The interband absorption spectra of sputterdeposited boron nitride analyzed using thecoherent potential approximationCarolyn Rubin Aita Citation: Journal of Applied Physics 66, 3750 (1989); doi: 10.1063/1.344061 View online: http://dx.doi.org/10.1063/1.344061 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/66/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Sputter deposition of boron nitride using neon–nitrogen discharges J. Vac. Sci. Technol. A 15, 93 (1997); 10.1116/1.580512 Nearultraviolet optical absorption in sputterdeposited cubic yttria J. Appl. Phys. 68, 2945 (1990); 10.1063/1.346428 Erratum: ‘‘The interband absorption spectra of sputterdeposited boron nitride analyzed using the coherentpotential approximation’’ [J. Appl. Phys. 6 6, 3750 (1989)] J. Appl. Phys. 67, 3906 (1990); 10.1063/1.346114 Optical behavior near the fundamental absorption edge of sputterdeposited microcrystalline aluminum nitride J. Appl. Phys. 66, 4360 (1989); 10.1063/1.343986 Radio frequency sputter deposited boron nitride films J. Vac. Sci. Technol. A 2, 322 (1984); 10.1116/1.572592

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The interband absorption spectra of sputter~deposited boron nitride analyzed using the coherent potential approximation

Carolyn Rubin Alta Materials Department and the Laboratory for Surface Studies, University of Wisconsin-Milwaukee, p. 0. Box 784, Milwaukee, Wisconsin 53201

(Received 13 March 1989; accepted for publication 26 June 1989)

The visible-near-ultraviolet optical absorption spectra for a family of sputter-deposited boron nitride films are reported here. The spectra of films that are nominally stoichiometric (BIN = 1.2-1.3 ± 20%) with short-range order equivalent to hexagonal BN were analyzed using the coherent potential approximation with Gaussian site disorder in the bands, as formulated by Abe and Toyozawa. The relative amount cfinterlayer B-N bond randomness determined from optical measurements is consistent with infrared spectrometry results.

I. BACKGROUND

Boron nitride, being a poor absorber of soft x-ray and visible radiation, is used as a mask membrane material for x­ray lithography. 1-5 Chemical vapor deposition is currently used to produce a hydrogenated form of boron nitride for this purpose. There are two serious consequences ofR in the film that affect its performance as a membrane: (1) a high mechanical stress in the as-deposited material, and (2) deg­radation in transparency and stress after irradiation, caused by changes in H-bonded species. Reactive sputter deposition is an attractive alternative for forming low H content, low stress BN films.

There are few reports of BN grown by sputter depo­sition,6--9 and only two of these studies6

,7 are concerned with optical behavior. The optical absorption coefficient in the vicinity of the fundamental absorption edge has yet to be reported. Here, we investigate the visible-near-ultraviolet absorption behavior of a family of BN films. These films have different BIN atomic concentrations and amounts of bond disorder, and no detectable B-H or N--H bonding.-\ The goal is to understand the differences in optical behavior in terms of what we have already determined by infrared spectroscopy to be differences in B-N bonding in the films.

II. EXPERIMENT

The films were deposited on (OOOO-cut a-A120 3 by sputtering a 13-cm-diam IC grade BN tltrget in Ar dis­charges containing 0%-50% N 2 operated at 300-W rf power and 7 X 10-3 Torr total pressure. Reference 7 gives details of the deposition process, as well as the results of film charac­terization, including chemical analysis and infrared absorp­tion behavior. Data relevant to the present study are record­ed in Table I. No long range order was detected by double-angle x-ray diffraction. The films are identified as having the short range order of hexagonal BN on the basis of the infrared B-N stretch (vs ) and the B-~N-B bend fre­quencies (Vb), associated with transverse optical photons E lu and A 2u' respectively.

Hexagonal BN has a layered structure il•t3 with strong

intralayer and weak interlayer bonds. Two extremes in layer stacking are (1) alignment of alternating Band N atoms

along the (0001> direction, as in pyrolytic BN shown in Fig. 1, and (2) random stacking, as in turbostratic BN.14 Atomic displacements associated with infrared-active normal modes are shown in Fig. 2.

In the experiment carried out here, a Perkin-Elmer Model 330 UV-visible-IR double-beam spectrophotometer was used to measure the transmittance T and reflectance R of near-nonnal incidence radiation of energy hv by the film at room temperature in laboratory air. In reflection mode, the spectrometer was calibrated using an Al mirror as stan­dard. The spectrophotometer was used in double-beam mode with a bare substrate in the reference beam to obtain transmission data through the film alone. For a film ofthick­ness x, the absorption coefficient a is related to T and R as follows 15:

T= [(1_R)2CXp( -ax)]I[1-R 2 cxp( -2ax)].

(l)

Figure 3 shows a as a function of hv. For each of the films, it can be seen from Fig. 3 that a varies slowly with hv at higher energy and exponentially with hv at lower energy. This behavior is typical of a disordered semiconductor.

III. DISCUSSION

In the following discussion, a theory for the optical be­havior of a disordered semiconductor formulated by Abe and Toyozawa 16, 17 is applied to the curves presented in Fig. 3. We will then show that the relative structural disorder,

TABLE 1. Chemical and infrared optical parameters ofsputtcr-deposited boron nitride.

Gas v, 'Vs

Film % N2 BIN" Appearance (cm- ')b (em ' )C

A 0 5.l brown 1355 782 B 10 1.3 yellow 1380 810 C 50 1.2 clear 1280 810

• Measured using wavelength dispersive spectroscopy, ± 20%. b In.(OOOl) plane B-N bond stretch, see Fig. 2. C Fun width at one half-peak maximum. d Out-of-(OOOl) plane B-N--B bond bend, see Fig. 2.

Av, (em-I)"

208 167 130

3750 J_ Appl. Phys_ 66 {S). 15 October 1989 0021-8979/89/203750-03$02.40 @ 1989 American Institute of PhySiCS 3750 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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(A)

Co

(B)

FIG.!. (a) The unit cell of hexagonal BN showing stacking of the B,N" hexagonsrclative to the crystal axes. (b) A projection of the (0001) crystal plane showing a B,N, hexagon relative to the lattice parameter a".

which can be quantified in films Band C using this analysis, is comparable to the relative structural disorder obtained from the half-width of the infrared-active B-N stretch vibra­tion peak. We will also discuss why bond disorder in film A cannot be quantitatively compared to that of the other films.

In brief, Abe and Toyozawa used the coherent potential approximate assumption 18 of statistical independence of wave functions describing electron behavior in the valence and conduction bands of a disordered semiconductor. The coherent potential approximation is an alternative to the random phase approximation 19 used by Tauc and widely ap­plied in the literature to amorphous materials. Within the framework of the coherent potentiai approximation, Abe and Toyozawa introduced a Gaussian distribution for site energy in the valence and conduction bands, where deviation from the mean site energy is an additive function of struc­tural and thermal disorder. 17

FIG. 2. The atomic displacements associated with two infrared-active nor· mal modcs in hexagonal BN. The optical phonons 1'1", u and A 2" are associat· ed with the in-layer B-N stretch and the out-of-layer B-N-B bend, respec­tively.

3751 J. Appl. Phys., Vol. 66, No.8, 15 October i 989

I FIL:1 GAS ZN2

0 A Q

• B 10

0 50

105

"' , 0 ?"5

104

w3 ~! ____ -L ____ -L ____ -L ____ ~ ____ ~ ____ ~

1

?ClDTON ENERGY (EV)

FIG. 3. The absorption coefficient as a function of in ciden I photon energy for three boron nitride films. The heavy lines represent Eq. (3). The light lines are the best fit through the data in the region in whkh Eq. (3) does not apply.

Three interrelated energy parameters are defined: (1) the energy band gap of the virtual crystal Eg , (2) the energy band gap of the disordered crystal Ex, and (3) the inverse slope of the exponential region Eo. where

(2)

T is the absolute temperature, and W is a measure of the structural disorder. The quantity Eo is proportional to W 2

/

B, where B is the half-width ofthe energy band under consi­deration,

The absorption coefficient due to band-to-tail (or tail­to-band) transitions, when hv is removed from Eg , is given by

(3)

where a Ex is the value of aRT at hv = Eg , The coordinates (Eg , a Eg ) define the point offocus, where curves with differ­ent values of Eo (the same band half-width but different val­ues of W) cross. 17 The absorption coefficient due to band-to­band transitions, when hvis near to but less than Eg , is given by

a Bs c:(hv-E,,)2. (4)

The Abe and Towozaya model is appealing because it integrates absorption behavior in the exponential and slowly varying regions. Its starting premise is that all real crystals are disordered, the amorphous state being one possible con­dition. Furthermore, although there are restrictions on the type of structural disorder to which the theory can be mean­ingfully applied, it is applicable to bond length disorder, 16.18

which is shown below to prevail in films Band C. With respect to boron nitride, the heavy lines in Fig. 3

are obtained by applying Eq. (3) to the data. The intersec­tion of the lines representing Eq. (3) for films Band C yields

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the values E = 6.88 eVandaE , = 7.S >< 105 em-I. For these two films, Eq. (2) can be rewritten as

a BT = (7.5X 105 cm-I)exp[ (hv - 6.88 eV)IEo]' (5)

Eo, measured from the inverse slope of a BT vs hv, is equal to 0.68 eV for film Band 0.47 eV for film C.

The region over which Eq. (4) holds is shown as light lines in Fig. 3. Ex for films Band C, calculated by extrapola­tion of (aBD ) 1/2 vs hv to a = 0, yields a value of 3.08 eV for film Band 4.10 eV for film C.

The assumption made in the above analysis is that the band width in films Band C is the same, and that changes in Ex and Eo are caused by a wider statistical distribution around the equilibrium intralayer B-N length in film B than in film C. This assumption is supported by the infrared spec­troscopy data presented in Table 1. Both the average stretch­ing and bending frequencies are identical in films Band C, and identical to that for pyrolytic BN, 10-12 indicating identi­cal average intralayer B-N bond strength and hence equi­librium bond length. However, llV, is greater in film B than in film C, indicating a greater statistical distribution about the average intralayer B--N bond length. Furthermore, since Eo ex: W 2 for films Band C (which have the same band­width), then [Eo(film B)/E(film C)] 1/2 is equal to [Avs (film B)/ Avs (film C) j. Substitution of the appropri~ ate values yields 1.20= 1.28. Optical and infrared data have therefore consistently shown that the relative disorder due to an intralayer B-N bond length distribution about an equi­librium length is 1.2-1.3 times greater in film B than in film C.

Equation (2) relatesEg , Ex, and Eo for each value of W, at a fixed bandwidth. If the above application of the Abe and Toyazawa theory is correct, then substitution of the values for the energy parameters into Eq. (2) should yield the same constant A for both films Band C. Carrying out the substitu­tion, A (film BY = 5.6 = A(film C) = 5.9. We can now write Eq. (2) applicable to films Band C (and all other hexagonal BN with the bandwidth of stoichiometric BN and in which structural disorder is manifest by bond length ran­domness) as follows:

Ex (w,n = 6.88 eV - 6EoC W,T). (6)

The BIN atomic concentration in film Band C is within experimental error of stoichiometric BN. The above analysis shows that the optical behavior of these films fits well to a model for a single-phase semiconductor where disorder is manifest by increased intralayer B-N bond length (or bond

3752 J. Appl. Phys., Vol. 66, No.8, 15 October 1989

strength) randomness, the mean value being characteristic of ordered stoichiometric BN. Physically, Eg is the zero­disorder limit (W,T= 0) of Ex, the optical band gap, and the constantA according to Cody17 "reflects conservation of states under the effect of disorder." Film A has a BIN atom­ic concentration of five times that of films Band C, and decreased Vs and Vb' indicating decreased mean bond strength, compared to films Band C. It is not expected that the optical absorption data shown in Fig. 3 for film A would

fit into the scheme developed for films Band C. Although Ex and Eo can be determined, both Eg and A are unknown for film A.

ACKNOWLEDGMENT

This work was supported by a gift from Johnson Con­trols, Inc. to the Wisconsin Distinguished Professorship pro­gram.

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