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Boron Nitride (BN)
Boron Nitride (BN) GARY L, DOLL Materials Science Department Timken Research Canton, Ohio
INTRODUCTION
The optical functions of the hexagonal and cubic phases of BN (hBN and cBN, respectively) are not nearly as well defined as those of other group III nitrides. This is due in large part to the fact that single-crystal samples either do not exist (which is the case for hexagonal boron nitride) or are extremely rare (as in the case of cubic boron nitride) [1]. Optical studies on the optically anisotropic hBN have ~been performed on preferentially oriented, polycrystalline samples with E_I_6 and E tl~ polarization. In these samples, it is difficult to obtain a complete separation of the two polarizations because the typical mosaic spread of the c-axes is greater than 20 ~, and because pure a-faces are not easily obtained. In this critique, we have not included experiments performed on B N films. The reasons for this are that the optical constants of these films can vary greatly with film properties such as stoichiometry, homogeneity, crystallinity, and purity, to name a few. For the most part, these types of film properties have not been correlated with optical properties that have been reported. As we shall see, the optical properties of bulk B N materials are not that well defined. The hexagonal phase of BN is isostructural to graphite in that it is composed of planes of BN hexagons stacked along the c-axis in an ABA configuration, hBN has the space group D64h(P63/mmc),which has the irreducible representation
I-'- 2E2g + A2, + Elu + 2Big, where the E2g modes are Raman-active, the Big modes are silent (optically inactive), and the A2, and El, modes are infrared-active. Whereas the A2, modes are outgof-plane vibrations excited by light polarized parallel to the hBN c-axis (Eli 0), the El, modes are in-plane vibrations excited by light 425 HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS III
Copyright 9 1998 by Academic Press. All rights of reproduction in any form reserved ISBN 0-12-544423-0/$25.00.
I
426
Gary L. Doll
polarized perpendicular to the c-axis (E.I_e). The A2u and Elu modes are polar, which means that the longitudinal-optical or LO mode has a higher energy than the transverse-optical or TO mode. cBN has the zincblende structure with the space group T2, (F43m). Its phonon modes are of T2 symmetry, and are polar, so that the energy of the cBN LO vibration is also higher than the TO polarization energy.
II
cBN
Selected optical constants n and k for cBN taken from three sources are collected in Table I and plotted in Fig. 1. Tabulated values of the optical constants were not included in any of the sources. Gielisse et al. [2] provided the first reported examination of the cBN optical constants. Although this study covered the energy range 400 to 4000 cm-1, the optical constants could only be deduced from their data over the energy range 400 to 1800 cm-1. In this study, Gielisse et al. measured the reflectivity of a collection of small single crystals compressed into compacts that were ground and polished. Their normal-incidence reflectivity was modeled using a four-parameter fit to the equations
0)02 -
0)2
e1(0)) = e~ + 4fro 0)2 (0)2_ 0)2)2 q_/-,20)2
E2(0))
/-'0) A 2 ~'"B'P0)O (COg- 0)2)2 ..]._/-'20)2'
(1)
(2)
where eo is the high-frequency limiting value of the dielectric constant, 0)0 is the Brillouin-zone-center, TO phonon-mode energy, 4fro is the strength of the resonance, F and is the phonon width or the damping constant. Good agreement between the calculated and measured reflectivity was found for the following parameters: e~ = 4.5, 47tO = 2.6, ~oo = 1065 cm -1, and F = 40.5 cm -1. The static dielectric constant eo was calculated to be 7.1 from the equation Eo = ~ + 4-rrp.
(3)
We calculated the values of EI(O ) and E2(0) ) using the above parameters, then derived n and k by the equations 2 n 2 = ~/e2 + ~2 + E1
(4) 2=
+
Boron Nitride (BN)
427
The results are shown in Fig. 1 and listed in Table I. The energy of the LO mode was deduced to be 1340 cm-~ from the Lyddane-Sachs-Teller relationship o~i~o = O~To(eo/E~)1/2. Eremets et al. [3] have reported the optical properties of cBN over the energy range 500 to 28,000 cm-1. Single crystals of cBN 0.45 ~m thick by 150/,m square were studied in reflection and transmission, and n and k were deduced by fitting the interference fringes with equations proposed by Heavens [4]. Although n and k were neither tabulated nor shown in a form suitable for our purposes, the dielectric functions were described by a Sellmeier model that considers the contribution to e(co) from phonons and electronic transitions. The Sellmeier model used by the authors is expressed as E -- Eph + Eelec m Ear
(5)
where eelec- 1 -
1 - - [ h o ~ / E o ] 2'
(6)
and Eph is described by Eqs. (1), (2), and (3). Using this approach, they were able to approximate the reflectance and transmittance over the measured energy range. We first calculated the dielectric functions using Eq. (5) with the parameters E o - 6.8, E ~ - 4.46, E o - 104,850 cm -1 coo - 1055.7 cm -~ and F - 0.005 cm-1, which were given by the authors. Eremets et al. also report the LO mode energy to be 1304.8 cm -~. We suspect that the value of F given by Eremets et al. in [3] is incorrect, since it appears to be too small to describe phonon linewidths in these types of samples. Nevertheless, using the preceding parameters, we calculated n and k from Eq. (4). The results of this calculation are gathered in Table I and plotted in Fig. 1. Miyata et al. [5] have reported the optical properties of a cBN single crystal having an area of 5 nlN12 and a thickness (d) of 0.16 mm. The sample was measured over the energy range 2 to 23 eV by reflectance and 2 to 6 eV by transmittance. In the energy range 2 to 6 eV where both R and T were measured, n and k were derived from the expressions (1
k-
4rrd
In
R + 1 + [(R + 1) 2 -
R) 2
-
T ( R - 1) 2 (1 + k2)] 1/2
(7)
1-R To determine the optical constants from the reflectance at higher photon energy, a Kramers-Kronig relation was employed where the values of the phase-change integral were set equal to those calculated from the optical
428
Gary L. Doll
constants in the energy region 2.5 to 5.5 eV. Their results for n and k, which we extracted from their figure, are listed in Table I and plotted in Fig. 1. As can be seen in Fig. 1, some discrepancy exists between the data published by Gielisse et al. [2] and Eremets et al. [3] in the vicinity of the cBN IR-active phonon. Whereas Gielisse et al. [2] quote the energy of the TO phonon of their sample to be 1065 cm-1, Eremets et al. [3] have determined the energy to be 1055.7 cm -1 for their material. One might expect this sort of discrepancy to be sample dependent. As we would expect from Eqs. (1) and (2), Fig. 1 shows us that the suspiciously low value of F = 0.005 cm-1 reported by Eremets et al. has a much more pronounced effect on k than on n in the region of the IR-active cBN phonon. Gielisse et al. [2] and Eremets et al. [3] derive similar values for eo and ~ . The method used to deduce n and k from Eremets et al. [3] does not account for multiphonon absorption that is present at energies between 2000 cm-~ and 4000 cm-1, so the optical constants in that energy range are not accurate. There is good agreement in the values of n derived from Eremets et al. [3] and Miyata et al. [5] where the data overlap in the energy region 2 to 3.5 eV. The onset for optical absorption was determined to be 6.1 +_ 0.2 eV from Miyata et al. [5], and several absorption edges are also present at higher photon energies.
III
heN
The first examination of the optical properties of hBN was performed by Geick et al. [6] on pyrolytic hBN with a mosaic spread in the c-axis of 30 ~ where the c-axis is the direction normal to the B N hexagonal planes. The reflectivity was measured at near-normal incidence in E_Ld and E I1~ polarizations over the energy range 300 to 2000 cm-1. With this mosaic spread, a complete separation of the polarizations is not possible, but the experiment did provide first evidence for the identification of the in-plane (Elu) and out-of-plane (A2u) IR-active phonons in hBN. The dielectric functions were obtained from a Kramers-Kronig transformation of the reflectance data. No details of how the phase integral was extended to lower and higher energies in order to perform the transformation were given. We have calculated n and k ~ i n g Eq. (4) from a digitization of their figures for ~1 and ~2 obtained with E_I_6 polarization. We show the results in Table II and Fig. 2. The presence of the low-frequency A2u phonon near 13 ~m illustrates the contribution that the crystallographic mosaic spread of the c-axis makes to the optical spectra of these types of samples. To our knowledge, there has been no optical spectrum taken on hBN samples that does not contain a mixture of these polarizations. The authors fit their dielectric functions to an oscillator model similar to Eqs. (1) and (2) but that contains contributions from both polarizations to account for the mosaic spread of the hBN crystallites. For the E II ~ polarization, the parameters that provided the best fit to
Boron Nitride (BN)
429
the data are e ~ - 4.10, eo ---~ 5.09, r A2u _ 783 cm -1 , (-OLo A2u _ 828 cm-1 , 3.26 • 105 c m - 2 , 1 - ' A 2 u - - 8.0 cm -1, LOT OElu _ 1510 cm -1, WL oE1. _ 1595 cm -~, 47rp E~" -- 1.04 • 106 cm -1 and F E~" = 80 cm -1 For the E_L6 polarization, the parameters that provided the best fit to the data are E~ = 4.95, ~o - 7.04, ~~ _ 767 c m - 1, ~0LoA2,_ 778 c m - l , 47rpA2, _-1.23 • 105 cm -2, F A2" ---- 35.0 cm-~, ~0TOEI" _ 1367 cm-~, 09LOEI" _-1610 c m - l , 4 7 r p el" = 3.49 • 106 cm -1, and F El" - 29 cm -~. We do not display the EII 6 optical constants in either Fig. 2 or Table II. Hoffman et al. [7] examined the E_L6 optical reflectivity spectrum on a similar sample of pyrolytic hBN, with a mosaic spread slightly larger than that of Geick et al. [6] over the energy range 0.05 to 10 eV. The dielectric functions were obtained from a Kramers-Kronig transformation of the reflectance data. For purposes of integrating the phase-shift integral of the transformation, the data were extended below 0.045 eV by treating R as a constant, from 10 to 30 eV by using data from Mamy et al. [8], from 30 to 100 eV as R ~ ~o-1 and thereafter as R ~ 0) - 4 . We have calculated n and k using Eq. (4) from a digitization of their figures for el and E2, and we show the results in Table II and Fig. 2. As is evident in the figure, there is agreement in the energies of the Ell, and A2u phonons between the two studies, but disagreement in the oscillator strengths of the vibrations. This is probably related to orientational and structural differences between the samples examined in the two studies. Another item of note is that the values of k are relatively high in the region between the ir-active phonons and the electronic band gap near 5 eV. The authors believe that this is not intrinsic to hBN, but rather is related to the rather large amounts of impurities and defects in the sample. The authors also examined the phonon region of E2 by fitting the data with an oscillator model similar to the one used by Geick et al. [6] for the E_L6 polarization. The best fit to the data was achieved with the following parameters: r 770 cm -~ , 4"/7"/9A 2 " - - 3 . 8 X 1 0 4 c m - 2 I - ' a 2 u - - 1 8 cm-1, OJTO E l , _ 1383 cm -~, 47rp e ~ " - 7.5 • 105 cm -~ , and 1 - ' E l u - - 30 cm -1 9 Values for Eo~ and r were not given in the paper, so a determination of the LO-mode energies from the data is not possible. 4"rrpA2u
- -
~
9
._..)
a z u
__
REFERENCES
1. J. H. Edgar, in "Properties of Group III Nitrides" (J. H. Edgar, ed.), p. 7. INSPEC, The Institute of Electrical Engineers, London, 1994. 2. P. J. Gielisse, S. S. Mitra, J. N. Plendl, R. D. Griffis, L. C. Mansur, R. Marshall, and E. A. Pascoe, Phys. Rev. 155, 1039 (1967). 3. M. I. Eremets, M. Gauthier, A. Polian, J. C. Chervin, J. M. Besson, G. A. Dubitskii, and Y. Y. Semenova, Phys. Rev. B 52, 8854 (1995). 4. O. S. Heavens, Rep. Prog. Phys. 23, 1 (1960). 5. N. Miyata, K. Moriki, O. Mishima, M. Fujisawa, and T. Hattori, Phys. Rev. B 40, 12028 (1989). 6. R. Geick, C. H. Perry, and G. Rupprecht, Phys. Rev. 146, 543 (1966). 7. D. M. Hoffman, G. L. Doll, and P. C. Eklund, Phys. Rev. B 30, 6052 (1984). 8. R. Mamy, J. Thomas, G. Jezequel, and J. C. Lemonnier, J. Phys. (Paris) Lett. 42, 473 (1981).
Gary L. Doll
430 '
''''1
101 4
k'l=
10 ~ "O.
"=
10-~
"A
10-&
Lk. -&
i
10-3E
10 -410-5-
Ii d
10 -6-
"1
10-7..
,,! =9
10 -& '
'
' ' ' I
'
'
'
'
'
' ' ' I
10 -1
'
'
'
'
'
' ' ' I
100
'
I
101
WAVELENGTH (#m) Fig. 1. Log-log plot of n (solid line) and k (dashed line) versus wavelength in micrometers for cBN. The data for n and k were derived from Gielisse et al. [2] (triangles), Eremets et al. [3] (squares), and Miyata et al. [5] (circles).
10110~
O, ....
"'-'O
.....
"O .....
~ .
10 4-
E
.i
. .....
10 -~-
10-3..
= , J,
10 .4_ '
'
' ' ' I
'
10 -1
'
'
'
'
' ' ' I
'
'
'
'
10 0
'
' ' ' I
'
'
101
WAVELENGTH (pm) Fig. 2. Log-log plot of n (solid line) and k (dashed line) versus wavelength in micrometers for hBN obtained from E_Ld polarization. The data for n and k were derived from Geick et al. [6] (squares) and Hoffman et al. [7] (circles).
Boron Nitride (BN)
431 TABLE I
Values of n a n d k for C u b i c B N f r o m V a r i o u s R e f e r e n c e s a
eV
cm-~
/xm
n
2.00El 1.98E1 1.96E 1 1.95E1 1.93E1 1.91 E1 1.89E1 1.87E1 1.85E1 1.84E1 1.82E1 1.80El 1.78E1 1.76E 1 1.75E 1 1.73E1 1.71E 1 1.69E1 1.67E 1 1.65E1 1.64E 1 1.62E 1 1.60E 1 1.58E1 1.56E 1 1.55E 1 1.53E1 1.51E 1 1.49E 1 1.47E1 1.45E1 1.44E 1 1.42E 1 1.40El 1.38E1 1.36E 1 1.35E 1 1.33E1 1.31E 1 1.29E 1 1.27E 1 1.25E 1 1.24E 1 1.22E1 1.20El 1.18E 1
1.613E5 1.599E5 1.584E5 1.569E5 1.555E5 1.540E5 1.525E5 1.511E5 1.496E5 1.481E5 1.467E5 1.452E5 1.437E5 1.423E5 1.408E5 1.393E5 1.379E5 1.364E5 1.349E5 1.335E5 1.320E5 1.305E5 1.291 E5 1.276E5 1.261 E5 1.247E5 1.232E5 1.217E5 1.203E5 1.188E5 1.173E5 1.159E5 1.144E5 1.129E5 1.115E5 1.100E5 1.085E5 1.071E5 1.056E5 1.041 E5 1.027E5 1.012E5 9.973E4 9.826E4 9.679E4 9.533E4
6.200E-2 6.257E-2 6.315E-2 6.374E-2 6.434E-2 6.495E-2 6.558E-2 6.621E-2 6.686E-2 6.752E-2 6.820E-2 6.889E-2 6.959E-2 7.031E-2 7.104E-2 7.179E-2 7.255E-2 7.333E-2 7.413E-2 7.495E-2 7.578E-2 7.663E-2 7.750E-2 7.839E-2 7.930E-2 8.024E-2 8.119E-2 8.217E-2 8.317E-2 8.420E-2 8.525E-2 8.633E-2 8.744E-2 8.857E-2 8.974E-2 9.093E-2 9.216E-2 9.342E-2 9.472E-2 9.606E-2 9.743E-2 9.884E-2 1.003E- 1 1.018E- 1 1.033E- 1 1.049E- 1
1.0389 [5] 1.0552 1.0872 1.1212 1.1534 1.1830 1.2125 1.2421 1.2735 1.3081 1.3427 1.3773 1.4112 1.4433 1.4776 1.5162 1.5547 1.5935 1.6344 1.6713 1.6835 1.6957 1.7079 1.7154 1.7178 1.7249 1.7388 1.7560 1.7780 1.8105 1.8516 1.8959 1.9390 1.9822 2.0369 2.0906 2.1344 2.1804 2.2249 2.2513 2.2628 2.2689 2.2648 2.2604 2.2583 2.2822
1.03E0 [51 1.05E0 1.07E0 1.09E0 1 IOE0 1 12E0 1 13E0 1 15E0 1 16E0 1 17E0 1 17E0 1 18E0 1 19E0 1.20E0 1.20E0 1.20E0 1.20E0 1.20E0 1.20E0 1.17E0 1.14E0 1.11E0 1.10E0 1.08E0 1.07E0 1.09E0 1.10E0 1.11E0 1.13E0 1.14E0 1.15E0 1 16E0 1 18E0 1 16E0 1 15E0 1 13E0 1 llE0 1.07E0 1.03E0 9.82E-1 9.35E-1 8.93E-1 8.60E-1 8.36E-1 8.45E-1 8.55E-1
(continued) a
The references from which the values were taken are given in brackets.
432
Gary L. Doll TABLE I
(Continued)
Cubic BN eV 1.16E1 1.15El 1.13El 1.11El 1.09El 1.07El 1.05E1 1.04El 1.02El 1.00E 1 9.82E0 9.64E0 9.45E0 9.27E0 9.09E0 8.91E0 8.73E0 8.55E0 8.36E0 8.18E0 8.00E0 7.82E0 7.64E0 7.45E0 7.27E0 7.09E0 6.91E0 6.73E0 6.55E0 6.36E0 6.18E0 6.00E0 5.82E0 5.64E0 5.45E0 5.27E0 5.09E0 4.91E0 4.73E0 4.55E0 4.36E0 4.18E0 4.00E0 3.82E0 3.64E0 3.55E0 3.45E0
cm
-1
9.386E4 9.239E4 9.093E4 8.946E4 8.799E4 8.653E4 8.506E4 8.359E4 8.213E4 8.066E4 7.919E4 7.773E4 7.626E4 7.479E4 7.333E4 7.186E4 7.039E4 6.893E4 6.746E4 6.599E4 6.453E4 6.306E4 6.159E4 6.013E4 5.866E4 5.720E4 5.573E4 5.426E4 5.280E4 5.133E4 4.986E4 4.840E4 4.693E4 4.546E4 4.400E4 4.253E4 4.106E4 3.960E4 3.813E4 3.666E4 3.520E4 3.373E4 3.226E4 3.080E4 2.933E4 2.862E4 2.786E4
/.Lm 1.066E-1 1.083E-1 1.100E- 1 1.118E-1 1.137E-1 1.156E-1 1.176E-1 1.197E-1 1.218E-1 1.240E- 1 1.263E-1 1.287E-1 1.312E-1 1.337E-1 1.364E-1 1.392E-1 1.421E-1 1.451E-1 1.483E-1 1.516E-1 1.550E-1 1.586E-1 1.624E-1 1.663E-1 1.705E-1 1.749E-1 1.795E-1 1.843E-1 1.894E-1 1.949E-1 2.006E- 1 2.067E-1 2.131E-1 2.200E- 1 2.273E-1 2.352E-1 2.436E-1 2.526E-1 2.623E-1 2.728E-1 2.842E-1 2.965E- 1 3.100E-1 3.248E-1 3.410E-1 3.490E-1 3.590E- 1
2.3384 2.4265 2.4467 2.4702 2.5046 2.5368 2.5357 2.5046 2.4598 2.4147 2.3900 2.3733 2.3647 2.3561 2.3470 2.3362 2.3268 2.3204 2.3086 2.2960 2.2835 2.2749 2.2690 2.2687 2.2733 2.2766 2.2762 2.2782 2.2919 2.3032 2.2913 2.2692 2.2160 2.1981 2.1912 2.1752 2.1471 2.1286 2.1258 2.1186 2.1148 2.1073 2.0969 2.0909 2.0852 2.1111 [3] 2.0791 [5]
8.65E-1 8.28E-1 7.62E-1 7.19E-1 6.76E-1 5.94E-1 5.13E-1 4.38E-1 4.15E-1 3.92E-1 3.69E-1 3.57E-1 3.45E-1 3.30E-1 3.11E-1 2.91E-1 2.70E-1 2.56E-1 2.44E-1 2.32E-1 2.26E-1 2.20E-1 2.14E-1 2.08E-1 2.03E-1 1.86E-1 1.65E-1 1.45E-1 1.24E-1 9.62E-2 5.15E-2 6.72E-3
Boron Nitride (BN)
433 TABLE I (Continued) Cubic BN
eV 3.30E0 3.27E0 3.09E0 3.07E0 2.91E0 2.86E0 2.73E0 2.66E0 2.55E0 2.47E0 2.36E0 2.30E0 2.18E0 2.14E0 2.00E0 1.99E0 1.85E0 1.72E0 1.60E0 1.49E0 1.39E0 1.29E0 1.20E0 1.12E0 1.04E0 9.67E-1 9.00E-1 8.37E-1 7.79E-1 7.25E-1 6.74E-1 6.27E-1 5.84E-1 5.43E-1 5.05E-1 4.70E-1 4.37E-1 4.07E-1 3.78E-1 3.52E-1 3.28E-1 3.05E-1 2.83E-1 2.64E-1 2.48E-1 2.47E-1 2.45E-1
cm
--1
2.663E4 2.640E4 2.493E4 2.477E4 2.346E4 2.305E4 2.200E4 2.144E4 2.053E4 1.995E4 1.907E4 1.856E4 1.760E4 1.727E4 1.613E4 1.606E4 1.494E4 1.390E4 1.293E4 1.203E4 1.120E4 1.042E4 9.690E3 9.015E3 8.387E3 7.803E3 7.259E3 6.754E3 6.283E3 5.846E3 5.438E3 5.060E3 4.707E3 4.379E3 4.074E3 3.790E3 3.526E3 3.281 E3 3.052E3 2.840E3 2.642E3 2.458E3 2.287E3 2.127E3 2.000E3 1.990E3 1.980E3
~m
3.760E- 1 3.789E-1 4.012E-1 4.040E-1 4.263E-1 4.340E-1 4.547E-1 4.660E- 1 4.871E-1 5.010E-1 5.246E- 1 5.390E-1 5.683E-1 5.790E-1 6.200E- 1 6.230E-1 6.690E- 1 7.190E-1 7.730E-1 8.310E-1 8.930E-1 9.600E- 1 1.032E0 1.109E0 1.193E0 1.282E0 1.378E0 1.481E0 1.592E0 1.711E0 1.839E0 1.977E0 2.125E0 2.284E0 2.455E0 2.639E0 2.836E0 3.049E0 3.277E0 3.522E0 3.786E0 4.069E0 4.374E0 4.701E0 5.001 E0 5.026E0 5.051 E0
2.111013] 2.0744 [5] 2.0794 2.1109 [3] 2.0815 [5] 2.1107 [31 2.0837 [5] 2.1105 [31 2.0935 [5] 2.1103 [31 2.1021 [51 2.1101 [3] 2.1109 [5] 2.1098 [3] 2.1231 [5] 2.1095 [3] 2.1091 2.1087 2.1082 2.1076 2.1069 2.1061 2.1052 2.1042 2.1029 2.1015 2.0999 2.0979 2.0957 2.0931 2.0901 [3] 2.0865 2.0823 2.0774 2.0716 2.0647 2.0566 2.0468 2.0351 2.0210 2.0037 1.9825 1.9559 1.9222 2.8450 [2] 2.8440 2.8430
2.11E-8 [3] 2.11E-8 2.98E-8 4.21E-8 5.16E-8 6.99E-8 8.69E-8 1.13E-7 1.46E-7 1.90E-7 2.50E-7 3.33E-7 4.51E-7 6.21E-7 1.75E-2 [2] 1.74E-2 1.73E-2
(continued)
434
Gary L. Doll TABLE I
(Continued)
Cubic BN
eV 2.45E-1 2.44E-1 2.43E-1 2.42E-1 2.41E-1 2.39E-1 2.38E-1 2.37E-1 2.36E-1 2.34E-1 2.33E-1 2.32E-1 2.31E-1 2.29E-1 2.28E-1 2.28E-1 2.27E-1 2.26E-1 2.24E-1 2.23E-1 2.22E-1 2.21E-1 2.19E-1 2.18E-1 2.17E-1 2.16E-1 2.14E-1 2.13E-1 2.12E-1 2.12E-1 2.11E-1 2.10E-1 2.08E-1 2.07E-1 2.06E- 1 2.05E-1 2.03E-1 2.02E-1 2.01E-1 2.00E- 1 1.98E-1 1.98E-1 1.97E-1 1.96E-1 1.95E-1 1.93E-1 1.92E-1
cm
-1
1.979E3 1.970E3 1.960E3 1.950E3 1.940E3 1.930E3 1.920E3 1.910E3 1.900E3 1.890E3 1.880E3 1.870E3 1.860E3 1.850E3 1.841E3 1.840E3 1.830E3 1.820E3 1.810E3 1.800E3 1.790E3 1.780E3 1.770E3 1.760E3 1.750E3 1.740E3 1.730E3 1.720E3 1.713E3 1.710E3 1.700E3 1.690E3 1.680E3 1.670E3 1.660E3 1.650E3 1.640E3 1.630E3 1.620E3 1.610E3 1.600E3 1.594E3 1.590E3 1.580E3 1.570E3 1.560E3 1.550E3
~m
5.053E0 5.077E0 5.103E0 5.129E0 5.156E0 5.182E0 5.209E0 5.237E0 5.264E0 5.292E0 5.320E0 5.349E0 5.377E0 5.406E0 5.432E0 5.436E0 5.465E0 5.496E0 5.526E0 5.557E0 5.588E0 5.619E0 5.651 E0 5.683E0 5.715E0 5.748E0 5.781E0 5.815E0 5.839E0 5.849E0 5.883E0 5.918E0 5.953E0 5.989E0 6.025E0 6.062E0 6.099E0 6.136E0 6.174E0 6.212E0 6.251 E0 6.276E0 6.290E0 6.330E0 6.371E0 6.411E0 6.453E0
1.8785 2.8420 2.8410 2.8400 2.8400 2.8390 2.8380 2.8370 2.8360 2.8350 2.8350 2.8340 2.8330 2.8320 1.8202 2.8310 2.8310 2.8300 2.8290 2.8280 2.8270 2.8270 2.8260 2.8250 2.8240 2.8240 2.8230 2.8220 1.7395 2.8210 2.8200 2.8200 2.8190 2.8180 2.8170 2.8170 2.8160 2.8150 2.8150 2.8140 2.8130 1.6215 2.8120 2.8120 2.8110 2.8100 2.8090
[3] [2]
[3] [2]
[3] [21
[31 [2]
8.75E-7 1.72E-2 1.72E-2 1.71E-2 1.70E-2 1.69E-2 1.69E-2 1.68E-2 1.67E-2 1.67E-2 1.66E-2 1.65E-2 1.65E-2 1.64E-2 1.27E-6 1.63E-2 1.63E-2 1.62E-2 1.61E-2 1.61E-2 1.60E-2 1.59E-2 1.59E-2 1.58E-2 1.57E-2 1.57E-2 1.56E-2 1.55E-2 1.94E-6 1.55E-2 1.54E-2 1.53E-2 1.53E-2 1.52E-2 1.52E-2 1.51E-2 1.50E-2 1.50E-2 1.49E-2 1.49E-2 1.48E-2 3.16E-6 1.47E-2 1.47E-2 1.46E-2 1.46E-2 1.45E-2
[3] [2]
[3] [2]
[3] [2]
[3] [2]
Boron Nitride (BN)
435 TABLE I (Continued) Cubic BN
eV 1.91E-1 1.90E-1 1.88E-1 1.87E-1 1.86E-1 1.85E-1 1.84E-1 1.83E-1 1.82E-1 1.81E-1 1.80E-1 1.79E-1 1.77E-1 1.76E-1 1.75E-1 1.74E-1 1.72E-1 1.71E-1 1.71E-1 1.70E-1 1.69E- 1 1.67E-1 1.66E- 1 1.65E-1 1.64E- 1 1.62E-1 1.61E-1 1.60E-1 1.59E-1 1.59E-1 1.57E-1 1.56E-1 1.55E-1 1.54E- 1 1.52E-1 1.51E-1 1.50E-1 1.49E-1 1.48E-1 1.48E-1 1.46E-1 1.45E-1 1.44E- 1 1.43E-1 1.41E-1 1.40E- 1 1.39E-1
cm-
1
1.540E3 1.530E3 1.520E3 1.510E3 1.500E3 1.490E3 1.483E3 1.480E3 1.470E3 1.460E3 1.450E3 1.440E3 1.430E3 1.420E3 1.410E3 1.400E3 1.390E3 1.380E3 1.379E3 1.370E3 1.360E3 1.350E3 1.340E3 1.330E3 1.320E3 1.310E3 1.300E3 1.290E3 1.283E3 1.280E3 1.270E3 1.260E3 1.250E3 1.240E3 1.230E3 1.220E3 1.210E3 1.200E3 1.194E3 1.190E3 1.180E3 1.170E3 1.160E3 1.150E3 1.140E3 1.130E3 1.120E3
/xm 6.495E0 6.537E0 6.580E0 6.624E0 6.668E0 6.713E0 6.745E0 6.758E0 6.804E0 6.851E0 6.898E0 6.946E0 6.994E0 7.044E0 7.094E0 7.144E0 7.196E0 7.248E0 7.251 E0 7.301 E0 7.354E0 7.409E0 7.464E0 7.520E0 7.577E0 7.635E0 7.694E0 7.753E0 7.793E0 7.814E0 7.875E0 7.938E0 8.001E0 8.066E0 8.132E0 8.198E0 8.266E0 8.335E0 8.377E0 8.405E0 8.476E0 8.549E0 8.622E0 8.697E0 8.774E0 8.851E0 8.930E0
2.8090 2.8080 2.8070 2.8070 2.8060 2.8050 1.4327 2.8050 2.8040 2.8030 2.8020 2.8020 2.8010 2.8000 2.8000 2.7990 2.7980 2.7980 1.0721 2.7970 2.7960 2.7960 2.7950 2.7940 2.7940 2.7930 2.7920 2.7920
[3] [21
[3] [2]
2.7910 [2] 2.7910 2.7900 2.7890 2.7890 2.7880 2.7870 2.7870 2.7860 2.7860 [2] 2.7850 2.7840 2.7840 2.7830 2.7820 2.7820 2.7810
1.44E-2 1.44E-2 1.43E-2 1.43E-2 1.42E-2 1.41E-2 5.75E-6 [3] 1.41E-2 [2] 1.40E-2 1.40E-2 1.39E-2 1.39E-2 1.38E-2 1.38E-2 1.37E-2 1.36E-2 1.36E-2 1.35E-2 1.35E-5 [3] 1.35E-2 [2] 1.34E-2 1.34E-2 1.33E-2 1.33E-2 1.32E-2 1.32E-2 1.31E-2 1.31E-2 6.64E-1 [3] 1.30E-2 [21 1.30E-2 1.29E-2 1.29E-2 1.28E-2 1.27E-2 1.27E-2 1.26E-2 1.26E-2 1.98E0 [3] 1.25E-2 [21 1.25E-2 1.24E-2 1.24E-2 1.23E-2 1.23E-2 1.23E-2 1.22E-2
(continued)
436
Gary L. Doll TABLE I
(Continued)
Cubic BN
eV 1.38E-1 1.38E-1 1.36E-1 1.35E-1 1.34E-1 1.33E-1 1.31E-1 1.30E-1 1.29E-1 1.28E-1 1.28E-1 1.26E-1 1.25E-1 1.24E-1 1.23E-1 1.21E-1 1.20E-1 1.19E-1 1.19E-1 1.18E-1 1.17E-1 1.15E-1 1.14E-1 1.13E-1 1.12E-1 1.11E-1 1.10E-1 1.09E-1 1.08E-1 1.07E-1 1.05E-1 1.04E-1 1.03E-1 1.03E-1 1.02E-1 1.00E- 1 9.92E-2 9.79E-2 9.67E-2 9.60E-2 9.55E-2 9.42E-2 9.30E-2 9.17E-2 9.05E-2 8.93E-2 8.93E-2
cm
--1
1.111E3 1.110E3 1.100E3 1.090E3 1.080E3 1.070E3 1.060E3 1.050E3 1.040E3 1.033E3 1.030E3 1.020E3 1.010E3 1.000E3 9.900E2 9.800E2 9.700E2 9.615E2 9.600E2 9.500E2 9.400E2 9.300E2 9.200E2 9.100E2 9.000E2 8.945E2 8.900E2 8.800E2 8.700E2 8.600E2 8.500E2 8.400E2 8.322E2 8.300E2 8.200E2 8.100E2 8.000E2 7.900E2 7.800E2 7.742E2 7.700E2 7.600E2 7.500E2 7.400E2 7.300E2 7.203E2 7.200E2
p,m 9.004E0 9.011E0 9.093E0 9.176E0 9.261 E0 9.348E0 9.436E0 9.526E0 9.617E0 9.678E0 9.711E0 9.806E0 9.903E0 1.000El 1.010El 1.021El 1.031El 1.040El 1.042E1 1.053E1 1.064E1 1.076E1 1.087E1 1.099E1 1.111El 1.118El 1.124E1 1.137E1 1.150El 1.163E1 1.177E1 1.191El 1.202E1 1.205E1 1.220E1 1.235E1 1.250E1 1.266E1 1.282E1 1.292E1 1.299E1 1.316E1 1.334E1 1.352E1 1.370E1 1.389E1 1.389E1
0.0001 2.7810 2.7800 2.7790 2.7790 2.7780 2.7780 2.7770 2.7770 7.7797 2.7760 2.7750 2.7750 2.7740 2.7740 2.7730 2.7720 4.2651 2.7720 2.7710 2.7710 2.7700 2.7700 2.7690 2.7690 3.5726 2.7680 2.7670 2.7670 2.7660 2.7660 2.7650 3.2627 2.7650 2.7640 2.7640 2.7630 2.7630 2.7620 3.0865 2.7620 2.7610 2.7610 2.7600 2.7600 2.9735 2.7590
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [21
4.17E0 [3] 1.22E-2 [2] 1.21E-2 1.21E-2 1.20E-2 1.20E-2 1.19E-2 1.19E-2 1.18E-2 4.00E-4 [3] 1.18E-2 [2] 1.17E-2 1.17E-2 1.16E-2 1.16E-2 1.15E-2 1.15E-2 4.07E-5 [3] 1.15E-2 [2] 1.14E-2 1.14E-2 1.13E-2 1.13E-2 1.12E-2 1.12E-2 1.65E-5 [3] 1.11E-2 [2] 1.11E-2 1.11E-2 1.10E-2 1.10E-2 1.09E-2 9.35E-6 [3] 1.09E-2 [2] 1.08E-2 1.08E-2 1.08E-2 1.07E-2 1.07E-2 6.17E-6 [3] 1.06E-2 [2] 1.06E-2 1.05E-2 1.05E-2 1.05E-2 4.45E-6 [3] 1.04E-2 [2]
Boron Nitride (BN)
437 TABLE I (Continued) Cubic BN
eV 8.80E-2 8.68E-2 8.55E-2 8.43E-2 8.31E-2 8.31E-2 8.18E-2 8.06E-2 7.93E-2 7.81E-2 7.73E-2 7.69E-2 7.56E-2 7.44E-2 7.31E-2 7.19E-2 7.19E-2 7.07E-2 6.94E-2 6.82E-2 6.69E-2 6.69E-2 6.57E-2 6.45E-2 6.32E-2 6.22E-2 6.20E-2 6.07E-2 5.95E-2 5.83E-2 5.79E-2 5.70E-2 5.58E-2 5.45E-2 5.39E-2 5.33E-2 5.21E-2 5.08E-2 5.01E-2 4.96E-2
cm-
1
7.100E2 7.000E2 6.900E2 6.800E2 6.701E2 6.700E2 6.600E2 6.500E2 6.400E2 6.300E2 6.234E2 6.200E2 6.100E2 6.000E2 5.900E2 5.800E2 5.800E2 5.700E2 5.600E2 5.500E2 5.400E2 5.396E2 5.300E2 5.200E2 5.100E2 5.020E2 5.000E2 4.900E2 4.800E2 4.700E2 4.670E2 4.600E2 4.500E2 4.400E2 4.345E2 4.300E2 4.200E2 4.100E2 4.043E2 4.000E2
/xm 1.409E1 1.429E1 1.450E1 1.471E1 1.493E1 1.493E1 1.515E1 1.539E1 1.563E1 1.588E1 1.604E1 1.613E1 1.640E1 1.667E1 1.695E1 1.724E1 1.725E1 1.755E1 1.786E1 1.819E1 1.852E1 1.854E1 1.887E1 1.923E1 1.961E1 1.992E1 2.000El 2.041E1 2.084E1 2.128E1 2.142E1 2.174E1 2.223E1 2.273E1 2.302E1 2.326E1 2.381E1 2.440E1 2.474E1 2.501E1
2.7590 2.7580 2.7570 2.7570 2.8952 2.7560 2.7560 2.7550 2.7550 2.7540 2.8383 2.7540 2.7530 2.7530 2.7530 2.7954 2.7520 2.7520 2.7510 2.7510 2.7500 2.7623 2.7500 2.7490 2.7490 2.7361 2.7480 2.7480 2.7470 2.7470 2.7151 2.7460 2.7460 2.7450 2.6981 2.7450 2.7440 2.7440 2.6841 2.7440
1.04E-2
[3] [2]
[3] [2]
[3] [21
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
1.03E-2 1.03E-2 1.03E-2 3.41E-6 1.02E-2 1.02E-2 1.01E-2 1.01E-2 1.01E-2 2.72E-6 1.00E-2 9.97E-3 9.93E-3 9.89E-3 2.24E-6 9.85E-3 9.81E-3 9.78E-3 9.74E-3 9.70E-3 1.88E-6 9.66E-3 9.62E-3 9.58E-3 1.61E-6 9.55E-3 9.51E-3 9.47E-3 9.43E-3 1.40E-6 9.40E-3 9.36E-3 9.32E-3 1.23E-6 9.28E-3 9.25E-3 9.21E-3 1.09E-6 9.17E-3
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
438
Gary L. Doll TABLE II Values of n and k for Hexagonal BN from Various References a
eV
cm- ~
/xm
n
k
1.000E 1 9.479E0 8.985E0 8.517E0 8.074E0 7.653E0 7.255E0 6.877E0 6.518E0 6.179E0 5.857E0 5.552E0 5.263E0 4.989E0 4.729E0 4.483E0 4.249E0 4.028E0 3.818E0 3.619E0 3.430E0 3.252E0 3.082E0 2.922E0 2.770E0 2.625E0 2.489E0 2.359E0 2.236E0 2.120E0 2.009E0 1.905E0 1.805E0 1.711 E0 1.622E0 1.538E0 1.458 E0 1.382E0 1.310E0 1.241 E0 1.177E0 1.116E0 1.057E0 1.002E0 9.501E-1 9.006E-1
8.066E4 7.646E4 7.248E4 6.870E4 6.512E4 6.173E4 5.852E4 5.547E4 5.258E4 4.984E4 4.724E4 4.478E4 4.245E4 4.024E4 3.814E4 3.616E4 3.427E4 3.249E4 3.079E4 2.919E4 2.767E4 2.623 E4 2.486E4 2.357E4 2.234E4 2.118E4 2.007E4 1.903E4 1.804E4 1.710E4 1.621 E4 1.536E4 1.456E4 1.380E4 1.308E4 1.240E4 1.176E4 1.114E4 1.056E4 1.001 E4 9.492E3 8.998E3 8.529E3 8.085E3 7.664E3 7.265E3
1.240E- 1 1.308E-1 1.380E- 1 1.456E- 1 1.536E-1 1.620E- 1 1.709E-1 1.803E-1 1.902E- 1 2.007E- 1 2.117E- 1 2.234E- 1 2.356E-1 2.486E- 1 2.622E- 1 2.766E- 1 2.918E- 1 3.079E- 1 3.248E-1 3.426E- 1 3.615E- 1 3.813 E- 1 4.023E- 1 4.244E- 1 4.477E- 1 4.723E- 1 4.983E- 1 5.256E-1 5.545E- 1 5.850E- 1 6.172E- 1 6.511E-1 6.868E- 1 7.246E- 1 7.644E-1 8.064E- 1 8.507E- 1 8.975E- 1 9.468E- 1 9.988E- 1 1.054E0 1.112E0 1.173E0 1.237E0 1.305E0 1.377E0
1.1905 [71 1.1903 1.1949 1.2040 1.1799 1.1281 1.0819 1.0470 1.1054 1.2790 1.3301 1.3589 1.5082 1.5987 1.5810 1.5631 1.5450 1.5266 1.5193 1.5270 1.5346 1.5422 1.5496 1.5566 1.5637 1.5707 1.5778 1.5849 1.5920 1.5992 1.6049 1.6050 1.6056 1.6061 1.6067 1.6072 1.6078 1.6084 1.6090 1.6096 1.6099 1.6094 1.6090 1.6088 1.6087 1.6088
3.3E- 1 [7] 3.3E-1 3.2E-1 3.1E-1 3.0E-1 3.7E-1 4.4E-1 5.3E-1 6.2E-1 8.3E-1 8.4E-1 5.6E-1 4.0E-1 2.8E-1 2.8E-1 2.8E-1 2.8E-1 2.8E-1 2.7E-1 2.7E-1 2.6E-1 2.6E-1 2.5E-1 2.5E-1 2.4E-1 2.3E-1 2.2E-1 2.2E-1 2.1E-1 2.0E-1 1.9E-1
a
The references from which the values were taken are given in brackets.
1.9E-1
1.8E-1 1.8E-1 1.8E-1 1.7E-1 1.7E-1 1.7E-1 1.7E-1 1.6E-1 1.6E-1 1.4E-1 1.3E-1 1.1E-1 9.9E-2 8.4E-2
Boron Nitride (BN)
439 TABLE II
(Continued)
Hexagonal BN eV 8.537E-1 8.092E- 1 7.671E-1 7.271E-1 6.893E-1 6.534E- 1 6.193E-1 5.871E-1 5.565E-1 5.275E-1 5.000E- 1 4.740E-1 4.493E-1 4.259E-1 4.037E-1 3.827E-1 3.627E-1 3.438E-1 3.259E-1 3.090E-1 2.929E-1 2.776E- 1 2.632E-1 2.494E-1 2.480E- 1 2.467E-1 2.455E-1 2.442E- 1 2.430E- 1 2.418E-1 2.405E- 1 2.393E-1 2.380E- 1 2.368E-1 2.365E-1 2.356E- 1 2.343E-1 2.331E-1 2.318E-1 2.306E- 1 2.294E-1 2.281E-1 2.269E-1 2.256E-1 2.244E- 1 2.241E-1 2.232E-1
cm
-1
6.886E3 6.527E3 6.187E3 5.865E3 5.560E3 5.270E3 4.995E3 4.735E3 4.489E3 4.255E3 4.033E3 3.823E3 3.624E3 3.435E3 3.256E3 3.087E3 2.926E3 2.773E3 2.629E3 2.492E3 2.362E3 2.239E3 2.123E3 2.012E3 2.000E3 1.990E3 1.980E3 1.970E3 1.960E3 1.950E3 1.940E3 1.930E3 1.920E3 1.910E3 1.907E3 1.900E3 1.890E3 1.880E3 1.870E3 1.860E3 1.850E3 1.840E3 1.830E3 1.820E3 1.810E3 1.808E3 1.800E3
~m 1.452E0 1.532E0 1.616E0 1.705E0 1.799E0 1.898E0 2.002E0 2.112E0 2.228E0 2.351E0 2.480E0 2.616E0 2.760E0 2.912E0 3.072E0 3.240E0 3.418E0 3.606E0 3.804E0 4.013E0 4.234E0 4.467E0 4.712E0 4.971 E0 5.001 E0 5.026E0 5.051E0 5.077E0 5.103E0 5.129E0 5.156E0 5.182E0 5.209E0 5.237E0 5.244E0 5.264E0 5.292E0 5.320E0 5.349E0 5.377E0 5.406E0 5.436E0 5.465E0 5.496E0 5.526E0 5.532E0 5.557E0
1.6093 1.6100 1.6109 1.6118 1.6128 1.6138 1.6149 1.6161 1.6173 1.6184 1.6196 1.6208 1.6142 1.6023 1.5904 1.5783 1.5661 1.5539 1.5415 1.5291 1.5166 1.5040 1.4913 1.4785 0.0337 0.0347 0.0358 0.0370 0.0382 0.0395 0.0409 0.0423 0.0439 0.0455 1.4657 0.0472 0.0491 0.0511 0.0532 0.0555 0.0579 0.06O5 0.0633 0.0663 0.0696 1.2721 0.0732
[6]
[71 [6]
[7] [6]
6.9E-2 5.7E-2 4.7E-2 3.7E-2 2.7E-2 1.7E-2 7.4E-3 6.3E-3 5.3E-3 4.2E-3 3.2E-3 2.2E-3 1.1E-3 1.0E-4 8.6E-4 2.2E-3 5.4E-3 8.6E-3 1.2E-2 1.5E-2 1.8E-2 2.2E-2 2.6E-2 3.4E-2 8.3E-1 [6] 8.4E-1 8.5E-1 8.6E-1 8.7E-1 8.8E-1 8.9E-1 9.0E-1 9.2E-1 9.3E-1 4.1E-2 [7] 9.4E-1 [6] 9.5E-1 9.7E-1 9.8E-1 9.9E-1 1.0E0 1.0E0 1.0E0 1.1E0 1.1E0 5.6E-2 [7] 1.1E0 [61
(continued)
440
Gary L. Doll TABLE II
(Continued)
Hexagonal BN
eV 2.219E-1 2.207E-1 2.194E-1 2.182E-1 2.170E-1 2.157E-1 2.145E-1 2.132E-1 2.125E-1 2.120E-1 2.108E-1 2.095E-1 2.083E-1 2.070E-1 2.058E-1 2.046E- 1 2.033E-1 2.021E-1 2.014E-1 2.008E- 1 1.996E- 1 1.984E-1 1.971E-1 1.959E-1 1.946E-1 1.934E-1 1.922E-1 1.909E-1 1.909E-1 1.897E-1 1.884E-1 1.872E-1 1.860E- 1 1.847E-1 1.835E-1 1.822E-1 1.810E-1 1.810E-1 1.798E-1 1.785E-1 1.773E-1 1.760E-1 1.748E-1 1.736E-1 1.723E-1 1.715E-1 1.711E-1
cm
--1
1.790E3 1.780E3 1.770E3 1.760E3 1.750E3 1.740E3 1.730E3 1.720E3 1.714E3 1.710E3 1.700E3 1.690E3 1.680E3 1.670E3 1.660E3 1.650E3 1.640E3 1.630E3 1.624E3 1.620E3 1.610E3 1.600E3 1.590E3 1.580E3 1.570E3 1.560E3 1.550E3 1.540E3 1.540E3 1.530E3 1.520E3 1.510E3 1.500E3 1.490E3 1.480E3 1.470E3 1.460E3 1.460E3 1.450E3 1.440E3 1.430E3 1.420E3 1.410E3 1.400E3 1.390E3 1.384E3 1.380E3
p,m 5.588E0 5.619E0 5.651E0 5.683E0 5.715E0 5.748E0 5.781E0 5.815E0 5.836E0 5.849E0 5.883E0 5.918E0 5.953E0 5.989E0 6.025E0 6.062E0 6.099E0 6.136E0 6.157E0 6.174E0 6.212E0 6.251 E0 6.290E0 6.330E0 6.371E0 6.411E0 6.453E0 6.495E0 6.495E0 6.537E0 6.580E0 6.624E0 6.668E0 6.713E0 6.758E0 6.804E0 6.851E0 6.852E0 6.898E0 6.946E0 6.994E0 7.044E0 7.094E0 7.144E0 7.196E0 7.229E0 7.248E0
0.0771 0.0813 0.0860 0.0911 0.0967 0.1029 0.1098 0.1175 0.9780 0.1261 0.1358 0.1469 0.1594 0.1739 0.1906 0.2101 0.2330 0.2603 0.9087 0.2930 0.3329 0.3821 0.4437 0.5220 0.6230 0.7549 0.9284 1.1541 1.4838 1.4357 1.7536 2.0515 2.2592 2.3459 2.3346 2.2666 2.1738 1.8762 2.0746 1.9778 1.8871 1.8035 1.7270 1.6572 1.5934 3.2662 1.5348
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
1.1E0 1.1E0 1.2E0 1.2E0 1.2E0 1.2E0 1.2E0 1.3E0 8.3E-2 [7] 1.3E0 [6] 1.3E0 1.4E0 1.4E0 1.4E0 1.5E0 1.5E0 1.6E0 1.6E0 7.4E- 1 [7] 1.7E0 [6] 1.8E0 1.8E0 1.9E0 2.0E0 2.1E0 2.2E0 2.3E0 2.4E0 1.lEO [7] 2.4E0 [6] 2.3E0 2.1E0 1.8E0 1.5E0 1.2E0 9.6E-1 7.8E-1 1.2E0 [7] 6.5E-1 [6] 5.4E-1 4.6E-1 4.0E-1 3.5E-1 3.1E-1 2.7E-1 3.0E-1 [7] 2.4E- 1 [6]
Boron Nitride (BN)
441 TABLE II (Continued) Hexagonal BN
eV 1.698E-1 1.686E-1 1.674E- 1 1.661E-1 1.649E- 1 1.636E-1 1.626E-1 1.624E-1 1.612E-1 1.599E-1 1.587E-1 1.575E-1 1.562E-1 1.550E-1 1.541 E- 1 1.537E-1 1.525E-1 1.513E-1 1.500E- 1 1.488E-1 1.475E-1 1.463E- 1 1.461E-1 1.451 E- 1 1.438E-1 1.426E- 1 1.413E-1 1.401E-1 1.389E-1 1.385E-1 1.376E- 1 1.364E- 1 1.351E-1 1.339E-1 1.327E-1 1.314E-1 1.313E-1 1.302E- 1 1.289E-1 1.277E-1 1.265E-1 1.252E-1 1.244E- 1 1.240E- 1 1.227E-1 1.215E-1 1.203E-1
cm
--I
1.370E3 1.360E3 1.350E3 1.340E3 1.330E3 1.320E3 1.311E3 1.310E3 1.300E3 1.290E3 1.280E3 1.270E3 1.260E3 1.250E3 1.243E3 1.240E3 1.230E3 1.220E3 1.210E3 1.200E3 1 190E3 1 180E3 1 178E3 1 170E3 1 160E3 1 150E3 1 140E3 1 130E3 1 120E3 1 117E3 1 l10E3 1 100E3 1.090E3 1.080E3 1.070E3 1.060E3 1.059E3 1.050E3 1.040E3 1.030E3 1.020E3 1.010E3 1.004E3 1.000E3 9.900E2 9.800E2 9.700E2
/.zm 7.301E0 7.354E0 7.409E0 7.464E0 7.520E0 7.577E0 7.626E0 7.635E0 7.694E0 7.753E0 7.814E0 7.875E0 7.938E0 8.001 E0 8.045E0 8.066E0 8.132E0 8.198E0 8.266E0 8.335E0 8.405E0 8.476E0 8.487E0 8.549E0 8.622E0 8.697E0 8.774E0 8.851E0 8.930E0 8.954E0 9.011E0 9.093E0 9.176E0 9.261E0 9.348E0 9.436E0 9.446E0 9.526E0 9.617E0 9.711E0 9.806E0 9.903E0 9.965E0 1.000El 1.010El 1.021El 1.031El
1.4808 1.4310 1.3847 1.3415 1.3010 1.2629 2.5572 1.2270 1.1929 1.1604 1.1293 1.0995 1.0707 1.0429 2.3066 1.0159 0.9896 0.9637 0.9383 0.9133 0.8884 0.8636 2.1397 0.8387 0.8137 0.7883 0.7625 0.7361 0.7089 2.0910 0.6806 0.6510 0.6198 0.5865 0.5506 0.5115 2.0411 0.4680 0.4189 0.3619 0.2943 0.2159 1.9899 0.1460 0.1060 0.0848 0.0721
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
2.2E-1 2.0E-1 1.8E-1 1.7E-1 1.6E-1 1.5E-1 9.5E-2 1.4E-1 1.3E-1 1.2E-1 1.1E-1 1.1E-1 1.0E-1 9.7E-2 5.2E-2 9.2E-2 8.8E-2 8.5E-2 8.2E-2 7.9E-2 7.6E-2 7.4E-2 1.5E-2 7.2E-2 7.1E-2 6.9E-2 6.8E-2 6.7E-2 6.7E-2 1.8E-2 6.7E-2 6.7E-2 6.8E-2 6.9E-2 7.1E-2 7.4E-2 2.1E-2 7.9E-2 8.6E-2 9.8E-2 1.2E-1 1.6E-1 2.5E-2 2.3E-1 3.2E-1 4.0E-1 4.7E-1
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
(continued)
442
Gary L. Doll TABLE II
(Continued)
Hexagonal BN eV 1.190E-1 1.180E-1 1.178E-1 1.165E-1 1.153E-1 1.141E-1 1.128E-1 1.118E-1 1.116E-1 1.103E-1 1.091E-1 1.079E-1 1.066E- 1 1.060E-1 1.054E-1 1.041E-1 1.029E-1 1.017E-1 1.005E- 1 1.004E-1 9.918E-2 9.794E-2 9.670E-2 9.546E-2 9.523E-2 9.422E-2 9.298E-2 9.174E-2 9.050E-2 9.027E-2 8.926E-2 8.802E-2 8.678E-2 8.557E-2 8.554E-2 8.430E-2 8.306E-2 8.182E-2 8.111E-2 8.059E-2 7.935E-2 7.811E-2 7.689E-2 7.687E-2 7.563E-2 7.439E-2 7.315E-2
cm
-1
9.600E2 9.514E2 9.500E2 9.400E2 9.300E2 9.200E2 9.100E2 9.019E2 9.000E2 8.900E2 8.800E2 8.700E2 8.600E2 8.549E2 8.500E2 8.400E2 8.300E2 8.200E2 8.104E2 8.100E2 8.000E2 7.900E2 7.800E2 7.700E2 7.682E2 7.600E2 7.500E2 7.400E2 7.300E2 7.281E2 7.200E2 7.100E2 7.000E2 6.902E2 6.900E2 6.800E2 6.700E2 6.600E2 6.543E2 6.500E2 6.400E2 6.300E2 6.202E2 6.200E2 6.100E2 6.000E2 5.900E2
/am 1.042E1 1.051El 1.053E1 1.064E1 1.075E1 1.087E1 1.099E1 1 109El 1 lllE1 1 124E1 1 137E1 1 150El 1 163E1 1 170El 1.177E1 1.191El 1.205E1 1.220E1 1.234E1 1.235E1 1.250E1 1.266E1 1.282E1 1.299E1 1.302E1 1.316E1 1.334E1 1.352E1 1.370E1 1.374E1 1.389E1 1.409E 1 1.429E1 1.449E1 1.450E1 1.471E1 1.493E1 1.515E1 1.529E1 1.539E1 1.563E1 1.588E1 1.613E1 1.613E1 1.640E 1 1.667E1 1.695E1
0.0637 1.9374 0.0579 0.0539 0.0511 0.0494 0.0486 1.8669 0.0487 0.0499 0.0521 0.0559 0.0616 1.7817 0.0703 0.0837 0.1053 0.1430 1.6951 0.2187 0.4147 1.3238 5.8255 3.9641 2.0660 3.0979 2.6422 2.3552 2.1550 2.0118 2.0058 1.8895 1.7958 1.9709 1.7184 1.6532 1.5973 1.5489 1.9582 1.5063 1.4687 1.4350 1.9517 1.4048 1.3774 1.3525 1.3297
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
5.4E-1 2.9E-2 [7] 6.1E-1 [6] 6.8E-1 7.5E-1 8.2E-1 9.0E-1 3.8E-2 [7] 9.7E-1 [6] 1.1E0 1.2E0 1.3E0 1.4E0 9.8E-2 [7] 1.5E0 [6] 1.7E0 1.9E0 2.2E0 1.7E-1 [7] 2.6E0 [6] 3.3E0 4.8E0 2.9E0 5.7E-1 2.6E- 1 [7] 2.5E-1 [6] 1.5E-1 9.9E-2 7.3E-2 8.3E-2 [7] 5.7E-2 [6] 4.6E-2 3.9E-2 6.9E-2 [7] 3.3E-2 [6] 2.9E-2 2.5E-2 2.3E-2 5.6E-2 [7] 2.1E-2 [6] 1.9E-2 1.7E-2 5.8E-2 [7] 1.6E-2 [6] 1.5E-2 1.4E-2 1.3E-2
Boron Nitride (BN)
443 TABLE II
(Continued)
Hexagonal BN eV 7.288E-2 7.191E-2 7.067E-2 6.943E-2 6.909E-2 6.819E-2 6.695E-2 6.571E-2 6.549E-2 6.447E-2 6.323E-2 6.208E-2 6.199E-2 6.075E-2 5.951E-2 5.884E-2 5.827E-2 5.703E-2 5.579E-2 5.578E-2 5.455E-2 5.331E-2 5.287E-2 5.207E-2 5.083E-2 5.012E-2 4.959E-2 4.835E-2 4.711E-2 4.587E-2 4.463E-2 4.339E-2 4.215E-2 4.091E-2 3.967E-2 3.843E-2 3.719E-2
cm
--1
5.879E2 5.800E2 5.700E2 5.600E2 5.572E2 5.500E2 5.400E2 5.300E2 5.282E2 5.200E2 5.100E2 5.007E2 5.000E2 4.900E2 4.800E2 4.746E2 4.700E2 4.600E2 4.500E2 4.499E2 4.400E2 4.300E2 4.265E2 4.200E2 4.100E2 4.043E2 4.000E2 3.900E2 3.800E2 3.700E2 3.600E2 3.500E2 3.400E2 3.300E2 3.200E2 3.100E2 3.000E2
/xm 1.701El 1.724E1 1.755E1 1.786E1 1.795E1 1.819E1 1.852E1 1.887E1 1.893E1 1.923E1 1.961E1 1.998E1 2.000E 1 2.041E1 2.084E1 2.107E1 2.128E1 2.174E1 2.223E1 2.223E1 2.273E1 2.326E1 2.345E1 2.381E1 2.439E1 2.474E1 2.500E1 2.565E1 2.632E1 2.703E1 2.778E1 2.858E1 2.942E1 3.031E1 3.126E1 3.226E1 3.334E1
1.9451 1.3087 1.2895 1.2716 1.9385 1.2551 1.2396 1.2253 1.9319 1.2118 1.1992 1.9260 1.1874 1.1763 1.1658 1.9216 1.1559 1.1466 1.1377 1.9172 1.1294 1.1214 1.9128 1.1139 1.1068 1.9084 1.1000 1.0935 1.0874 1.0816 1.0760 1.0707 1.0657 1.0609 1.0563 1.0520 1.0479
[7] [6]
[7] [6]
[7] [6] [7] [6]
[7] [61
[7] [6] [7] [6] [7] [6]
6.1E-2 1.2E-2 1.2E-2 1.1E-2 6.3E-2 1.1E-2 1.0E-2 9.6E-3 6.6E-2 9.2E-3 8.8E-3 6.8E-2 8.4E-3 8.1E-3 7.7E-3 6.4E-2 7.4E-3 7.1E-3 6.9E-3 6.0E-2 6.6E-3 6.4E-3 5.6E-2 6.1E-3 5.9E-3 5.2E-2 5.7E-3 5.5E-3 5.3E-3 5.1E-3 4.9E-3 4.7E-3 4.5E-3 4.3E-3 4.2E-3 4.0E-3 3.9E-3
[7] [6]
[7] [6]
[7] [6] [7] [6]
[7] [6]
[7] [6] [7] [6] [7] [6]
INTRODUCTION
The optical functions of the hexagonal and cubic phases of BN (hBN and cBN, respectively) are not nearly as well defined as those of other group III nitrides. This is due in large part to the fact that single-crystal samples either do not exist (which is the case for hexagonal boron nitride) or are extremely rare (as in the case of cubic boron nitride) [1]. Optical studies on the optically anisotropic hBN have ~been performed on preferentially oriented, polycrystalline samples with E_I_6 and E tl~ polarization. In these samples, it is difficult to obtain a complete separation of the two polarizations because the typical mosaic spread of the c-axes is greater than 20 ~, and because pure a-faces are not easily obtained. In this critique, we have not included experiments performed on B N films. The reasons for this are that the optical constants of these films can vary greatly with film properties such as stoichiometry, homogeneity, crystallinity, and purity, to name a few. For the most part, these types of film properties have not been correlated with optical properties that have been reported. As we shall see, the optical properties of bulk B N materials are not that well defined. The hexagonal phase of BN is isostructural to graphite in that it is composed of planes of BN hexagons stacked along the c-axis in an ABA configuration, hBN has the space group D64h(P63/mmc),which has the irreducible representation
I-'- 2E2g + A2, + Elu + 2Big, where the E2g modes are Raman-active, the Big modes are silent (optically inactive), and the A2, and El, modes are infrared-active. Whereas the A2, modes are outgof-plane vibrations excited by light polarized parallel to the hBN c-axis (Eli 0), the El, modes are in-plane vibrations excited by light 425 HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS III
Copyright 9 1998 by Academic Press. All rights of reproduction in any form reserved ISBN 0-12-544423-0/$25.00.
I
426
Gary L. Doll
polarized perpendicular to the c-axis (E.I_e). The A2u and Elu modes are polar, which means that the longitudinal-optical or LO mode has a higher energy than the transverse-optical or TO mode. cBN has the zincblende structure with the space group T2, (F43m). Its phonon modes are of T2 symmetry, and are polar, so that the energy of the cBN LO vibration is also higher than the TO polarization energy.
II
cBN
Selected optical constants n and k for cBN taken from three sources are collected in Table I and plotted in Fig. 1. Tabulated values of the optical constants were not included in any of the sources. Gielisse et al. [2] provided the first reported examination of the cBN optical constants. Although this study covered the energy range 400 to 4000 cm-1, the optical constants could only be deduced from their data over the energy range 400 to 1800 cm-1. In this study, Gielisse et al. measured the reflectivity of a collection of small single crystals compressed into compacts that were ground and polished. Their normal-incidence reflectivity was modeled using a four-parameter fit to the equations
0)02 -
0)2
e1(0)) = e~ + 4fro 0)2 (0)2_ 0)2)2 q_/-,20)2
E2(0))
/-'0) A 2 ~'"B'P0)O (COg- 0)2)2 ..]._/-'20)2'
(1)
(2)
where eo is the high-frequency limiting value of the dielectric constant, 0)0 is the Brillouin-zone-center, TO phonon-mode energy, 4fro is the strength of the resonance, F and is the phonon width or the damping constant. Good agreement between the calculated and measured reflectivity was found for the following parameters: e~ = 4.5, 47tO = 2.6, ~oo = 1065 cm -1, and F = 40.5 cm -1. The static dielectric constant eo was calculated to be 7.1 from the equation Eo = ~ + 4-rrp.
(3)
We calculated the values of EI(O ) and E2(0) ) using the above parameters, then derived n and k by the equations 2 n 2 = ~/e2 + ~2 + E1
(4) 2=
+
Boron Nitride (BN)
427
The results are shown in Fig. 1 and listed in Table I. The energy of the LO mode was deduced to be 1340 cm-~ from the Lyddane-Sachs-Teller relationship o~i~o = O~To(eo/E~)1/2. Eremets et al. [3] have reported the optical properties of cBN over the energy range 500 to 28,000 cm-1. Single crystals of cBN 0.45 ~m thick by 150/,m square were studied in reflection and transmission, and n and k were deduced by fitting the interference fringes with equations proposed by Heavens [4]. Although n and k were neither tabulated nor shown in a form suitable for our purposes, the dielectric functions were described by a Sellmeier model that considers the contribution to e(co) from phonons and electronic transitions. The Sellmeier model used by the authors is expressed as E -- Eph + Eelec m Ear
(5)
where eelec- 1 -
1 - - [ h o ~ / E o ] 2'
(6)
and Eph is described by Eqs. (1), (2), and (3). Using this approach, they were able to approximate the reflectance and transmittance over the measured energy range. We first calculated the dielectric functions using Eq. (5) with the parameters E o - 6.8, E ~ - 4.46, E o - 104,850 cm -1 coo - 1055.7 cm -~ and F - 0.005 cm-1, which were given by the authors. Eremets et al. also report the LO mode energy to be 1304.8 cm -~. We suspect that the value of F given by Eremets et al. in [3] is incorrect, since it appears to be too small to describe phonon linewidths in these types of samples. Nevertheless, using the preceding parameters, we calculated n and k from Eq. (4). The results of this calculation are gathered in Table I and plotted in Fig. 1. Miyata et al. [5] have reported the optical properties of a cBN single crystal having an area of 5 nlN12 and a thickness (d) of 0.16 mm. The sample was measured over the energy range 2 to 23 eV by reflectance and 2 to 6 eV by transmittance. In the energy range 2 to 6 eV where both R and T were measured, n and k were derived from the expressions (1
k-
4rrd
In
R + 1 + [(R + 1) 2 -
R) 2
-
T ( R - 1) 2 (1 + k2)] 1/2
(7)
1-R To determine the optical constants from the reflectance at higher photon energy, a Kramers-Kronig relation was employed where the values of the phase-change integral were set equal to those calculated from the optical
428
Gary L. Doll
constants in the energy region 2.5 to 5.5 eV. Their results for n and k, which we extracted from their figure, are listed in Table I and plotted in Fig. 1. As can be seen in Fig. 1, some discrepancy exists between the data published by Gielisse et al. [2] and Eremets et al. [3] in the vicinity of the cBN IR-active phonon. Whereas Gielisse et al. [2] quote the energy of the TO phonon of their sample to be 1065 cm-1, Eremets et al. [3] have determined the energy to be 1055.7 cm -1 for their material. One might expect this sort of discrepancy to be sample dependent. As we would expect from Eqs. (1) and (2), Fig. 1 shows us that the suspiciously low value of F = 0.005 cm-1 reported by Eremets et al. has a much more pronounced effect on k than on n in the region of the IR-active cBN phonon. Gielisse et al. [2] and Eremets et al. [3] derive similar values for eo and ~ . The method used to deduce n and k from Eremets et al. [3] does not account for multiphonon absorption that is present at energies between 2000 cm-~ and 4000 cm-1, so the optical constants in that energy range are not accurate. There is good agreement in the values of n derived from Eremets et al. [3] and Miyata et al. [5] where the data overlap in the energy region 2 to 3.5 eV. The onset for optical absorption was determined to be 6.1 +_ 0.2 eV from Miyata et al. [5], and several absorption edges are also present at higher photon energies.
III
heN
The first examination of the optical properties of hBN was performed by Geick et al. [6] on pyrolytic hBN with a mosaic spread in the c-axis of 30 ~ where the c-axis is the direction normal to the B N hexagonal planes. The reflectivity was measured at near-normal incidence in E_Ld and E I1~ polarizations over the energy range 300 to 2000 cm-1. With this mosaic spread, a complete separation of the polarizations is not possible, but the experiment did provide first evidence for the identification of the in-plane (Elu) and out-of-plane (A2u) IR-active phonons in hBN. The dielectric functions were obtained from a Kramers-Kronig transformation of the reflectance data. No details of how the phase integral was extended to lower and higher energies in order to perform the transformation were given. We have calculated n and k ~ i n g Eq. (4) from a digitization of their figures for ~1 and ~2 obtained with E_I_6 polarization. We show the results in Table II and Fig. 2. The presence of the low-frequency A2u phonon near 13 ~m illustrates the contribution that the crystallographic mosaic spread of the c-axis makes to the optical spectra of these types of samples. To our knowledge, there has been no optical spectrum taken on hBN samples that does not contain a mixture of these polarizations. The authors fit their dielectric functions to an oscillator model similar to Eqs. (1) and (2) but that contains contributions from both polarizations to account for the mosaic spread of the hBN crystallites. For the E II ~ polarization, the parameters that provided the best fit to
Boron Nitride (BN)
429
the data are e ~ - 4.10, eo ---~ 5.09, r A2u _ 783 cm -1 , (-OLo A2u _ 828 cm-1 , 3.26 • 105 c m - 2 , 1 - ' A 2 u - - 8.0 cm -1, LOT OElu _ 1510 cm -1, WL oE1. _ 1595 cm -~, 47rp E~" -- 1.04 • 106 cm -1 and F E~" = 80 cm -1 For the E_L6 polarization, the parameters that provided the best fit to the data are E~ = 4.95, ~o - 7.04, ~~ _ 767 c m - 1, ~0LoA2,_ 778 c m - l , 47rpA2, _-1.23 • 105 cm -2, F A2" ---- 35.0 cm-~, ~0TOEI" _ 1367 cm-~, 09LOEI" _-1610 c m - l , 4 7 r p el" = 3.49 • 106 cm -1, and F El" - 29 cm -~. We do not display the EII 6 optical constants in either Fig. 2 or Table II. Hoffman et al. [7] examined the E_L6 optical reflectivity spectrum on a similar sample of pyrolytic hBN, with a mosaic spread slightly larger than that of Geick et al. [6] over the energy range 0.05 to 10 eV. The dielectric functions were obtained from a Kramers-Kronig transformation of the reflectance data. For purposes of integrating the phase-shift integral of the transformation, the data were extended below 0.045 eV by treating R as a constant, from 10 to 30 eV by using data from Mamy et al. [8], from 30 to 100 eV as R ~ ~o-1 and thereafter as R ~ 0) - 4 . We have calculated n and k using Eq. (4) from a digitization of their figures for el and E2, and we show the results in Table II and Fig. 2. As is evident in the figure, there is agreement in the energies of the Ell, and A2u phonons between the two studies, but disagreement in the oscillator strengths of the vibrations. This is probably related to orientational and structural differences between the samples examined in the two studies. Another item of note is that the values of k are relatively high in the region between the ir-active phonons and the electronic band gap near 5 eV. The authors believe that this is not intrinsic to hBN, but rather is related to the rather large amounts of impurities and defects in the sample. The authors also examined the phonon region of E2 by fitting the data with an oscillator model similar to the one used by Geick et al. [6] for the E_L6 polarization. The best fit to the data was achieved with the following parameters: r 770 cm -~ , 4"/7"/9A 2 " - - 3 . 8 X 1 0 4 c m - 2 I - ' a 2 u - - 1 8 cm-1, OJTO E l , _ 1383 cm -~, 47rp e ~ " - 7.5 • 105 cm -~ , and 1 - ' E l u - - 30 cm -1 9 Values for Eo~ and r were not given in the paper, so a determination of the LO-mode energies from the data is not possible. 4"rrpA2u
- -
~
9
._..)
a z u
__
REFERENCES
1. J. H. Edgar, in "Properties of Group III Nitrides" (J. H. Edgar, ed.), p. 7. INSPEC, The Institute of Electrical Engineers, London, 1994. 2. P. J. Gielisse, S. S. Mitra, J. N. Plendl, R. D. Griffis, L. C. Mansur, R. Marshall, and E. A. Pascoe, Phys. Rev. 155, 1039 (1967). 3. M. I. Eremets, M. Gauthier, A. Polian, J. C. Chervin, J. M. Besson, G. A. Dubitskii, and Y. Y. Semenova, Phys. Rev. B 52, 8854 (1995). 4. O. S. Heavens, Rep. Prog. Phys. 23, 1 (1960). 5. N. Miyata, K. Moriki, O. Mishima, M. Fujisawa, and T. Hattori, Phys. Rev. B 40, 12028 (1989). 6. R. Geick, C. H. Perry, and G. Rupprecht, Phys. Rev. 146, 543 (1966). 7. D. M. Hoffman, G. L. Doll, and P. C. Eklund, Phys. Rev. B 30, 6052 (1984). 8. R. Mamy, J. Thomas, G. Jezequel, and J. C. Lemonnier, J. Phys. (Paris) Lett. 42, 473 (1981).
Gary L. Doll
430 '
''''1
101 4
k'l=
10 ~ "O.
"=
10-~
"A
10-&
Lk. -&
i
10-3E
10 -410-5-
Ii d
10 -6-
"1
10-7..
,,! =9
10 -& '
'
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'
'
'
'
' ' ' I
10 -1
'
'
'
'
'
' ' ' I
100
'
I
101
WAVELENGTH (#m) Fig. 1. Log-log plot of n (solid line) and k (dashed line) versus wavelength in micrometers for cBN. The data for n and k were derived from Gielisse et al. [2] (triangles), Eremets et al. [3] (squares), and Miyata et al. [5] (circles).
10110~
O, ....
"'-'O
.....
"O .....
~ .
10 4-
E
.i
. .....
10 -~-
10-3..
= , J,
10 .4_ '
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10 -1
'
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10 0
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101
WAVELENGTH (pm) Fig. 2. Log-log plot of n (solid line) and k (dashed line) versus wavelength in micrometers for hBN obtained from E_Ld polarization. The data for n and k were derived from Geick et al. [6] (squares) and Hoffman et al. [7] (circles).
Boron Nitride (BN)
431 TABLE I
Values of n a n d k for C u b i c B N f r o m V a r i o u s R e f e r e n c e s a
eV
cm-~
/xm
n
2.00El 1.98E1 1.96E 1 1.95E1 1.93E1 1.91 E1 1.89E1 1.87E1 1.85E1 1.84E1 1.82E1 1.80El 1.78E1 1.76E 1 1.75E 1 1.73E1 1.71E 1 1.69E1 1.67E 1 1.65E1 1.64E 1 1.62E 1 1.60E 1 1.58E1 1.56E 1 1.55E 1 1.53E1 1.51E 1 1.49E 1 1.47E1 1.45E1 1.44E 1 1.42E 1 1.40El 1.38E1 1.36E 1 1.35E 1 1.33E1 1.31E 1 1.29E 1 1.27E 1 1.25E 1 1.24E 1 1.22E1 1.20El 1.18E 1
1.613E5 1.599E5 1.584E5 1.569E5 1.555E5 1.540E5 1.525E5 1.511E5 1.496E5 1.481E5 1.467E5 1.452E5 1.437E5 1.423E5 1.408E5 1.393E5 1.379E5 1.364E5 1.349E5 1.335E5 1.320E5 1.305E5 1.291 E5 1.276E5 1.261 E5 1.247E5 1.232E5 1.217E5 1.203E5 1.188E5 1.173E5 1.159E5 1.144E5 1.129E5 1.115E5 1.100E5 1.085E5 1.071E5 1.056E5 1.041 E5 1.027E5 1.012E5 9.973E4 9.826E4 9.679E4 9.533E4
6.200E-2 6.257E-2 6.315E-2 6.374E-2 6.434E-2 6.495E-2 6.558E-2 6.621E-2 6.686E-2 6.752E-2 6.820E-2 6.889E-2 6.959E-2 7.031E-2 7.104E-2 7.179E-2 7.255E-2 7.333E-2 7.413E-2 7.495E-2 7.578E-2 7.663E-2 7.750E-2 7.839E-2 7.930E-2 8.024E-2 8.119E-2 8.217E-2 8.317E-2 8.420E-2 8.525E-2 8.633E-2 8.744E-2 8.857E-2 8.974E-2 9.093E-2 9.216E-2 9.342E-2 9.472E-2 9.606E-2 9.743E-2 9.884E-2 1.003E- 1 1.018E- 1 1.033E- 1 1.049E- 1
1.0389 [5] 1.0552 1.0872 1.1212 1.1534 1.1830 1.2125 1.2421 1.2735 1.3081 1.3427 1.3773 1.4112 1.4433 1.4776 1.5162 1.5547 1.5935 1.6344 1.6713 1.6835 1.6957 1.7079 1.7154 1.7178 1.7249 1.7388 1.7560 1.7780 1.8105 1.8516 1.8959 1.9390 1.9822 2.0369 2.0906 2.1344 2.1804 2.2249 2.2513 2.2628 2.2689 2.2648 2.2604 2.2583 2.2822
1.03E0 [51 1.05E0 1.07E0 1.09E0 1 IOE0 1 12E0 1 13E0 1 15E0 1 16E0 1 17E0 1 17E0 1 18E0 1 19E0 1.20E0 1.20E0 1.20E0 1.20E0 1.20E0 1.20E0 1.17E0 1.14E0 1.11E0 1.10E0 1.08E0 1.07E0 1.09E0 1.10E0 1.11E0 1.13E0 1.14E0 1.15E0 1 16E0 1 18E0 1 16E0 1 15E0 1 13E0 1 llE0 1.07E0 1.03E0 9.82E-1 9.35E-1 8.93E-1 8.60E-1 8.36E-1 8.45E-1 8.55E-1
(continued) a
The references from which the values were taken are given in brackets.
432
Gary L. Doll TABLE I
(Continued)
Cubic BN eV 1.16E1 1.15El 1.13El 1.11El 1.09El 1.07El 1.05E1 1.04El 1.02El 1.00E 1 9.82E0 9.64E0 9.45E0 9.27E0 9.09E0 8.91E0 8.73E0 8.55E0 8.36E0 8.18E0 8.00E0 7.82E0 7.64E0 7.45E0 7.27E0 7.09E0 6.91E0 6.73E0 6.55E0 6.36E0 6.18E0 6.00E0 5.82E0 5.64E0 5.45E0 5.27E0 5.09E0 4.91E0 4.73E0 4.55E0 4.36E0 4.18E0 4.00E0 3.82E0 3.64E0 3.55E0 3.45E0
cm
-1
9.386E4 9.239E4 9.093E4 8.946E4 8.799E4 8.653E4 8.506E4 8.359E4 8.213E4 8.066E4 7.919E4 7.773E4 7.626E4 7.479E4 7.333E4 7.186E4 7.039E4 6.893E4 6.746E4 6.599E4 6.453E4 6.306E4 6.159E4 6.013E4 5.866E4 5.720E4 5.573E4 5.426E4 5.280E4 5.133E4 4.986E4 4.840E4 4.693E4 4.546E4 4.400E4 4.253E4 4.106E4 3.960E4 3.813E4 3.666E4 3.520E4 3.373E4 3.226E4 3.080E4 2.933E4 2.862E4 2.786E4
/.Lm 1.066E-1 1.083E-1 1.100E- 1 1.118E-1 1.137E-1 1.156E-1 1.176E-1 1.197E-1 1.218E-1 1.240E- 1 1.263E-1 1.287E-1 1.312E-1 1.337E-1 1.364E-1 1.392E-1 1.421E-1 1.451E-1 1.483E-1 1.516E-1 1.550E-1 1.586E-1 1.624E-1 1.663E-1 1.705E-1 1.749E-1 1.795E-1 1.843E-1 1.894E-1 1.949E-1 2.006E- 1 2.067E-1 2.131E-1 2.200E- 1 2.273E-1 2.352E-1 2.436E-1 2.526E-1 2.623E-1 2.728E-1 2.842E-1 2.965E- 1 3.100E-1 3.248E-1 3.410E-1 3.490E-1 3.590E- 1
2.3384 2.4265 2.4467 2.4702 2.5046 2.5368 2.5357 2.5046 2.4598 2.4147 2.3900 2.3733 2.3647 2.3561 2.3470 2.3362 2.3268 2.3204 2.3086 2.2960 2.2835 2.2749 2.2690 2.2687 2.2733 2.2766 2.2762 2.2782 2.2919 2.3032 2.2913 2.2692 2.2160 2.1981 2.1912 2.1752 2.1471 2.1286 2.1258 2.1186 2.1148 2.1073 2.0969 2.0909 2.0852 2.1111 [3] 2.0791 [5]
8.65E-1 8.28E-1 7.62E-1 7.19E-1 6.76E-1 5.94E-1 5.13E-1 4.38E-1 4.15E-1 3.92E-1 3.69E-1 3.57E-1 3.45E-1 3.30E-1 3.11E-1 2.91E-1 2.70E-1 2.56E-1 2.44E-1 2.32E-1 2.26E-1 2.20E-1 2.14E-1 2.08E-1 2.03E-1 1.86E-1 1.65E-1 1.45E-1 1.24E-1 9.62E-2 5.15E-2 6.72E-3
Boron Nitride (BN)
433 TABLE I (Continued) Cubic BN
eV 3.30E0 3.27E0 3.09E0 3.07E0 2.91E0 2.86E0 2.73E0 2.66E0 2.55E0 2.47E0 2.36E0 2.30E0 2.18E0 2.14E0 2.00E0 1.99E0 1.85E0 1.72E0 1.60E0 1.49E0 1.39E0 1.29E0 1.20E0 1.12E0 1.04E0 9.67E-1 9.00E-1 8.37E-1 7.79E-1 7.25E-1 6.74E-1 6.27E-1 5.84E-1 5.43E-1 5.05E-1 4.70E-1 4.37E-1 4.07E-1 3.78E-1 3.52E-1 3.28E-1 3.05E-1 2.83E-1 2.64E-1 2.48E-1 2.47E-1 2.45E-1
cm
--1
2.663E4 2.640E4 2.493E4 2.477E4 2.346E4 2.305E4 2.200E4 2.144E4 2.053E4 1.995E4 1.907E4 1.856E4 1.760E4 1.727E4 1.613E4 1.606E4 1.494E4 1.390E4 1.293E4 1.203E4 1.120E4 1.042E4 9.690E3 9.015E3 8.387E3 7.803E3 7.259E3 6.754E3 6.283E3 5.846E3 5.438E3 5.060E3 4.707E3 4.379E3 4.074E3 3.790E3 3.526E3 3.281 E3 3.052E3 2.840E3 2.642E3 2.458E3 2.287E3 2.127E3 2.000E3 1.990E3 1.980E3
~m
3.760E- 1 3.789E-1 4.012E-1 4.040E-1 4.263E-1 4.340E-1 4.547E-1 4.660E- 1 4.871E-1 5.010E-1 5.246E- 1 5.390E-1 5.683E-1 5.790E-1 6.200E- 1 6.230E-1 6.690E- 1 7.190E-1 7.730E-1 8.310E-1 8.930E-1 9.600E- 1 1.032E0 1.109E0 1.193E0 1.282E0 1.378E0 1.481E0 1.592E0 1.711E0 1.839E0 1.977E0 2.125E0 2.284E0 2.455E0 2.639E0 2.836E0 3.049E0 3.277E0 3.522E0 3.786E0 4.069E0 4.374E0 4.701E0 5.001 E0 5.026E0 5.051 E0
2.111013] 2.0744 [5] 2.0794 2.1109 [3] 2.0815 [5] 2.1107 [31 2.0837 [5] 2.1105 [31 2.0935 [5] 2.1103 [31 2.1021 [51 2.1101 [3] 2.1109 [5] 2.1098 [3] 2.1231 [5] 2.1095 [3] 2.1091 2.1087 2.1082 2.1076 2.1069 2.1061 2.1052 2.1042 2.1029 2.1015 2.0999 2.0979 2.0957 2.0931 2.0901 [3] 2.0865 2.0823 2.0774 2.0716 2.0647 2.0566 2.0468 2.0351 2.0210 2.0037 1.9825 1.9559 1.9222 2.8450 [2] 2.8440 2.8430
2.11E-8 [3] 2.11E-8 2.98E-8 4.21E-8 5.16E-8 6.99E-8 8.69E-8 1.13E-7 1.46E-7 1.90E-7 2.50E-7 3.33E-7 4.51E-7 6.21E-7 1.75E-2 [2] 1.74E-2 1.73E-2
(continued)
434
Gary L. Doll TABLE I
(Continued)
Cubic BN
eV 2.45E-1 2.44E-1 2.43E-1 2.42E-1 2.41E-1 2.39E-1 2.38E-1 2.37E-1 2.36E-1 2.34E-1 2.33E-1 2.32E-1 2.31E-1 2.29E-1 2.28E-1 2.28E-1 2.27E-1 2.26E-1 2.24E-1 2.23E-1 2.22E-1 2.21E-1 2.19E-1 2.18E-1 2.17E-1 2.16E-1 2.14E-1 2.13E-1 2.12E-1 2.12E-1 2.11E-1 2.10E-1 2.08E-1 2.07E-1 2.06E- 1 2.05E-1 2.03E-1 2.02E-1 2.01E-1 2.00E- 1 1.98E-1 1.98E-1 1.97E-1 1.96E-1 1.95E-1 1.93E-1 1.92E-1
cm
-1
1.979E3 1.970E3 1.960E3 1.950E3 1.940E3 1.930E3 1.920E3 1.910E3 1.900E3 1.890E3 1.880E3 1.870E3 1.860E3 1.850E3 1.841E3 1.840E3 1.830E3 1.820E3 1.810E3 1.800E3 1.790E3 1.780E3 1.770E3 1.760E3 1.750E3 1.740E3 1.730E3 1.720E3 1.713E3 1.710E3 1.700E3 1.690E3 1.680E3 1.670E3 1.660E3 1.650E3 1.640E3 1.630E3 1.620E3 1.610E3 1.600E3 1.594E3 1.590E3 1.580E3 1.570E3 1.560E3 1.550E3
~m
5.053E0 5.077E0 5.103E0 5.129E0 5.156E0 5.182E0 5.209E0 5.237E0 5.264E0 5.292E0 5.320E0 5.349E0 5.377E0 5.406E0 5.432E0 5.436E0 5.465E0 5.496E0 5.526E0 5.557E0 5.588E0 5.619E0 5.651 E0 5.683E0 5.715E0 5.748E0 5.781E0 5.815E0 5.839E0 5.849E0 5.883E0 5.918E0 5.953E0 5.989E0 6.025E0 6.062E0 6.099E0 6.136E0 6.174E0 6.212E0 6.251 E0 6.276E0 6.290E0 6.330E0 6.371E0 6.411E0 6.453E0
1.8785 2.8420 2.8410 2.8400 2.8400 2.8390 2.8380 2.8370 2.8360 2.8350 2.8350 2.8340 2.8330 2.8320 1.8202 2.8310 2.8310 2.8300 2.8290 2.8280 2.8270 2.8270 2.8260 2.8250 2.8240 2.8240 2.8230 2.8220 1.7395 2.8210 2.8200 2.8200 2.8190 2.8180 2.8170 2.8170 2.8160 2.8150 2.8150 2.8140 2.8130 1.6215 2.8120 2.8120 2.8110 2.8100 2.8090
[3] [2]
[3] [2]
[3] [21
[31 [2]
8.75E-7 1.72E-2 1.72E-2 1.71E-2 1.70E-2 1.69E-2 1.69E-2 1.68E-2 1.67E-2 1.67E-2 1.66E-2 1.65E-2 1.65E-2 1.64E-2 1.27E-6 1.63E-2 1.63E-2 1.62E-2 1.61E-2 1.61E-2 1.60E-2 1.59E-2 1.59E-2 1.58E-2 1.57E-2 1.57E-2 1.56E-2 1.55E-2 1.94E-6 1.55E-2 1.54E-2 1.53E-2 1.53E-2 1.52E-2 1.52E-2 1.51E-2 1.50E-2 1.50E-2 1.49E-2 1.49E-2 1.48E-2 3.16E-6 1.47E-2 1.47E-2 1.46E-2 1.46E-2 1.45E-2
[3] [2]
[3] [2]
[3] [2]
[3] [2]
Boron Nitride (BN)
435 TABLE I (Continued) Cubic BN
eV 1.91E-1 1.90E-1 1.88E-1 1.87E-1 1.86E-1 1.85E-1 1.84E-1 1.83E-1 1.82E-1 1.81E-1 1.80E-1 1.79E-1 1.77E-1 1.76E-1 1.75E-1 1.74E-1 1.72E-1 1.71E-1 1.71E-1 1.70E-1 1.69E- 1 1.67E-1 1.66E- 1 1.65E-1 1.64E- 1 1.62E-1 1.61E-1 1.60E-1 1.59E-1 1.59E-1 1.57E-1 1.56E-1 1.55E-1 1.54E- 1 1.52E-1 1.51E-1 1.50E-1 1.49E-1 1.48E-1 1.48E-1 1.46E-1 1.45E-1 1.44E- 1 1.43E-1 1.41E-1 1.40E- 1 1.39E-1
cm-
1
1.540E3 1.530E3 1.520E3 1.510E3 1.500E3 1.490E3 1.483E3 1.480E3 1.470E3 1.460E3 1.450E3 1.440E3 1.430E3 1.420E3 1.410E3 1.400E3 1.390E3 1.380E3 1.379E3 1.370E3 1.360E3 1.350E3 1.340E3 1.330E3 1.320E3 1.310E3 1.300E3 1.290E3 1.283E3 1.280E3 1.270E3 1.260E3 1.250E3 1.240E3 1.230E3 1.220E3 1.210E3 1.200E3 1.194E3 1.190E3 1.180E3 1.170E3 1.160E3 1.150E3 1.140E3 1.130E3 1.120E3
/xm 6.495E0 6.537E0 6.580E0 6.624E0 6.668E0 6.713E0 6.745E0 6.758E0 6.804E0 6.851E0 6.898E0 6.946E0 6.994E0 7.044E0 7.094E0 7.144E0 7.196E0 7.248E0 7.251 E0 7.301 E0 7.354E0 7.409E0 7.464E0 7.520E0 7.577E0 7.635E0 7.694E0 7.753E0 7.793E0 7.814E0 7.875E0 7.938E0 8.001E0 8.066E0 8.132E0 8.198E0 8.266E0 8.335E0 8.377E0 8.405E0 8.476E0 8.549E0 8.622E0 8.697E0 8.774E0 8.851E0 8.930E0
2.8090 2.8080 2.8070 2.8070 2.8060 2.8050 1.4327 2.8050 2.8040 2.8030 2.8020 2.8020 2.8010 2.8000 2.8000 2.7990 2.7980 2.7980 1.0721 2.7970 2.7960 2.7960 2.7950 2.7940 2.7940 2.7930 2.7920 2.7920
[3] [21
[3] [2]
2.7910 [2] 2.7910 2.7900 2.7890 2.7890 2.7880 2.7870 2.7870 2.7860 2.7860 [2] 2.7850 2.7840 2.7840 2.7830 2.7820 2.7820 2.7810
1.44E-2 1.44E-2 1.43E-2 1.43E-2 1.42E-2 1.41E-2 5.75E-6 [3] 1.41E-2 [2] 1.40E-2 1.40E-2 1.39E-2 1.39E-2 1.38E-2 1.38E-2 1.37E-2 1.36E-2 1.36E-2 1.35E-2 1.35E-5 [3] 1.35E-2 [2] 1.34E-2 1.34E-2 1.33E-2 1.33E-2 1.32E-2 1.32E-2 1.31E-2 1.31E-2 6.64E-1 [3] 1.30E-2 [21 1.30E-2 1.29E-2 1.29E-2 1.28E-2 1.27E-2 1.27E-2 1.26E-2 1.26E-2 1.98E0 [3] 1.25E-2 [21 1.25E-2 1.24E-2 1.24E-2 1.23E-2 1.23E-2 1.23E-2 1.22E-2
(continued)
436
Gary L. Doll TABLE I
(Continued)
Cubic BN
eV 1.38E-1 1.38E-1 1.36E-1 1.35E-1 1.34E-1 1.33E-1 1.31E-1 1.30E-1 1.29E-1 1.28E-1 1.28E-1 1.26E-1 1.25E-1 1.24E-1 1.23E-1 1.21E-1 1.20E-1 1.19E-1 1.19E-1 1.18E-1 1.17E-1 1.15E-1 1.14E-1 1.13E-1 1.12E-1 1.11E-1 1.10E-1 1.09E-1 1.08E-1 1.07E-1 1.05E-1 1.04E-1 1.03E-1 1.03E-1 1.02E-1 1.00E- 1 9.92E-2 9.79E-2 9.67E-2 9.60E-2 9.55E-2 9.42E-2 9.30E-2 9.17E-2 9.05E-2 8.93E-2 8.93E-2
cm
--1
1.111E3 1.110E3 1.100E3 1.090E3 1.080E3 1.070E3 1.060E3 1.050E3 1.040E3 1.033E3 1.030E3 1.020E3 1.010E3 1.000E3 9.900E2 9.800E2 9.700E2 9.615E2 9.600E2 9.500E2 9.400E2 9.300E2 9.200E2 9.100E2 9.000E2 8.945E2 8.900E2 8.800E2 8.700E2 8.600E2 8.500E2 8.400E2 8.322E2 8.300E2 8.200E2 8.100E2 8.000E2 7.900E2 7.800E2 7.742E2 7.700E2 7.600E2 7.500E2 7.400E2 7.300E2 7.203E2 7.200E2
p,m 9.004E0 9.011E0 9.093E0 9.176E0 9.261 E0 9.348E0 9.436E0 9.526E0 9.617E0 9.678E0 9.711E0 9.806E0 9.903E0 1.000El 1.010El 1.021El 1.031El 1.040El 1.042E1 1.053E1 1.064E1 1.076E1 1.087E1 1.099E1 1.111El 1.118El 1.124E1 1.137E1 1.150El 1.163E1 1.177E1 1.191El 1.202E1 1.205E1 1.220E1 1.235E1 1.250E1 1.266E1 1.282E1 1.292E1 1.299E1 1.316E1 1.334E1 1.352E1 1.370E1 1.389E1 1.389E1
0.0001 2.7810 2.7800 2.7790 2.7790 2.7780 2.7780 2.7770 2.7770 7.7797 2.7760 2.7750 2.7750 2.7740 2.7740 2.7730 2.7720 4.2651 2.7720 2.7710 2.7710 2.7700 2.7700 2.7690 2.7690 3.5726 2.7680 2.7670 2.7670 2.7660 2.7660 2.7650 3.2627 2.7650 2.7640 2.7640 2.7630 2.7630 2.7620 3.0865 2.7620 2.7610 2.7610 2.7600 2.7600 2.9735 2.7590
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [21
4.17E0 [3] 1.22E-2 [2] 1.21E-2 1.21E-2 1.20E-2 1.20E-2 1.19E-2 1.19E-2 1.18E-2 4.00E-4 [3] 1.18E-2 [2] 1.17E-2 1.17E-2 1.16E-2 1.16E-2 1.15E-2 1.15E-2 4.07E-5 [3] 1.15E-2 [2] 1.14E-2 1.14E-2 1.13E-2 1.13E-2 1.12E-2 1.12E-2 1.65E-5 [3] 1.11E-2 [2] 1.11E-2 1.11E-2 1.10E-2 1.10E-2 1.09E-2 9.35E-6 [3] 1.09E-2 [2] 1.08E-2 1.08E-2 1.08E-2 1.07E-2 1.07E-2 6.17E-6 [3] 1.06E-2 [2] 1.06E-2 1.05E-2 1.05E-2 1.05E-2 4.45E-6 [3] 1.04E-2 [2]
Boron Nitride (BN)
437 TABLE I (Continued) Cubic BN
eV 8.80E-2 8.68E-2 8.55E-2 8.43E-2 8.31E-2 8.31E-2 8.18E-2 8.06E-2 7.93E-2 7.81E-2 7.73E-2 7.69E-2 7.56E-2 7.44E-2 7.31E-2 7.19E-2 7.19E-2 7.07E-2 6.94E-2 6.82E-2 6.69E-2 6.69E-2 6.57E-2 6.45E-2 6.32E-2 6.22E-2 6.20E-2 6.07E-2 5.95E-2 5.83E-2 5.79E-2 5.70E-2 5.58E-2 5.45E-2 5.39E-2 5.33E-2 5.21E-2 5.08E-2 5.01E-2 4.96E-2
cm-
1
7.100E2 7.000E2 6.900E2 6.800E2 6.701E2 6.700E2 6.600E2 6.500E2 6.400E2 6.300E2 6.234E2 6.200E2 6.100E2 6.000E2 5.900E2 5.800E2 5.800E2 5.700E2 5.600E2 5.500E2 5.400E2 5.396E2 5.300E2 5.200E2 5.100E2 5.020E2 5.000E2 4.900E2 4.800E2 4.700E2 4.670E2 4.600E2 4.500E2 4.400E2 4.345E2 4.300E2 4.200E2 4.100E2 4.043E2 4.000E2
/xm 1.409E1 1.429E1 1.450E1 1.471E1 1.493E1 1.493E1 1.515E1 1.539E1 1.563E1 1.588E1 1.604E1 1.613E1 1.640E1 1.667E1 1.695E1 1.724E1 1.725E1 1.755E1 1.786E1 1.819E1 1.852E1 1.854E1 1.887E1 1.923E1 1.961E1 1.992E1 2.000El 2.041E1 2.084E1 2.128E1 2.142E1 2.174E1 2.223E1 2.273E1 2.302E1 2.326E1 2.381E1 2.440E1 2.474E1 2.501E1
2.7590 2.7580 2.7570 2.7570 2.8952 2.7560 2.7560 2.7550 2.7550 2.7540 2.8383 2.7540 2.7530 2.7530 2.7530 2.7954 2.7520 2.7520 2.7510 2.7510 2.7500 2.7623 2.7500 2.7490 2.7490 2.7361 2.7480 2.7480 2.7470 2.7470 2.7151 2.7460 2.7460 2.7450 2.6981 2.7450 2.7440 2.7440 2.6841 2.7440
1.04E-2
[3] [2]
[3] [2]
[3] [21
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
1.03E-2 1.03E-2 1.03E-2 3.41E-6 1.02E-2 1.02E-2 1.01E-2 1.01E-2 1.01E-2 2.72E-6 1.00E-2 9.97E-3 9.93E-3 9.89E-3 2.24E-6 9.85E-3 9.81E-3 9.78E-3 9.74E-3 9.70E-3 1.88E-6 9.66E-3 9.62E-3 9.58E-3 1.61E-6 9.55E-3 9.51E-3 9.47E-3 9.43E-3 1.40E-6 9.40E-3 9.36E-3 9.32E-3 1.23E-6 9.28E-3 9.25E-3 9.21E-3 1.09E-6 9.17E-3
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
[3] [2]
438
Gary L. Doll TABLE II Values of n and k for Hexagonal BN from Various References a
eV
cm- ~
/xm
n
k
1.000E 1 9.479E0 8.985E0 8.517E0 8.074E0 7.653E0 7.255E0 6.877E0 6.518E0 6.179E0 5.857E0 5.552E0 5.263E0 4.989E0 4.729E0 4.483E0 4.249E0 4.028E0 3.818E0 3.619E0 3.430E0 3.252E0 3.082E0 2.922E0 2.770E0 2.625E0 2.489E0 2.359E0 2.236E0 2.120E0 2.009E0 1.905E0 1.805E0 1.711 E0 1.622E0 1.538E0 1.458 E0 1.382E0 1.310E0 1.241 E0 1.177E0 1.116E0 1.057E0 1.002E0 9.501E-1 9.006E-1
8.066E4 7.646E4 7.248E4 6.870E4 6.512E4 6.173E4 5.852E4 5.547E4 5.258E4 4.984E4 4.724E4 4.478E4 4.245E4 4.024E4 3.814E4 3.616E4 3.427E4 3.249E4 3.079E4 2.919E4 2.767E4 2.623 E4 2.486E4 2.357E4 2.234E4 2.118E4 2.007E4 1.903E4 1.804E4 1.710E4 1.621 E4 1.536E4 1.456E4 1.380E4 1.308E4 1.240E4 1.176E4 1.114E4 1.056E4 1.001 E4 9.492E3 8.998E3 8.529E3 8.085E3 7.664E3 7.265E3
1.240E- 1 1.308E-1 1.380E- 1 1.456E- 1 1.536E-1 1.620E- 1 1.709E-1 1.803E-1 1.902E- 1 2.007E- 1 2.117E- 1 2.234E- 1 2.356E-1 2.486E- 1 2.622E- 1 2.766E- 1 2.918E- 1 3.079E- 1 3.248E-1 3.426E- 1 3.615E- 1 3.813 E- 1 4.023E- 1 4.244E- 1 4.477E- 1 4.723E- 1 4.983E- 1 5.256E-1 5.545E- 1 5.850E- 1 6.172E- 1 6.511E-1 6.868E- 1 7.246E- 1 7.644E-1 8.064E- 1 8.507E- 1 8.975E- 1 9.468E- 1 9.988E- 1 1.054E0 1.112E0 1.173E0 1.237E0 1.305E0 1.377E0
1.1905 [71 1.1903 1.1949 1.2040 1.1799 1.1281 1.0819 1.0470 1.1054 1.2790 1.3301 1.3589 1.5082 1.5987 1.5810 1.5631 1.5450 1.5266 1.5193 1.5270 1.5346 1.5422 1.5496 1.5566 1.5637 1.5707 1.5778 1.5849 1.5920 1.5992 1.6049 1.6050 1.6056 1.6061 1.6067 1.6072 1.6078 1.6084 1.6090 1.6096 1.6099 1.6094 1.6090 1.6088 1.6087 1.6088
3.3E- 1 [7] 3.3E-1 3.2E-1 3.1E-1 3.0E-1 3.7E-1 4.4E-1 5.3E-1 6.2E-1 8.3E-1 8.4E-1 5.6E-1 4.0E-1 2.8E-1 2.8E-1 2.8E-1 2.8E-1 2.8E-1 2.7E-1 2.7E-1 2.6E-1 2.6E-1 2.5E-1 2.5E-1 2.4E-1 2.3E-1 2.2E-1 2.2E-1 2.1E-1 2.0E-1 1.9E-1
a
The references from which the values were taken are given in brackets.
1.9E-1
1.8E-1 1.8E-1 1.8E-1 1.7E-1 1.7E-1 1.7E-1 1.7E-1 1.6E-1 1.6E-1 1.4E-1 1.3E-1 1.1E-1 9.9E-2 8.4E-2
Boron Nitride (BN)
439 TABLE II
(Continued)
Hexagonal BN eV 8.537E-1 8.092E- 1 7.671E-1 7.271E-1 6.893E-1 6.534E- 1 6.193E-1 5.871E-1 5.565E-1 5.275E-1 5.000E- 1 4.740E-1 4.493E-1 4.259E-1 4.037E-1 3.827E-1 3.627E-1 3.438E-1 3.259E-1 3.090E-1 2.929E-1 2.776E- 1 2.632E-1 2.494E-1 2.480E- 1 2.467E-1 2.455E-1 2.442E- 1 2.430E- 1 2.418E-1 2.405E- 1 2.393E-1 2.380E- 1 2.368E-1 2.365E-1 2.356E- 1 2.343E-1 2.331E-1 2.318E-1 2.306E- 1 2.294E-1 2.281E-1 2.269E-1 2.256E-1 2.244E- 1 2.241E-1 2.232E-1
cm
-1
6.886E3 6.527E3 6.187E3 5.865E3 5.560E3 5.270E3 4.995E3 4.735E3 4.489E3 4.255E3 4.033E3 3.823E3 3.624E3 3.435E3 3.256E3 3.087E3 2.926E3 2.773E3 2.629E3 2.492E3 2.362E3 2.239E3 2.123E3 2.012E3 2.000E3 1.990E3 1.980E3 1.970E3 1.960E3 1.950E3 1.940E3 1.930E3 1.920E3 1.910E3 1.907E3 1.900E3 1.890E3 1.880E3 1.870E3 1.860E3 1.850E3 1.840E3 1.830E3 1.820E3 1.810E3 1.808E3 1.800E3
~m 1.452E0 1.532E0 1.616E0 1.705E0 1.799E0 1.898E0 2.002E0 2.112E0 2.228E0 2.351E0 2.480E0 2.616E0 2.760E0 2.912E0 3.072E0 3.240E0 3.418E0 3.606E0 3.804E0 4.013E0 4.234E0 4.467E0 4.712E0 4.971 E0 5.001 E0 5.026E0 5.051E0 5.077E0 5.103E0 5.129E0 5.156E0 5.182E0 5.209E0 5.237E0 5.244E0 5.264E0 5.292E0 5.320E0 5.349E0 5.377E0 5.406E0 5.436E0 5.465E0 5.496E0 5.526E0 5.532E0 5.557E0
1.6093 1.6100 1.6109 1.6118 1.6128 1.6138 1.6149 1.6161 1.6173 1.6184 1.6196 1.6208 1.6142 1.6023 1.5904 1.5783 1.5661 1.5539 1.5415 1.5291 1.5166 1.5040 1.4913 1.4785 0.0337 0.0347 0.0358 0.0370 0.0382 0.0395 0.0409 0.0423 0.0439 0.0455 1.4657 0.0472 0.0491 0.0511 0.0532 0.0555 0.0579 0.06O5 0.0633 0.0663 0.0696 1.2721 0.0732
[6]
[71 [6]
[7] [6]
6.9E-2 5.7E-2 4.7E-2 3.7E-2 2.7E-2 1.7E-2 7.4E-3 6.3E-3 5.3E-3 4.2E-3 3.2E-3 2.2E-3 1.1E-3 1.0E-4 8.6E-4 2.2E-3 5.4E-3 8.6E-3 1.2E-2 1.5E-2 1.8E-2 2.2E-2 2.6E-2 3.4E-2 8.3E-1 [6] 8.4E-1 8.5E-1 8.6E-1 8.7E-1 8.8E-1 8.9E-1 9.0E-1 9.2E-1 9.3E-1 4.1E-2 [7] 9.4E-1 [6] 9.5E-1 9.7E-1 9.8E-1 9.9E-1 1.0E0 1.0E0 1.0E0 1.1E0 1.1E0 5.6E-2 [7] 1.1E0 [61
(continued)
440
Gary L. Doll TABLE II
(Continued)
Hexagonal BN
eV 2.219E-1 2.207E-1 2.194E-1 2.182E-1 2.170E-1 2.157E-1 2.145E-1 2.132E-1 2.125E-1 2.120E-1 2.108E-1 2.095E-1 2.083E-1 2.070E-1 2.058E-1 2.046E- 1 2.033E-1 2.021E-1 2.014E-1 2.008E- 1 1.996E- 1 1.984E-1 1.971E-1 1.959E-1 1.946E-1 1.934E-1 1.922E-1 1.909E-1 1.909E-1 1.897E-1 1.884E-1 1.872E-1 1.860E- 1 1.847E-1 1.835E-1 1.822E-1 1.810E-1 1.810E-1 1.798E-1 1.785E-1 1.773E-1 1.760E-1 1.748E-1 1.736E-1 1.723E-1 1.715E-1 1.711E-1
cm
--1
1.790E3 1.780E3 1.770E3 1.760E3 1.750E3 1.740E3 1.730E3 1.720E3 1.714E3 1.710E3 1.700E3 1.690E3 1.680E3 1.670E3 1.660E3 1.650E3 1.640E3 1.630E3 1.624E3 1.620E3 1.610E3 1.600E3 1.590E3 1.580E3 1.570E3 1.560E3 1.550E3 1.540E3 1.540E3 1.530E3 1.520E3 1.510E3 1.500E3 1.490E3 1.480E3 1.470E3 1.460E3 1.460E3 1.450E3 1.440E3 1.430E3 1.420E3 1.410E3 1.400E3 1.390E3 1.384E3 1.380E3
p,m 5.588E0 5.619E0 5.651E0 5.683E0 5.715E0 5.748E0 5.781E0 5.815E0 5.836E0 5.849E0 5.883E0 5.918E0 5.953E0 5.989E0 6.025E0 6.062E0 6.099E0 6.136E0 6.157E0 6.174E0 6.212E0 6.251 E0 6.290E0 6.330E0 6.371E0 6.411E0 6.453E0 6.495E0 6.495E0 6.537E0 6.580E0 6.624E0 6.668E0 6.713E0 6.758E0 6.804E0 6.851E0 6.852E0 6.898E0 6.946E0 6.994E0 7.044E0 7.094E0 7.144E0 7.196E0 7.229E0 7.248E0
0.0771 0.0813 0.0860 0.0911 0.0967 0.1029 0.1098 0.1175 0.9780 0.1261 0.1358 0.1469 0.1594 0.1739 0.1906 0.2101 0.2330 0.2603 0.9087 0.2930 0.3329 0.3821 0.4437 0.5220 0.6230 0.7549 0.9284 1.1541 1.4838 1.4357 1.7536 2.0515 2.2592 2.3459 2.3346 2.2666 2.1738 1.8762 2.0746 1.9778 1.8871 1.8035 1.7270 1.6572 1.5934 3.2662 1.5348
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
1.1E0 1.1E0 1.2E0 1.2E0 1.2E0 1.2E0 1.2E0 1.3E0 8.3E-2 [7] 1.3E0 [6] 1.3E0 1.4E0 1.4E0 1.4E0 1.5E0 1.5E0 1.6E0 1.6E0 7.4E- 1 [7] 1.7E0 [6] 1.8E0 1.8E0 1.9E0 2.0E0 2.1E0 2.2E0 2.3E0 2.4E0 1.lEO [7] 2.4E0 [6] 2.3E0 2.1E0 1.8E0 1.5E0 1.2E0 9.6E-1 7.8E-1 1.2E0 [7] 6.5E-1 [6] 5.4E-1 4.6E-1 4.0E-1 3.5E-1 3.1E-1 2.7E-1 3.0E-1 [7] 2.4E- 1 [6]
Boron Nitride (BN)
441 TABLE II (Continued) Hexagonal BN
eV 1.698E-1 1.686E-1 1.674E- 1 1.661E-1 1.649E- 1 1.636E-1 1.626E-1 1.624E-1 1.612E-1 1.599E-1 1.587E-1 1.575E-1 1.562E-1 1.550E-1 1.541 E- 1 1.537E-1 1.525E-1 1.513E-1 1.500E- 1 1.488E-1 1.475E-1 1.463E- 1 1.461E-1 1.451 E- 1 1.438E-1 1.426E- 1 1.413E-1 1.401E-1 1.389E-1 1.385E-1 1.376E- 1 1.364E- 1 1.351E-1 1.339E-1 1.327E-1 1.314E-1 1.313E-1 1.302E- 1 1.289E-1 1.277E-1 1.265E-1 1.252E-1 1.244E- 1 1.240E- 1 1.227E-1 1.215E-1 1.203E-1
cm
--I
1.370E3 1.360E3 1.350E3 1.340E3 1.330E3 1.320E3 1.311E3 1.310E3 1.300E3 1.290E3 1.280E3 1.270E3 1.260E3 1.250E3 1.243E3 1.240E3 1.230E3 1.220E3 1.210E3 1.200E3 1 190E3 1 180E3 1 178E3 1 170E3 1 160E3 1 150E3 1 140E3 1 130E3 1 120E3 1 117E3 1 l10E3 1 100E3 1.090E3 1.080E3 1.070E3 1.060E3 1.059E3 1.050E3 1.040E3 1.030E3 1.020E3 1.010E3 1.004E3 1.000E3 9.900E2 9.800E2 9.700E2
/.zm 7.301E0 7.354E0 7.409E0 7.464E0 7.520E0 7.577E0 7.626E0 7.635E0 7.694E0 7.753E0 7.814E0 7.875E0 7.938E0 8.001 E0 8.045E0 8.066E0 8.132E0 8.198E0 8.266E0 8.335E0 8.405E0 8.476E0 8.487E0 8.549E0 8.622E0 8.697E0 8.774E0 8.851E0 8.930E0 8.954E0 9.011E0 9.093E0 9.176E0 9.261E0 9.348E0 9.436E0 9.446E0 9.526E0 9.617E0 9.711E0 9.806E0 9.903E0 9.965E0 1.000El 1.010El 1.021El 1.031El
1.4808 1.4310 1.3847 1.3415 1.3010 1.2629 2.5572 1.2270 1.1929 1.1604 1.1293 1.0995 1.0707 1.0429 2.3066 1.0159 0.9896 0.9637 0.9383 0.9133 0.8884 0.8636 2.1397 0.8387 0.8137 0.7883 0.7625 0.7361 0.7089 2.0910 0.6806 0.6510 0.6198 0.5865 0.5506 0.5115 2.0411 0.4680 0.4189 0.3619 0.2943 0.2159 1.9899 0.1460 0.1060 0.0848 0.0721
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
2.2E-1 2.0E-1 1.8E-1 1.7E-1 1.6E-1 1.5E-1 9.5E-2 1.4E-1 1.3E-1 1.2E-1 1.1E-1 1.1E-1 1.0E-1 9.7E-2 5.2E-2 9.2E-2 8.8E-2 8.5E-2 8.2E-2 7.9E-2 7.6E-2 7.4E-2 1.5E-2 7.2E-2 7.1E-2 6.9E-2 6.8E-2 6.7E-2 6.7E-2 1.8E-2 6.7E-2 6.7E-2 6.8E-2 6.9E-2 7.1E-2 7.4E-2 2.1E-2 7.9E-2 8.6E-2 9.8E-2 1.2E-1 1.6E-1 2.5E-2 2.3E-1 3.2E-1 4.0E-1 4.7E-1
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
(continued)
442
Gary L. Doll TABLE II
(Continued)
Hexagonal BN eV 1.190E-1 1.180E-1 1.178E-1 1.165E-1 1.153E-1 1.141E-1 1.128E-1 1.118E-1 1.116E-1 1.103E-1 1.091E-1 1.079E-1 1.066E- 1 1.060E-1 1.054E-1 1.041E-1 1.029E-1 1.017E-1 1.005E- 1 1.004E-1 9.918E-2 9.794E-2 9.670E-2 9.546E-2 9.523E-2 9.422E-2 9.298E-2 9.174E-2 9.050E-2 9.027E-2 8.926E-2 8.802E-2 8.678E-2 8.557E-2 8.554E-2 8.430E-2 8.306E-2 8.182E-2 8.111E-2 8.059E-2 7.935E-2 7.811E-2 7.689E-2 7.687E-2 7.563E-2 7.439E-2 7.315E-2
cm
-1
9.600E2 9.514E2 9.500E2 9.400E2 9.300E2 9.200E2 9.100E2 9.019E2 9.000E2 8.900E2 8.800E2 8.700E2 8.600E2 8.549E2 8.500E2 8.400E2 8.300E2 8.200E2 8.104E2 8.100E2 8.000E2 7.900E2 7.800E2 7.700E2 7.682E2 7.600E2 7.500E2 7.400E2 7.300E2 7.281E2 7.200E2 7.100E2 7.000E2 6.902E2 6.900E2 6.800E2 6.700E2 6.600E2 6.543E2 6.500E2 6.400E2 6.300E2 6.202E2 6.200E2 6.100E2 6.000E2 5.900E2
/am 1.042E1 1.051El 1.053E1 1.064E1 1.075E1 1.087E1 1.099E1 1 109El 1 lllE1 1 124E1 1 137E1 1 150El 1 163E1 1 170El 1.177E1 1.191El 1.205E1 1.220E1 1.234E1 1.235E1 1.250E1 1.266E1 1.282E1 1.299E1 1.302E1 1.316E1 1.334E1 1.352E1 1.370E1 1.374E1 1.389E1 1.409E 1 1.429E1 1.449E1 1.450E1 1.471E1 1.493E1 1.515E1 1.529E1 1.539E1 1.563E1 1.588E1 1.613E1 1.613E1 1.640E 1 1.667E1 1.695E1
0.0637 1.9374 0.0579 0.0539 0.0511 0.0494 0.0486 1.8669 0.0487 0.0499 0.0521 0.0559 0.0616 1.7817 0.0703 0.0837 0.1053 0.1430 1.6951 0.2187 0.4147 1.3238 5.8255 3.9641 2.0660 3.0979 2.6422 2.3552 2.1550 2.0118 2.0058 1.8895 1.7958 1.9709 1.7184 1.6532 1.5973 1.5489 1.9582 1.5063 1.4687 1.4350 1.9517 1.4048 1.3774 1.3525 1.3297
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
[7] [6]
5.4E-1 2.9E-2 [7] 6.1E-1 [6] 6.8E-1 7.5E-1 8.2E-1 9.0E-1 3.8E-2 [7] 9.7E-1 [6] 1.1E0 1.2E0 1.3E0 1.4E0 9.8E-2 [7] 1.5E0 [6] 1.7E0 1.9E0 2.2E0 1.7E-1 [7] 2.6E0 [6] 3.3E0 4.8E0 2.9E0 5.7E-1 2.6E- 1 [7] 2.5E-1 [6] 1.5E-1 9.9E-2 7.3E-2 8.3E-2 [7] 5.7E-2 [6] 4.6E-2 3.9E-2 6.9E-2 [7] 3.3E-2 [6] 2.9E-2 2.5E-2 2.3E-2 5.6E-2 [7] 2.1E-2 [6] 1.9E-2 1.7E-2 5.8E-2 [7] 1.6E-2 [6] 1.5E-2 1.4E-2 1.3E-2
Boron Nitride (BN)
443 TABLE II
(Continued)
Hexagonal BN eV 7.288E-2 7.191E-2 7.067E-2 6.943E-2 6.909E-2 6.819E-2 6.695E-2 6.571E-2 6.549E-2 6.447E-2 6.323E-2 6.208E-2 6.199E-2 6.075E-2 5.951E-2 5.884E-2 5.827E-2 5.703E-2 5.579E-2 5.578E-2 5.455E-2 5.331E-2 5.287E-2 5.207E-2 5.083E-2 5.012E-2 4.959E-2 4.835E-2 4.711E-2 4.587E-2 4.463E-2 4.339E-2 4.215E-2 4.091E-2 3.967E-2 3.843E-2 3.719E-2
cm
--1
5.879E2 5.800E2 5.700E2 5.600E2 5.572E2 5.500E2 5.400E2 5.300E2 5.282E2 5.200E2 5.100E2 5.007E2 5.000E2 4.900E2 4.800E2 4.746E2 4.700E2 4.600E2 4.500E2 4.499E2 4.400E2 4.300E2 4.265E2 4.200E2 4.100E2 4.043E2 4.000E2 3.900E2 3.800E2 3.700E2 3.600E2 3.500E2 3.400E2 3.300E2 3.200E2 3.100E2 3.000E2
/xm 1.701El 1.724E1 1.755E1 1.786E1 1.795E1 1.819E1 1.852E1 1.887E1 1.893E1 1.923E1 1.961E1 1.998E1 2.000E 1 2.041E1 2.084E1 2.107E1 2.128E1 2.174E1 2.223E1 2.223E1 2.273E1 2.326E1 2.345E1 2.381E1 2.439E1 2.474E1 2.500E1 2.565E1 2.632E1 2.703E1 2.778E1 2.858E1 2.942E1 3.031E1 3.126E1 3.226E1 3.334E1
1.9451 1.3087 1.2895 1.2716 1.9385 1.2551 1.2396 1.2253 1.9319 1.2118 1.1992 1.9260 1.1874 1.1763 1.1658 1.9216 1.1559 1.1466 1.1377 1.9172 1.1294 1.1214 1.9128 1.1139 1.1068 1.9084 1.1000 1.0935 1.0874 1.0816 1.0760 1.0707 1.0657 1.0609 1.0563 1.0520 1.0479
[7] [6]
[7] [6]
[7] [6] [7] [6]
[7] [61
[7] [6] [7] [6] [7] [6]
6.1E-2 1.2E-2 1.2E-2 1.1E-2 6.3E-2 1.1E-2 1.0E-2 9.6E-3 6.6E-2 9.2E-3 8.8E-3 6.8E-2 8.4E-3 8.1E-3 7.7E-3 6.4E-2 7.4E-3 7.1E-3 6.9E-3 6.0E-2 6.6E-3 6.4E-3 5.6E-2 6.1E-3 5.9E-3 5.2E-2 5.7E-3 5.5E-3 5.3E-3 5.1E-3 4.9E-3 4.7E-3 4.5E-3 4.3E-3 4.2E-3 4.0E-3 3.9E-3
[7] [6]
[7] [6]
[7] [6] [7] [6]
[7] [6]
[7] [6] [7] [6] [7] [6]