_ _- C.?,.-: _ _ . _

NASA Technical Memorandum 102356-ii

Optical Dispersaon Relations for

' : _'-"'Diamondlike" Carbon.... Films

(NA_A-IM-!O?356) OPTICAL

_rL_TIONS FOb O!AMONDLIKt

(NASA) 9 p

Samuel A. Alterovitz

Lewis Research Center

DISPERSION

CARqON FILMS

CqCL ?OL

N90-1073_

Unclas

G3/76 023_6B9

Cleveland, Ohio

Robert M. Sieg

Cleveland State University

_:2_- __--: _i_7/_-Cleveland, Ohio

Neil S. Shoemaker

Case Western Reserve University

Cleveland, Ohio

and

John J. Pouch

_Lewis Research Center

Cleveland, Ohio

................ Prepared for the

....... 1989 Spring Meeting of the Materials Research Society

San Diego, California, Apr_ 24,29, 1989

OPTICAL DISPERSION RELATIONS FOR "DIAMONDLIKE" CARBON FILMS

Samuel A. Alterovltz

National Aeronautics and Space Admlnistratlon

Lewis Research Center

Cleveland, Ohio 44135

Robert M. Sieg*

Cleveland State University

Department of Electrical Engineering

Cleveland, Ohlo 44115

Neil S. Shoemaker*

Case Western Reserve Universlty

Physics Department

Cleveland, Ohio 44106

and

John 3. Pouch

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohlo 44135

SUMMARY

Ellipsometrlc 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 temr--perature Cup to 750 °C) anneals The real in) and imaginary (k) parts of

the complex index of refraction N were obtained simultaneously. Following the theory of Forouhi and Bloomer (Phys. Rev. B!4, 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 vaiue of the energy gap Eg obtained

in this 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

using a Tauc plot [I], 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 refractive 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 glve the refractive index

through the Kramers-Kronlg 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 Ill. The onset for this regime varies and values of order

*Undergraduate Student Intern at NASA Lewis Research Center.

l
= 103 cm-I [I] up to

Tauc plots also start to deviate from a straight line at high _ values

[4,5].

Recently, an extension of the theory of optical absorption has been

publlshed for amorphous materials [2]. Later, the theory was extended to

Include more than one critical point, and was applied to crystalline semiconductors [6]. In the Tauc plot derivation [I], the main assumptions are

a constant matrix element and parabolic density of states for both the

valence and the conduction bands. However, if the excited state has a

finite llfetime _, 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

lifetime concept, obtaining.

A(E-E_ 2

k(E) E2 - BE + C

: 104 cm-1 [3] have been used. Empirically, many

(1)

Here A Is k(_) and is proportional to M2/_ where M Is the position

matrix element (M = (flxIi>); B : 2(Ec,crit - Ev,crlt), where Ec,crlt and

Ev crit are energles in the conduction and valence band respectively corresp6nding to a critical point, i.e., where k(Ec,crit - Ev crit) Is a maximum. C Is related to the llfetlme _ through _/_ : (46 - B2) I/2 and

Eg = Ec,bottom - Ev ton, l.e., the optical bandgap. Using the KramersKronig relation, th_ r_fractive Index was obtained [2]"

BoE + Co

n(k) = n(_) + (2)

E2 - BE + C

Here Bo and CO are related to A,B and C through slmple algebralc

formulas, and n(_) is a constant.

In thls paper we will examine if this new result applles to "diamondllke" carbon, also denoted a-C:H (amorphous hydrogenated carbon). If

applicable, the result can glve the n(E) function From a known absorptlon

spectrum k(E) and a single refractlve index measurement. Also, the functlons n(E) and/or k(E) can be used when their analytical form is requlred,

e.g., optimizing antlreflection filters. In addition, this paper will dlscuss the meaning of the experimental constants, A,B, C, and Eg.

Amorphous hydrogenated carbon material Is made almost exclusively in

form of thin films. The natural choice for an experimental technlque is

e111psometry. The multiple angle of incidence, multiple wavelengths (MAW)

technlque [? to 9] was used. MAN gives n and k of the film simultaneously at a11 wavelengths measured, wlthout the use of elther a known

dispersion relation or appllcation 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 determined by

e11_psometry is of order 0.005, correspondlng to m m lO00 cm-I In the visible. Thus, the Urbach edge regime is almost elimlnated from this work.

Reflection elllpsometry has the added benefit of measuring the thin film

samples on any substrate, In contrast to transmission experlments. As the

optical energy bandgap Eg depends on the substrate material [5], possibly

due to differences In conductivity, this advantage of elllpsometry 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 50 to 200 W,

with a constant flow rate of 7xlO -5 m3/mln. Details of the growth chamber

are given in [12]. Several samples cut from the 150 N wafer were annealed

in nitrogen for IO sec using a rapid thermal anneal module [5]. The

rotating analyzer elllpsometer set-up [13] is essentially similar to the

one described in [IO]. At each angle of incidence, data was taken in the

wavelength range 3500 to 7300 A, with lO0 X intervals. Five angles of incidence were used, usually in the range 55° to 75°. Each measurement conslsted of IOO 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 elllpsometric parameters _ 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 acquistlon and analysis. _ and _ were

obtained by Fourier analysis. The MAN inversion process was done by

minimizing experimental _ and 6 (or tan _ and cos 4) versus their calculated values [9]. The model used included only the substrate and a homogeneous film. This is a reasonable approxlmation, as the interface of

a-C:H on $i includes only the native oxide and ~5 A SiC x [15], and our

Films were above I000 A thick.

RESULTS

Seven samples were measured. Simplified and regular Tauc plots were

done for all samples. A representative plot (50 N sample) is glven In

Fig. l, showing a slightly concave result versus the theory. As the annealIng temperature and/or deposition power rlses, the experimental Tauc function first becomes a stralght line and later turns convex. We kept the

extrapolation range to the linear part of the experlmental functlon. A summary of the energy bandgaps obtained from regular and slmplified Tauc plots,

together with sample thlcknesses t, are given in Table I. Results of n(E)

and k(E) for the 50 and 150 N, 600 °C samples are glven In Figs 2 and 3

respectively. Figure 2 shows a rising n versus E whlle Fig. 3 show a

decreasing n(E). All other samples have an Interlm type of behavior. Grid

least square fits to Eq. (1) were done to obtaln A,B,C and Eg simultaneously. With these 4 parameters fixed, the value of n(_) was set to get

the best n(E) fits. The solid lines in Figs. 2 and 3 were calculated using

these parameters. Results for all samples are given in Table If, while Eg

is also displayed in Table I.

3
TABLE I a-C:H OPTICAL ENERGY GAPS IN eV

P, W T,°C t, A Sqrt(_E) Sqrt(_En) Grid

5O

i00

150

2O0

150

150

150

m

w

400

600

750

1490

2305

2810

2960

2560

1320

950

I .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 A B, eV C, (eV)Z Eg, eV n(m)

5O

I00

150

2O0

150

150

150

i

i

m

400

600

750

.06

.01

.05

.II

.06

.40

.85

6.39

6.46

5.90

5.99

5.10

3.66

1.21

12.67

10.51

9.75

11.73

7.20

4.22

1.85

1.64

2.70

2.23

1.65

1.90

1.03

O. 39

1.63

1.70

1.67

1.69

1.70

1.58

I .71

o

c3

C3

C3

0

i_

E

O

2g

d

Q

0

d

a-C:H 50 W 70 sccm

I I'

÷

_- 4- ÷

+.

I I I I I

1.75 2.00

FIGURE I.

LINES SHOW

2.25 2.50 2.75 3.O0

ENERGY [eV]

TAUC PLOT FOR THE 50 W

THE FITTING RANGE.

9.25 3.50 3.75

SAMPLE. VERTICAL
X m

L.LJ

Cq

Z

LLJ

(...3

CZ

OC

Lt_ o

,LJ

OZ _

s-C:H 50 N 70 sccm

L/3

OJ

i

4- ÷ +

4, ÷ 4- 4- ÷

+ ,, BEFRRCTIVE INDEX

t I I I I I

0

l:3

El)

u_ (_3

t"-

0

EZ)

F---

-(57

I----.-I

F-

_ x

R t.J

0

0

0

I. 75 2. O0 2.25 2.50 2.75 3. O0 3.25 3.50 3.75

ENERGY (eV)

FIGURE 2. REFRACTIVE INDEX AND EXTINCTION COEFFICIENT

OF THE 50 M SAMPLE. SOLID LINES ARE DUE TO EQUATIONS

(t) AND (2).

0 O:D _-C:H 1SO N 70 sccm 600°C O{)

Le) 4-

CB N. *÷,, _

(_._)

It _ 4-

LJ.J x - EXTINCTION LL_I

IT- _ F +- REFRRCTIVE INDEX

:::},,

l , t l 1 i 6

2.oo 2.2s 2.5o 2.7s 3.oo 3.2s. 3.so 3.7s

ENERGY (eV)

FIGURE 3, REFRACTIVE INDEX AND EXTINCTION COEFFICIENT

OF THE 150 W, 600"C SAMPLE, SOLID LINES ARE DUE TO

EQUATIONS (1) AND (2),

5
DISCUSSION

Optical energy bandgaps Eg found using the two Tauc procedures are

identical. 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 exponentlal

in the Urbach edge [I]. 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 with prior results [4,5]. The thickness increases with power [16] and decreases with anneaIlng temperature.

The quallty of the fits shown in Figs. 2 and 3 Is quite good. The

n(E) flts are the real test of the theory and the figures show a reasonable

agreement between experiment and calculation. All other n(E) experimental

curves show an equal or better fit to theory, as they include almost constant n(E) values. In addition, the k(E) fit is deflnitely better than

the Tauc fits.

The value of the A,B,C parameters, as shown in Table II, are essentlally constant as function of deposition power, but they change significantly versus annea1_ng,_emperature. The value of the lifetime _/_,

deduced from (4C - BL) _zL, has quite an amount of scatter. However, all

results are around _/_ _ 2 eV. This is a large value, but it is comparable with other amorphous materials [2]. The values of A are In general

lower than for other materlals [2], denoting a smaller position matrix element M In a-C:H. There is an order of magnitude Increase in M with

heatlng to 750 °C. It would be Interesting to correlate thls increase with

the changes In the composition and crystall|vity 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 anneallng temperature. The value of B/2 is characteristlc of the critical point bandgap

[6], denoting a sharp decrease in thls bandgap, in parallel with the sharp

Eg drop. However, we did not see signs of a peak in k(E) at E : B/2, as

expected for a critical point.

CONCLUSION

Dispersion relations suggested in [2] are obeyed, although the n(E)

function does not have a perfect fit. Values of the parameters for the

bandgaps B and Eg show reasonable agreement with Tauc plots and with

prior results. The posltlon matrix element increases with Increasing

anneallng temperature.

REFERENCES

I. N.F. Mort and E.A. Davis, Electronic Processes In Non-Crystalllne

Materials, 2nd ed. (Clarendon Press, Oxford, 1979).

2. A.R. Forouh| and I. Bloomer, Phys. Rev. B, 34, 7018 (1986).

3. J. Robertson, Adv. Phys., 35, 317 (1986).
°

,

S.A. Alterovitz, J.D. Warner, D.C. Liu and J.J. Pouch, J. Electrochem.

Soc., I!3, 2339 (1986).

S.A. Alterovitz, J.O. Pouch and J.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. Forouhi and I. Bloomer, Phys. Rev. B, 3.._88, 1865 (1988).

°

,

o

lO.

II.

12.

13.

14.

15.

16.

S.A. Alterovitz, G.H. Bu-Abbud, J.A. Woollam, and D.C. Liu, J. Appl.

Phys., 54, 1559 (1983).

G.H. Bu-Abbud, S.A. Alterovitz, N.M. Bashara and J.A. Woollam, J. Vac.

Sci. Techno1., A, _, 619 (1983).

G.H. Bu-Abbud, N.M. Bashara, and J.A. Woollam, Thin Solid Fllms, 13.___88,

27 (1986).

P.G. Snyder, M.C. Rost, G.H. Bu-Abbud, J.A. Woollam, and S.A.

Alterovitz, J. App]. Phys., 60, 3293 (1986).

S.A. Alterovitz, J.A. Woollam, and P.G. Snyder, Sol. State Tech., 31

(3), 99 (1988).

J.J. Pouch, J.D. Warner, D.C. Liu and S.A. Alterovltz, Thin Solid

Films, 15__Z,97 (1988).

J.A. Woollam Co., Lincoln, NB.

D.E. Aspnes and A.A. Studna, Appl. Opt., L4, 220 (1975).

R.W. Collins, Appl. Phys. Left., 5._22,2025 (1988).

J.J. Pouch, S.A. Alterovitz, J.D. Namer, 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__77,Pittsburgh,

PA, 1985) pp. 201-204.
National Aeronautics and

Space Administration

Report Documentation Page

1. Report No. i 2. Government Accession No.

NASA TM-102356

4. Title and Subtitle

Optical Dispersion Relations for "Diamondlike" Carbon Films

7. Author(s)

Samuel A. Alterovitz, Robert M. Sieg, Neil S. Shoemaker, and John J. Pouch

9. Performing Organization Name and Address

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

3. Recipient's Catalog No.

5. Report Date

6. Performing Organization Code

8, Performing Organization Report No.

E-4769

10. Work Unit No.

506-44-21

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

t4. Sponsoring Agency Code

15. Supplementary Notes

Prepared for the 1989 Spring Meeting of the Materials Research Society, San Diego, California, April 24-29, 1989.

Samuel Alterovitz and John J. Pouch, NASA Lewis Research Center; Robert M. Sieg, Undergraduate Student

Intern from Cleveland State University, Dept. of Electrical Engineering, Cleveland, Ohio 44115; Neil S. Shoemaker,

Undergraduate Student Intern from Case Western Reserve University, Physics Dept., Cleveland, Ohio 44106.

16. Abstract

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 (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 this

way was compared to the Eg value using conventional Tauc plots and reasonably good agreement was obtained.

17. Key Words (Suggested by Author(s))

Ellipsometry

Diamondlike film

18. Distribution Statement

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Subject Category 76

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