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phys. stat. sol. (RRL) 2, No. 5, 227–229 (2008) / DOI 10.1002/pssr.200802152

REPR

INT

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.pss-rapid.com

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phys. stat. sol. (RRL) 2, No. 5, 227–229 (2008) / DOI 10.1002/pssr.200802152

First-principles study on the concentrations of native point defects in high-dielectric-constant binary oxide materials

J. X. Zheng1, G. Ceder1, 2, and W. K. Chim*, 1, 3

1 Singapore-MIT Alliance, 4 Engineering Drive 3, Singapore 117576 2 Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge,

MA 02139-66307, USA 3 Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576

Received 5 July 2008, revised 28 July 2008, accepted 30 July 2008

Published online 5 August 2008

PACS 71.20.Ps, 74.62.Dh, 77.84.–s

* Corresponding author: e-mail elecwk@nus.edu.sg

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction As feature sizes of the metal–oxide–semiconductor field-effect transistor device continue to shrink towards nanometer dimensions, high-dielectric-constant (high-k) materials are urgently needed to replace the silicon dioxide (SiO2) gate dielectric. According to the International Technology Roadmap for Semiconductors, a progression from hafnium-based dielectrics to Group III and rare-earth oxides to ternary oxides might be required [1]. It is known that there are higher concentrations of pre-existing defects in high-k gate dielectrics that cause thresh-old voltage instability and give rise to the charge scattering of channel carriers, which in turn reduces the channel car-rier mobility [2]. The origin of these imperfections has been attributed to oxygen defects [3–8]. In the present ar-ticle, we extend our previous work [9, 10] to investigate the dominant point defects under the constraint of charge neutrality in bulk hafnium oxide (HfO2), zirconium oxide (ZrO2), yttrium oxide (Y2O3) and lanthanum oxide (La2O3). By calculating the defect concentrations, our results sup-port the speculation that oxygen-related defects are the dominant point defects in these binary high-k oxides. In HfO2 and ZrO2, oxygen Frenkel pairs are particularly likely to form. There are higher concentrations of charged oxygen defects in Y2O3 and La2O3 than in HfO2 and ZrO2.

2 Computational methods The calculations are based on the density functional theory (DFT) in the gener-alized gradient approximation using the projector aug-mented wave method [11, 12], as implemented in the VASP (Vienna ab-initio simulation package) program [13]. The detailed computational procedure to obtain defect formation energies can be found in Refs. [9] and [10]. In these studies, the stable point defects were determined as a function of Fermi level and oxygen chemical potential without a local electroneutrality constraint as would be ap-plicable to the interfacial regions between the high-k oxide and silicon. In the bulk regions of the oxides, charges from positively charged defects have to be balanced by charges from negatively charged defects to maintain charge neu-trality. This condition can be fulfilled at least a few atomic layers away from interfacial region where the bulk form of material is resumed and hence a higher energy barrier is present to carriers in the channel region. The charge neu-trality condition is given by

net charge 0 ,i i

i

q c= =Â (1)

where qi is the charge associated with a particular de- fect i and ci is its concentration. Under equilibrium con-

The intrinsic concentrations of point defects in high-k binary

oxide materials of HfO2, ZrO

2, Y

2O

3 and La

2O

3 are evaluated

on the basis of first-principles calculations. Oxygen defects

are found to dominate over a wide range of the oxygen

chemical potential. Neutral oxygen vacancies are likely to

be responsible for electron trapping in the investigated mate-

rials. In HfO2 and ZrO

2, oxygen Frenkel pairs are likely to

form.

228 J. X. Zheng et al.: First-principles study on the concentrations of native point defects

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-rapid.com

stat

us

solid

i

ph

ysic

a rrl

ditions, the concentration of a point defect is given by

sites f Bexp ( / ) ,

ic N E k T= - (2)

where Nsites is the number of lattice sites on which the de-fect can occur (per unit volume), Ef is the formation energy of the point defect, kB is the Boltzmann constant, and T is the growth temperature of the material. The formation en-ergies for native point defects are a function of Fermi level and chemical potentials, and their values for HfO2, ZrO2 and Y2O3 have been reported in Refs. [9] and [10]. It is noted that although a thermodynamic equilibrium condi-tion is assumed, the formation energies can serve as a good indicator as to which defects are more likely to form and which material is more prone to the formation of certain type of defects, even when the equilibrium condition is not completely reached. The supercell approach used in the calculations introduces artificial interactions between charge defects and their image charges [14]. In this study, the formation energies for charged defects are corrected for the image charge interactions using the leading term (L–1 term where L is the supercell size) in the Makov–Payne correction scheme [14]. The values for the image charge corrections for different charge states in HfO2 and ZrO2 were reported in Ref. [10]. The image charge correc-tions in Y2O3 (k = 16) and La2O3 (k = 25) are 0.12 eV and 0.07 eV, respectively for ±1 charge defects and they scale proportionally with q2 for ±q charge defects. The possible oxygen chemical potential is bound by the stability of the compounds with respect to the pure metal and molecular oxygen [9, 10]. The allowable range for oxygen chemical potential in HfO2 or ZrO2 is given as

2 2o MO MO o1

O f O O2Δ ,Eµ µ µ+ < < (3)

where 2MOO

µ is the chemical potential for oxygen in MO2 (M = Hf or Zr), o

Oµ is the energy of an oxygen atom in O2

gas, and 2MOf

ΔE is the formation enthalpy of MO2. Simi-larly the range for oxygen chemical potential in M2O3 (M = Y or La) is given as

2 3 2 3M O M Oo o1

O f O O3Δ .Eµ µ µ+ < < (4)

The formation energies for the neutral oxygen vacancy (VO) and oxygen interstitial (Oi) in these four oxides are shown in Table 1 under oxidation condition.

The large concentration of pre-existing bulk defects that is usually present in high-k oxides can trap electrons during device operation [2]. The shift in the threshold volt-age due to trapped charges can be estimated as Q t*tox/Cox, where Qt is the total trapped charge concentration, tox is the physical thickness of the high-k oxide and Cox is the gate Table 1 Formation energies in eV for VO and Oi under oxidation condition o

O O( ).µ µ=

HfO2 ZrO

2 Y

2O

3 La

2O

3

VO 6.63 6.15 6.92 6.64

Oi 1.58 1.31 0.48 0.47

oxide capacitance per unit area. For a high-k gate oxide with a dielectric constant of k = 20 and tox = 4 nm (corre-sponding to an equivalent oxide thickness of less than 1 nm), the defect concentration needs to be approximately 7 × 1017 cm–3 to cause a 10 mV shift in the threshold volt-age, assuming that all defects are fully charged.

It is known that the defect concentration cannot be significantly reduced by annealing after deposition of the gate dielectric, and is largely determined by the source/drain activation anneal that is carried out at about 1000 °C [2]. Thus, T = 1300 K is used to calculate the de-fect concentrations. We have considered all the native point defects, including oxygen and metal vacancies, oxy-gen and metal interstitials, and oxygen and metal antisites. The negative charge states for oxygen vacancies are also considered [7].

3 Results and discussion The concentrations of na-

tive point defects in bulk HfO2 are shown in Fig. 1a for those defects that reach a concentration greater than 105 cm–3. From the figure, the first observation is that the dominant defects are all oxygen-related defects. When the local electroneutrality constraint is not imposed, different types of defects can become dominant depending on the Fermi level and oxygen chemical potential [10]. In general, positively charged defects can only dominate at the Fermi level near the valence band as their formation energies in-crease with the Fermi level, while negatively charged de-fects usually dominate at a high Fermi level as their forma-tion energies decrease with the Fermi level. When the local electroneutrality is constrained, the Fermi level is no longer an independent variable, but it has to equilibrate to a value which keeps the average charges of all the defects neutral. For instance, under oxidation condition in HfO2 without the local electroneutrality constraint, the formation energies for metal vacancies become negative over a large range of the Fermi level near the conduction band, leading to a substantial trend to form such defects. At the Fermi level where metal vacancies are dominant, there are no compensating defects with positive charges. To satisfy the charge neutrality requirement, the Fermi level has to move closer to the valence band where charged oxygen intersti-tials eventually dominate over charged metal vacancies and at the same time positively charged oxygen vacancies be-come the charge compensating defects.

In HfO2, the dominant charged defects are positively charged oxygen vacancies 2

O(V )+ and negatively charged

oxygen interstitials 2i

(O ).- Their concentrations are almost independent of the oxygen partial pressure, indicating that they form as oxygen Frenkel pairs in HfO2. The concentra-tions for these charged defects are too low (

phys. stat. sol. (RRL) 2, No. 5 (2008) 229

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Rapid

Research Letter

cancies are expected to be the most dominant native point defects. This is in agreement with Ref. [2] where it has been argued that the vacancies are initially neutral since no strong threshold voltage shift with increasing oxide thick-ness is observed. Although the coexistence of an equal amount of positively and negatively charged defects would also be consistent with that observation, this is not the case in HfO2 as the concentrations of all charged defects are too low. The concentrations of dominant defects as a function of temperature in HfO2 under reducing conditions are shown in Fig. 2. It can be seen that the defect concentra-tions can be lowered dramatically when the temperature is decreased. It should be noted that the following assump-tions are used to calculate the defect concentrations: (1) Eq. (2) does not account for the formation entropy of the point defect, which could increase the concentrations by two to three orders of magnitude [15]. (2) No corrections were applied to correct for band gap errors using DFT as it is still an ongoing debate on how to apply such corrections [16, 17]. Recently, various hybrid functionals have been employed to study defects in HfO2 [6, 7]. Although these methods produce a band gap value closer to experimental measurement, they are not widely adopted in the defect en-ergy calculations and thus further investigation is needed. (3) An equilibrium condition is assumed.

The concentrations of point defects in ZrO2 are shown in Fig. 1b. The types of dominant defects are the same as those in HfO2. However, the concentrations of neutral oxy-gen vacancies and oxygen interstitials in ZrO2 are about two orders of magnitude higher than those in HfO2 under the same oxygen chemical potential. This is consistent with the conclusion that HfO2 is less prone to the formation of oxygen point defects than ZrO2 [10].

-5 -4 -3 -2 -1 0

105

1010

1015

1020

-5 -4 -3 -2 -1 0

105

1010

1015

1020

-6 -5 -4 -3 -2 -1 0

105

1010

1015

1020

-6 -5 -4 -3 -2 -1 0

105

1010

1015

1020

Defec

tco

nce

ntration(#/cm

3 )

VO4 V

O3O

i

-2 Oi

(a) HfO2

+2

-5.6

VO3

VO4

+2

Oxygen chemical potential (eV)

VO4

VO3Oi

-2 Oi

(b) ZrO2

VO3

+2

+2

-5.3

VO4

VO

Oi

-2

VO V

O

+

Oi

(c) Y2O

3

+2

-6.4

VO

Oi

-2

VO

VO

+

Oi

(d) La2O

3

+2

Figure 1 (online colour at: www.pss-rapid.com) Defect concen-trations at 1300 K as a function of oxygen chemical potential un-

der charge neutrality condition for (a) HfO2, (b) ZrO

2, (c) Y

2O

3

and (d) La2O

3. Image charge corrections have been applied to the

formation energies of charged defects. The range of oxygen

chemical potential for each material is shown in Eqs. (3) or (4).

Here oO,µ which is the oxygen chemical potential in molecular

oxygen, is chosen to be 0 eV.

600 800 1000 1200100

105

1010

1015

1020

-4

+2

VHf

Defec

tco

nce

ntration(#/cm

3 )

Temperature (K)

VO4

VO3

Oi

VO3

VO4

HfO2

-2

+2

Figure 2 (online colour at: www.pss-rapid.com) Defect concen-trations in the bulk HfO2 as a function of temperature under re-

ducing condition 2o HfOO O f

( (1/2) Δ ).Eµ µ= +

The concentrations of point defects in Y2O3 and La2O3 are shown in Fig. 1c and d, respectively. The dominant defects are also oxygen-related defects. The concentrations of 2

OV

+ and 2i

O- are not entirely independent of the oxygen

chemical potential due to the existence of O

V ,+ as no nega-

tive-U behavior for oxygen vacancies in Y2O3 and La2O3 is observed. The concentration of

OV

+ can be larger than that of 2

OV

+ under reducing condition, thus becoming the dom-inant defect to compensate the charges from 2

iO .

- When two

OV

+ compensate for one 2i

O ,- the concentrations of

2

OV

+ and 2i

O- become dependent on the oxygen partial

pressure. Compared to HfO2 and ZrO2, the concentrations of 2

OV

+ and 2i

O- are higher in Y2O3 and La2O3. Thus besides

the neutral oxygen vacancies that can act as electron traps in Y2O3 and La2O3, charged oxygen vacancies could also be responsible for electron trapping in these materials. The concentration of neutral oxygen interstitials is high in Y2O3 and La2O3 under oxidation conditions due to the existence of structural anion vacancies in the cubic bixbyite structures.

References

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2005 Edition: http://public.itrs.net.

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[15] D. B. Laks et al., Phys. Rev. B 45, 10965 (1992).

[16] A. F. Kohan et al., Phys. Rev. B 61, 15019 (2000).

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