optical and electrical properties between 0.4 and 12 μm for sn-doped in_2o_3 films by pulsed laser...

Optical and electrical properties between 0.4 and 12 �mfor Sn-doped In2O3 films by pulsed laser deposition and

cathode sputtering

Daniel Dubreuil,1,* Jean-Pierre Ganne,1 Gérard Berginc,2 and Frédéric Terracher2

1Thales Research & Technology, Route Départementale 128, 91767 Palaiseau cedex, France2Thales Optronics SA, rue Guynemer, BP 55, 78283 Guyancourt Cedex, France

*Corresponding author: [email protected]

Received 4 April 2007; accepted 22 May 2007;posted 22 May 2007 (Doc. ID 81850); published 8 August 2007

Optical properties of Sn-doped In2O3 (ITO) have been studied in the optical range of 0.4–12 �m. Adeposition has been made on BK7 glass, magnesium fluoride, sapphire, and zinc sulfide substrates. Thelayers have been characterized by their optical properties, DC electrical sheet resistivity, and Hallmobility. Sheet resistivity lies in the range of 6.8–318 ��sq for thicknesses between 16 and 280 nm. Thebest carrier mobility is obtained on BK7 and sapphire substrates, up to �50 cm2�V s. The material showsgood infrared transparency in the 3–5 �m range on magnesium fluoride and 0.4–4 �m on sapphire, andit is usable for practical applications up to 12 �m on zinc sulfide. Simulations have been carried out foroptical indices and spectra calculations. The Drude model has been used to exploit the results in eitherdirection: from electrical measured data to the simulation of optical spectra and indices, and frommeasured optical spectra to simulated optical indices and electrical parameters (mobility, carrier den-sity). Hall mobility is considered a worthy and convenient material quality criteria for materials aimedat optics. © 2007 Optical Society of America

OCIS codes: 310.6860, 310.6870, 260.3060, 260.3090, 160.6000.

1. Introduction

Sn-doped In2O3 (ITO) films have been widely usedand investigated [1] for their combined optical trans-parency and conductivity. Primary applications arein the visible spectrum [2–8]. Their infrared reflec-tivity and�or absorption makes them also useful forenergy-efficient windows [1]. They can be transpar-ent in the infrared region if not too thick, with appli-cations in forward-looking infrared systems ormissile domes [9]. Nevertheless, particularly for elec-tromagnetic shielding, the layer design is often theresult of a compromise between high transparencyand low sheet resistivity. If good transparency in thevisible spectrum is easy enough to obtain, the opticalproperties in the infrared spectrum can strongly dif-fer between different layers: they can be considered asensitive quality criteria. We will show that the elec-

trical Hall mobility can be a good quality criterion.The idea is that optical absorption is due to freecharge carriers. Hence, for a desired sheet resistivity,the best layer is expected to be the one with fewer freecarriers and higher mobility. The interest for optimi-zation is that the electrical mobility is an intrinsicmaterial quantity, which can be readily obtainedfrom Hall measurements, even if the layer thicknessis unknown. Interpretation of optical measurementsis more difficult: transmission and reflection areneeded, and they combine intrinsic material proper-ties (real and imaginary parts of the refractive index)with layer thickness and substrate contribution. Us-ing the Drude model [10,11], one can quantitativelyrelate optical and electrical properties of conductivelayers. Despite its simplicity, it gives good simula-tions if used in its validity domain. By means of thismodel, consistency between measured values (op-tical and electrical) can be tested and dispersiveoptical indices can be inferred, usable for futuresimulations. Knowledge of the indices of ITO ob-

0003-6935/07/235709-10$15.00/0© 2007 Optical Society of America

10 August 2007 � Vol. 46, No. 23 � APPLIED OPTICS 5709

tained in given conditions is useful because its prop-erties depend on the deposition technique, thickness,etc.

2. Deposition Techniques

A. Pulsed Laser Deposition

We first used pulsed laser deposition (PLD) for afeasibility demonstration. Apart from being availablein our lab, important advantages of this techniqueare its flexibility and its relative ease of use. Forexample, target composition is easily reproduced ondeposition in most operating conditions. It is thusideal for study purposes. Its weakness is that depo-sition is made on a small area �1–3 cm2� without spe-cial arrangements.

The source was a KrF excimer laser �248 nm wave-length, �20 ns pulse duration, 20 mm � 6 mm initialsize). The beam was focused on the 45° tilted target toobtain �1 J�cm2 fluence. On the target, the beamenergy was about 117 mJ�pulse and the spot sizeabout 7.4 mm � 1.6 mm. The target was rotated toavoid successive pulse superposition. The repetitionrate for deposition was 1 Hz. A target preablationwas carried out for 3 min at 5 Hz before deposition.The target-to-substrate distance was 60 mm. Thespot impact on the target was shifted at half depo-sition to improve film uniformity. These conditionsresulted in a 0.05–0.06 nm�pulse deposition rate(measured by a step profilometer or X-ray reflecto-metry).

The heating system consisted of a copper soleheated by an infrared lamp. The substrate wasclamped on a gold foil for better thermal contact. Thetemperature was measured by a thermocouple em-bedded in the sole just under the substrate. Thisparameter is important but its accuracy does notseem to be critical.

The base vacuum was better than 1 � 10�6 mbar.Deposition was made under oxygen atmosphere;the temperature was then decreased for 1 h to cooldown, under the same oxygen pressure as deposi-tion.

B. Magnetron Sputtering

For most applications, the layers must have a largearea. Magnetron sputtering is well fitted for suchpurposes. Its drawback is that it is more difficult tocarry out than laser ablation, due to a greater sensi-tivity of layer properties (composition, electrical) todeposition parameters (power, temperature, oxygenpressure . . .). Examples of ITO deposition by sputter-ing can be found in Refs. [2]–[7]. Magnetron sputteredlayers have been subcontracted to CS Developpe-ments [12]. Their deposition conditions are propri-etary. They made the depositions with, as objectives,the best optical transmission for a given sheet resis-tivity (��sq); we made the optical, electrical measure-ments and simulations. Optimization has been doneby feedback.

3. Substrates

Depending on the optical spectrum to be covered, dif-ferent substrates were used: BK7 Schott optical glassfor 0.4–2 �m, sapphire �Al2O3� for 0.4–5 �m, magne-sium fluoride �MgF2� for 3–6 �m, and zinc sulfide(ZnS) for 2–12 �m. Optical data can be found inRef. [13].

A. BK7 Glass Substrate

BK7 Schott optical glass shows excellent transpar-ency from the visible to near infrared spectrum. Itstransmittance is close to 92% and reflectance 8%along the spectral range 0.4–2 �m. Gap absorptionoccurs under approximately 0.35 �m.

B. MgF2 Substrate

This substrate is usable in the mid-infrared spec-trum, between 2 and 6 �m. It may be found underits trade name “Irtran1.” Absorption peaks, typical ofthis sintered polycrystalline material, are seen at 2.8,5, and 6.7 �m.

C. Sapphire Substrate

Sapphire is a good material, fairly transparent fromthe visible to the mid-infrared. Absorption occursabove 4 �m, noticeably dependent on thickness. Thissubstrate will be used for a “large” area deposition bysputtering.

D. ZnS Substrate

This substrate is usable for the medium to far infra-red spectrum. The material used here is obtained bychemical vapor deposition (CVD). Data can be ob-tained from the website in Ref. [14]. Absorption peaksnear 6 and 11 �m are typical of this kind of material.

4. Pulsed Laser Deposition: Parameter Effect

We do not aim to detail the results of a PLD study; wewill just summarize some general tendencies. Studiescan be found in literature, such as in Refs. [8] and[15].

The following deposition parameters have beentested: target composition, deposition temperature,and oxygen pressure. Three target compositions havebeen used for ITO. These are in weight percentage ofIn2O3:SnO2, [97%:3%], [94%:6%], and [90%:10%]. Forconcision, they will be written 97–3, 94–6, and 90–10. Considering resistivity, mobility, and opticalproperties of deposited films, the 97–3 target compo-sition was close to or slightly better than the 94–6one, and the two of them close to or better than the90–10 one. The best choice was dependent on otherdeposition parameters, substrates, and which qualitycriterion was used. 97–3 has been retained, but thechoice was not straightforward. In2O3 was tried too,starting from the assumption that a lower carrierconcentration may give a higher mobility. As a mat-ter of fact, mobility in these “dirty” semiconductors isnot only governed by the doping ionized impurities,and In2O3 showed poorer properties than ITO withmore difficulties for oxidation control.

5710 APPLIED OPTICS � Vol. 46, No. 23 � 10 August 2007

The optimal deposition temperature is strongly de-pendent on the substrate: on BK7, the best resultswere obtained near 450 °C (thermocouple tempera-ture, kept at �10 °C during deposition), but, on MgF2and ZnS (less stable than BK7), it had to be loweredto 250 °C ��5 °C�.

Concerning oxygen pressure during depositionand cooling down, good ITO films were obtainedbetween 5 � 10�5 and 5 � 10�3 mbar; 5 � 10�4 mbarwas retained. Several In2O3 films showed high re-sistivity after this process. A post heating and cool-ing down under vacuum was found to improve theirquality.

5. Optical and Electrical Results

A. General

Layers are characterized by their thickness t andmaterial properties. Material data are optical ones:complex dielectric permittivity or indices � � �� i�� n � ik�2, and electrical ones: sheet resistivityRsq ��sq� and carrier mobility �. All these data arelinked together.

To explain the methodology and identify the mainsources of uncertainty, one needs to know the rela-tionship between the quantities. The relationshipamong electrical mobility, effective mass, carrier den-sity, resistivity, and sheet resistivity, can be found innumerous textbooks and articles, i.e., see Refs. [11]and [16]–[18]. For the Drude model see Refs. [1],[10], and [11].

Optical measurements were made with nonpolar-ized light, and normal (or near-normal for reflec-tance) incidence. An accuracy of �0.01 (absolute) ontransmittance and reflectance seems reasonable toassume. Sheet resistivity was measured by the four-probe technique, with in-line and�or Van der Pauwgeometries. Accuracy is estimated to be about �5%.Repeatability is better, but the final value is oftendependent on the geometry used (in-line probes orVan der Pauw, which imply a different electricalweight for the center and periphery of the layer, anda different geometrical factor). One possible reasonmay be some thickness nonuniformity.

Hall measurements have been carried out withVan der Pauw geometry, under a 5000 G field inten-sity. Repeatability was about �2%. Hall mobility � isobtained, probably dominated by error on sheet re-sistivity Rsq ��sq�. The volume carrier density ne canalso be calculated if the thickness is known. Accuracyon ne is thus dependent on t uncertainty.

Dielectric permittivity and optical indices arestrongly frequency-dependent, and different modelsmust be used for a large range of photon energy [1,19–21]. The Drude model [1,10,11] can be used when freeelectrons play a significant role in the optical perfor-mance. It relates intrinsic material values such as mo-bility and carrier density to phenomenological onessuch as complex dielectric permittivity and optical in-dices. In this model, the real and imaginary parts ofthe dielectric permittivity are given by

�� N

2

2 � �2, (1)

��

N2

�2 � �2�, (2)

where � is the high frequency dielectric constant,which includes the effect of bound electrons, and N isdefined by

N2 �

neq2

�0meff, (3)

where ne is the volume carrier density, q is the ele-mentary charge, �0 is the permittivity of free space,meff is the effective mass of carriers in the conductionband, � is a damping constant �s�1�, associated withenergy dissipation. The pulsation p associated withthe plasma frequency (at which �� 0) is given by

p2 �

N2

�� 2. (4)

The damping constant � is related to �, the averagetime for carriers between collisions by � � 1��.

After that, we can calculate the high frequency(optical) mobility by

� �q�

meff. (5)

Therefore, the knowledge of �, p, and � (i.e., byoptical fit of a measured spectrum using the Drudeformalism), with meff taken from literature, enablesus to calculate ne and �. Inversely, having ne and �(by DC sheet resistivity and Hall measurements) andtaking meff and �, from literature or other personaldata, enables us to calculate the complex dielectricpermittivity. A difference is usually found betweenthe values obtained from optics and those obtainedfrom DC measurements. Several sources of discrep-ancy can exist: experimental uncertainties on theelectrical and optical data, on thickness, etc. Also tobe mentioned are the approximations of the Drudemodel. Among others, this way does not take intoaccount that � is expected to be different for DC andoptical frequencies. Moreover, the contribution ofbound electrons to permittivity is assumed to befrequency-independent (via �). Moreover, the Drudemodel is made for conductors; it fails if the materialbehavior is too dielectric and, of course, near and atthe band gap (that is, for ITO, under about 0.6 �m).In this case, other models are needed, such as Cauchyor Lorentz [19–21]. Therefore, even if measurementsare presented, we have excluded the Drude calcula-tions for this domain.

Optical simulations can be classified into two sets: (i)“direct simulations,” where the optical constants (n, k)


and thickness are known, and the spectrum is simu-lated; (ii) “inverse simulations,” where a measuredspectrum is known, and the optical constants are cal-culated in order to fit this spectrum. Special care has tobe taken when carrying out measurements aimed atinverse simulations, because the simulation parame-ters are often very sensitive to the measured spectrumused as a target for fitting.

Optical simulations have been carried out usingFilmstar software, in which several dispersive indexfunctions are included (Cauchy, Lorentz, Sellmeier,Drude . . .). These functions can be used for directsimulations (to build a spectrum or calculate a set ofdispersive indices, starting from the material param-eters) or inverse simulations (to fit a measured spec-trum and deduce material parameters). The Drudemodel has been used to exploit the results in theinfrared range, where light absorption by carriers isnoticeable. Calculations of the Drude parametershave been made using two approaches: (i) from DCelectrical measurements, giving “Electrical Drudeparameters,” allowing the calculation of n and k, thenof the spectrum by direct simulation with t knownby another way; and (ii) from inverse simulationfitting of a measured spectrum, giving “OpticalDrude parameters,” and possibly the thickness,which can be included in the fitting parameters.Whatever the approach, the effective mass of theconduction-band electrons is required. For this, weused meff � 0.35me [1].

From the optical Drude parameters (obtained byinverse simulation), one can calculate the carrierdensity ne and the (high frequency) mobility �. Fromthese values, the corresponding resistivity can be cal-culated by

�1

neq�. (6)

If the thickness t is known, by physical measurementor from the optical fit, the sheet resistivity Rsq can bealso calculated. The two approaches are summarizedin Table 1.

Starting from optical measurements (inverse sim-ulation), each of the results �ne, �, �, Rsq) can becompared with its counterpart obtained from electri-cal measurements. Alternatively, starting from DCelectrical measurements (giving ne and �, the thick-

ness supposed to be known by another way), theDrude model enables us to compute �� and �� (equiv-alent to n and k), then to simulate a spectrum andcompare it with the measured one. In this latter case,the high frequency permittivity � is needed, asknown by other means. For such simulations basedon DC electrical measurements, we used � � 3.95from Ref. [1].

B. Visible—Near Infrared Spectrum

An ITO layer has been deposited by PLD onto a 2 mmthick BK7 substrate. Figure 1 shows its measuredtransmittance and reflectance (with calculated ab-sorptance � 1 � T � R). Layer sheet resistivity was6.8 ��sq (DC measurement), thickness was 280 nm��20 nm, step profilometer). Gap absorption occursunder 0.36 �m.

Optical simulation has been carried out on thisspectrum, in order to compute (by inverse simulation)the material properties. A Drude model has thus beenfitted on measured transmittance and reflectance.The thickness was included in the fitting parameters.The only input taken from the literature is meff �0.35me. The result of the fitting is shown in Fig. 2 (see“Drude optic”) compared with the measured spec-trum. The fitting converges on optical Drude param-eters, which are shown in Table 2, under layer ITO 36on BK7 substrate, “optical fit”. The more relevantresults are the ones intrinsic to the material, i.e., �,ne, �, and �.

Measured sheet resistivity and thickness give ma-terial resistivity. DC Hall mobility measured for thislayer is about 50 cm2�V s. After that, carrier densitycan be calculated by Eq. (6). These values are in Table2. This mobility is among the best reported in theliterature, although some higher ones can also beencountered [1,22]. Bellingham et al. [23] calculateda lower limit to the attainable resistivity with noother scattering mechanisms for free electrons thanthose with ionized impurities. For carrier concentra-tions between 1020 and 1021�cm3, we give an upper

Fig. 1. Measured spectral transmittance, reflectance and ab-sorptance for an ITO layer on BK7 substrate. ITO layer: 280 nmthickness, 6.8 ��sq sheet resistivity.

Table 1. Methodology: Direct and Inverse Simulations

DirectSimulation

InverseSimulation

Measured, startingdata

Rsq, � Transmittance,reflectancet ¡ ne

External inputs meff, ε� meff

Calculated data Electrical Drudeparameters

Optical Drudeparameters

Results ofsimulations

Transmittance,reflectance

ε�, ne, �, t�, Rsq

n, k


limit on the electron mobility of 90–100 cm2�V s.Coming back to the present layer in Table 2, thevalues obtained from electrical measurements areclose to the ones obtained using the optical approach.The spectrum has then been simulated using theelectrical Drude parameters. For the electrical Drudecalculations; we introduced � � 3.95 [1]. The resultis plotted in Fig. 2. The agreement is satisfactory,taking into account the different approaches. Thelargest differences are about 5% from the measure-ments, near 1.5 �m.

The effect of optical measurement uncertainty��0.01 absolute on transmittance and reflectance) onoptical fit is far from straightforward and can bestrongly layer dependent. It has been investigated byinverse simulation and its effect can be seen in Table2. Uncertainty brackets are consistent. To make acomparison with publications such as Ref. [1] easier,�h� and �hp have been added (note that, for a givenmeff, they are equivalent to � and ne, respectively).The values, like that for �, are in agreement withthose presented in Ref. [1].

In this way, the optical and electrical Drude param-eters have been used to calculate the optical constantsof the ITO layer. The real part (n) and imaginary part(k) of the refractive index in the 0.6–2 �m range areshown in Fig. 3. The optical constants obtained by theoptical and electrical methods have been plotted, show-ing small differences on the spectrum range. Theplasma wavelength �p (corresponding to the plasmafrequency) has been marked. It roughly gives thewavelength above which reflection becomes large, evenwithout losses. Let us not forget that the lower the ne

and the p, the higher the �p. This is one more reasonfor moderate-doping, high-mobility layers.

C. Visible and Mid-Infrared Spectrum

An ITO layer has been deposited by PLD onto a mag-nesium fluoride substrate. For this optical range, thecompromise between optical transmission and elec-tromagnetic shielding led to a higher sheet resistivity(smaller thickness) for the layer. The spectrum isshown in Fig. 4 (substrate transmission is superim-

Table 2. Data for All ITO Films. Thickness and Electrical Measurements are Presented, as well as Results Issued from Fitting the OpticalMeasurements by the Drude Model (“Optical Drude Parameters”). The Effect of Experimental Uncertainties on Final Values is also Shown, Either

Direct (Thickness and Electrical Measurements) or Indirect (Via Fitting of Measured Optical Spectra by Inverse Simulation)

Layer Nr ITO 36 ITO 47 0118603 ITO 51 MethodSubstrate BK7 MgF2 Sapphire ZnSRange (�m) 0.6–2 3–5 0.6–4 2–12Thickness (nm) 280 � 20a 16 � 1.6b 17.4 � 0.5c 23.3 � 2.3b

252–263d Optical fitRsq (��sq) 6.8 � 0.34 205 � 10 318 � 16 180 � 9 Electric. meas.

7.8 502 252 Optical fit6.6–9.1d 147–100d 162–363d

ε� 3.92 4.4 4.3 Optical fit3.75–4.10d 3.6–5.2d �0.64–16d

ne (1020�cm3) 6.6 � 0.5 4.7 � 0.5 2.2 � 0.1 4.2 � 0.4 Electric. meas.6.9 2.6 4.2 Optical fit

6.5–7.3d 2.1–3.7d 3.9–4.7d

� (cm2�V s) 50 � 2.5 41 � 2 51 � 2.5 36 � 2 Electric. meas.45 27 25 Optical fit41–49d 16–64d 21–32d

� (m� cm) 0.19 0.33 0.55 0.42 Electric. meas.0.20 0.87 0.59 Optical fit

�h� (eV) 0.074 0.12 0.13 Optical fit�hp (eV) 0.83 0.47 0.61 Optical fitp (�m) 1.5 2.6 2.0 Optical fit

aStep profilometer.bEstimated from PLD conditions.cX-ray reflectometry.dOptical fit, measured T, R �0.01.

Fig. 2. Measured and simulated transmittance and reflectancefor the ITO layer shown in Fig. 1. Drude model has been used forfitting and simulations (optical and electrical Drude parametersgiven in Table 2).


posed for comparison). On this MgF2 substrate, wehad to lower the deposition temperature down to250 °C (instead of 450 °C on BK7), presumably be-cause of interface diffusion from this less stable ma-terial.

DC sheet resistivity and Hall mobility have beenmeasured and resulting Drude parameters are givenin Table 2, under ITO 47 on MgF2. Carrier mobility isa bit lower than the one on BK7; this could be due tothe thinness of the layer combined with some resid-ual interface diffusion. The Drude parameters ex-tracted from these DC measurements have been usedto calculate the optical spectrum of this layer, whichis shown in Fig. 4. We took � � 3.95 [1]. For thisdirect simulation, the agreement with the measuredspectrum is good enough to be indicative in futurepredictions. Unfortunately, fitting the spectrum (byinverse simulation) leads to erratic Drude parame-ters. This discrepancy can be due to differences be-tween the substrate used for this layer and thereference one, excessive sensitivity to measurementuncertainties, which possibly added to imperfec-

Fig. 3. (a) Real and (b) imaginary parts of the refractive indexfor the ITO layer on BK7 shown in Fig. 1, calculated by theDrude model (optical an electrical Drude parameters, given inTable 2).

Fig. 4. Measured and simulated transmittance, reflectance andabsorptance for an ITO layer (16 nm thickness, 205 ��sq sheetresistivity) on magnesium fluoride substrate. The electrical Drudeparameters (from DC measurements) have been used for this sim-ulation (given in Table 2). Substrate transmission has been addedfor comparison.

Fig. 5. (a) Real and (b) imaginary parts of the refractive index forthe ITO layer on MgF2 shown in Fig. 4, calculated by the Drudemodel (DC Drude parameters, given in Table 2).


tions of the Drude model. Nevertheless, the op-tical constants calculated from DC measurementscan be a useful indication. They are plotted inFig. 5.

Figure 6 shows the visible to mid-infrared spec-trum for an ITO layer deposited on a small sapphiresubstrate (25.4 mm diameter, 1 mm thickness) bymagnetron sputtering. The layer thickness has beendetermined by X-ray reflectometry at 17.4 � 0.5 nm.By DC measurements, the sheet resistivity is318 ��sq and mobility 51 cm2�V s (good for such alow thickness).

Reflectance and transmittance of this layer havebeen simulated by the two approaches. The opticalDrude fit is very good, but the electrical Drude sim-ulation gives a transmission in the mid-infrared up to5% higher than the measurements.

The optical fitting converges on the data gatheredin Table 2, under layer 0118603 on sapphire. Thehigh frequency permittivity � is somewhat differentfrom the one (3.95) found in Ref. [1], but the uncer-tainty bracket is consistent with this value. More-over, one can notice that it is close to � � 4.45 foundin Ref. [4]. The mobility value is clearly different fromthe one issued from electrical measurements (whichimplies a discrepancy on the subsequent calculatedsheet resistivity). This is consistent with and may bedue to the large uncertainty on mobility calculated byoptical fitting, but it can be justified by the discussionin Subsection 5.A. We often encountered such a dif-ference for ITO layers, with optical mobility lowerthan the electrical (by Hall effect) one. Discrepancyup to a factor of 2 also exists in Table 1 of Ref. [1],between mobility determined by the Hall effect on theone hand, and by optical methods involving theplasma frequency p on the other hand. Such a dif-ference was also reported in Ref. [4] but, in this paper,the optical mobility was higher than the Hall mobil-

ity. One can notice that the optical Drude parametersassociated with this layer are much more sensitive tooptical measurement uncertainties than the previousone �280 nm on BK7 substrate). It can be attributedto its low thickness and low absorption, leading to arelatively small influence of this layer on overall op-tical performances.

Whatever these uncertainties, this layer is a goodexample of a process where the optical quality im-provement has been made by means of the carriermobility. The best layer from the optical point of viewwas also the one with the best Hall mobility. Theoptical measurements alone were not so straightfor-ward to read because the layers had different sheetresistivity values.

The real and imaginary parts of the refractive in-dex of this layer are shown in Fig. 7. Values resultingfrom the optical and electrical methods have beenplotted. For the same reason as explained earlier, anoticeable difference is seen between them. More-over, a minimum in the real index n clearly appearsnear the plasma wavelength. It is associated with the

Fig. 6. Measured and simulated transmittance and reflectancefor an ITO layer on a small sapphire substrate. ITO layer: 17.4 nmthickness, 318 ��sq sheet resistivity. Drude model has been usedfor fitting and simulations (optical and electrical Drude parame-ters given in Table 2). Substrate transmission has been added forcomparison.

Fig. 7. (a) Real and (b) imaginary parts of the refractive indexfor the ITO layer on sapphire shown in Fig. 6, calculated by theDrude model (optical and electrical Drude parameters, given inTable 2).


frequency at which �� goes down through zero, while�� stays � unity. Another point is that the plasmawavelength (thus the minimum of n) is �2.6–3 �m,instead of 1.5–2 �m for the PLD layer on BK7 (Fig.3). This is an illustration of the differences betweenlayers obtained in unlike conditions.

An ITO layer has been deposited by magnetronsputtering on a large sapphire substrate, with a 100mm diameter and a 5 mm thickness. The depositionconditions obviously had to be adapted, aimed at ob-taining a layer similar to the one whose spectrum isseen in Fig. 6. The sheet resistivity of the layer is271 ��sq, the Hall mobility could not be measuredbecause of its large size. Its spectrum is shown in Fig.8. The step ��2%� at 2 �m (also seen on the sapphiresubstrate) is an artifact associated with the switchingfrom one spectrometer to another (a Fourier trans-form infrared spectrometer is used above 2 �m). Itcan be partly attributed to an instrumental malfunc-tion, most probably the 0.3–2 �m spectrophotometer(lacking in precision, perhaps not perfect mechanicalalignment). A second contribution may be somelayer nonuniformity: the transmission above 2 �mwas measured in the center region, whereas the oneunder 2 �m was taken near the periphery because ofthe UV–visible–NIR spectrometer compartment con-figuration. A simulation has been superimposed, us-ing the optical Drude parameters deduced from thelayer in Fig. 6 �318 ��sq on the small substrate). Forthis simulation, the thickness has been increasedfrom 17.4 to 20.4 nm in order to adapt for the lowersheet resistivity. The carrier mobility of this layer isprobably not as good as the previous one because itsmeasured transmission is 2–3% lower than the sim-ulation in the 2.5–4 �m range, but this quality wasobtained on a 100 mm diameter.

D. Medium to Far Infrared Spectrum

An ITO layer has been deposited by PLD onto a ZnSsubstrate. As for the deposition on the MgF2 sub-strate, we had to lower the deposition temperature to250 °C. The measured optical spectra are seen in Fig.9. A Drude model has then been fitted on the mea-sured spectra. To fit this layer, the thickness wasfixed to 23.3 nm estimated from PLD conditions (aconvergence including it in the variable parametersled to aberrant results); it gives the data shown inTable 2 (ITO 51, optical fit), besides the results issuedfrom DC electrical measurements. As usual, the op-tical mobility is lower than the Hall value, and con-sequently the optical sheet resistivity is higher thanthe DC one. The calculated spectra resulting from theoptical fit and DC electrical measurements have beensuperimposed on the measured ones (Fig. 9). The fit isgood. However, (see Table 2) the effect of the opticalmeasurement uncertainty ��0.01 absolute on trans-mittance and reflectance) on � is strong, giving alarge bracket down to a (mathematical) negativevalue. This is an illustration about the difficultysometimes encountered when trying to reach the op-tical parameters by inverse simulation, even withsmall experimental measurement errors. This has tobe kept in mind when trying to explain discrepancies.The positive point is that in this case, when onewants to simulate layers not too far from the originalone, these differences (giving differences on n and k)result only in small variations on simulated spectrafor the same reason. In such cases, choosing the morerealistic or a mean value to calculate indices andspectra may be a good compromise. The other data�ne, �� are consistent.

The real and imaginary parts of the refractive in-dex calculated by the Drude model are shown in Fig.10. Both sets of indices are plotted, the parametersbased on DC electrical measurements and optical fit.Computing of electrical parameters has been donewith � � 3.95 (from Ref. [1]).

Fig. 8. Measured transmittance, reflectance, and absorptancefor an ITO layer on a 100 mm diameter, 5 mm thickness sapphiresubstrate. Drude model has been used for transmittance andreflectance simulations, by taking the optical Drude parametersof the layer shown in Fig. 6, but 20.4 nm thickness, 271 ��sqsheet resistivity. Substrate transmission has been added for com-parison.

Fig. 9. Measured and simulated spectra for an ITO layer on zincsulfide substrate. ITO layer: 23.3 nm thickness, 180 ��sq sheetresistivity. The optical and electrical Drude parameters have beenused for simulation (given in Table 2). Substrate transmission hasbeen added for comparison.


6. Conclusion

Optical and electrical properties of ITO layers on dif-ferent substrates have been presented. Overall opti-cal range covers 0.4–12 �m. Layer thickness variesfrom 16 to 280 nm, sheet resistivity from 6.8 to318 ��sq. Hall electron mobility has been considereda worthy criterion for improving material transpar-ency in the infrared range. The best mobility valuesare measured on BK7 and sapphire substrates, at50–51 cm2�V s. They are lower on magnesium fluo-ride and zinc sulfide; nevertheless the search for thebest mobility on these substrates resulted in a mate-rial suitable for practical applications in the mediumand far infrared. Good transparency was obtained inthe 3–5 �m range for 205 ��sq on MgF2, 0.4–4 �mfor 271 ��sq on sapphire, and the material is stillusable up to 12 �m for 180 ��sq on ZnS. Optical andelectrical properties, each measured and simulated,have been related by the Drude model. Despite itslimits and simplicity, this model leads to good simu-lations for optical spectra and allows easy calculationof optical indices; however, differences between opti-cal and electrical-issued parameters have been en-

countered in all cases. Although such differences arealso encountered in literature and can be justified bytheoretical considerations, uncertainties have to bekept in mind particularly when inverse simulationsare done to determine electrical or optical data fromoptical measurements. The dielectric constant � istypically found between 3.92 and 4.4. Indices calcu-lated from the Drude model can be a good start forfuture simulations involving a similar material.

The authors acknowledge the excellent collabora-tion with Sabatino Cohen and Daniel Cohen from CSDeveloppements Company, as well as their remark-able flexibility and reactivity. Olivier Durand, fromThales Research and Technology, carried out thick-ness measurements by X-ray reflectometry. We alsoexpress thanks to Guy Garry who has introducedlaser deposition in Thales Research.

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optical and electrical properties between 0.4 and 12 μm for sn-doped in_2o_3 films by pulsed laser...

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