Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenatedamorphous silicon carbide between 300 and 500 K at 1.55 μmFrancesco G. Della Corte, Maurizio Esposito Montefusco, Luigi Moretti, Ivo Rendina, and Alfredo Rubino Citation: Applied Physics Letters 79, 168 (2001); doi: 10.1063/1.1383056 View online: http://dx.doi.org/10.1063/1.1383056 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/79/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Light switching via thermo-optic effect of micromachined silicon prism Appl. Phys. Lett. 88, 243501 (2006); 10.1063/1.2212278 6-H single-crystal silicon carbide thermo-optic coefficient measurements for ultrahigh temperatures up to 1273 Kin the telecommunications infrared band J. Appl. Phys. 98, 103512 (2005); 10.1063/1.2133897 The thermo-optic effect of Si nanocrystals in silicon-rich silicon oxidethin films Appl. Phys. Lett. 85, 2526 (2004); 10.1063/1.1798395 Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 Kat the wavelength of 1.5 μm Appl. Phys. Lett. 77, 1614 (2000); 10.1063/1.1308529 Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550K at the wavelength of 1523 nm Appl. Phys. Lett. 74, 3338 (1999); 10.1063/1.123337

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Study of the thermo-optic effect in hydrogenated amorphous siliconand hydrogenated amorphous silicon carbide between 300 and 500 Kat 1.55 mm

Francesco G. Della Corte, Maurizio Esposito Montefusco, Luigi Moretti,a)

and Ivo RendinaInstitute of Research for Electromagnetics and Electronic Components, National Research Council(IRECE–CNR), Via Diocleziano 328, 80124 Naples, Italy

Alfredo RubinoEnte per le Nuove Tecnologie, l’Energia e l’Ambiente (ENEA–CP), LocalitaGranatello,80055 Portici-Naples, Italy

~Received 16 April 2001; accepted for publication 10 May 2001!

The thermo-optic coefficients of hydrogenated amorphous silicon (a-Si:H) and hydrogenatedamorphous silicon carbide (a-SiC:H!—two of the main amorphous semiconductors inoptoelectronics—have been measured and critically analyzed in the practical device operationtemperature range 300–500 K, at the communication wavelength of 1.55mm. The experimentaldata have been fitted using a single-oscillator model that takes into account the shape of thee2

spectrum of the amorphous materials. In particular, fora-Si:H, the extracted parameterssignificantly extend, and are consistent with, the few data reported in the literature; an interestinganalogy with crystalline silicon is also found and discussed. Complete results fora-SiC:H arefinally reported. ©2001 American Institute of Physics.@DOI: 10.1063/1.1383056#

The design of optoelectronic devices requires the preciseknowledge and characterization of the material optical pa-rameters. In particular, the temperature dependence of therefractive indexn @viz., the thermo-optic effect~TOE!# is ofconsiderable interest in semiconductors because it can deter-mine the misfunctioning of passive and active devices, suchas distributed feedback lasers, optical couplers, interferom-eters, and waveguides. On the other hand, the TOE is widelyexploited for switching, routing, and wavelength tuning pur-poses. The parameter measuring the strength of this effect isthe thermo-optic coefficientdn/dT, whose wavelength de-pendence has been widely studied in many photonic semi-conductors, but in limited temperature ranges around roomtemperature.1–3 Therefore, a substantial lack of data has to beregistered for temperature excursions of hundreds of degreesCelsius, often occurring in the lifetime of thermo-optic de-vices or in optical components for harsh environments. Stud-ies on the TOE and its temperature dependence are at aneven more preliminary stage in amorphous semiconductors.For instance, hydrogenated amorphous silicon (a-Si:H) andhydrogenated amorphous silicon carbide (a-SiC:H), bothshowing interesting features making them attractive for pho-tonics, have been never characterized thermo-optically, withthe exception of a few data at room temperature reported fora-Si:H.4,5 In an attempt to gain more insight into the analysisof this phenomenon, in this letter, we report a complete char-acterization of the thermo-optic coefficient ofa-Si:H anda-SiC:H in the temperature range 300–500 K, at the impor-tant fiber-optic communication wavelength of 1.55mm.

Moreover, a generalizable interpretation of the measureddata in terms of a single-oscillator model is presented.

The extraction ofdn/dT from refractive index standardmeasurements is usually limited by the weakness of theTOE, and usually requires extremely high accuracy duringexperiments. For this reason, a simple and direct measure-ment technique of the thermo-optic coefficient was proposedin a previous work.6 It is based on the multiple-beam inter-ference principle that arises in a Fabry–Pe´rot cavity interro-gated by a monochromatic light beam. The intensity of theradiation transmitted~or reflected! by the cavity shows a pe-riodic fringe pattern when measured as a function of thesample temperature. The temperature difference between twosubsequent transmission~or reflection! fringe maxima orminima allows the direct determination ofdn/dT.

The measures have been carried out in Fabry–Pe´rot in-terferometers with a thin-film planar waveguiding configura-tion ~see Fig. 1!. Each planar waveguide is formed on ahighly doped crystalline silicon (c-Si) substrate, on which a200-nm-thick undercladding layer of ZnO~nZnO'2! was de-posited by sputtering from a ZnO target in an Ar-plasmaatmosphere. The deposition was performed at room tempera-ture in a rf~13.56 MHz! reactor at a power of 150 W, and atthe pressure of 6 mTorr. The waveguiding layers~i.e.,a-Si:Hor a-SiC:H, respec-

a!Author to whom correspondence should be addressed; electronic mail:moretti@irece.na.cnr.it FIG. 1. Schematics of the planar waveguides ina-Si:H ~a! anda-SiC:H ~b!.

APPLIED PHYSICS LETTERS VOLUME 79, NUMBER 2 9 JULY 2001

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tively! were then deposited by plasma-enhanced chemical-vapor deposition. In particular,a-Si:H 5-mm-thick filmsamples were obtained by loading the substrate ZnO stackinto a different reactor, and then flowing 20 sccm of SiH4 , ata substrate temperature of 180 °C, a pressure of 0.8 mbar,and a 13.56 MHz rf power of 4 W. Thea-SiC:H 2.75-mm-thick film samples were deposited in analogous conditions,except for the substrate temperature~170 °C! and the processgas, a SiH4/CH4 50% mixture with a total flow of about 80sccm. The waveguiding cavity samples were obtained bycleavage of the crystalline silicon substrate wafer. With thisoperation, the two mirrors of each cavity were also defined,with no further smoothing or polishing treatments.

The experimental setup used for the measurements issimilar to that described in Ref. 7. However, the presentwaveguiding configuration of the samples has suggested theuse of a single-mode fiber to butt couple the probing radia-tion to the amorphous films under test. The fiber was, in turn,connected to a distributed-feedback laser-diode emitting at1.55 mm. A multimode fiber was butt coupled at the wave-guide output to collect and send the transmitted beam to anInGaAs photodiode.

The measureddn/dT versus temperature fora-Si:H anda-SiC:H are reported in Figs. 2 and 3, respectively. The ex-perimental uncertainties on the data are 631026 K21 fora-Si:H and 1026 K21 for a-SiC:H. In the given tempera-ture range, the second-order-polynomial interpolation returnsthe following relations, which are useful for design purposes:

dn

dT527.363102511.43310263T21.44310293T2

for a-Si:H, ~1!

dn

dT522.033102514.65310273T23.053102103T2

for a-SiC:H. ~2!

In a previous work on crystalline silicon,8 the experi-mental data on the thermo-optic coefficient have been ana-lyzed using both single- and double-oscillator models. Infact, we demonstrated that the latter is more meaningful from

a physical point of view, being thee2 spectrum ofc-Si char-acterized by two peaks, while the single-oscillator approxi-mation is more convenient to look at the average behavior ofthe crystal band gap.

In the present case, the temperature dependence ofdn/dT for amorphous semiconductors has been analyzedonly by a single-oscillator approximation because of thesingle resonance peak in thee2 near-infrared spectrum ofthese materials.9 Approximating this spectrum with a deltafunction centered at the energyEg where the absorption hasa maximum, the Kramers–Kronig relations give the follow-ing expression for the refractive index at the photon energyE in the transparency region:

n2511Ep

2

~Eg22E2!

, ~3!

where

Ep5A4pN\2e2/m, ~4!

is the electronic plasma energy,N is the number of oscilla-tors per unit volume, ande andm are the electron charge andmass. From Eq.~4! we have8

dEp2

dT523kEp

2, ~5!

wherek is the material thermal expansion coefficient. FromEqs.~3! and ~5! we obtain the thermo-optic coefficient

dn

dT5

n221

2n F23k22

Eg

dEg

dT

1

12~E/Eg!2G , ~6!

with n and k both depending on the temperature. For thetemperature dependence ofEg the following Varshnirelation10 can be exploited:11

Eg~T!5Eg~0!2aT2

~T1b!, ~7!

wherea andb are dimensional parameters characterizing thematerial. For the thermal expansion we have adopted theexpression given in Ref. 12 for crystalline silicon:

FIG. 2. Experimental data showing the thermo-optic coefficient vs tempera-ture in hydrogenated amorphous silicon (a-Si:H). The best-fit curve ob-tained in single-oscillator approximation is reported as a solid line.

FIG. 3. Experimental data showing the thermo-optic coefficient vs tempera-ture in hydrogenated amorphous silicon carbide (a-SiC:H). The best-fitcurve obtained in single-oscillator approximation is reported as a solid line.

169Appl. Phys. Lett., Vol. 79, No. 2, 9 July 2001 Della Corte et al.

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k~T!53.72531026$12exp@25.8831023~T2124!#%

15.548310210T. ~8!

As a matter of fact, the expansion of the thin waveguidingamorphous layer samples is determined by that one of the500-mm-thick c-Si substrates.

The fitting procedure involves the four floating param-etersEg(0), Ep , a, andb. In particular, the parameterEp isvaried in the range found in Ref. 13, i.e., between 10.9 and13 eV. Moreover, we assume that its temperature dependenceis negligible in the explored temperature range.8 No limitsare set for the other parameters.

Table I summarizes the parameter values resulting fromthe fitting procedure with the corresponding uncertainties. Inspite of the well-known dependence of thea-Si:H opticalproperties on the deposition process parameters, the resultsare in fair agreement with those reported in the literature. Inparticular, the value ofEg at room temperature~3.2660.20eV! is consistent with those reported in Ref. 9~i.e., 3.7 eV!and in Ref. 13~i.e., 3.3–3.6 eV for various growth condi-tions!. Also, the estimated values ofa and b are consistentwith the values reported in Ref. 11~4.9431024 eV K21 and669.7 K, respectively! for the temperature dependence of theTauc gap. Finally, it is worthwhile noting that the fittingresults carried out for amorphous silicon are similar to thosereported in Ref. 8 for crystalline silicon in the single-oscillator approximation. This behavior seems to confirmthat, to a first approximation, certain optical properties ofcrystalline materials, averaged over the conduction and va-lence bands, are closely related to similar averaged proper-ties of the corresponding amorphous materials. This certainlyholds for Eg and Ep , which depend more on the materialdensity and chemistry than on lattice symmetry issues.14

The fitting curves are also reported in Figs. 2 and 3. Thethermo-optic coefficient ofa-Si:H at room temperature isestimated to be 2.331024 K21. This value is consistentwith those carried out in a previous work,4 and is about 20%higher than that of crystalline silicon.6–8 Anyway, the tem-

perature dependences of the thermo-optic coefficients in theamorphous and in the crystalline silicon are strictly related.

The estimated thermo-optic coefficient ofa-SiC:H atroom temperature is 9.231025 K21, and is, therefore,much higher than that of the crystalline silicon carbide,which is 2.7731025 K21.15 The TOE variation with thetemperature is also different for amorphous and crystallinesilicon carbide, being in the temperature range 300–500 K,of about 35% and 100%,15 respectively.

In conclusion, we have adopted a simple technique tomeasure the thermo-optic coefficient ofa-Si:H anda-SiC:Hin the temperature range between 300 and 500 K, at thefiber-optic communication wavelength of 1.55mm. A single-oscillator approximation was used to model the temperature-dependence effects. The results obtained fora-Si:H are con-sistent with the few ones reported to date in the literature. Astrict analogy has also been found with the previously re-ported values of the electronic plasma energy and of theaveraged band gap of crystalline silicon. Finally, the originaldata reported fora-SiC:H on the thermo-optic coefficientand on its temperature dependence have shown significantdifferences with respect to the corresponding values in amor-phous silicon and in crystalline SiC.

This work was supported by the CNR-PF MADESS II-Sensor and Microsystem Project, and by Regione Campania~Italy!, FESR-POP 94-99, Misura 5.4.2.

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TABLE I. Parameters involved in the fitting procedure. The uncertainitesare given in parentheses.

Material Ep ~eV! Eg(0) ~eV! a(1024 eV K21) b ~K!

a-Si:H 12.3~1.9! 3.3~0.2! 3.4~0.5! 538~182!a-SiC:H 21.6~0.8! 7.2~0.2! 7.1~0.2! 546~46!c-Si ~Ref. 8! 13.31 4.03~0.02! 3.41~0.03! 439~13!

170 Appl. Phys. Lett., Vol. 79, No. 2, 9 July 2001 Della Corte et al.

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