- Email: [email protected]
Ab initio study of point defects in dielectrics based on Pr oxides
ARTICLE IN PRESS
Materials Science in Semiconductor Processing 9 (2006) 897–903
Ab initio study of point defects in dielectrics based on Pr oxides J. Da¸browskia,, A. Fleszarb, G. Łupinaa, Ch. Wengera a
IHP, Im Technologiepark 25, 15236 Frankfurt (Oder), Germany Unviersita¨t Wu¨rzburg, Am Hubland, 97074 Wu¨rzburg, Germany
b
Available online 6 December 2006
Abstract We discuss the influence of band structures and point defects (oxygen vacancies and interstitials, and praseodymium vacancies) in Pr2O3, PrO2, and PrSiO3.5 on the electrical properties of high-K gate dielectrics for the application in CMOS technology. In particular, we consider the origin of fixed charges and leakage currents. We address these issues mostly from the perspective of ab initio calculations for formation energies, electronic structures, and band alignment between the film and the silicon substrate. r 2006 Elsevier Ltd. All rights reserved. Keywords: Praseodymium oxide; Silicate; Oxidation state; Point defects; Vacancy; Interstitial; Formation energy; Chemical potential; Charge state; Band offset; Leakage current; Ab initio calculations; Density functional theory
1. Introduction In the nearest future, a dielectric with a dielectric constant K several times higher than that of SiO2 will be needed for the fabrication of CMOS (complementary metal–oxide–semiconductor) devices [1]. But despite previous announcements, the industry sticks to SiO2 as the MOSFET gate dielectric, although this means that the capacitance density cannot be further increased. A major obstacle in the way to substitute SiO2 by a new material is the need to assure high electrical quality of the dielectric film. At least a part of the problem is associated with the presence of point defects in the new dielectrics. In this work we consider the point defects in the dielectrics based on Pr oxides. While Corresponding author.
E-mail address: [email protected] (J. Da¸browski). 1369-8001/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mssp.2006.10.049
Hf silicate, a material with a moderately high dielectric constant K, appears to be the closest to industrial implementation [2], Pr oxides are among the candidates for truly high-K materials [3]. Pr silicate forms at Pr2 O3 /Si(0 0 1) interfaces in a natural way [4], and it itself is an interesting gate oxide with a moderately high dielectric constant [5,6]. Defects which can trap charge carriers make a contribution to the leakage (through trap-assisted transport of carriers across the film) and/or to mobility degradation of carriers in the channel (through scattering of carriers by the electric field), jeopardizing the gain from the increased dielectric constant. Previous calculations have shown [7,8] that oxygen vacancies in HfO2 and in ZrO2 may be responsible for leakages and threshold voltage instabilities. We find that the energy positions of oxygen vacancy charge transition states in Pr oxides are not so critical from the point of view of leakage
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currents as in HfO2 and ZrO2 , but the concern still remains. We also address the influence of the film stoichiometry (oxygen content in PrOx ) on the leakage current and the role of oxygen interstitials and metal vacancies in the processes responsible for the electrical quality of the film. 2. Approach Total energy calculations were done with the ab initio plane wave code fhi96md [9,10]. We applied the local density approximation (LDA, [11,12]) and nonlocal pseudopotentials [13,14] with 40 Ry cutoff for plane waves; in some cases, generalized gradient approximation (GGA [15]) was used. The Brillouin zone was sampled at a set of special k-points, akin to the (0.25, 0.25, 0.25) point family generated for cells of dimensions close to these of the Pr2 O3 unit cell (cube with the lattice constant of 1 nm). Because of the open f-shell of Pr atoms, a key problem in calculations involving Pr is the construction of a reliable Pr pseudopotential [16,17]. Our band structure calculations taking into account the whole f-shell of Pr as valence shell have shown that such an approach is unpracticable within LSDA and also within GW. The position of the occupied f-band is much too high and there is no tendency to localize these electrons. It turns out that in practice two different Pr pseudopotentials are needed: a pseudopotential with two core f electrons for Pr2 O3 (trivalent PrIII, +3 ionic charge), and with only one f electron for PrO2 (tetravalent PrIV, +4 ionic charge). We calibrate the pseudopotential energy difference between PrIII and PrIV in such a way that the experimental difference in the formation enthalpies of Pr2 O3 and PrO2 is reproduced [18,19]. The computed lattice constants of Pr2 O3 and PrO2 are in agreement with experiment.
The drawback is that the wavefunctions responsible for the (4 þ =3þ) electron transition level of Pr cannot be computed. However, from total energy difference between the perfect crystal and the crystal with one Pr atom in the other charge state one can calculate the energy position of the highest occupied f-band in Pr2 O3 and PrSiO3:5 , and the lowest unoccupied f-band in PrO2 . The location of the occupied f-band top is obtained as the (0/+) electron transition state of the isolated f-shell of a Pr atom in the crystal, that is, as the Fermi energy at which the charge state of the Pr atom changes from +3 to +4. We find these bands at 0.5 above the topmost occupied oxygen states in Pr2 O3 , and at about 0.16 eV below the top of the non-f valence band in PrSiO3:5 . This is roughly compatible with out XPS measurements, which show the f peak at the valence band top; however, its measured position is typically about 0.5 eV above the position estimated from the calculation. The empty f-band in PrO2 is computed to be located 1.3 eV above the topmost occupied oxygen states and corresponds to the (=0) electron transition state of the f shell. 3. Band offsets Since point defects are usually charged, we must consider the dependence of the defect formation energy G f on the electron chemical potential, that is, on the Fermi energy E F . This means that the formation energy of charged defects in a dielectric remaining in electrical contact with the Si substrate is determined by the position of the Fermi level in the substrate and by the valence band offset between Si and the dielectric. We compute the band offsets (Table 1) using the conjunction that when two materials with an energy gap are brought into contact, their charge neutrality levels (CNLs) tend to match: electrons flow from the
Table 1 Band offsets to Si and charge transition states of oxygen-related defects OV , energy below CB
Band offsets to
PrO2 Pr2 O3 PrSiO3:5
OI , energy above VB
Si VB
Si CB
(++/+) (eV)
ðþ=0Þ (eV)
ð0=Þ (eV)
2.6 2.1 2.7
2.3 2.1 1.8
0.37 1.09 (n)
– 0.85 (n)
– 0.21 (n)
ð0=Þ (eV) 1.80 0.04 1.16
For vacancy levels the distance to the conduction band (CB) edge is given, while for interstitial levels the distance to the valence band (VB) edge is specified. For Pr2 O3 , the VB offset and the OI levels are given with respect to estimated position of f-type VB top. (n) - see text.
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Fig. 1. Band gap of Pr2 O3 film deposited on Si, as measured by XPS from the offset between the O1s peak and the loss peak. The O1s peak has been subtracted by gaussian fit. The position of the O1s peak and the onset of the loss peak are indicated by vertical lines.
material with the higher CNL to the material with the lower CNL, whereby the electrical dipole moment produced in this way is screened, so that the matching is usually not complete [20,21]. Since the mechanism of CNL alignment is akin to the appearance of metal induced gap states (states from one material enter into the other material and change the effective density of states, thus producing an interface dipole), f-state density is not included in these calculations. Namely, f-states are localized and their contribution to the metal induced gap States should be minimal, given that all Pr atoms are separated from Si by O atoms. This is fortunate, because although the position of the occupied f-band can be reasonably estimated, the position of the empty f-band is difficult to obtain. When the conduction band offset is known, the valence band offset is found by subtracting the conduction band offset and Si energy gap from the band gap of the dielectric. For this purpose, we used experimental energy gaps (Fig. 1). 4. Charge states of oxygen-related defects For most of Fermi energies, oxygen vacancies in Pr oxides are double positively charged. In the upper part of the gap there are, however, charge transition states. They correspond to Fermi energies at which the vacancy traps an additional electron, changing its charge state. This electron is trapped in a state of conduction-band type (Fig. 2). This is because the oxides are strongly ionic and the
removed oxygen atom is a negatively charged ion, that is, the removal of oxygen is equivalent to the creation of a positive perturbation potential. This potential is attractive to electrons, i.e., it locally pulls the band structure to lower energies. It follows that when the LDA gap is corrected to the experimental one by a rigid shift of the conduction band, the vacancy states should be shifted by the same amount (Fig. 2, right). This conjunction can be easily verified by changing the exchange-correlation potential such that the band structure does not change dramatically but the band gap changes. Indeed, when the calculation is done with GGA exchange-correlation, the band gap increases by about 0.5 eV but the position of the transition state relative to the conduction band edge does not change. The positions of vacancy transition states in the gap of Pr2 O3 and PrO2 with respect to the conduction band edge are listed in Table 1. Oxygen vacancy in PrSiO3:5 is not a charged defect at Fermi levels of interest. This is because O atoms in PrSiO3:5 have either only Si neighbors or both Si and Pr neighbors. The vacancy created by removing oxygen from between two Si atoms results in an electrically neutral Si–Si bridge, with the highest occupied electronic orbital located about 2 eV below the valence band top of Si. This defect is labeled OV (SiSi) in Fig. 3. (One expects that this bridge is the precursor of the family of defects similar to the E0 family in SiO2). The removal of oxygen from a site where it had Pr neighbors results in the formation of a Si dangling bond. This defect
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Fig. 2. (Left) Charge density of an electron trapped on oxygen vacancy in Pr2 O3 ; Pr atoms are blue, O atoms are yellow. It is clear that this is a conduction band state. (Right) Therefore, the LDA energy of the transition state measures the relative position between the conduction band and the Fermi energy at which the defect changes its charge state. When the gap is corrected to the experimental one by a rigid shift of the conduction band (‘‘scissors operator’’), the transition state should be therefore shifted together with the conduction band.
Fig. 3. (Left) Free Si dangling bond, Si(db). Si atoms are white, O atoms are light gray, Pr atoms are dark gray, the H atom saturating the spurious dangling bond is black, and the dangling bond is also rendered in black. In order to make the figure more readable, some atoms are removed from the panels (the bonds are retained). (Right) Formation energies of oxygen-vacancy related native defects in PrSiO3:5 as a function of the chemical potential of oxygen. For the chemical potential of Si, equilibrium with bulk Si is assumed. The Fermi level corresponds to that of intrinsic Si. Formation energy of Si(db) has been corrected as explained in the text.
is labeled OV (SiPr) in Fig. 3. Its formation energy is nearly equal to that of OV (SiSi). Although this dangling bond does capture an electron, this electron comes locally from the metal neighbors. The negative charge localized now at the Si dangling
bond is the same as the charge that was collected from the metal atoms by the removed O atom; the defect is thus electrically neutral. The electrons in this negatively charged dangling bond are bound by the electric field of the positively charged Pr ion;
ARTICLE IN PRESS J. Da¸browski et al. / Materials Science in Semiconductor Processing 9 (2006) 897–903
they occupy an orbital located roughly 1 eV below the valence band of Si. If an isolated Si dangling bond Si(db) is far enough from Pr atoms, typical dangling bond transition states are produced. We have built a model of such a dangling bond (Fig. 3) starting from the OV (SiSi) Si bridge. We stretch and break the bridge by moving one of the Si neighbors along the Si–Si bond until this atom arrives at the sp3 site on the other side of the plane defined by its three O neighbors. We then saturate this atom with hydrogen and treat the dangling bond on the other Si atom as a free Si dangling bond. The computed formation energy of such a defect consists of two major contributions: one is the formation energy of the dangling bond, the other is the formation energy of the O3SiH defect. In Fig. 3 we adjusted this formation energy to represent the free dangling bond. We did this by adding a corrective term DE bringing the formation energy of the uncharged defect to the value of 1.1 eV at the equilibrium with SiO2. Indeed, since the oxygen atom was removed from a configuration closely resembling that in SiO2 and—for this choice of the chemical potential—was moved to SiO2, the formation energy of the (uncharged) dangling bond should be roughly equal to half of the SiSi bond energy, that is, to 1.1 eV. From Fig. 3 we now conclude that oxygen vacancies in PrSiO3:5 may be stable with respect to dissociation at least in thin films. Oxygen vacancies may be created in PrSiO3:5 when the silicate is in the chemical contact with a strongly reducing medium, e.g., with Pr or Ti metal layer. According to the computed formation energies, the chemical potential of oxygen at the equilibrium between PrSiO3:5 , Pr metal, and crystalline Si is equal to 5:65 eV (cf. Fig. 3; zero of the chemical potential corresponds to oxygen in O2). The defect formation energy of about 1 eV, computed for O vacancies at these strongly reducing conditions (Fig. 3), is equivalent to the equilibrium concentration of about 1017 cm3 at 600 C. At the chemical potential of oxygen corresponding to the equilibrium between Pr2 O3 , SiO2, and Si, this concentration drops to about 1014 cm3 . As for oxygen interstitials, OI , they are double negatively charged when the Fermi level is high enough. This is because oxygen valence orbitals have low energy; this translates into a large energy gain when electrons move from Fermi energy to the interstitial. When the Fermi level is low, OI makes a bond with an oxygen atom from the lattice to form O2 2 . This
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substitutional molecule is an electrically neutral defect, because lattice oxygen atoms are also double negatively charged. The single negative charge state is unstable, because hole capture is associated with a strong relaxation of the atomic structure. The same behavior of interstitial oxygen has been found by ab initio calculations in HfO2 [7], ZrO2 [8], and ZrSiO4 [22]. The position of the ð0=Þ state depends on the atomic structure of the host (Table 1). In Pr2 O3 , OI can go into the formal vacancy site (cubic Pr2 O3 is obtained from cubic PrO2 by removing one quarter of O atoms). The formation energy of O2 is thus low I and the charge transition state is close to the valence band top. But O2 I in PrO2 and PrSiO3:5 must occupy truly interstitial sites, so that the formation energies of 0 O2 I are higher, making OI relatively more stable and shifting the transition states to higher energies. 5. Discussion We are now in position to sketch the band diagram of a Pr oxide deposited on Si (Fig. 4). Since Pr2 O3 reacts with Si and oxygen to form Pr silicate, and with oxygen to form a higher oxide, we will assume a stack consisting of Si, PrSiO3:5 , Pr2 O3 , and PrO2 . Band offsets are estimated by the CNL alignment procedure described in Section 3. Let us begin with the Pr2 O3 layer. Its rightmost part (the closest to Si) sees the Fermi level as determined by the Si substrate (and by the influence of the PrSiO3:5 layer, which we ignore for a while). This means that the formation of negatively charged oxygen interstitials (and negatively charged Pr vacancies, Pr3 V [23,24]) is energetically favorable in this region, and the concentration of these defects is determined only by electrostatic repulsion. Consequently, a negative fixed charge appears there, pushing the bands upwards as the distance from Si increases. Therefore, the energy gain from the creation of deep acceptors diminishes with increasing distance from the substrate. The formation of O2 ceases to be I favorable when the Fermi level drops to about 1.5 eV above the f-band edge. Since Pr2 O3 is a widegap material, only a small amount of acceptors (of the order of 1015 cm3 ) suffices for such a movement of Fermi level in a free-standing material, hence there are virtually no negatively charged oxygen interstitials in Pr2 O3 bulk. For Pr3 V , this happens earlier, for Fermi energy about 2.1 eV above the f-band edge. In other words, band bending due to charge accumulation removes the tendency to form negatively charged defects, and the bands flatten out.
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Fig. 4. Band diagram for a Si/PrSiO3:5 /Pr2 O3 /PrO2 stack. Charge transition states of several point defects are indicated. The valence band edges marked by thick sold lines correspond to topmost occupied states of O. The estimated position of the topmost occupied f band in PrSiO3:5 and Pr2 O3 is marked by thin solid lines, the position of the lowest unoccupied f band in PrO2 is marked by a dotted line. The broken line is the Fermi energy, assumed to coincide with that of intrinsic Si. See text for more discussion, and Table 1 for numerical data.
At the same time, the negative charge hinders the in-diffusion of negatively charged oxygen from the ambient atmosphere to PrSiO3:5 (although in-diffusion of neutral species is not affected). PrSiO3:5 can thus develop positive fixed charge, associated with Si [23,24] and partially compensating the negative charge in the oxide. The rest of the negative charge must be compensated in the substrate, leading to band bending there, visible in CV characteristics as a flatband voltage shift. On the opposite side of the Pr2 O3 layer, there is a growing tendency for oxidation, particularly during annealing (even ‘‘inert’’ N2 ambient contains enough oxygen to oxidize Pr2 O3 to PrOx with x41:5). Oxidation of Pr2 O3 is more difficult in deeper regions because the transition from PrIV (the charge state of Pr in PrO2 ) to PrIII (the charge state of Pr in PrIII) occurs in PrO2 already at low Fermi energies. According to our estimate, Pr would trap an electron when the Fermi level is higher than about 1.3 eV above the valence band edge of PrO2 . This opposes the oxidation by forcing Pr to the charge state it has in the suboxide. The current calculations are not exact enough to describe this effect quantitatively, particularly because it takes place in PrOx , which is a structurally complex material when x differs from its limiting values of 1.5 (Pr2 O3 ) and 2 (PrO2 ). It is nevertheless clear that the presence of the f-band at Fermi energies within (or close to) the energy gap of Si leads to electron hopping conductivity [26,25]. This
Fig. 5. The quality factor of a Pr oxide MOS film decreases with the film thickness.
conductivity can be avoided only if the stoichiometry of the oxide is Pr2 O3 , which is possible to maintain if the film is sufficiently thin to allow for an efficient reduction of PrOx to Pr2 O3 by the combined action of the Si substrate and the metal gate. Indeed, the electrical quality of the film deteriorates with increasing thickness (Fig. 5). Even though the electron hopping from Pr atom to Pr atom is not a problem in Pr2 O3 , the latter material is likely to contain a high concentration of
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oxygen vacancies. Although the formation energy of an electrically neutral group of defects consisting of 3Oþ2 and 2Pr3 amounts to 2 eV per defect, V V meaning that the concentration of these defects would be negligible when the film is grown under thermal equilibrium conditions, such defects can easily be formed under non-equilibrium growth. Since oxygen vacancies are the major species compensating the negative charge of Pr vacancies and oxygen interstitials, removing them (e.g., by oxidation) would upset the charge balance. Therefore, we expect that the concentration of these defects cannot be neglected even after annealing. Fortunately, the charge transition levels of oxygen vacancies are above the energy of the conduction band bottom in Si. Trap-assisted leakage (tunneling or Poole–Frenkel emission [27]) through the vacancy states of Pr2 O3 is therefore of a less concern than electron hopping through f states of Pr in a mixed oxide (PrOx ). However, our experimental data indicate that Poole–Frenkel emission characterized by the energy barrier of about 1.0 eV plays a role in the leakage through Pr2 O3 films on Si substrates. This energy barrier is compatible with the computed position of the ðþ= þ þÞ charge transition state of oxygen vacancy in Pr2 O3 . 6. Summary and conclusions Using ab initio data, we analysed the influence of charged point defects in Pr2 O3 , PrSiO3:5 , and PrO2 on electrical properties of the dielectric deposited on Si. We estimated the band diagram of a Pr-oxide stack; up to our knowledge, this estimate is compatible with the experimental data. We discussed the leakage mechanisms as suggested by the results of the calculation (trap-assisted leakage through oxygen vacancies, and electron hopping through empty fband). From experiment, we have hints that both mechanisms contribute noticeably to gate leakage. Acknowledgment The calculations have been done on IBM Regatta in von Neumann Institute for Computing, Ju¨lich, Germany (project hfo06).
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References [1] Huff HR, Gilmer DC. High dielectric constant materials— VLSI MOSFET applications, Springer series in advanced microelectronics, vol. 16, 2005. [2] Wilk GD, Green ML, Ho MY, Busch BW, Sorsch TW, Klemens FP, et al. Technical Digest VLSI Symposium, 2002. p. 88. [3] Schwalke U, Stefanov Y. Microelectron Reliab 2005;45:790. [4] Schmeisser D, Mu¨ssig H-J, Dabrowski J. Appl Phys Lett 2004;85:88. [5] Schro¨der T, Lupina G, Dabrowski J, Mane A, Wenger C, Lippert G, et al. Appl Phys Lett 2005;87:022902. [6] Lupina G, Schro¨der T, Dabrowski J, Wenger C, Mane A, Lippert G, et al. Appl Phys Lett 2005;87:092901. [7] Foster AS, Gejo FL, Shluger AL, Nieminen RM. Phys Rev B 2002;65:174117. [8] Foster AS, Sulimov VB, Gejo FL, Shluger AL, Nieminen RM. Phys Rev B 2001;64:224108. [9] Fissel A, Da¸browski J, Osten HJ. J Appl Phys 2002;91: 8986. [10] Bockstedte M, Kley A, Neugebauer J, Scheffler M. Comp Phys Comm 1997;107:187. [11] M Ceperley D, Alder BJ. Phys Rev Lett 1980;45:367. [12] Perdew JP, Zunger A. Phys Rev B 1981;23:5048. [13] Haman DR. Phys Rev B 1989;40:2980. [14] Bachelet GB, Hamann DR, Schlu¨ter MA. Phys Rev B 1982;26:4199. [15] Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, et al. Phys Rev B 1992;46:6671. [16] Mu¨ssig H-J, Osten HJ, Bugiel E, Da¸browski J, Fissel A, Guminskaya T, et al. Proceedings of the 2001 IEEE Integrated Reliability Workshop, 2001. p. 1. [17] Da¸browski J, Zavodinsky V, Fleszar A. Microelectron Reliab 2001;41:1093. [18] H. Bergman, Gmelin Handbuch der Anorganischen Chemie, Seltenerdelemente, Teil C1 (Springer, Berlin 1974). [19] David R. Lide, editor. Handbook of chemistry and physics, 73rd ed. Boca Raton, FL: CRC Press; 1993–1994). [20] Tersoff J. Phys Rev B 1984;30:4874. [21] Robertson J. J Vac Sci Technol B 2000;18:1785. [22] Pruneda JM, Archer TD, Artacho E. Phys Rev B 2004;70:104111. [23] Dabrowski J, Fleszar A, Lippert G, Lupina G, Mane A, Muessig H-J, et al. Adv Solid State Phys 2005;45:339. [24] Dabrowski J, Fleszar A, Lippert G, Łupina G, Mane A, Wenger Ch. In: Fanciulli M, Scarel G, editors, Rare earth oxide thin films: growth, characterization, and applications, Topics in applied physics, vol. 106, Berlin: Springer; 2006. p. 247. [25] Subba Rao GV, Ramdas S, Mehrotra PN, Rao CNR. J Solid State Chem 1970;2:377. [26] Biswas RG, Rajendran M, Walker GS, Williams W, Bhattacharya AK. J Mater Sci 1998;33:3001. [27] Hill RM. Phil Mag 1971;23:59.
Materials Science in Semiconductor Processing 9 (2006) 897–903
Ab initio study of point defects in dielectrics based on Pr oxides J. Da¸browskia,, A. Fleszarb, G. Łupinaa, Ch. Wengera a
IHP, Im Technologiepark 25, 15236 Frankfurt (Oder), Germany Unviersita¨t Wu¨rzburg, Am Hubland, 97074 Wu¨rzburg, Germany
b
Available online 6 December 2006
Abstract We discuss the influence of band structures and point defects (oxygen vacancies and interstitials, and praseodymium vacancies) in Pr2O3, PrO2, and PrSiO3.5 on the electrical properties of high-K gate dielectrics for the application in CMOS technology. In particular, we consider the origin of fixed charges and leakage currents. We address these issues mostly from the perspective of ab initio calculations for formation energies, electronic structures, and band alignment between the film and the silicon substrate. r 2006 Elsevier Ltd. All rights reserved. Keywords: Praseodymium oxide; Silicate; Oxidation state; Point defects; Vacancy; Interstitial; Formation energy; Chemical potential; Charge state; Band offset; Leakage current; Ab initio calculations; Density functional theory
1. Introduction In the nearest future, a dielectric with a dielectric constant K several times higher than that of SiO2 will be needed for the fabrication of CMOS (complementary metal–oxide–semiconductor) devices [1]. But despite previous announcements, the industry sticks to SiO2 as the MOSFET gate dielectric, although this means that the capacitance density cannot be further increased. A major obstacle in the way to substitute SiO2 by a new material is the need to assure high electrical quality of the dielectric film. At least a part of the problem is associated with the presence of point defects in the new dielectrics. In this work we consider the point defects in the dielectrics based on Pr oxides. While Corresponding author.
E-mail address: [email protected] (J. Da¸browski). 1369-8001/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mssp.2006.10.049
Hf silicate, a material with a moderately high dielectric constant K, appears to be the closest to industrial implementation [2], Pr oxides are among the candidates for truly high-K materials [3]. Pr silicate forms at Pr2 O3 /Si(0 0 1) interfaces in a natural way [4], and it itself is an interesting gate oxide with a moderately high dielectric constant [5,6]. Defects which can trap charge carriers make a contribution to the leakage (through trap-assisted transport of carriers across the film) and/or to mobility degradation of carriers in the channel (through scattering of carriers by the electric field), jeopardizing the gain from the increased dielectric constant. Previous calculations have shown [7,8] that oxygen vacancies in HfO2 and in ZrO2 may be responsible for leakages and threshold voltage instabilities. We find that the energy positions of oxygen vacancy charge transition states in Pr oxides are not so critical from the point of view of leakage
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currents as in HfO2 and ZrO2 , but the concern still remains. We also address the influence of the film stoichiometry (oxygen content in PrOx ) on the leakage current and the role of oxygen interstitials and metal vacancies in the processes responsible for the electrical quality of the film. 2. Approach Total energy calculations were done with the ab initio plane wave code fhi96md [9,10]. We applied the local density approximation (LDA, [11,12]) and nonlocal pseudopotentials [13,14] with 40 Ry cutoff for plane waves; in some cases, generalized gradient approximation (GGA [15]) was used. The Brillouin zone was sampled at a set of special k-points, akin to the (0.25, 0.25, 0.25) point family generated for cells of dimensions close to these of the Pr2 O3 unit cell (cube with the lattice constant of 1 nm). Because of the open f-shell of Pr atoms, a key problem in calculations involving Pr is the construction of a reliable Pr pseudopotential [16,17]. Our band structure calculations taking into account the whole f-shell of Pr as valence shell have shown that such an approach is unpracticable within LSDA and also within GW. The position of the occupied f-band is much too high and there is no tendency to localize these electrons. It turns out that in practice two different Pr pseudopotentials are needed: a pseudopotential with two core f electrons for Pr2 O3 (trivalent PrIII, +3 ionic charge), and with only one f electron for PrO2 (tetravalent PrIV, +4 ionic charge). We calibrate the pseudopotential energy difference between PrIII and PrIV in such a way that the experimental difference in the formation enthalpies of Pr2 O3 and PrO2 is reproduced [18,19]. The computed lattice constants of Pr2 O3 and PrO2 are in agreement with experiment.
The drawback is that the wavefunctions responsible for the (4 þ =3þ) electron transition level of Pr cannot be computed. However, from total energy difference between the perfect crystal and the crystal with one Pr atom in the other charge state one can calculate the energy position of the highest occupied f-band in Pr2 O3 and PrSiO3:5 , and the lowest unoccupied f-band in PrO2 . The location of the occupied f-band top is obtained as the (0/+) electron transition state of the isolated f-shell of a Pr atom in the crystal, that is, as the Fermi energy at which the charge state of the Pr atom changes from +3 to +4. We find these bands at 0.5 above the topmost occupied oxygen states in Pr2 O3 , and at about 0.16 eV below the top of the non-f valence band in PrSiO3:5 . This is roughly compatible with out XPS measurements, which show the f peak at the valence band top; however, its measured position is typically about 0.5 eV above the position estimated from the calculation. The empty f-band in PrO2 is computed to be located 1.3 eV above the topmost occupied oxygen states and corresponds to the (=0) electron transition state of the f shell. 3. Band offsets Since point defects are usually charged, we must consider the dependence of the defect formation energy G f on the electron chemical potential, that is, on the Fermi energy E F . This means that the formation energy of charged defects in a dielectric remaining in electrical contact with the Si substrate is determined by the position of the Fermi level in the substrate and by the valence band offset between Si and the dielectric. We compute the band offsets (Table 1) using the conjunction that when two materials with an energy gap are brought into contact, their charge neutrality levels (CNLs) tend to match: electrons flow from the
Table 1 Band offsets to Si and charge transition states of oxygen-related defects OV , energy below CB
Band offsets to
PrO2 Pr2 O3 PrSiO3:5
OI , energy above VB
Si VB
Si CB
(++/+) (eV)
ðþ=0Þ (eV)
ð0=Þ (eV)
2.6 2.1 2.7
2.3 2.1 1.8
0.37 1.09 (n)
– 0.85 (n)
– 0.21 (n)
ð0=Þ (eV) 1.80 0.04 1.16
For vacancy levels the distance to the conduction band (CB) edge is given, while for interstitial levels the distance to the valence band (VB) edge is specified. For Pr2 O3 , the VB offset and the OI levels are given with respect to estimated position of f-type VB top. (n) - see text.
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Fig. 1. Band gap of Pr2 O3 film deposited on Si, as measured by XPS from the offset between the O1s peak and the loss peak. The O1s peak has been subtracted by gaussian fit. The position of the O1s peak and the onset of the loss peak are indicated by vertical lines.
material with the higher CNL to the material with the lower CNL, whereby the electrical dipole moment produced in this way is screened, so that the matching is usually not complete [20,21]. Since the mechanism of CNL alignment is akin to the appearance of metal induced gap states (states from one material enter into the other material and change the effective density of states, thus producing an interface dipole), f-state density is not included in these calculations. Namely, f-states are localized and their contribution to the metal induced gap States should be minimal, given that all Pr atoms are separated from Si by O atoms. This is fortunate, because although the position of the occupied f-band can be reasonably estimated, the position of the empty f-band is difficult to obtain. When the conduction band offset is known, the valence band offset is found by subtracting the conduction band offset and Si energy gap from the band gap of the dielectric. For this purpose, we used experimental energy gaps (Fig. 1). 4. Charge states of oxygen-related defects For most of Fermi energies, oxygen vacancies in Pr oxides are double positively charged. In the upper part of the gap there are, however, charge transition states. They correspond to Fermi energies at which the vacancy traps an additional electron, changing its charge state. This electron is trapped in a state of conduction-band type (Fig. 2). This is because the oxides are strongly ionic and the
removed oxygen atom is a negatively charged ion, that is, the removal of oxygen is equivalent to the creation of a positive perturbation potential. This potential is attractive to electrons, i.e., it locally pulls the band structure to lower energies. It follows that when the LDA gap is corrected to the experimental one by a rigid shift of the conduction band, the vacancy states should be shifted by the same amount (Fig. 2, right). This conjunction can be easily verified by changing the exchange-correlation potential such that the band structure does not change dramatically but the band gap changes. Indeed, when the calculation is done with GGA exchange-correlation, the band gap increases by about 0.5 eV but the position of the transition state relative to the conduction band edge does not change. The positions of vacancy transition states in the gap of Pr2 O3 and PrO2 with respect to the conduction band edge are listed in Table 1. Oxygen vacancy in PrSiO3:5 is not a charged defect at Fermi levels of interest. This is because O atoms in PrSiO3:5 have either only Si neighbors or both Si and Pr neighbors. The vacancy created by removing oxygen from between two Si atoms results in an electrically neutral Si–Si bridge, with the highest occupied electronic orbital located about 2 eV below the valence band top of Si. This defect is labeled OV (SiSi) in Fig. 3. (One expects that this bridge is the precursor of the family of defects similar to the E0 family in SiO2). The removal of oxygen from a site where it had Pr neighbors results in the formation of a Si dangling bond. This defect
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Fig. 2. (Left) Charge density of an electron trapped on oxygen vacancy in Pr2 O3 ; Pr atoms are blue, O atoms are yellow. It is clear that this is a conduction band state. (Right) Therefore, the LDA energy of the transition state measures the relative position between the conduction band and the Fermi energy at which the defect changes its charge state. When the gap is corrected to the experimental one by a rigid shift of the conduction band (‘‘scissors operator’’), the transition state should be therefore shifted together with the conduction band.
Fig. 3. (Left) Free Si dangling bond, Si(db). Si atoms are white, O atoms are light gray, Pr atoms are dark gray, the H atom saturating the spurious dangling bond is black, and the dangling bond is also rendered in black. In order to make the figure more readable, some atoms are removed from the panels (the bonds are retained). (Right) Formation energies of oxygen-vacancy related native defects in PrSiO3:5 as a function of the chemical potential of oxygen. For the chemical potential of Si, equilibrium with bulk Si is assumed. The Fermi level corresponds to that of intrinsic Si. Formation energy of Si(db) has been corrected as explained in the text.
is labeled OV (SiPr) in Fig. 3. Its formation energy is nearly equal to that of OV (SiSi). Although this dangling bond does capture an electron, this electron comes locally from the metal neighbors. The negative charge localized now at the Si dangling
bond is the same as the charge that was collected from the metal atoms by the removed O atom; the defect is thus electrically neutral. The electrons in this negatively charged dangling bond are bound by the electric field of the positively charged Pr ion;
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they occupy an orbital located roughly 1 eV below the valence band of Si. If an isolated Si dangling bond Si(db) is far enough from Pr atoms, typical dangling bond transition states are produced. We have built a model of such a dangling bond (Fig. 3) starting from the OV (SiSi) Si bridge. We stretch and break the bridge by moving one of the Si neighbors along the Si–Si bond until this atom arrives at the sp3 site on the other side of the plane defined by its three O neighbors. We then saturate this atom with hydrogen and treat the dangling bond on the other Si atom as a free Si dangling bond. The computed formation energy of such a defect consists of two major contributions: one is the formation energy of the dangling bond, the other is the formation energy of the O3SiH defect. In Fig. 3 we adjusted this formation energy to represent the free dangling bond. We did this by adding a corrective term DE bringing the formation energy of the uncharged defect to the value of 1.1 eV at the equilibrium with SiO2. Indeed, since the oxygen atom was removed from a configuration closely resembling that in SiO2 and—for this choice of the chemical potential—was moved to SiO2, the formation energy of the (uncharged) dangling bond should be roughly equal to half of the SiSi bond energy, that is, to 1.1 eV. From Fig. 3 we now conclude that oxygen vacancies in PrSiO3:5 may be stable with respect to dissociation at least in thin films. Oxygen vacancies may be created in PrSiO3:5 when the silicate is in the chemical contact with a strongly reducing medium, e.g., with Pr or Ti metal layer. According to the computed formation energies, the chemical potential of oxygen at the equilibrium between PrSiO3:5 , Pr metal, and crystalline Si is equal to 5:65 eV (cf. Fig. 3; zero of the chemical potential corresponds to oxygen in O2). The defect formation energy of about 1 eV, computed for O vacancies at these strongly reducing conditions (Fig. 3), is equivalent to the equilibrium concentration of about 1017 cm3 at 600 C. At the chemical potential of oxygen corresponding to the equilibrium between Pr2 O3 , SiO2, and Si, this concentration drops to about 1014 cm3 . As for oxygen interstitials, OI , they are double negatively charged when the Fermi level is high enough. This is because oxygen valence orbitals have low energy; this translates into a large energy gain when electrons move from Fermi energy to the interstitial. When the Fermi level is low, OI makes a bond with an oxygen atom from the lattice to form O2 2 . This
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substitutional molecule is an electrically neutral defect, because lattice oxygen atoms are also double negatively charged. The single negative charge state is unstable, because hole capture is associated with a strong relaxation of the atomic structure. The same behavior of interstitial oxygen has been found by ab initio calculations in HfO2 [7], ZrO2 [8], and ZrSiO4 [22]. The position of the ð0=Þ state depends on the atomic structure of the host (Table 1). In Pr2 O3 , OI can go into the formal vacancy site (cubic Pr2 O3 is obtained from cubic PrO2 by removing one quarter of O atoms). The formation energy of O2 is thus low I and the charge transition state is close to the valence band top. But O2 I in PrO2 and PrSiO3:5 must occupy truly interstitial sites, so that the formation energies of 0 O2 I are higher, making OI relatively more stable and shifting the transition states to higher energies. 5. Discussion We are now in position to sketch the band diagram of a Pr oxide deposited on Si (Fig. 4). Since Pr2 O3 reacts with Si and oxygen to form Pr silicate, and with oxygen to form a higher oxide, we will assume a stack consisting of Si, PrSiO3:5 , Pr2 O3 , and PrO2 . Band offsets are estimated by the CNL alignment procedure described in Section 3. Let us begin with the Pr2 O3 layer. Its rightmost part (the closest to Si) sees the Fermi level as determined by the Si substrate (and by the influence of the PrSiO3:5 layer, which we ignore for a while). This means that the formation of negatively charged oxygen interstitials (and negatively charged Pr vacancies, Pr3 V [23,24]) is energetically favorable in this region, and the concentration of these defects is determined only by electrostatic repulsion. Consequently, a negative fixed charge appears there, pushing the bands upwards as the distance from Si increases. Therefore, the energy gain from the creation of deep acceptors diminishes with increasing distance from the substrate. The formation of O2 ceases to be I favorable when the Fermi level drops to about 1.5 eV above the f-band edge. Since Pr2 O3 is a widegap material, only a small amount of acceptors (of the order of 1015 cm3 ) suffices for such a movement of Fermi level in a free-standing material, hence there are virtually no negatively charged oxygen interstitials in Pr2 O3 bulk. For Pr3 V , this happens earlier, for Fermi energy about 2.1 eV above the f-band edge. In other words, band bending due to charge accumulation removes the tendency to form negatively charged defects, and the bands flatten out.
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Fig. 4. Band diagram for a Si/PrSiO3:5 /Pr2 O3 /PrO2 stack. Charge transition states of several point defects are indicated. The valence band edges marked by thick sold lines correspond to topmost occupied states of O. The estimated position of the topmost occupied f band in PrSiO3:5 and Pr2 O3 is marked by thin solid lines, the position of the lowest unoccupied f band in PrO2 is marked by a dotted line. The broken line is the Fermi energy, assumed to coincide with that of intrinsic Si. See text for more discussion, and Table 1 for numerical data.
At the same time, the negative charge hinders the in-diffusion of negatively charged oxygen from the ambient atmosphere to PrSiO3:5 (although in-diffusion of neutral species is not affected). PrSiO3:5 can thus develop positive fixed charge, associated with Si [23,24] and partially compensating the negative charge in the oxide. The rest of the negative charge must be compensated in the substrate, leading to band bending there, visible in CV characteristics as a flatband voltage shift. On the opposite side of the Pr2 O3 layer, there is a growing tendency for oxidation, particularly during annealing (even ‘‘inert’’ N2 ambient contains enough oxygen to oxidize Pr2 O3 to PrOx with x41:5). Oxidation of Pr2 O3 is more difficult in deeper regions because the transition from PrIV (the charge state of Pr in PrO2 ) to PrIII (the charge state of Pr in PrIII) occurs in PrO2 already at low Fermi energies. According to our estimate, Pr would trap an electron when the Fermi level is higher than about 1.3 eV above the valence band edge of PrO2 . This opposes the oxidation by forcing Pr to the charge state it has in the suboxide. The current calculations are not exact enough to describe this effect quantitatively, particularly because it takes place in PrOx , which is a structurally complex material when x differs from its limiting values of 1.5 (Pr2 O3 ) and 2 (PrO2 ). It is nevertheless clear that the presence of the f-band at Fermi energies within (or close to) the energy gap of Si leads to electron hopping conductivity [26,25]. This
Fig. 5. The quality factor of a Pr oxide MOS film decreases with the film thickness.
conductivity can be avoided only if the stoichiometry of the oxide is Pr2 O3 , which is possible to maintain if the film is sufficiently thin to allow for an efficient reduction of PrOx to Pr2 O3 by the combined action of the Si substrate and the metal gate. Indeed, the electrical quality of the film deteriorates with increasing thickness (Fig. 5). Even though the electron hopping from Pr atom to Pr atom is not a problem in Pr2 O3 , the latter material is likely to contain a high concentration of
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oxygen vacancies. Although the formation energy of an electrically neutral group of defects consisting of 3Oþ2 and 2Pr3 amounts to 2 eV per defect, V V meaning that the concentration of these defects would be negligible when the film is grown under thermal equilibrium conditions, such defects can easily be formed under non-equilibrium growth. Since oxygen vacancies are the major species compensating the negative charge of Pr vacancies and oxygen interstitials, removing them (e.g., by oxidation) would upset the charge balance. Therefore, we expect that the concentration of these defects cannot be neglected even after annealing. Fortunately, the charge transition levels of oxygen vacancies are above the energy of the conduction band bottom in Si. Trap-assisted leakage (tunneling or Poole–Frenkel emission [27]) through the vacancy states of Pr2 O3 is therefore of a less concern than electron hopping through f states of Pr in a mixed oxide (PrOx ). However, our experimental data indicate that Poole–Frenkel emission characterized by the energy barrier of about 1.0 eV plays a role in the leakage through Pr2 O3 films on Si substrates. This energy barrier is compatible with the computed position of the ðþ= þ þÞ charge transition state of oxygen vacancy in Pr2 O3 . 6. Summary and conclusions Using ab initio data, we analysed the influence of charged point defects in Pr2 O3 , PrSiO3:5 , and PrO2 on electrical properties of the dielectric deposited on Si. We estimated the band diagram of a Pr-oxide stack; up to our knowledge, this estimate is compatible with the experimental data. We discussed the leakage mechanisms as suggested by the results of the calculation (trap-assisted leakage through oxygen vacancies, and electron hopping through empty fband). From experiment, we have hints that both mechanisms contribute noticeably to gate leakage. Acknowledgment The calculations have been done on IBM Regatta in von Neumann Institute for Computing, Ju¨lich, Germany (project hfo06).
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