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Optical constants and spectral selectivity of titanium carbonitrides
Thin Solid Films, 87 (1982) 181-187 ELECTRONICS AND OPTICS
181
OPTICAL CONSTANTS AND SPECTRAL SELECTIVITY OF TITANIUM CARBONITRIDES * BJORN KARLSSON Department of Solid State Physics, University of Uppsala, Uppsala (Sweden)
JAN-ERIK SUNDGREN AND BENGT-OLOFJOHANSSON University of Link@ing, Link@ing (Sweden)
(ReceivedAugust 31, 1981; accepted October 19, 1981)
Thin films of titanium compounds were prepared by the reactive r.f. sputtering of a titanium target in an atmosphere of nitrogen and/or methane. Auger electron spectroscopy and X-ray diffraction were used for sample characterization. Reflectance measurements were carried out between 0.2 and 50 Ixm and the optical constants were determined by means of K r a m e r s - K r o n i g analysis. A separation into contributions from interband transitions and from free-electron behaviour was carried out. The optical properties of the TiN and the shifts in them which are obtained when carbon is introduced are interpreted in terms of the density of states distribution.
1. INTRODUCTIONAND THEORETICALBACKGROUND The optical properties of transition metal carbides and nitrides are important since these compounds are a m o n g the few which are promising for use as single surface selective absorbers. It is also of fundamental interest that closely related compounds exhibit radically different optical behaviour. This can be seen in Fig. 1 where the optical constants of TiC and TiN are shown. Like most other transition metal compounds, the carbide has a reflectance curve which fails off continuously from a high value at low energies, while the nitride shows a high Drude-like IR reflectance combined with an edge in the visible region. F r o m the electronic density of states 1, as seen in Fig. 2, a model which explains these properties has recently been suggested 2. The total density of states in Fig. 2 is decomposed into partial linear combination of atomic orbital (LCAO) densities. The Fermi energy EF of TiN is situated above the minimum of the density of states, where the L C A O partial density of metal d states dominates. The contribution of the L C A O partial density of metalloid p states is very small. This means that interband transitions at low energies must be weak since selection rules prevent transitions between d bands. The low energy interval, where the optical properties of TiN are characterized by intraband * Paper presented at the 5th International Conference on Thin Films, Herzlia-on-Sea,Israel, September 21-25, 1981. 0040-6090/82/0000-0000/$02.75
© ElsevierSequoia/Printed in The Netherlands
182
B. KARLSSON, J.-E. SUNDGREN, B.-O. JOHANSSON
transitions, is i n t e r r u p t e d b y an onset o f i n t e r b a n d t r a n s i t i o n s at 2.5 eV. T h e y c a n be identified as t r a n s i t i o n s b e t w e e n the increasing n u m b e r s of p states 2.5 eV b e l o w EF a n d of d states at EF. T h e energy of these t r a n s i t i o n s is d e n o t e d Eo in Fig. 2. T h e s i t u a t i o n for T i C is different. I n this case the F e r m i energy EF intersects the density of states curve where the c o n t r i b u t i o n s from metallic d o r b i t a l s a n d m e t a l l o i d p o r b i t a l s are c o m p a r a b l e a n d the i n t e r b a n d t r a n s i t i o n s m a y occur at low energies. This is clearly e x h i b i t e d in the reflectance curve which shows no D r u d e - l i k e b e h a v i o u r at low energies. I n the low energy r e g i o n the o p t i c a l p r o p e r t i e s of T i N are therefore freee l e c t r o n like with a gas of d electrons. I n Fig. 2 we can see t h a t the density of states a l m o s t vanishes at the m i n i m u m 2.5 eV b e l o w EF. It is therefore r e a s o n a b l e to 10
.
.
.
2' ",,./" 4 ~
X ,' ,'i
.
.
.
'
'
'
100
80_ .-e iii
" "E(eV) 6o70 ,~ I .--. .... ~ . ~ ' ~ o
......
u. .i Q2
2O
/ / 10 /
I ,
/
.
.
.
.
.
Fig. 1. Spectral reflectance and real and imaginary parts of the dielectric constant for stoichiometric TiN ( ) and TiC ( - - -).
tt
I I I
'
92.5
i
f EF
(a) -8
;
-L,
8
4
ii -oB
12
(eV)
!,
i!
~
-o4
o
} '
oz,
o8
E (Ryd)
EF
~2
(b) Fig. 2 LCAO partial density of states gt(E) (the number of states of both spins per Rydberg and per unit cell) for (a) TiC and (b) TiN (X denotes carbon or nitrogen):..., gXs(E);- - -, gXp(E); , ggio(E ). (From Neckel et al. 1)
OPTICAL CONSTANTS OF
Ti
CARBONITRIDES
183
estimate the number of electrons, active in the Drude excitation, from the density of states between the minimum and E r. The area under the density of states curve in Fig. 2 corresponds to approximately 0.9 electrons per formula unit TiN. This electron density gives a plasma energy hcop = 8.04 eV, which can be fitted to experimental data by assuming an effective mass m* different from 1.0. As can be seen in Fig. 1, the position of the plasma knee is situated at a much lower energy than the predicted plasma resonance at 8.04 eV. This difference can partly be explained by an electron effective mass greater than 1.0, but it depends mainly on a positive contribution to e x from bound electrons. These contributions to el shift the point at which el(C0) = 0 to a lower energy. At this energy a screened plasma resonance occurs and the reflectance decreases sharply. This behaviour is strikingly similar to that of the noble metals. In silver, interband transitions cause e~(Co) to change sign at 3.9eV instead of 9.2eV as expected 3 from the Drude value of hCop. The high IR reflectance and the steep reflectance step make the nitride promising as a selectively absorbing layer on a solar absorber. To increase the solar absorptance, however, the reflectance knee should be displaced towards a lower energy value. Within the framework of our interpretation this is achieved if the total number of electrons is reduced. Such a reduction lowers E v which makes the area under the density of states curve smaller. This in turn lowers the plasma energy and, more importantly, the threshold energy E 0 for the onset of p electron excitation to the Fermi level. Both these effects would cause el to change sign at lower energy, would move the reflectance knee to a lower energy and would also increase the solar absorptance. One way to shift the Fermi energy down is to replace some nitrogen atoms with carbon atoms 4 (which have one p electron less). This was tested by preparing a number of titanium carbonitrides for optical analysis. 2.
SAMPLE PREPARATION AND CHARACTERIZATION
The samples were prepared by reactive sputtering in an r.f. diode sputtering system equipped with a diffusion pump capable of keeping a constant pumping speed of 2501s -1 up to pressures as high as 1.5 x 10 -2 Torr. To get as clean a v a c u u m as possible a titanium sublimation pump was also used. The ultimate pressure in the system is 5 × 10-7 Torr. The depositions were carried out in an a~mosphere of argon (99.9997~ pure) and nitrogen (99.9992~o pure) and/or methane (99.998~o pure) at a total pressure of 7 x 10- 3 Torr. The partial pressures of nitrogen and methane are given in Table I. The fused silica substrates were kept at 770 K, and the films were deposited to thicknesses ranging from 1000 to 2500,~, which are sufficient to give opaque samples over the measured spectral region. Auger electron spectroscopy was used to determine the impurity content and the composition of the films. Excluding the extreme surface the films were very pure, only minor amounts of oxygen (less than I at.Y/o) being found. The composition of the films was estimated by comparison with pure titanium, TiC and TiN standard samples. The crystallographic structure was determined by using X-ray diffraction analysis. The X-ray diffraction patterns were recorded with Guinier camera using filtered Cu K ~ I , ~ 2 radiation. The lattice parameters obtained as a function of
184
B. K A R L S S O N , J . - E . S U N D G R E N , B . - O . J O H A N S S O N
TABLE I PREPARATION
PARAMETERS
Sample
PN (Torr)
1 2 3 4 5 6 7 8 9
2× 3x 3x 3x 3x 3x 3x 3x --
FOR THIN
FILM SAMPLES
Composition (mol.%)
P c . (Torr)
10 -4
--
10 - 4 10 - 4 10 - 4 10 - 4 10 - 4 10 - 4 10 - 4
1x 2.5 5x 7.5 1x 3x 6 x 5x
10 - s x 10 - s 10 - s x 10 - 5 10 - 4 10 - 4 10 - 4 10 - 4
4.34[
TiN
TiC
100 81 79 68 61 58 42 33 --
-19 21 32 39 42 58 67 i00
Lattice constant (~)
4.250 4.244 4.241 4.259 4.265 4.277 4.288 4.292 4.328
100 80 z60 ~40
~
8
4.26 a: 20
4.2/-, TiC
xx 20
/.0
60
80
TiN
01 .8
.
.
. 1.2
.
. . 1.6
COMPOSITION [ mote*/,J Fig. 3. L a t t i c e p a r a m e t e r vs. c o m p o s i t i o n : x , o u r s a m p l e s ;
.
. 2.0
. 2~
2.8
E (eV) , b u l k v a l u e s 5.
Fig. 4. S p e c t r a l r e f l e c t a n c e for s a m p l e s 1 - 9 d e s c r i b e d in T a b l e I.
composition are shown in Fig. 3. Also shown in the figure are data obtained by Duwez and Odell 5. 3.
OPTICAL RESULTS
3.1. R e f l e c t i v i t y m e a s u r e m e n t s
T h e specular reflectance of the samples at r o o m temperature was measured over the wavelength range 0.195-3.0 I~m with a Beckman 5240 spectrophotometer and from 2.5 to 50 I~m with a Perkin-Elmer model 599B spectrophotometer. The reflectance was measured relative to that of a freshly evaporated aluminium mirror. The aluminium mirror was flash evaporated at 1 0 - 6 T o r r in a diffusion-pumped vacuum system. Above 0.4 ~tm the reflectance values of the aluminium reference were assumed to agree with those obtained by Bennett et al. 6"7 for similar preparation conditions. Below 0.4 pm the reflectance of the aluminium reference was calibrated in a Beckman D K - 2 A spectrophotometer equipped with a V-W
O P T I C A L C O N S T A N T S OF
Ti
CARBONITRIDES
185
attachment for absolute reflectance measurements. The ratio of diffuse to specular reflectance was measured at 0.3 ~tm in the 5240 spectrophotometer (which was equipped with an integrating sphere) and was found to be less than 0.01. The reflectance of the samples for p-polarized light at 60 ° incidence was measured at wavelengths corresponding to 2.5, 3.0, 4.0 and 5.0eV. The reflectance was reproducible to within 1~. The spectral reflectances of the pure TiN and TiC are shown in Fig. 1 and those of the TiNxC~ _x compounds in Fig. 4. The TiN data are in agreement with measurements on chemically vapour-deposited TiN described in ref. 2 and references therein. A comparison of the TiC reflectance data with those from measurements on single-crystal TiC performed by Lynch et al. s shows good overall agreement even though differences in the fine structure occur.
3.2. Optical analysis The reflectance spectra of the samples were analysed by means of the K r a m e r s Kronig relation. The reflectance below 0.05 eV was found by extrapolation with
in accordance with the Hagen-Rubens relation where s is chosen to adjust the extrapolation to the low energy part of the measured spectra. The extrapolation of the reflectance in the UV beyond 6.3 eV was made by setting the reflectance constant at the 6.3 eV value up to hto I and assuming that R ~ co-P for h~o > ho91. The parameters co1 and p were chosen to adjust the optical constants from the KramersKronig analysis to the known optical constants at 2.5, 3.0, 4.0 and 5.0 eV, deduced from reflectance measurements for p-polarized light 9 at normal incidence and at 60 ° incidence. Typical values of the parameters were ha~ = 12 eV and p = 3.7. The optical constants of the stoichiometric TiN and TiC are shown in Fig. 1. Drude plots were prepared to separate the contributions to the optical constants from intraband and interband transitions. F r o m these plots the freeelectron collision time r and the plasma frequency Ogpwere deduced. The values of h/r and hogp are given in Table II. From these parameters the contribution to the optical constants from intraband transitions was calculated over the full experimental range and the total dielectric constant was separated into contributions from TABLE II SELECTED OPTICAL PARAMETERS
Compound TiN TiNo.slCo.19 TiN0.79Co.21
TiNo.68C0.32 TiNo.61Co.~9 TiNo.ssCo.42 TiNo.42Co.ss TiNo.aaC0.67
TiC
ho~p
h/¢
(eV)
(eV) (eV)
6.29 5.87 5.68 5.52 5.22 4.79 3.41 2.53 .
0.30 0.31 0.30 0.33 0.30 0.29 0.45 0.61 .
- AEF
0 0.17 0.25 0.32 0.44 0.61 1.2 1.5 .
.
- Ae2a (eV)
- Ae2b (eV)
hog[{Im(e-1)}max] (eV)
R(0.2 eV)
0 0.22 0.35 0.56 0.67 0.72 --.
0 0.30 0.40 0.50 0.70 ----
2.52 2.37 2.33 2.25 2.18 2.17 2.0 --
0.923 0.923 0.918 0.906 0.904 0.901 0.850 0.778 0.858
.
186
B. KARLSSON, J.-E. SUNDGREN, B.-O. JOHANSSON
free and bound electrons as shown in Fig. 5. Finally the energy loss function Ira{e- 1(~)} --
e2 /~12 --[-g2 2
was calculated. The spectral positions of the peak of the loss function, indicating a screened plasma resonance, are listed in Table II. 8 i
4 6
E (eV)
Fig. 5. Contribution e2b to ~2from bound electronsfor samples 1-6 describedin Table I.
4. DISCUSSION
4.1. Conduction electron properties The plasma energy h~op for TiN calculated from the density of states distribution, as explained in Section 1, has a value of 8.04 eV. The experimental value of the plasma energy obtained from the Drude plot is 6.28 eV. If the freeelectron mass is considered as a free parameter an effective optical mass m* = 1.64 gives agreement between the experimental and theoretical values of the plasma energy. When carbon replaces nitrogen in the compound the plasma energy decreases, as seen in Table II. Under the assumption that m* is constant, which is reasonable in a rigid-band approximation if no new unfilled band is created, this can be explained if a decreasing number of conduction electrons contribute to the plasma frequency. This can be further analysed if the area between the minimum and E F in the density of states distribution is approximated by a triangle. Since it is assumed that the band structure is rigid and that only the Fermi energy shifts when carbon is introduced, the plasma energy will be proportional t o the distance of E F above the minimum in the density of states curve. The proportionality comes from the square root dependence of the plasma energy on the electron density. The shifts in EF, calculated from h~%, are also given in Table II. The relaxation energy h/z is surprisingly constant up to a carbon content of 42~o. This implies that the contribution to the scattering from the carbon atoms is small. This is also verified by the reflectance curves in Fig. 4 and by the low energy reflectance given in Table II. The figure shows that the reflectance step is not smeared out, and the IR reflectances in the table are relatively constant when the carbon-to-nitrogen ratio is increased. Both these facts indicate a nearly constant relaxation time z.
OPTICAL CONSTANTS OF
Ti
CARBONITRIDES
187
4.2. Interband transitions
The contribution to 82 in TiN from interband transitions, as shown in Fig. 5, indicates a threshold for strong interband excitations at around 2.6 eV with peaks at 3.5 eV and 5.1 eV. These energies, denoted E o, E1 and E 2 respectively in Fig. 2, are in good agreement with the results in ref. 2 and references therein. When carbon is introduced, the Fermi energy is decreased and the transitions are shifted to lower energies. These shifts are given in Table II as A82a and AgEb. A82a is the energy shift at constant e 2 ( = 3.5) close to the onset of the interband transitions and A82b corresponds to the shift in 82 at the peak around 5 eV. In our simple model, where the position o f E F is the only important parameter, the shift in E F should be equal to the shift in energy of the transitions from the p states below E F to the d states at E F. Table II shows that the A82 shifts are larger than the AE F shift, but considering the simplicity of our model the agreement is reasonable. 4.3. Optical selectivity
Properties such as the high IR reflectance, the steep reflectance knee and the extremely good high temperature stability which make TiN promising as a singlesurface high temperature stable selective surface have to be supplemented with an increased solar absorptance. This investigation showed that the reflectance knee can be shifted by about 0.4 eV without significantly lowering the IR reflectance and the steepness of the reflectance knee. The shifts in the reflectance R are indicated in Table II, as given by the position of the m a x i m u m of the energy loss function. The reflectance shifts are comparable with the AEF shifts up to a carbon content of 32~o. 5. CONCLUSIONS
A model has been developed which explains the extended free-electron region and the onset of strong interband transitions for TiN. The model gives reasonable agreement between predicted and measured optical shifts when carbon replaces nitrogen in the compound. The optical selectivity is increased by the introduction of carbon, but the solar absorptance of the c o m p o u n d is still insufficient for practical applications. ACKNOWLEDGMENT This work was supported by the Swedish Natural Science Research Council under Contract E - E G 4231-101. REFERENCES 1 A. Neckel, P. Rastl, R. Eibler, P. Weinbergerand K. Schwarz, J. Phys. C, 9 (1976) 579. 2 B. Karlsson, R. P. Shimshock, B. O. Seraphin and J. C. Haygarth, in Proc. Nordic Solid State Physics Conf. 1981, University of Copenhagen, August 10-12, 1981,in Phys. Scr., to be published. 3 H. Ehrenreich and H. R. Philipp, Phys. Rev., 128 (1962) 1622. 4 P. Weinberger,Phys. Status Solidi B, 98 (1980) 207. 5 P. Duwez and F. Odell, J. Electrochem. Soc., 97 (1950) 299. 6 H.E. Bennett, J. M. Bennett and E. J. Ashley,J. Opt. Soc. Am., 52 (1962) 1245. 7 H.E. Bennett, M. Silverand E. J. Ashley,J. Opt. Soc. Am., 53 (1963) 1089. 8 D.N. Lynch, C. G. Olson and D. J. Peterman, Phys. Rev. B, 22 (1980) 3991. 9 J.E. Nestell and R. W. Christy, Appl. Opt., 11 (1972) 643.
181
OPTICAL CONSTANTS AND SPECTRAL SELECTIVITY OF TITANIUM CARBONITRIDES * BJORN KARLSSON Department of Solid State Physics, University of Uppsala, Uppsala (Sweden)
JAN-ERIK SUNDGREN AND BENGT-OLOFJOHANSSON University of Link@ing, Link@ing (Sweden)
(ReceivedAugust 31, 1981; accepted October 19, 1981)
Thin films of titanium compounds were prepared by the reactive r.f. sputtering of a titanium target in an atmosphere of nitrogen and/or methane. Auger electron spectroscopy and X-ray diffraction were used for sample characterization. Reflectance measurements were carried out between 0.2 and 50 Ixm and the optical constants were determined by means of K r a m e r s - K r o n i g analysis. A separation into contributions from interband transitions and from free-electron behaviour was carried out. The optical properties of the TiN and the shifts in them which are obtained when carbon is introduced are interpreted in terms of the density of states distribution.
1. INTRODUCTIONAND THEORETICALBACKGROUND The optical properties of transition metal carbides and nitrides are important since these compounds are a m o n g the few which are promising for use as single surface selective absorbers. It is also of fundamental interest that closely related compounds exhibit radically different optical behaviour. This can be seen in Fig. 1 where the optical constants of TiC and TiN are shown. Like most other transition metal compounds, the carbide has a reflectance curve which fails off continuously from a high value at low energies, while the nitride shows a high Drude-like IR reflectance combined with an edge in the visible region. F r o m the electronic density of states 1, as seen in Fig. 2, a model which explains these properties has recently been suggested 2. The total density of states in Fig. 2 is decomposed into partial linear combination of atomic orbital (LCAO) densities. The Fermi energy EF of TiN is situated above the minimum of the density of states, where the L C A O partial density of metal d states dominates. The contribution of the L C A O partial density of metalloid p states is very small. This means that interband transitions at low energies must be weak since selection rules prevent transitions between d bands. The low energy interval, where the optical properties of TiN are characterized by intraband * Paper presented at the 5th International Conference on Thin Films, Herzlia-on-Sea,Israel, September 21-25, 1981. 0040-6090/82/0000-0000/$02.75
© ElsevierSequoia/Printed in The Netherlands
182
B. KARLSSON, J.-E. SUNDGREN, B.-O. JOHANSSON
transitions, is i n t e r r u p t e d b y an onset o f i n t e r b a n d t r a n s i t i o n s at 2.5 eV. T h e y c a n be identified as t r a n s i t i o n s b e t w e e n the increasing n u m b e r s of p states 2.5 eV b e l o w EF a n d of d states at EF. T h e energy of these t r a n s i t i o n s is d e n o t e d Eo in Fig. 2. T h e s i t u a t i o n for T i C is different. I n this case the F e r m i energy EF intersects the density of states curve where the c o n t r i b u t i o n s from metallic d o r b i t a l s a n d m e t a l l o i d p o r b i t a l s are c o m p a r a b l e a n d the i n t e r b a n d t r a n s i t i o n s m a y occur at low energies. This is clearly e x h i b i t e d in the reflectance curve which shows no D r u d e - l i k e b e h a v i o u r at low energies. I n the low energy r e g i o n the o p t i c a l p r o p e r t i e s of T i N are therefore freee l e c t r o n like with a gas of d electrons. I n Fig. 2 we can see t h a t the density of states a l m o s t vanishes at the m i n i m u m 2.5 eV b e l o w EF. It is therefore r e a s o n a b l e to 10
.
.
.
2' ",,./" 4 ~
X ,' ,'i
.
.
.
'
'
'
100
80_ .-e iii
" "E(eV) 6o70 ,~ I .--. .... ~ . ~ ' ~ o
......
u. .i Q2
2O
/ / 10 /
I ,
/
.
.
.
.
.
Fig. 1. Spectral reflectance and real and imaginary parts of the dielectric constant for stoichiometric TiN ( ) and TiC ( - - -).
tt
I I I
'
92.5
i
f EF
(a) -8
;
-L,
8
4
ii -oB
12
(eV)
!,
i!
~
-o4
o
} '
oz,
o8
E (Ryd)
EF
~2
(b) Fig. 2 LCAO partial density of states gt(E) (the number of states of both spins per Rydberg and per unit cell) for (a) TiC and (b) TiN (X denotes carbon or nitrogen):..., gXs(E);- - -, gXp(E); , ggio(E ). (From Neckel et al. 1)
OPTICAL CONSTANTS OF
Ti
CARBONITRIDES
183
estimate the number of electrons, active in the Drude excitation, from the density of states between the minimum and E r. The area under the density of states curve in Fig. 2 corresponds to approximately 0.9 electrons per formula unit TiN. This electron density gives a plasma energy hcop = 8.04 eV, which can be fitted to experimental data by assuming an effective mass m* different from 1.0. As can be seen in Fig. 1, the position of the plasma knee is situated at a much lower energy than the predicted plasma resonance at 8.04 eV. This difference can partly be explained by an electron effective mass greater than 1.0, but it depends mainly on a positive contribution to e x from bound electrons. These contributions to el shift the point at which el(C0) = 0 to a lower energy. At this energy a screened plasma resonance occurs and the reflectance decreases sharply. This behaviour is strikingly similar to that of the noble metals. In silver, interband transitions cause e~(Co) to change sign at 3.9eV instead of 9.2eV as expected 3 from the Drude value of hCop. The high IR reflectance and the steep reflectance step make the nitride promising as a selectively absorbing layer on a solar absorber. To increase the solar absorptance, however, the reflectance knee should be displaced towards a lower energy value. Within the framework of our interpretation this is achieved if the total number of electrons is reduced. Such a reduction lowers E v which makes the area under the density of states curve smaller. This in turn lowers the plasma energy and, more importantly, the threshold energy E 0 for the onset of p electron excitation to the Fermi level. Both these effects would cause el to change sign at lower energy, would move the reflectance knee to a lower energy and would also increase the solar absorptance. One way to shift the Fermi energy down is to replace some nitrogen atoms with carbon atoms 4 (which have one p electron less). This was tested by preparing a number of titanium carbonitrides for optical analysis. 2.
SAMPLE PREPARATION AND CHARACTERIZATION
The samples were prepared by reactive sputtering in an r.f. diode sputtering system equipped with a diffusion pump capable of keeping a constant pumping speed of 2501s -1 up to pressures as high as 1.5 x 10 -2 Torr. To get as clean a v a c u u m as possible a titanium sublimation pump was also used. The ultimate pressure in the system is 5 × 10-7 Torr. The depositions were carried out in an a~mosphere of argon (99.9997~ pure) and nitrogen (99.9992~o pure) and/or methane (99.998~o pure) at a total pressure of 7 x 10- 3 Torr. The partial pressures of nitrogen and methane are given in Table I. The fused silica substrates were kept at 770 K, and the films were deposited to thicknesses ranging from 1000 to 2500,~, which are sufficient to give opaque samples over the measured spectral region. Auger electron spectroscopy was used to determine the impurity content and the composition of the films. Excluding the extreme surface the films were very pure, only minor amounts of oxygen (less than I at.Y/o) being found. The composition of the films was estimated by comparison with pure titanium, TiC and TiN standard samples. The crystallographic structure was determined by using X-ray diffraction analysis. The X-ray diffraction patterns were recorded with Guinier camera using filtered Cu K ~ I , ~ 2 radiation. The lattice parameters obtained as a function of
184
B. K A R L S S O N , J . - E . S U N D G R E N , B . - O . J O H A N S S O N
TABLE I PREPARATION
PARAMETERS
Sample
PN (Torr)
1 2 3 4 5 6 7 8 9
2× 3x 3x 3x 3x 3x 3x 3x --
FOR THIN
FILM SAMPLES
Composition (mol.%)
P c . (Torr)
10 -4
--
10 - 4 10 - 4 10 - 4 10 - 4 10 - 4 10 - 4 10 - 4
1x 2.5 5x 7.5 1x 3x 6 x 5x
10 - s x 10 - s 10 - s x 10 - 5 10 - 4 10 - 4 10 - 4 10 - 4
4.34[
TiN
TiC
100 81 79 68 61 58 42 33 --
-19 21 32 39 42 58 67 i00
Lattice constant (~)
4.250 4.244 4.241 4.259 4.265 4.277 4.288 4.292 4.328
100 80 z60 ~40
~
8
4.26 a: 20
4.2/-, TiC
xx 20
/.0
60
80
TiN
01 .8
.
.
. 1.2
.
. . 1.6
COMPOSITION [ mote*/,J Fig. 3. L a t t i c e p a r a m e t e r vs. c o m p o s i t i o n : x , o u r s a m p l e s ;
.
. 2.0
. 2~
2.8
E (eV) , b u l k v a l u e s 5.
Fig. 4. S p e c t r a l r e f l e c t a n c e for s a m p l e s 1 - 9 d e s c r i b e d in T a b l e I.
composition are shown in Fig. 3. Also shown in the figure are data obtained by Duwez and Odell 5. 3.
OPTICAL RESULTS
3.1. R e f l e c t i v i t y m e a s u r e m e n t s
T h e specular reflectance of the samples at r o o m temperature was measured over the wavelength range 0.195-3.0 I~m with a Beckman 5240 spectrophotometer and from 2.5 to 50 I~m with a Perkin-Elmer model 599B spectrophotometer. The reflectance was measured relative to that of a freshly evaporated aluminium mirror. The aluminium mirror was flash evaporated at 1 0 - 6 T o r r in a diffusion-pumped vacuum system. Above 0.4 ~tm the reflectance values of the aluminium reference were assumed to agree with those obtained by Bennett et al. 6"7 for similar preparation conditions. Below 0.4 pm the reflectance of the aluminium reference was calibrated in a Beckman D K - 2 A spectrophotometer equipped with a V-W
O P T I C A L C O N S T A N T S OF
Ti
CARBONITRIDES
185
attachment for absolute reflectance measurements. The ratio of diffuse to specular reflectance was measured at 0.3 ~tm in the 5240 spectrophotometer (which was equipped with an integrating sphere) and was found to be less than 0.01. The reflectance of the samples for p-polarized light at 60 ° incidence was measured at wavelengths corresponding to 2.5, 3.0, 4.0 and 5.0eV. The reflectance was reproducible to within 1~. The spectral reflectances of the pure TiN and TiC are shown in Fig. 1 and those of the TiNxC~ _x compounds in Fig. 4. The TiN data are in agreement with measurements on chemically vapour-deposited TiN described in ref. 2 and references therein. A comparison of the TiC reflectance data with those from measurements on single-crystal TiC performed by Lynch et al. s shows good overall agreement even though differences in the fine structure occur.
3.2. Optical analysis The reflectance spectra of the samples were analysed by means of the K r a m e r s Kronig relation. The reflectance below 0.05 eV was found by extrapolation with
in accordance with the Hagen-Rubens relation where s is chosen to adjust the extrapolation to the low energy part of the measured spectra. The extrapolation of the reflectance in the UV beyond 6.3 eV was made by setting the reflectance constant at the 6.3 eV value up to hto I and assuming that R ~ co-P for h~o > ho91. The parameters co1 and p were chosen to adjust the optical constants from the KramersKronig analysis to the known optical constants at 2.5, 3.0, 4.0 and 5.0 eV, deduced from reflectance measurements for p-polarized light 9 at normal incidence and at 60 ° incidence. Typical values of the parameters were ha~ = 12 eV and p = 3.7. The optical constants of the stoichiometric TiN and TiC are shown in Fig. 1. Drude plots were prepared to separate the contributions to the optical constants from intraband and interband transitions. F r o m these plots the freeelectron collision time r and the plasma frequency Ogpwere deduced. The values of h/r and hogp are given in Table II. From these parameters the contribution to the optical constants from intraband transitions was calculated over the full experimental range and the total dielectric constant was separated into contributions from TABLE II SELECTED OPTICAL PARAMETERS
Compound TiN TiNo.slCo.19 TiN0.79Co.21
TiNo.68C0.32 TiNo.61Co.~9 TiNo.ssCo.42 TiNo.42Co.ss TiNo.aaC0.67
TiC
ho~p
h/¢
(eV)
(eV) (eV)
6.29 5.87 5.68 5.52 5.22 4.79 3.41 2.53 .
0.30 0.31 0.30 0.33 0.30 0.29 0.45 0.61 .
- AEF
0 0.17 0.25 0.32 0.44 0.61 1.2 1.5 .
.
- Ae2a (eV)
- Ae2b (eV)
hog[{Im(e-1)}max] (eV)
R(0.2 eV)
0 0.22 0.35 0.56 0.67 0.72 --.
0 0.30 0.40 0.50 0.70 ----
2.52 2.37 2.33 2.25 2.18 2.17 2.0 --
0.923 0.923 0.918 0.906 0.904 0.901 0.850 0.778 0.858
.
186
B. KARLSSON, J.-E. SUNDGREN, B.-O. JOHANSSON
free and bound electrons as shown in Fig. 5. Finally the energy loss function Ira{e- 1(~)} --
e2 /~12 --[-g2 2
was calculated. The spectral positions of the peak of the loss function, indicating a screened plasma resonance, are listed in Table II. 8 i
4 6
E (eV)
Fig. 5. Contribution e2b to ~2from bound electronsfor samples 1-6 describedin Table I.
4. DISCUSSION
4.1. Conduction electron properties The plasma energy h~op for TiN calculated from the density of states distribution, as explained in Section 1, has a value of 8.04 eV. The experimental value of the plasma energy obtained from the Drude plot is 6.28 eV. If the freeelectron mass is considered as a free parameter an effective optical mass m* = 1.64 gives agreement between the experimental and theoretical values of the plasma energy. When carbon replaces nitrogen in the compound the plasma energy decreases, as seen in Table II. Under the assumption that m* is constant, which is reasonable in a rigid-band approximation if no new unfilled band is created, this can be explained if a decreasing number of conduction electrons contribute to the plasma frequency. This can be further analysed if the area between the minimum and E F in the density of states distribution is approximated by a triangle. Since it is assumed that the band structure is rigid and that only the Fermi energy shifts when carbon is introduced, the plasma energy will be proportional t o the distance of E F above the minimum in the density of states curve. The proportionality comes from the square root dependence of the plasma energy on the electron density. The shifts in EF, calculated from h~%, are also given in Table II. The relaxation energy h/z is surprisingly constant up to a carbon content of 42~o. This implies that the contribution to the scattering from the carbon atoms is small. This is also verified by the reflectance curves in Fig. 4 and by the low energy reflectance given in Table II. The figure shows that the reflectance step is not smeared out, and the IR reflectances in the table are relatively constant when the carbon-to-nitrogen ratio is increased. Both these facts indicate a nearly constant relaxation time z.
OPTICAL CONSTANTS OF
Ti
CARBONITRIDES
187
4.2. Interband transitions
The contribution to 82 in TiN from interband transitions, as shown in Fig. 5, indicates a threshold for strong interband excitations at around 2.6 eV with peaks at 3.5 eV and 5.1 eV. These energies, denoted E o, E1 and E 2 respectively in Fig. 2, are in good agreement with the results in ref. 2 and references therein. When carbon is introduced, the Fermi energy is decreased and the transitions are shifted to lower energies. These shifts are given in Table II as A82a and AgEb. A82a is the energy shift at constant e 2 ( = 3.5) close to the onset of the interband transitions and A82b corresponds to the shift in 82 at the peak around 5 eV. In our simple model, where the position o f E F is the only important parameter, the shift in E F should be equal to the shift in energy of the transitions from the p states below E F to the d states at E F. Table II shows that the A82 shifts are larger than the AE F shift, but considering the simplicity of our model the agreement is reasonable. 4.3. Optical selectivity
Properties such as the high IR reflectance, the steep reflectance knee and the extremely good high temperature stability which make TiN promising as a singlesurface high temperature stable selective surface have to be supplemented with an increased solar absorptance. This investigation showed that the reflectance knee can be shifted by about 0.4 eV without significantly lowering the IR reflectance and the steepness of the reflectance knee. The shifts in the reflectance R are indicated in Table II, as given by the position of the m a x i m u m of the energy loss function. The reflectance shifts are comparable with the AEF shifts up to a carbon content of 32~o. 5. CONCLUSIONS
A model has been developed which explains the extended free-electron region and the onset of strong interband transitions for TiN. The model gives reasonable agreement between predicted and measured optical shifts when carbon replaces nitrogen in the compound. The optical selectivity is increased by the introduction of carbon, but the solar absorptance of the c o m p o u n d is still insufficient for practical applications. ACKNOWLEDGMENT This work was supported by the Swedish Natural Science Research Council under Contract E - E G 4231-101. REFERENCES 1 A. Neckel, P. Rastl, R. Eibler, P. Weinbergerand K. Schwarz, J. Phys. C, 9 (1976) 579. 2 B. Karlsson, R. P. Shimshock, B. O. Seraphin and J. C. Haygarth, in Proc. Nordic Solid State Physics Conf. 1981, University of Copenhagen, August 10-12, 1981,in Phys. Scr., to be published. 3 H. Ehrenreich and H. R. Philipp, Phys. Rev., 128 (1962) 1622. 4 P. Weinberger,Phys. Status Solidi B, 98 (1980) 207. 5 P. Duwez and F. Odell, J. Electrochem. Soc., 97 (1950) 299. 6 H.E. Bennett, J. M. Bennett and E. J. Ashley,J. Opt. Soc. Am., 52 (1962) 1245. 7 H.E. Bennett, M. Silverand E. J. Ashley,J. Opt. Soc. Am., 53 (1963) 1089. 8 D.N. Lynch, C. G. Olson and D. J. Peterman, Phys. Rev. B, 22 (1980) 3991. 9 J.E. Nestell and R. W. Christy, Appl. Opt., 11 (1972) 643.