15兲

共16兲

共12兲

= 143 kJ/mol兲,

= 302 kJ/mol兲.

K

0 共⌬G1000

K

= − 97 kJ/mol兲. 共19兲

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In contrast to the Zr–O–Si case, these calculations suggest that TiO2 in contact with Si will react and lead to the formation of Ti silicides. However, if a stable interface layer can be inserted between TiO2 and Si, then Ti-silicide formation will be suppressed or at least delayed during an annealing process. Such an interface layer could, for instance, be the stable ZrO2 mentioned above and would allow us to take advantage of the higher dielectric constant of TiO2 共80兲. Moreover, thin SiO2 or SiON layers 共⬇1 nm兲 have already been used for this purpose. The same logic has also been used to grow single-crystal perovskites such as SrTiO3 epitaxially on Si.28–31 In this case, an interface is engineered using a SrO and/or 共Ba,Sr兲O 0 that is much template layer. Both SrO and BaO have a ⌬Gox lower than that of SiO2, so that the reaction in Eq. 共5兲 does not occur. Accordingly, their equilibrium PO2 is also much lower than that of SiO2 共Fig. 10兲, 2SrO + Si = 2Sr + SiO2

0 共⌬G1000

K

= 252 kJ/mol兲. 共20兲

In addition, the formation of Sr silicate is not thermodynamically favored, 3SrO + Si = 2Sr + SrSiO3

0 共⌬G1000

K

= 121 kJ/mol兲. 共21兲

Unfortunately, not enough thermodynamic data on the Sr and Ba silicides are available to quantify the reactions in Eqs. 共6兲 and 共8兲 for SrO and BaO. However, those groups that grew SrTiO3 on Si using a SrO / 共Ba, Sr兲O buffer did not report the appearance of thick Sr and/or Ba silicides28–30 nor was this predicted using numerical computations.31 In those cases where such a buffer was not used, the formation of Ti silicides could not be avoided.32

C. Role of suboxides

Since the initial thermodynamic predictions regarding the stability of ZrO2 and HfO2 were made, a number of contradicting results have appeared. These contradictions were recently reviewed by Stemmer.33 In particular, several groups—including our own—simultaneously observed ZrO2 共or HfO2兲 as well as the presence of Zr or Hf silicide together with SiO2 and/or Si suboxides, as illustrated in Fig. 9. This figure shows the x-ray photoelectron spectroscopy 共XPS兲 data as a function of binding energy of a 3 nm thick HfO2 film grown on Si 共100兲 at 625 K. The Hf4f signature consists of a doublet around 18 eV and a much weaker feature around 14 eV. The former corresponds to Hf atoms in an oxide matrix 共HfO2兲 whereas the latter corresponds to Hf atoms in silicide matrix 共Hf silicides兲. The inset shows the Si2p signature with a large Si peak 共99 eV兲 and a broad SiOx peak 共102 eV兲. The peak position of pure SiO2 is indicated by an arrow. The position of the SiOx peak in this figure suggests a majority of Si+2 and Si+3. Hence, the reaction mechanisms described above do not provide a correct picture of what happens. To account for these discrepancies, Stemmer33 proposed reactions that include gaseous species 关such as SiO共g兲兴 as well as the nonstoichiometry 共such as ZrO2−x兲 of the oxides. In this subsec-

FIG. 9. Experimental XPS spectrum vs binding energy for a HfO2 film grown 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.

tion, we propose an additional mechanism based on the existence of a solid Si suboxide SiO共S2兲 phase. Most metallic species can form stable oxides with different oxidation states. A good example is Ti, where stable phases with oxidation state +II 共TiO兲, +III 共Ti2O3兲, and +IV 共TiO2兲 exist. Additional phases with intermediate valence states, such as Ti3O5 and TiO4O7, also exist and their thermodynamic properties have been tabulated.26 From the val0 ues in Table III, ⌬Gox of the Ti suboxides can be calculated, using the same procedure as demonstrated in the previous subsections. These values were then used to estimate the equilibrium oxygen pressure in Fig. 10. As the Ti oxidation 0 at 1000 K for an oxistate increases from +II to +IV, ⌬Gox 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 a Ti+II phase, in agreement with these estimates, as illustrated in Fig. 10. Silicon can also have solid suboxide species, such as Si2O, SiO, and Si2O3. These can be synthesized as amorphous thin films during the evaporation of Si under different

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

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oxidizing conditions. Although the detailed structure of these phases still is a topic of discussion,34,35 there is no doubt that the average Si valence in these films varies according to their chemical formula. Upon heating above 1000 K, the films have a strong tendency to disproportionate into the phases SiO2 and Si,34–36 which is one reason for the many contradictory results reported. The disproportionation reaction, which may take place on a nanometer scale, makes it difficult to measure the thermodynamic properties of the pure suboxide phases over a large temperature window. Summarizing the recent literature, Hohl34 proposes a phase diagram that includes SiO and Si2O3 as metastable phases that can exist up to 870 and 470 K, respectively. Two nearly identical estimates for G0f of SiO are available in the literature37,38 and are included in Table III as SiO共S1兲. Note that these models start from the premise that SiO is less stable than Si and SiO2, which is derived from the experimental disproportionation observation. The consequence of this premise is that, not surprisingly, the G0f 共SiO兲 are estimated such that 0 ⌬G1000 K of the following reaction must be positive, SiO2 + Si = 2SiO共S1兲

0 共⌬G1000

K

= 353 kJ/mol兲.

共22兲

As a consequence the equilibrium oxygen pressure 共Fig. 10兲 for this SiO共S1兲 phase is larger than that for SiO2, which suggest that upon oxidation first SiO2 forms before SiO forms. From an interface reaction point of view this does not make sense. Here we explore a different approach. While it is correct that most of the thin film deposited SiO will decompose into areas of Si and SiO2 upon annealing, the interface 关3-4 ML 共monolayer兲兴 between the two phases always contains Si suboxides, as shown, for instance, in Fig. 9. This may well be a different phase 共S2兲 or structural arrangement than the SiO deposited originally. For instance, in the case of high temperature 共1200 ° C兲 thermally grown SiO2 on Si, XPS has shown that the interface actually contains all Si valence states.39 The amount of suboxide phases present at such interfaces can be limited to 3-4 ML, but not eliminated, by high temperature annealing experiments.36 Whether this is purely a consequence of steric hinderance that prevents a sharp Si– SiO2 interface or a signature of a specific phase that can only exist between Si and SiO2 cannot be resolved at this point. As this SiO共S2兲 phase cannot be completely reacted away despite the high temperature anneals, it poses a dilemma. If this phase is described using the thermodynamic parameters for SiO共S1兲 mentioned above then, this SiO共S1兲 is not stable 关see reaction in Eq. 共22兲兴 and should not exist in the experimental data. As a consequence, it should also not play a role in the thermodynamic considerations between Si and the high-K dielectrics. However, since the 3-4 ML interface region cannot be reacted away, there is no point in ignoring it. For the purpose of this paper, we consider the interface phase a more stable phase than SiO共S1兲 and call it SiO共S2兲. In that case, the reaction in Eq. 共22兲 should therefore have the opposite sign. That is, whenever Si and SiO2 come in contact, this SiO共S2兲 phase is formed. In addition, we further speculate that the same stable interphase may exist between Si and all high-K dielectrics. Although thermodynamic considerations strictly

only apply to large systems, we nevertheless attempt to extend the same line of reasoning to this interface phase. Clearly, its thermodynamic properties must be quite different from those of the reported SiO共S1兲 phase.37,38 Since the goal is to describe a situation where SiO共S2兲 will be formed, different values of G0f must be provided. To illustrate this, we have—in a gedanken experiment— created an average SiO共S2兲 solid suboxide and made an educated guess about its thermodynamic parameters. This is a didactic example and hence neither the precise value of the G0f chosen, or the particular Si valence chosen plays a big role in demonstrating the argument. There are different ways to make such a guess. In this case, we have evaluated other four-valent metals that have a stable MO2 phase as well as known stable suboxides. This limits the search to elements such as Ti, Sn, and Pb, Ti and Sn exhibit a very similar behavior, whereas in the case of Pb the most stable oxide is PbO and not PbO2. It turns out that for the following discussion either the Ti–O or the Sn–O system would lead to nearly identical values of the estimated G0f 共SiO兲共S2兲. Hence, we have used the Ti–O system as the model system. As expected, TiO2 in contact with Ti will decompose into TiO according to 0 TiO2 + Ti = 2TiO 共⌬G1000

K

= − 130 kJ/mol兲,

共23兲

which is the type of reaction we are looking for. As a starting point, G0f 共SiO兲共S2兲 was estimated from G0f 共TiO兲, adjusted for the observed relative difference between G0f 共SiO2兲 and G0f 共TiO2兲. Hence G0f 共SiO兲 = 共1 − x兲 G0f 共TiO兲 with x = 关G0f 共TiO2兲 − G0f 共SiO2兲兴 / G0f 共TiO2兲. This procedure was used to estimate the values of G0f SiO共S2兲 reported in Table III. 0 Not surprisingly, the estimated ⌬Gox = −866 kJ/ mol at 1000 K and the corresponding PO2 in Fig. 10 are not far from those of TiO. To estimate the effect of this phase on the thermodynamic considerations developed above, the reactions in the Zr–O–Si phase diagram will now be reevaluated against the appearance of this SiO共S2兲 phase. First, ZrO2 on Si will not decompose into Zr and SiO as indicated by ZrO2 + 2Si = Zr + 2SiO

0 共⌬G1000

K

= 41.3 kJ/mol兲. 共24兲

However, the next series of reactions show that the stability against silicide formation is completely lost, ZrO2 + 4Si = Si2Zr + 2SiO

0 共⌬G1000

K

= − 112 kJ/mol兲, 共25兲

ZrO2 + 3Si = SiZr + 2SiO

2ZrO2 + 5Si = SiZr2 + 4SiO

0 共⌬G1000

K

0 共⌬G1000

= − 113 kJ/mol兲, 共26兲

K

= − 129 kJ/mol兲, 共27兲

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5ZrO2 + 13Si = Si3Zr5 + 10SiO

0 共⌬G1000

K

= − 378 kJ/mol兲. 共28兲

Hence, as soon as ZrO2 comes in contact with Si, some SiO共S2兲 and Zr silicide will be formed at the interface. Compared with the case discussed in the previous subsections, it costs much less energy to form this SiO phase than to form SiO2. Hence the equilibrium of the reaction shifts towards the right-hand side. Thermodynamically this may already suffice to transform the entire ZrO2 film; kinetically, however, the reaction depends on the availability of Si 共through diffusion兲 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, 0 the ⌬G1000 K for the reaction of SiO2 in contact with Si leading to the SiO共S2兲 phase can also be estimated according to

SiO2 + Si = 2SiO共S2兲

0 共⌬G1000

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

D. Gaseous species K

= − 136 kJ/mol兲. 共29兲

These predictions are completely in agreement with the observations in the literature33 and with our own measurements. Considering the local bonding configuration at the Si interface, an abrupt transition from Si to SiO2 has never been observed using XPS. The same is true for an abrupt bonding configuration from Si to ZrO2 or HfO2. In general, the presence of several ML of Si suboxide is observed at this interface, and silicides may also be observed, as seen in Fig. 9. This is frequently the case for high-K films grown under high vacuum conditions. One way to limit the interface reactions is to prepare the films at low temperature and not to perform any postgrowth annealing experiments. However, this is not compatible with the standard industry procedures, which require, for instance, an annealing in forming gas at ⬇700 K. As mentioned above, another practical solution to avoid silicide formation is to use an interface layer, typically a 0.5– 1.0 nm thick SiO2 or SiON film. If such an SiO2 layer is inserted between Si and the high-K dielectric, then the formation of SiO共S2兲 and silicide can be avoided 共or delayed兲 at the SiO2 / high-K interface. While this approach limits silicide formation, its impact on the capacity is detrimental, and it does not offer a solution for EOT below 0.5 nm. At this point, the material recommendations of Hubbard Schlomm,27 see previous subsection, can be reevaluated against the thermodynamic parameters of this SiO共S2兲 phase. Virtually none of the materials suggested will pass the test with the G0f 共SiO兲共S2兲 chosen here. However, it should also be noted that for many relevant silicides, the thermodynamic properties have not yet been reported and tabulated. In addition, the somewhat arbitrarily chosen G0f of this Si suboxide may turn out to be not as negative as assumed in this gedanken experiment, and its values must be consistent with overall thermodynamic properties in the Si–O phase diagram. Nevertheless, it is clear that this suggestion may have implications regarding the search for high-K dielectrics that are stable in contract with Si. It may well turn out that no oxide is thermodynamically stable against Si suboxides.

Up to now we have only considered the solid phases and solid-state reactions. However, during both growth and annealing, the gaseous environment plays an important role. To review all the possible reactions with process gases would require an additional section. As we have already taken solid SiO into consideration, we will briefly explore the role of its gaseous counterpart, SiO共g兲 in some reactions. First, the vapor pressure of SiO共g兲 in equilibrium with the solid SiO, Si, and SiO2 phases can be estimated from SiO共S1兲 = SiO共g兲

0 共⌬G1000

K

= 160 kJ/mol兲,

共30兲

SiO共S2兲 = SiO共g兲

0 共⌬G1000

K

= 246 kJ/mol兲,

共31兲

SiO2 + Si = 2SiO共g兲

0 共⌬G1000

K

= 355 kJ/mol兲.

共32兲

In all three cases, the favorable side of the reaction is on the side of the solids. Nevertheless a SiO pressure 共PSiO兲 in equilibrium with the solids can be derived using ⌬G0 = −RT ln共PSiO / 760 Torr兲. For the three reactions, PSiO at 1000 K is 3.3⫻ 10−6, 1.1⫻ 10−10, and 4.0⫻ 10−7 Torr, respectively, as illustrated in Fig. 11. Next the decomposition of ZrO2 is explored in the following reactions, where L stands for ZrO2 + 4Si, ZrO2 + 2Si = Zr + 2SiO共g兲

0 共⌬G1000

ZrO2 + 4Si = Si2Zr + 2SiO共g兲

K

= 533 kJ/mol兲,

0 共⌬G1000

K

共33兲

= 380 kJ/mol兲, 共34兲

L = Si2Zr + SiO共g兲 + SiO共S1兲

0 共⌬G1000

K

= 220 kJ/mol兲, 共35兲

L = Si2Zr + SiO共g兲 + SiO共S2兲

0 共⌬G1000

K

= 143 kJ/mol兲. 共36兲

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

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mental observation of both Si suboxides and Zr silicides together with ZrO2 on Si. As in the above case, ⌬G remains positive at 1000 K for these reactions, and the equilibrium PSiO 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 not decompose, it should be pointed out that all of the above considerations used the tabulated G0f values for standard temperature and pressure 共760 Torr兲 共STP兲 conditions. However, besides the variation of G0f as a function of temperature, which has already been illustrated in many graphs here, there is also a pressure variation. For a solid the pressure dependence is negligible, whereas for 1 mol of an ideal gas G0f 共P兲 = G0f 共760 Torr兲 + RT ln共P / 760 Torr兲. For instance, for P = 10−9 Torr, G0f 共SiO兲 共g兲 at 1000 K will decrease from −328 to − 556 kJ/ mol. This decrease in energy can be understood to result from the correspondingly larger volume that one mol O2 at 10−9 Torr occupies. This will of course change the energy balance of the above reactions, and ⌬G will be less positive, or in other words, the SiO pressure in equilibrium with the solids will increase. The pressure ratio 共10−9 / 760兲 corresponds to 12 orders of magnitude, and all the equilibrium PSiO’s mentioned above will be increased by this amount. In that case, PSiO at 1000 K of all of the above 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 conditions may provide an additional mechanism for oxide decomposition, that is complementary to previous suggestions.33 E. Interface stability

To improve the usability of certain oxides that are not stable in contact with Si, we have seen that one method is to use an interface layer, typically 0.5– 1 nm SiO2 or SiON. In this subsection the thermodynamic justification for such a process is provided. For instance, the stability of ZrO2 on SiO2 can be tested using the following reactions, where L⬘ = ZrO2 + 4 SiO2. The solid-state reaction, ZrO2 + SiO2 = ZrSiO4

0 共⌬G1000

K

= − 6.5 kJ/mol兲, 共37兲

0 has a slightly negative ⌬G1000 K and hence a tendency towards formation of the silicate. As the silicate has a lower ⑀ 共11兲 than ZrO2, this may be detrimental to the EOT, which depends on the thickness ratio SiO2 / ZrSiO4, but not necessarily to the leakage. As there are no other solids in the Zr–Si–O system with equal 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 共S1 and S2兲,

L⬘ = Si2Zr + 2SiO共S1兲 + 4O2

0 共⌬G1000

K

= 36.6 kJ/mol兲 共38兲

0 ⌬G1000 K,

but already also a negative one yields at positive of −71.8 kJ/ mol at 1100 K. For the SiO共S2兲 phase, ⌬G0 is negative 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 an increased stability but that it may come at the price of silicate formation or be restricted to a limited temperature window. In line with the ideas developed in the previous subsections, the stability of ZrO2 against the solid SiO phases at the Si interface is also briefly explored. In particular, the presence of SiO共S1兲 will enhance both the silicate formation as well as Si precipitation and diffusion according to L⬙ = ZrSiO4 + Si

0 共⌬G1000

K

= − 41.9 kJ/mol兲,

共39兲

where L⬙ is ZrO2 + 2SiO共S1兲. F. Issues

While the focus of this paper is on high-K dielectrics, there is another area where these conclusions may also have an impact. The high-K dielectric needs a metallic top contact. Traditionally this has been done using heavily doped p or n polycrystalline silicon. However, it turned out that there are quite a number of issues at that contact. The above results again suggest that this contact interface will not be stable and that a silicide as well as SiO may be formed. Finally, there are number of issues regarding the practical validity of the thermodynamic considerations for this application that should be mentioned. First, in the thin film configuration, materials are in contact with a specific surface orientation. In the case of complex oxide on Si, such a surface may include an element that either easily forms a silicide 共for instance, the TiO2 surface of SrTiO3兲 or one that does not easily form a silicide 共for instance, the SrO surface of SrTiO3兲. There can be a significant difference in stability between these two cases. Second, the thermodynamic quantities used here are derived from bulk samples under standard conditions. However, it is often difficult to make completely phase-pure material, which will affect the correctness of the tabulated G0f values. For instance, different values for the Zr silicides have recently been proposed,40 which will shift the phase balances mentioned above.33 An additional concern is that the properties of thin films can vary considerably from bulk samples. Differences may be related to strain and interface energies. In particular, for very thin films, a huge amount of strain as well as metastable phases can easily be induced. VI. KINETIC CONSIDERATIONS

In the previous section the thermodynamic stability of oxides deposited on top of Si was considered in detail. However, during the deposition step, the growing film fortunately is not under equilibrium conditions. The oxygen partial pressures used during oxide growth are many orders of magnitude above those at which Si and SiO2 are in thermodynamic equilibrium. Hence, the entire Si wafer should become oxidized immediately. However, the speed at which this reaction can proceed is limited by kinetic considerations. One example of such considerations is to estimate the molecular incidence rate. The molecular incidence rate of a gas species is the number of gas molecules that will impinge on 1 cm2 / s. This is a function of the pressure P 共Torr兲 and

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

temperature T 共K兲 as well as the mass M 共a.u.兲 of the gas molecules and is given by41 R = 3.513 ⫻ 1022P/共MT兲1/2 .

共40兲

For example, the incidence rate R of O2 at 300 K and 1 Torr equals 3.59⫻ 1020 O2 molecules/ cm2 s. Assuming a sticking and oxidation coefficient of unity, that is, every impinging oxygen molecule will oxidize Si into SiO2, and considering the surface density of Si 共001兲 atoms NSi = 6.74⫻ 1014 / cm2, the time to oxidize a Si 共001兲 surface is 1.9⫻ 10−6 s. If the goal is to prevent any Si oxidation, then either the Si surface must be protected or the evaporation rate of the metallic species 共such as Zr兲 must be large enough to consume all impinging O2 molecules. In this case, the Zr deposition rate should exceed 1 ML per 1.9⫻ 10−6 s, which is clearly not practical. These assumptions will only provide a lower limit on the oxidation time. When the sticking and oxidation coefficient are smaller than unity, the time needed to oxidize the surface will increase accordingly. If the goal is to control the oxidation better than in the above example, then different process conditions are needed, for instance, a reduction of the O2 pressure during growth. At 10−6 Torr, the time needed to oxidize a Si surface into SiO2 is now increased to 1.9 s. Under such low-pressure conditions it then becomes feasible to control the oxidation state of different materials. This is illustrated in Fig. 12, which shows the total oxygen budget needed to oxidize different materials. The oxygen budget is defined as the product of pressure and exposure time. For the above example, considering the oxidation of one Si ML, the required minimum oxygen budget is 1.9⫻ 10−6 Torr s. For simplicity, the lattice parameters of all materials in this plot were scaled to lead to the same number of surface atoms as Si 共001兲 共NSi = 6.74 ⫻ 1014 / cm2兲. Under these conditions, the amount of O2 needed to form a monolayer of HfO2, ZrO2, or SiO2 is the same. In practice, such an assumption may work only for the first few monolayers, where epitaxy tends to keep the atoms aligned. However, for thicker films the lattice parameters will differ considerably, and thus the values must be corrected accordingly.

In Fig. 12 the oxygen budgets for the different oxidation states of Si and various other materials are estimated. Under low-pressure conditions 共10−6 Torr兲, it is thus in principle simple to tune the oxidation state from Si+I to Si+IV by changing the exposure time by a factor of 4. For the suboxides, each data series in the figure can correspond to a phase separation line. If an oxygen budget is chosen that falls between two lines, then a mixture of two phases becomes possible. For instance, in the case of HfO2, applying an oxygen budget that exceeds the calculated one will allow excess oxygen in the reactor, which may lead to the formation of some SiO below the HfO2 film. Alternatively if not enough oxygen is provided to completely oxidize HfO2, then this may lead to Hf suboxides, a large density of oxygen vacancies, or promote the formation of Hf silicides. The likelihood of any of the above reactions can then again be determined by the above thermodynamic considerations. But clearly the availability of sufficient oxygen on the time scale at which the deposition takes place is an essential kinetic parameter for the successful growth of high-K dielectrics on Si. The above figure provides a good first-order estimation of the O2 pressure needed. However, the oxidation coefficients of different materials—and different oxidation states—turn out to change considerably. For instance, the oxidation coefficient of Si at 600 K is below 10−3, whereas those of Sr and Ba are close to 1. Hence in practice, a series of experiments is needed to accurately determine the oxygen budget needed for each case. Another good example of kinetic considerations is related to diffusion. For instance, in the previous section, it was shown that ZrO2 on Si is not stable against the formation of a Zr silicide and SiO. Yet, for this reaction to proceed, Si must be in contact with ZrO2. For a deposition process that occurs at sufficiently low temperature, Si diffusion can be restricted to the region near the interface. However, at higher temperature, this is not the case and as Si atoms diffuse into the 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 reported to date, there is an interfacial SiOx or SiON 共⬇1 nm兲 layer— intentionally or accidentally—present between the high-K dielectric and Si. Even if this layer is very thin, it is connected in series with the dielectric and has a profound impact on the electrical properties. For instance, if a 3 nm thick high-K layer with ⑀ = 20 共C / A = 5.9⫻ 10−6 F / cm2兲 such as the HfO2-based oxides has a 1 nm thick SiO2 interfacial layer with ⑀ = 3.9 共C / A = 3.45⫻ 10−6 F / cm2兲, then the C / A of the total stack will drop to 2.18⫻ 10−6 F / cm2 or the EOT will increase from 0.58 to about 1.6 nm. Even a 0.5 nm thick SiO2 layer will almost double the EOT to about 1.08 nm and hence cut the expected Ids in half 关Eq. 共1兲兴. The leakage current is also strongly affected. With two capacitors in series 共CSiO2 and Chigh K兲, a part of VG will fall across each capacitor. As the charge on each capacitor face will be the same, Qox = −QSi, the voltage drops will be VSiO2 = −QSi / CSiO2 and Vhigh K = −QSi / Chigh K, respectively,

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FIG. 13. The band bending 共⌿ / q兲, the voltage over the corresponding oxides VSiO2 and VHfO2, as well as their total as a function of VG calculated using Eq. 共3兲 for a bilayer consisting of 1.0 nm SiO2 and 3 nm HfO2.

and determine Jt through each barrier. For capacitors in series, the largest voltage drop falls across the smallest capacitor, in this case the SiO2 layer, as illustrated in Fig. 13. At the reference 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. At these voltages, Jt through each individual layer would be 900 and 3.16 A / cm2. To evaluate Jt of the bilayer, a simple first-order approximation is to consider a thickness-averaged tunnel barrier, where ␾ = 共␾SiO2tSiO2 + ␾high Kthigh K兲 / 共tSiO2 + thigh K兲 = 2.06 eV * * and m* = 共mSiO tSiO2 + mhigh Kthigh K兲 / 共tSiO2 + thigh K兲 = 0.16. The 2 quantities are then used in Eq. 共2兲 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 single 3 nm HfO2-based film to −2.38⫻ 10−3 A / cm2 for the bilayer. The drastic changes to the EOT and Jt of these bilayers substantially alter the predictions of the previous FOM and necessitate a modified version, see Fig. 14. Starting from Jt共VG兲 of single HfO2-based layers, with ⑀ = 20, ␾ = 1.4 eV, and m* = 0.14me 共solid circles兲, the SiO2 thickness is increased gradually from 0 to 1 nm in steps of 0.25 nm. For each monolayer of SiO2 added, Jt drops by about an order of magnitude, following a line more or less parallel to that of single SiO2 layers 共solid squares兲. While Jt of a 3 nm HfO2-based layer with a 0.5 nm SiO2 interface decreases below 1 A / cm2, the EOT unfortunately is now larger than 1 nm, which does not fulfill the long-term ITRS requirements illustrated in Fig. 2. Of course, taken at constant EOT of 1 nm—which corresponds to the vertical line in Fig. 14— the leakage current density in such bilayers decreases as the SiO2 content decreases. The above figure is derived from simple model calculations only. For a precise correlation of these predictions with experiment, a very accurate determination of the SiO2 interface thickness is required. Is that possible? Figure 15 shows a transmission electron microscope 共TEM兲 cross section of a

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

3.4 nm thick HfO2 film with ⬇1 nm SiO2. A precise thickness estimate is hampered because the diffraction contrast must be sharp and not vary significantly over the area investigated. Here both interfaces are not sharp—structurally or chemically—with a transition region from Si to SiO2 as well as a transition region from SiO2 to HfO2. In addition, the TEM image contrast originates from a two-dimensional projection of the sample, and the structural and/or chemical variation along the viewing direction can generate a very complex contrast which cannot be easily interpreted and may lead to blurring, even for sharp interfaces. In this particular case, the SiO2 thickness cannot be determined to better than 1.0± 0.25 nm, which leaves an error bar of two orders of magnitude on Jt! The precision of other techniques such as spectroscopic ellipsometry and XPS is also not better and with their limited spatial resolution of about 1 ␮m, they average over the entire interface. Several other complications make an accurate determination difficult. First, the presence of charges 共mobile and fixed兲 in the oxide or at the interface adds additional voltages

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

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FIG. 16. High-field mobility vs EOT for a broad range of materials showing a severely reduced mobility at low EOT values. The legend specifies the surface treatment 共O3, NH3兲, the high-K material, and the gate metal used.

over the gate 关Eq. 共3兲兴 and, if not taken into account properly, changes the reference voltage 共VG = VFB − 1 V兲, at which the different samples are compared in Fig. 14. For the example of 3 nm HfO2, a fixed charge density Q f = 5 ⫻ 102 / cm2 will lead to an induced voltage Q f A / Cox = 0.135 V and an error on Jt of at least a factor of 2. This amount of charge is far from insignificant and must be compared with QSi in Fig. 3. In that example the onset of inversion takes place for a surface charge of about 1012 q / cm2. Compared with the number of Si 共100兲 surface atoms, NSi = 6.74⫻ 1014 / cm2, this number of defects corresponds to about 1% of the Si atoms. Such a defect concentration is quite common in high-K dielectrics. Many possible sources for defects have been discussed in the literature, and we refer the reader to the reviews mentioned in the Introduction. However, in view of the thermodynamic considerations in Sec. V, the presence of the Si suboxide phase at the interface as well as the silicide may well be at the origin of these defects. A second error, similar to the previous one, can occur owing to variations in the metal work function 共Wm兲 itself and how it is modified by the presence of silicides at the high-K/metal-gate interface. Third, as discussed in detail above, the precise nature of the interfacial SiO2 共SiOx兲 layer is not well known and can vary from sample to sample. As mentioned, XPS results demonstrated that all Si valence states are present at the interface between Si and SiO2.39 The electrical properties of these Si suboxides are not well known, except for the deposited SiO films. The presence of such SiO phases—with an increased ⑀ ⬇ 6 and a reduced Eg ⬇ 6 eV—will increase Jt, reduce EOT, and increase the uncertainty. VIII. MOBILITY

There is a second essential FOM that is widely used in the literature. It connects the high-field 共艌1 MV/ cm兲 carrier mobility with the EOT, as illustrated in Fig. 16. For the data taken from Murto et al.,42 ␮ is severely depressed at small EOT values compared with its “universal” value

共170 cm2 / V s at 1.3 MV/ cm兲 which corresponds to that of a standard SiO2 / Si system. This is a very disappointing result, as the gain in Ids achieved by reducing EOT may be completely lost through the ␮ degradation. Although today the situation might have improved somewhat thanks to extensive postgrowth annealing treatments, the precise origin of this phenomenon has not yet been elucidated. There are two main models to explain the mobility degradation, namely, a scattering mechanism via remote phonons and Coulomb scattering with charged defects/ roughness. The remote phonon scattering model, developed by Fischetti et al.,43 is based on the observation that all highK dielectrics intrinsically have low energy phonons. Although “remote” from the carriers in the channel by at least 1 nm, these lattice vibrations correspond to dipole displacements in the dielectric, which couple electrically to the carriers. The second model44 is based on the observed excess of trapped charges and/or interface states.42 Many experiments confirm the large number of charged defects in high-K dielectrics, observed, for instance, through the shift of VFB in IV and CV measurements. Most of these may be located near the SiOx / Si interface, the SiOx / high-K interface, or in the high-K dielectric itself. At this point, it seems likely that the mobility degradation is due to a combination of these two mechanisms.

IX. CONCLUSION

We have “selectively” looked at the current state of the art in the field of high-K dielectrics for the gate stack. Two figures of merit were presented that illustrate two major challenges. On the one hand, the materials currently being studied—while improving Jt—do not yet provide a good solution for EOT down to 0.5 nm. To get there will require materials with higher ⑀ and/or higher ␾, while maintaining an interfacial SiOx thickness of less than 1 ML. Another possibility may be to remove any Si–O bonds by creating a “metallic” silicide submonolayer—as occurs probably for the

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3 Å EOT LaAlO3 on Si 共Ref. 45兲—but at the expense of a mobility reduction related to an increased Coulomb scattering. As the phases, including interface phases, experimentally observed do not agree with the thermodynamic predictions, an in-depth review was provided that covers most relevant aspects. By introducing the solid SiO phases, either from literature values or by estimation, reactions that can explain the observed results are proposed. Finally, the highfield ␮ values at low EOT are also reported. These values are unacceptably low which seriously hampers the introduction of high-K dielectrics into CMOS devices. ACKNOWLEDGMENTS

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