lattice parameters

Influence of lattice parameters on the dielectric constant of tetragonal ZrO2 and La-doped ZrO2 crystals in thin films deposited by atomic layer deposition on Ge(001)

C. Wiemer, A. Debernardi, A. Lamperti, A. Molle, O. Salicio et al.

Citation: Appl. Phys. Lett. 99, 232907 (2011); doi: 10.1063/1.3666237

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Influence of lattice parameters on the dielectric constant of tetragonal ZrO2 and La-doped ZrO2crystals in thin films deposited by atomic layer deposition on Ge(001)

C.Wiemer,1,a)A.Debernardi,https://www.wendangku.net/doc/fa5470150.html,mperti,1A.Molle,1O.Salicio,https://www.wendangku.net/doc/fa5470150.html,magna,1

and M.Fanciulli1,2

1Laboratorio MDM,IMM-CNR,Via C.Olivetti2,20864Agrate Brianza,(MB),Italy

2Dipartimento di Scienza dei Materiali,Universita`di Milano Bicocca,20125Milano,Italy

(Received13September2011;accepted16November2011;published online7December2011)

In ZrO2crystals,the highest dielectric constant(k)is ascribed to the tetragonal phase.By the use of

density functional theory and synchrotron radiation x-ray diffraction,we show how the a and c

lattice parameters of the tetragonal phase in?uence the resulting k.Highest k values are obtained at

increasing both a and c,while k is reduced for compressive strained cells.The determination of a

and c on La-doped ZrO2and ZrO2thin?lms deposited by atomic layer deposition on Ge(001)

allowed us to elucidate the in?uence of La doping and Ge diffusion on the k value.V C2011

American Institute of Physics.[doi:10.1063/1.3666237]

The distorted?uorite tetragonal phase(P42/NMCS)of ZrO2and HfO2has been reported to be the polymorph that corresponds to the highest value of the respective dielectric constant(k).1In bulk stoichiometric systems,this structure develops at high temperature(1525 C for ZrO2and1670 C for HfO2(Ref.2)).Due to the demand of a gate oxide with high dielectric constant for logic and memory applications, the stabilization of the tetragonal phase at room temperature is widely explored.3–5Tetragonal ZrO2can be stabilized by the use of different dopant elements,6,7by the introduction of oxygen vacancies,8or also by the reduced size of the crystallites.9

In particular,for gate dielectrics in logic devices on Si(001)and Ge(001),high values of k measured in thin ZrO2?lms have been often inferred to the occurrence of the tetrag-onal phase,although an unambiguous signature cannot be supplied,due to the dif?culty in conventional x-ray diffrac-tion(XRD)to discriminate between the tetragonal and cubic polymorphs of ZrO2.3,10Moreover,the reported experimen-tal k values of doped10and un-doped11–14thin ZrO2layers vary in a wide range(from25to44),therefore suggesting that either not only the tetragonal structure is present in the measured thin?lms,or the doping element has a strong impact on the k value.However,the k value of tetragonal ZrO2might be also in?uenced by additional structural properties.

In this Letter,we demonstrate that tuning the lattice pa-rameters of the tetragonal structure may severely in?uence the entity of the dielectric constant.The a and c lattice pa-rameters were precisely determined by dedicated synchro-tron radiation(SR)XRD experiments on La-doped ZrO2 (La-ZrO2)and ZrO2thin?lms on Ge(001).The extracted a and c of the tetragonal cell determine the range of lattice pa-rameters used to compute the corresponding k of ZrO2by density functional theory(DFT)with plane-wave pseudopo-tential techniques15with Perdew Zunger parameterization for exchange-correlation energy functional.Ultra-soft pseu-dopotentials16are used for O,and Zr,with6and10valence electrons,respectively.The Zr pseudopotential was gener-ated according to Ref.17with4p electrons as semi-core states and checked for the presence of any ghost state.We used a kinetic energy cutoff of55Ry and of600Ry for elec-tronic and for augmentation density,respectively.The static k was computed by linear response as previously reported for the HfO2structure.18The obtained k values are then com-pared to those extracted from C-V characteristics of metal oxide semiconductor capacitors including La-ZrO2and ZrO2 on Ge(001)and Al metal electrodes.The role of lattice dis-tortions and doping elements are?nally elucidated.

La-ZrO2(La?2%atomic)and ZrO2have been depos-ited by atomic layer deposition at300 C on pristine n-type Ge(001)surfaces alternating cycles of(i PrCp)3La and (MeCp)2ZrMe(OMe)with O3.10La-ZrO2and ZrO2/Ge stacks of the same total thickness were annealed at400 C in N2atmosphere for one minute to promote Ge diffusion from the substrate,since it is known that incorporation of Ge atoms can induce the stabilization of the tetragonal phase in ZrO2,3while in the same layers grown on Si(001)this ther-mal treatment promotes the monoclinic phase.19,20After annealing,the stack structure was determined by combined spectroscopic ellipsometry and x-ray re?ectivity analysis proving that the stacks consist of a12.5(12.9)nm thick La-ZrO2(ZrO2)and a2.5(2.3)nm thick,germanate-like,inter-facial region.10

Complementary time of?ight secondary ion mass spec-trometry(ToF SIMS),C-V characteristics and laboratory XRD are performed using conventional setups.21SR-XRD experiments have been conducted at ESRF BM28beam line with photons of9keV to limit the excitation of the Ge(113) asymmetric re?ection that might be excited in grazing inci-dence con?guration and to avoid the?uorescence from Ge K a(9.886keV)that would sensibly increase the back-ground.19Measurements have been performed with grazing incidence both in wide and grazing exit angle con?gurations. Due to the strong overlap between the corresponding

a)Author to whom correspondence should be addressed.Electronic mail:

claudia.wiemer@https://www.wendangku.net/doc/fa5470150.html,r.it.

0003-6951/2011/99(23)/232907/3/$30.00V C2011American Institute of Physics

99,232907-1

APPLIED PHYSICS LETTERS99,232907(2011)

diffraction lines 19and the reduced crystallite size of our sam-ples,the presence of the cubic phase cannot be ruled out in both La-ZrO 2and ZrO 2layers.The detection of the tetrago-nal phase was pursued by measuring the well isolated tetrag-onal (102)re?ection (t(102)).By scanning this 1/d region,it was also possible to evidence the appearance of the mono-clinic phase,thanks to the detection of the monoclinic (à121)and (112)(m(à121)and m(112))re?ections.22Fig-ure 1(a)shows the comparison between the La-ZrO 2and ZrO 2diffraction patterns.In both cases,only the tetragonal phase was detected,with no signs of the monoclinic poly-morph.Variations in the peak position were found both as a function of doping and geometry,suggesting that crystals with slightly different a and c lattice parameters coexist in our samples.Since for the explored a and c values the angle between t(101)and t(102)directions is $19 ,and at 9keV the Bragg angle of t(102)is also $19 ,complementary Bragg-Brentano measurements of the t(101)re?ection (Fig-ure 1(b))identi?es the lattice parameters (a ,c/a )belonging

to two different families of crystals.The measured (a ,c/a)values are reported in Figure 2.Both families have the t[101]direction oriented perpendicular to the substrate plane.Their t[102]direction is either 20 from the substrate normal (cor-responding to the higher a values),or parallel to the substrate plane (corresponding to the lower a values).

We have then computed the k value of the tetragonal crystals by relaxation of internal parameters for a given set of lattice parameters.The (a ,c/a)corresponding to the bulk structure are obtained in correspondence of vanishing stress.The calculated lattice parameters and k values for the bulk structure are (theoretical results from Ref.1are in parenthe-ses):a ?3.68A

?(3.56),c ?5.24A ?(5.10),k xx ?k yy ?37.4(46.6),k zz ?22.1(19.9),while the phonon frequencies of infrared active modes are the following:195(154),333(334),and 441(437)cm à1.As for HfO 2,the high k xx (k yy )can be explained by the lower frequency of infrared active phonon modes,as compared to the corresponding ones of the baddeleyte and ?uorite structures.18The computed c/a $1.42is slightly lower than the one (c/a $1.43)found by Zhao and Vanderbilt,1which gives an anisotropy in our dielectric tensor lower than the one of Ref.1.Different exchange correlation functional or different choice in build-ing up the pseudopotential can modify the frequencies of phonon modes,1,18thus in?uencing the dielectric constant value.The differences in the experimental frequency modes reported in literature do not allow to de?nitively identify the best choice of pseudopotential.As far as the one used in the present work is concerned,a good agreement between the calculated and the measured k values is obtained.Figure 2shows the computed average k (i.e.,one-third of the trace of the dielectric tensor)at different (a ,c/a),c/a ranging from cubic ?uorite,c/a ?H 2,to the highest measured value.According to our computation,k decreases for compressive strain,while k increases at increasing the lattice parameters.

The k values of La-ZrO 2and ZrO 2are extracted from C-V curves taken at room temperature in dark.Due to the presence of frequency dispersion,10k was extracted from the accumulation capacitance at the lowest possible frequency of 1kHz (Figure 3(a)).This value constitutes an inferior

limit

FIG.1.(a)SR-XRD analysis around the position of the t(102)peak in wide and grazing exit geometry,and (b)Bragg Brentano analysis of the t(101)re?ection,of La-ZrO 2(black)and ZrO 2(grey)thin ?lms.Powder diffraction patterns of cubic,tetragonal,and monoclinic ZrO 2are also added for

comparison.

a ( )oA

c /a

La:ZrO 2

ZrO 2

Bulk ZrO 2

3.56 3.58 3.6

3.62 3.64 3.66 3.68

1.42

1.431.44

1.451.461.471.4825

3035404550FIG.2.(Color online)Distribution of the calculated k values as a function

of the lattice parameters of tetragonal ZrO 2.The experimentally measured lattice parameters of ZrO 2(squares)and La-ZrO 2(diamonds)are also reported,together with those of nanosized and high temperature tetragonal ZrO 2phases reported in database

(asterisks).FIG.3.(Color online)(a)C-V characteristics at 1kHz of ZrO 2(full sym-bols)and La-ZrO 2(open symbols)stacks on Ge (b):ToF SIMS depth pro?les of as deposited (full symbols)and 400 C annealed (open symbols)La-ZrO 2and ZrO 2stacks on Ge.In La-ZrO 2:Ge:^,ZrO 2:!,LaO:3.In ZrO 2:Ge: ,ZrO 2:~,LaO:".

of the dielectric constant value.Interface state densities of 3.960.3?1011eVà1cmà2and3.260.1?1012eVà1cmà2 for ZrO2and La-ZrO2based MOS capacitors,respectively, have been extracted at room temperature and with a fre-quency of1MHz.By considering a two layers structure and an interfacial region with k?6.2,10k?1862for ZrO2and 4261for La-ZrO2are estimated.10The stabilization of the tetragonal polymorph occurs through the diffusion of Ge atoms from the substrate.Figure3(b)shows ToF SIMS depth pro?les taken before and after annealing of La-ZrO2and ZrO2stacks on Ge(001).As evidenced,in La-ZrO2stacks Ge diffusion occurs only after annealing.Conversely,in ZrO2,the diffusion takes place already during the growth process and,after annealing,the level of Ge atoms inside ZrO2?lm is1.5orders of magnitude higher than in La-ZrO2. Therefore,the insertion of La atoms limits the Ge diffusion from the substrate.On the other hand,the low k value meas-ured for ZrO2can be related to the high amount of diffused Ge.Actually,incorporation of Ge atoms inside the metallic sublattice of the tetragonal phase is known to reduce the cor-responding k value.7In particular,the reduction of k by increasing Ge content is signi?cant for Ge concentration below15%,23as it might be the case in our stacks.

Taking into account that the layers are polycrystalline, i.e.,other(a,c/a)of the constituent crystals along with those we measured by SR-XRD might be present,we observe that for two different families of crystals the lattice parameters of La-ZrO2tetragonal phase are larger than the corresponding ones of ZrO2.This effect might be related to the larger size of the La3tionic radius(1.06A?)as compared to Zr4t(0.72A?).We can therefore expect a similar effect for other orientations of the crystals.Indeed,the obtained values of k for ZrO2and La-ZrO2are in agreement with the general trend that higher values of a and c/a correspond to higher k values,as calculated by DFT.

In conclusion,this work demonstrates that in addition to the crystallographic structure,the speci?c values of the lat-tice parameters within the same polymorph can also have a strong in?uence on the dielectric constant of transition metal oxides.In the tetragonal P42/NMCS structure of ZrO2,we explained this behavior by the theoretical evaluation of the dependence of the lowest infrared active phonon mode on the lattice parameters.For a and c higher than the bulk val-ues,the corresponding frequency is lower,and therefore a higher k value can be reached.The combined experimental and theoretical work presented here elucidate that the inser-tion of La inside the metallic sublattice of ZrO2has a bene?-cial effect on the ZrO2k value due to several reasons:(i)La has a higher polarisability than Zr,24therefore intrinsically increases k,to values even higher than those shown in Figure2.(ii)La limits the Ge diffusion to an amount suf?-cient to promote the stabilization of the tetragonal phase,and to still take advantage of the high k value typical of low dop-ing levels of Ge.23(iii)La doping promotes the stabilization of La-ZrO2tetragonal crystals,with lattice parameters larger than those of ZrO2,and thus enhancing the resulting k value.

The authors are grateful to Oier Bikondoa(ESRF, BM28)and Silvia Baldovino(MDM).Computational resour-ces are provided by CASPUR within the OSE project.

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