for low diffusion constant), is likely to be rare. One could obtain a high dielectric constant in a high band gap solid by increasing ionicity (ionic polarization),5 ...
Correlation between the Material Properties of the High-K Gate Dielectrics Samares Kar1 and Rajendra Singh2 1Department
of Electrical Engineering, Indian Institute of Technology, Kanpur-208016, India 2Holcombe Department of Computer and Electrical Engineering, Clemson University, Clemson, SC 29634 Currently, an active area of research in microelectronics, is dielectrics, with a high dielectric constant, κ, as a possible replacement for SiO2 as the gate dielectric, in future MISFETs.1 The high-κ dielectrics have been reviewed recently.2-4 For carrying out a comparative evaluation of the merits and the demerits of the high-κ materials in a systematic manner, it is necessary, first, to identify the critical issues, on which a gate dielectric is to be assessed, and then analyze their inter-linkages, so that the profile of an optimal high-κ gate dielectric can be outlined, against which the different high-κ dielectrics can be compared and ranked. These were the aims of this work. In many respects, the dry thermal SiO2 is as perfect a gate dielectric as any can get.2 Interestingly, its near perfection in some respects can be said to be its unmaking, when its application in sub-70-nm MISFETs is concerned. The basic factors, that promote its huge band gap (nearly 9.0 eV), which provides large energy barriers (nearly 3.2 and 4.7 eV, respectively) to both electron and hole transport, and its higher covalency and fourfold coordination, which contribute to very low interface/bulk defect density, inevitably lead to one of the lowest dielectric constants among all inorganic insulators and also one of the lowest specific densities. In a high quality solid with structural symmetry and low defect density, the combination of high band gap (desirable for low MISFET off current) and covalent bond (desirable for high quality interface with resultant higher carrier mobility and device reliability), with high dielectric constant (to satisfy the perennial need for higher drain current) and high specific density (desirable for low diffusion constant), is likely to be rare. One could obtain a high dielectric constant in a high band gap solid by increasing ionicity (ionic polarization),5 structural asymmetry (dipolar polarization),5 and/or defect density (defect and/or space charge polarization),6 however, these may generate reliability problems and frequency-dependent dielectric constant with multiple relaxation frequencies (fr), some of which will be lower than the clock frequency (>> 1 GHz). Most of the important material constants of the high-κ dielectrics are interlinked. Perhaps, the most basic element that links these properties is the nearest neighborhood, which may be represented by the coordination number (CN), the cation-anion distances, ionicity of the mixed bond, and the cation size, the combination of which influence the crystal structure, the specific density (ρ), the melting point (m.p.), the coefficient of thermal expansion (α), the band gap (EG), the electron affinity (χ), the tunneling electron/hole mass (m*), and the dielectric constant (κ). In the case of a mixed bond, the coordination number reflects the radius ratio, the bond ionicity/covalency (an increase in ionicity increases the CN as in Zr silicate), and the cation size (an increase in which increases CN, as in BaZrO3). Smaller constituent elements lead to smaller cation-anion distances, consequently stronger bonds, culminating in large band gaps and small electron affinities (as in SiO2, Al2O3). From the point of view of reliability, higher bond covalency may be desirable. But, as covalent bonds are strongly directional, covalent solids have low packing density with a relatively open network, susceptible to atomic diffusion, which may lead to the contamination of the gate dielectric, the interface, and silicon. The coordination number (CN) may be an important parameter determining the stability of the high-κ dielectrics as well the quality of the Si/ high-κ-dielectric interfaces. For this objective, the most desirable CN may be 4 (which both Si and SiO2 have,
facilitating the highest quality interface, technology has ever achieved), which, unfortunately, none of the high-κ dielectrics has, because of higher ionicity. For some high-κ gate dielectrics, high CN appears to lead to structural asymmetry and inter-conversion between alternate nearest neighbor configurations. The uncommon CN of 7, which occurs for a number of the high-κ dielectrics (such as ZrO2, HfO2, La2O3) appears to have uncommon features, including unequal cation-anion distances, (in ZrO2, HfO2, all seven M-O distances are reported to be different, while in La2O3, 3 different sets of distances may exist). It has been suggested, that in the case of sevenfold coordination, stoichiometry and charge balance are maintained with half the anions having a coordination of 3 and the rest of the anions having a coordination of 4. Whether the center of gravity of the cations is the same as that of the anions in these dielectrics (when the CNc = 7) is an important question. If not, there may be a contribution to κ from dipolar polarization. The contribution of the electronic polarization to the dielectric constant, κelectronic (fr ≈1015-1016 Hz), should be about n2 (where n is the refractive index),7,8 which even in the case of low bandgap (e.g. TiO2) or heavy cations (e.g. HfO2) does not exceed 7. (In Si and diamond, κstatic=n2, which confirms that there is no polarization in these solids other than electronic. The Moss Rule suggests an inverse relation between (κelectronic)2 and EG.7) The remaining dielectric constant, ∆κ=κstatic-n2, is contribution from ionic, κionic (fr ≈1011-1013 Hz),8 dipolar (fr ≈106-108 Hz),8defect (fr ≈103-105 Hz),6 and space-charge (fr ≈100-10-2 Hz)6 polarizations. In dry thermal SiO2 and in Al2O3, the dielectric constant has been found to be independent of frequency from low to very high frequencies. Therefore, it can be assumed that in dry thermal SiO2 and in Al2O3, there is only electronic and ionic polarizations with κionic=1.6 and 6.6, respectively. As already pointed out, only κelectronic and κionic will be useful for the gate dielectric capacitance at the clock frequency, while the other polarizations will only create reliability problems. Based on our identification of the critical material constants and our analysis of their inter-linkages, we have outlined an approximate profile of the optical high-K gate dielectric with clock-frequency κ = 18, EG = 6.0 eV, me* = 1.0 m, χ = 1.6 eV, ρ = 5.0 g/cm3, α = 2.5X10-6/K, and CNc = 4.0. Compared to this (hypothetical) benchmark gate dielectric, HfO2 has the highest rank, followed by Al2O3, ZrSiO4, ZrO2, La2O3, and Y2O3, while BaZrO3, Ta2O5, and TiO2 compare poorly. From our analysis, it appears unlikely that any high-κ binary dielectric will attain the optimal values of all the important bulk parameters. (The score for HfO2 is 7.46 against 10 for the optimal gate dielectric.) High-κ silicates or oxide solid solutions have to be found that effectively combine the attractive properties of the high band gap oxides (e.g. EG, χ, and CNc of SiO2) with those of the high- κ oxides (e.g. κ, ρ of HfO2 and Ta2O5). 1. Semiconductor Industry Association, "International Technology Roadmap for Semiconductors", 2001 Edition, http://public.itrs.net/ . 2. G. D. Wilk, R. M. Wallace, and J. M. Anthony, J. Appl. Phys. 89, 5243(2001). 3. J. D. Plummer and P. B. Griffin, Proc. IEEE 89, 240(2001). 4. H. Iwai and S. Ohmi, Electrochem. Soc. Proc. 2001-2, 3(2001). 5. A. R. von Hippel, Dielectrics and Waves, M.I.T. Press, Cambridge, 1954, p. 96. 6. R. G. Breckenridge, in Imperfections in Nearly Perfect Crystals, eds. W. Shockley, J. H. Solomon, R. Maurer, and F. Seitz, John Wiley, New York, 1952, p. 219. 7. J. I. Pankove, Optical Processes in Semiconductors, Prentice Hall, Englewood Cliffs, 1971, p. 267. 8. C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1967.
