Ellipsometric measurements on plasma deposited diamondlike amorphous carbon (a-C:H) films were taken in the visible, (E = 1.75 to 3.5 eV). The films were deposited on Si and their properties were varied using high temperature (up to 750 C) anneals. The real (n) and imaginary (k) parts of the complex index of refraction, N, were obtained simultaneously. Following the theory of Forouhi and Bloomer, a least squares fit was used to find the dispersion relations n(E) and k(E). Reasonably good fits were obtained, showing that the theory can be used for a-C:H films. Moreover, the value of the energy gap, Eg, obtained in this way was compared the the Eg value using conventional Tauc plots and reasonably good agreement was obtained

Alterovitz, Samuel A.

Pouch, John J.

Shoemaker, Neil S.

Sieg, Robert M.

English

NASA Technical Reports Server

N91 - 18305 !
"DIAMONDLIKE CARBON FILMSOPTICAL DISPERSION RELATIONS FOR " "
Samuel A. A]terovitz*, Robert M. Siegt, Neil S. Shoemaker*, and
John J. Pouch"
"NASA Lewis Research Center, Cleveland, Ohio 44135
tUndergraduate Student Intern at NASA Lewis ReSearch Center from Cleveland,
State University, Dept. of Electrical Engineering, Cleveland, Ohio 44106
*Undergraduate Student Intern at NASA Lewis Research Center from Case
Western Reserve University, Physics Dept., Cleveland, Ohio 44115
ABSTRACT
Elllpsometrlc measurements on plasma deposited "diamondIike" amorphous
carbon (a-C:H) films were taken in the visible, (E - 1.75 to 3.5 eV). The
films were deposited on SI and their propertles were varied using high tem-
perature (up to 750 °C) anneals. The real (n) and Imaglnary (k) parts of
the complex index of refraction N were obtained slmultaneously. Follow-
ing the theory of Forouhl and Bloomer (Phys. Rev. B34, 7018 (1986)), a
least squares fit was used to find the dispersion relations n(E) and
k(E). Reasonably good fits were obtained, showing that the theory can be
used for a-C:H films. Morever, the value of the energy gap Eg obtained
in thls way was compared to the Eg. value using conventional Tauc plots
and reasonably good agreement was obtained.
INTRODUCTION
The optical energy band gap of amorphous materials Is usually found
uslng a Tauc plot Ill, I.e., an extrapolation of (:nE) I/2 versus E. Here
Is the optical absorption coefficient, n Is the refractive index and
E Is the energy. In many cases, the refractlve index is almost constant
or is unavailable, and (:E)I/2 versus E is used (simplified Tauc).
There are several drawbacks to the Tauc theory and procedure. First, the
theory relates to absorption only, and cannot give the refractive index
through the Kramers-Kronig relation [2]. Second, there is ambiguity on
the energy range that the Tauc extrapolation is correct. Below a certain
value of _, the absorption falls exponentially. This regime Is called
the Urbach edge []]. The onset for this reglme varies and values of order
= lO3 cm-l [I] up to : = IO4 cm-l [3] have been used. Empirically, many
Tauc plots also start to deviate from a straight line at high _ values
[4,5].
Recently, an extension of the theory of optical absorptlon has been
published for amorphous materials [2]. Later, the theory was extended to
include more than one critical point, and was applied to crystalline semi-
conductors [6]. In the Tauc plot derivation CI], the maln assumptions are
a constant matrix element and parabolic denslty of states for both the
valence and the conduction bands. However, if the excited state has a
finite lifetime _, the absorption probability has a damping factor [2]
and Tauc plots are theoretically incorrect. The extinction coefficient k
(k . :c_/2E where E Is the energy) Is calculated in [2,6] using the
lifetlme concept, obtalnlng.
A(E - Eg)2
k(E) _ (l)
E2 - BE + C
Here A is k(®) and Is proportional to M21_ where M is the position
matrix element (M = (flxll)); B - 2(EC crit - Ev crit ), where Ec crlt and
Ev,crlt are energies in the conductioA and valence band respectively corre-
sponding to a crltlcal polnt, i.e., where k(Er rrif - Ev rr_f) iS a maxi-
mum. C is related to the lifetime _ through"_/_ , (4_-'B2) I/2 and
Mat. Res. Soc. Symp. Proc. Vol. 152. ©1989 Materials Research Society
240
https://ntrs.nasa.gov/search.jsp?R=19910008992 2020-03-19T19:44:06+00:00Z
Eg - Ec,bottem - Ev,top, i.e., the optical bandgap. Using the Kramers-
Kronlg relation, the refractive index was obtained [2]:
BoE * CO
n(k) - n(®) • E2 _ BE + C
(Z)
Here Bo and CO are related to A,B and C through simple algebraic
formulas, and n(_) is a constant.
In this paper we will examine if this new result applies to "diamond-
like" carbon, also denoted a-C:H (amorphous hydrogenated carbon). If
applicable, the result can give the n(E) function from a known absorption
spectrum k(E) and a single refractive index measurement. Also, the func-
tions n(E) and/or k(E) can be used when their analytical Form is required,
e.g., optimizing antlreflection filters. In addition, this paper will dis-
cuss the meaning of the experimental constants, A,B, C, and Eg.
Amorphous hydrogenated carbon material is made almost exclusivelj in
Form of thin films. The natural choice for an experimental technique _s
ellipsometry. The multiple angle of incidence, multiple wavelengths (MAW)
technique [7 to 9] was used. MAW gives n and k of the film simulta-
neously at all wavelengths measured, without the use of either a known
dispersion relation or application of the Kramers-Kronig analysis. This
technique was commonly used to analyze various semiconductor multilayer
structures [lO,ll] when n and k of the constituents were known. Here,
the MAW technique Is used in a spectroscopic way, to measure unknown n(E)
and k(E). The smallest value of k that is accurately determlned by
ellipsometry is of order 0.005, corresponding to _ _ _000 cm-l in the visi-
ble. Thus, the Urbach edge regime is almost eliminated From this work.
Reflection ellipsometry has the added benefit of measuring the thin Film
samples on any substrate, in contrast to transmission experiments. As the
optical energy bandgap Eg depends on the substrate mater_al [5], possibly
due to differences in conductivity, thls advantage of ellipsometry can be
crucial for actual applications.
EXPERIMENTAL
Samples were prepared on 3 In. diameter Si substrates using a 30 kHz
plasma deposition unit. The power P used was in the range _0 to 200 W,
with a constant flow rate of 7xlO-5 m3/min. Details of the growth chamber
are glven In [12]. Several samples cut from the 150 W wafer were annealed
In nltrogen for lO sec using a rapid thermal anneal module [5]. The
rotating analyzer ellipsometer set-up [13] is essentially similar to the
one described in [lO]. At each angle of Incidence, data was taken in the
wavelength range 3500 to 7300 A, with lO0 A intervals. Five angles of inci-
dence were used, usually In the range 5S° to 75°. Each measurement con-
sisted of lO0 rev, with 72 points per rev, taken at a rate of -50 rev/sec.
Background subtraction was done at each point. Calibration of the absolute
value of the elIipsometrlc parameters g and a was done using [14]. The
double grating monchromator was controlled by a IBM-AT personal computer
that was also used For all data acquistion and analysis. _ and a were
obtained by Fourier analysis. The MAW inversion process was done by
mlnlmizing experimental 9 and 6 (or tan 9 and cos 6) versus thelr cal-
culated values [9]. The model used included only the substrate and a homo-
geneous fl]m. Thls is a reasonable approximation, as the interface of
a-C:H on Si includes only the native oxlde and ~5 A SiCX [15], and our
fllms were above I000 A thick.
RESULTS
Seven samples were measured. Simplified and regular Tauc plots were
done for all samples. A representative plot (50 W sample) is given In
241
Fig. I, showlng a slightly concave result versus the theory. As the anneal-
ing temperature and/or deposition power rises, the experimental Tauc func-
tion first becomes a straight line and later turns convex. He kept the
extrapolation range to the linear part of the experimental function. A sum-
mary of the energy bandgaps obtained From regular and simplified Tauc plot_,
together with sample thicknesses t, are given in Table I. Results of n(E)
and k(E) for the 50 and 150 N, 600 °C samples are given in Figs 2 and 3
respectively. Figure 2 shows a rising n versus E while Fig. 3 show a
decreasing n(E). All other samples have an interim t'ype of behavior. Grid
least square fits to Eq. (1) were done to obtain A,B,C and Eg simulta-
neously. With these 4 parameters fixed, the value of n(=) was set to get
the best n(E) fits, The solid llnes in Figs. 2 and 3 ,Mere calculated using
these parameters. Results for all samples are given in Table I!, while Eg
is also displayed in Table I.
TABLE I a-C:H OPTICAL ENERGY GAPS IN eV
P, W T,°C t, A Sqrt(_E) Sqrt(_En) Grid
50
100
150
200
150 400
150 600
150 750
1490
2305
2810
2960
2580
1320
950
1 .90
2.65
2.36
2.02
2.05
1.08
O. 57
1.90
2.65
2.36
2.02
2.06
0.89
0.39
1 .64
2.70
2.23
1.65
1 .90
1.03
0.39
TABLE II DISPERSION RELATION PARAMETERS FOR a-C:H FILMS
P, W T, C
50
100
150
200
150 400
150 600
150 750
A B, eV
.06
.01
.05
.II
•06
.40
.85
6.39
6.46
5.90
5.99
5.10
3.66
I .21
C, (eV)Z
12.67
10.51
9.75
11.73
7.20
4.22
1.85
Eg, eV
i .64
2.70
2.23
i .65
I. 90
I .03
0.39
n(=)
I .63
1.70
I .67
I .69
i. 70
I .58
I .71
242
c;
lZ'l"
O
CD _'"
11
E
t_
C_J
0
0
0
a-C:H ,50 W 70 sccm
÷
I 1 I I I
.Ts 2.o_ 2.2s 2.so 2.;s 3.00 3.25
ENERGY (eV)
FrGURE I. TAUC PLOT FOR THE SO U SAMPLE.
L!NES SHOW THE FITTING RANGE.
I |
3.50 3.75
VERT I CAL
_= a-C:H 50 N 70 sccm
r_ c_
:>< -.
1,1
g
Z _ m
2- Z
2
• Q + x
_ t* x x
2-I _.f" x - _TINCTION C_EF. -_
./X + 4_CTIVE INDEX
o
_ -" | _............... r I 1 I I I
1.75 2.00 2.25 2.50 2.7S 3.00 3.25 3.50 _.75
ENERGY (eV)
FIGURE 2. REFRACTIVE INDEX AND EXTINCTION COEFFICIENT
OF THE 50 W SAMPLE. SOLID LINES ARE DUE TO EQUATIONS
(1 AND (2).
243
o
_-C:H
X
LJ
Z _-
C_)
_R
.,,i
FIGURE 3.
OF THE _50 W, 600°C SAMPLE.
EQUATIONS (£) AND (2).
!50 N 70 sccm 600 C
• i
(_)
Z
N_
w - EXTINCTION X
/ ÷ - BEF_QCTIVE INOEX tJ._]
_=_
2" ' ' ' '•25 2.50 2.75 .00 3.25 . 3.50 _. "/5
ENERGY (eV]
REFRACTIVE INDE× AND EXT[NCTION COEFFICIENT
SOLID LINES ARE DUE TO
DISCUSSION
Optical energy bandgaps Eg found using the two Tauc procedures are
identlcal. However, Eg found using the dispersion relation fits are almost
always smaller than the Tauc plots, although the differences are not very
large. It Is impossible to rule which bandgap is the "correct" one. The
dispersion relation functions do take into account, at least qualitatively,
the existence of absorption at lower energy than the regular Tauc regime,
the Urbach tail. This can be seen by the very small slope of K(E) near
Eg, as shown in Fig. 2. However, :<E) Is expected to be purely exponential
In the Urbach edge Ill. Thus, theoretically, the dispersion relations do
not describe this regime. Table I also shows a decrease In Eg with
increasing deposition power, (except the 50 W sample) and with increasing
annealing temperature, in agreement wlth prlor results [4,5]. The thick-
ness Increases with power [16] and decreases wlth annealing temperature.
The quality of the fits shown in Figs. 2 and 3 is quite good. The
n(E) fits are the real test of the theory and the figures show a reasonable
agreement between experlment and calculation. All other n(E) experlmental
curves show an equal or better fit to theory, as they include almost con-
stant n(E) values. In addition, the k(E) fit Is definitely better than
the Tauc fits.
The value of the A,B,C parameters, as shown in Table IT, are essen-
tially constant as function of deposition power, but they change signifi-
cantly versus anneal!ng.temperature. The value of the lifetime _/_,
deduced from (4C - BZ) I/z, has quite an amount of scatter. However, all
results are around _/_ _ 2 eV. This is a large value, but it Is compara-
ble with other amorphous materials [2]. The values of A are in general
lower than for other materials [2], denoting a smaller position matrix ele-
ment M In a-C:H. There Is an order of magnltude increase in M with
heating to 750 °C. It would be interesting to correlate this increase with
the changes in the composition and crystalllvlty of a-C:H. The value of
B for the room temperature deposited samples, is equal to the lowest values
obtained for other materials [2], and drops markedly with annealing tempera-
ture. The value of BI2 Is characteristlc of the critical point bandgap
[6], denoting a sharp decrease In this bandgap, in parallel with the sharp
Eg drop. However, we did not see signs of a peak in k(E) at E - BI2, as
expected for a critical point.
244
CONCLUSION , .
Oisoersion relations suggested in [2] are obeyed, although the n(E)
Function does not have a perfect Fit. Values of the @arameters For the
bandgaos B and Eg show reasonable agreement with Tauc plots and with
prior results. The position matrix element Increases with Increasing
annealing temperature.
REFERENCES
I. N.F. Mort and E.A. Davis, Electronic Processes in Non-Crystalline
Materials, 2nd ed. (Clarendon Press, OxFord, 1979).
2. A.R. Forouhi and I. Bloomer, Phys. Re,/.B, 34, 7018 (1986).
3. J. Robertson, Adv. Phys., 3_5.5,317 (1986).
4. S.A. Alterovitz, i.D. Warner, D.C. Liu and J.J. Pouch, J. Electrochem.
Soc., 13__.33,2 39 (1986).
5. S.A. Alterovitz, J.J. Pouch and 3.D. Warner, in Rapid Thermal
Processing of Electronic Materials, edited by S.R. Wilson, R. Powell,
and D.E. Davies, (Mater. Res. Soc. Proc. 92, Pittsburgh, PA, 1987)
pp. 311-318.
6. A.R. Forouhl and I. Bloomer, Phys. Rev. B, 38, 1865 (1988).
7. S.A. A1terovitz, G.H. Bu-Abbud, J.A. Hoollam, and D.C. Liu, J. Appl.
Phys., L4, 1559 (1983).
8. G.H. Bu-Abbud, S.A. Alterovitz, N.M. Bashara and J.A. Hoollam, J. Vac.
Sci. Techno1., A, _, 619 (1983).
9. G.H. Bu-Abbud, N.M. Bashara, and J]A. Wcollam, Thin Solid Films, 13J,
27 (1986).
lO. P.G. Snyder, M.C. Rost, G.H. Bu-Abbud, J.A. Woollam, and S.A.
Alterovitz, J. Appl. Phys., 60, 3293 (1986).
11. S.A. Alterovitz, J.A. Woollam, and P.G. Snyder, Sol. State Tech., 31
(3), 99 (1988).
12. J.J. Pouch, 3.D. Warner, D.C. Liu and S.A. Alterbvitz, Thin Solid
Films, 157, 97 (1988).
13. 3.A. Wcollam Co., Lincoln, NB.
14. D.E. Aspnes and A.A. Studna, Appl. Opt., 14, 220 (1975).
15. R.W. Collins, Appl. Phys. Left., 5__22,025 (1988).
16. J.3. Pouch, S.A. Alterovltz, J.D. Warner, D.C. Liu, and W.A. Lanford,
In Thin Films" The Relationship of Structure to Properties, edited by
C.R Aita and K.S. Sreeharsha, (Mater. Res. Soc, Proc. 4__Z, Pittsburgh,
PA, 1985) pp. 201-204.
This paper also appears in Mat, Res Soc. Extended Abstract (EA-lg)
245


Optical dispersion relations for diamondlike carbon films

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server