Tunable optical properties of amorphous Tantalalayers in a quantizing structureTHOMAS WILLEMSEN,1,2,* MARCO JUPÉ,2 LAURENT GALLAIS,3 DOMINIC TETZLAFF,4 AND DETLEV RISTAU1,2

1Institute of Quantenoptics Quest, Leibniz Universität, 30167 Hanover, Germany2Laser Zentrum Hannover e.V., Hollerithallee 8, 30419 Hanover, Germany3Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France4Institute of Electronic Materials and Devices, Leibniz Universität, 30167 Hanover, Germany*Corresponding author: t.willemsen@lzh.de

Received 17 August 2017; revised 27 September 2017; accepted 3 October 2017; posted 3 October 2017 (Doc. ID 304631);published 30 October 2017

Plasma deposition techniques like ion-beam-sputtering(IBS) are state of the art to manufacture high quality opticalcomponents for laser applications. Besides the well opti-mized process and monitoring systems, the coating materialselection is integral to achieve optimum optical perfor-mances. Applying the IBS technology, an approach is pre-sented to create novel materials by the direct application ofbinary oxides in a quantizing structure. By reducing thephysical thickness of the high refractive index material toa few nm, within a classical high-low index stack, the elec-tron confinement can be changed. Optical characterizationsof the manufactured samples with decreasing quantum wellthicknesses result in an increasing blue shift of the absorp-tion gap and offer a method to approximate the effectivemass of the high refractive index material in conjunctionwith theoretical models. Laser-induced damage thresholdtests of coating samples prepared with different well thick-nesses indicate an increase of the measured threshold valueswith optical gap energy. © 2017 Optical Society of America

OCIS codes: (310.0310) Thin films; (310.3840) Materials and process

characterization; (310.6860) Thin films, optical properties.

https://doi.org/10.1364/OL.42.004502

During the last years, industrial and fundamental research ap-plications imposed increasing demands on optical coatings tofulfill the new technological challenges of high end lasers. Interms of losses, defect distributions, and laser-induced damagethresholds, plasma deposition techniques like ion-beam-sput-tering (IBS) are well approved to deposit complex optical com-ponents. In combination with the best suited broad bandmonitoring systems and in situ re-optimization tools, challeng-ing designs with the necessary layer accuracy to a few atomicmono layers can be manufactured [1–3]. This accuracy requiresdetailed knowledge of optical and electronic properties of thesputtered material to achieve the best optical performances. Ingeneral, only a limited spectrum of well characterized coatingbinary materials is applied for high quality optics production.

In this context, the ion-beam-co-sputter technique can enablealternative prospects for optical designs [4]. In particular, di-electric ternary composite layers with improved electricaland optical properties can be deposited to increase the laser-in-duced damage threshold (LIDT) of optical components [5,6].In semiconductor materials, a different concept has been suc-cessfully applied. If the thickness (quantum well) of the crys-talline material is small enough, in the range of a few nm, thenthe electronic states are changed [7,8]. This well-establishedprinciple is mainly applied for the fabrication of diode lasers[9]. Amorphous structures lack a microscopic periodic longrange order and have no well-defined band gaps in the solid,in contrast to crystalline materials. However, a defined opticalgap between the ground and excited state imposes a necessarycondition for the creation of a well structure. In a previousstudy of amorphous layer structures, so-called nanolaminateswere investigated, indicating a shift of the optical gap forHafnia embedded in silica [10]. Nevertheless a detailed studyof the samples to exclude a blue shift because of increased silicacontent and a microscopic analysis of the layer structures couldnot be performed.

This Letter reports on the manufacturing and characteriza-tion of dielectric quantized amorphous Tantala nanolaminatesapplying IBS technology. A method is presented to tune theelectronic confinement parameters correlated to theoreticalmodels. The geometric layer structures of the nanolaminatesare analyzed by transmission electron microscopy (TEM), aswell as the influence of different total contents of the highrefractive index material with respect to the change of the op-tical gaps. Resulting LIDT values are measured in a 10,000 to 1procedure at a center wavelength of 800 nm.

The description of the quantization of the introduced di-electric nanolaminates requires consideration of energetic statesof the quasi free electrons in the conduction band, as well as thecorresponding hole in the valence band (compare depictedprinciple in Fig. 1). The reduction of the thickness leads tothe generation of new states for both the electrons and holes,which are related by the quantum well thickness Lwell. The highrefractive index material H with a lower optical gap (quantumwell) changes the carrier confinement, while the low refractive

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0146-9592/17/214502-04 Journal © 2017 Optical Society of America

index material L (barrier) sets up a finite limit of the energylevel. According to the 1D finite potential well model andSchrödinger formalism, boundary conditions lead to transcend-ent equations f 1�z� and f 2�z�. The dimensionless parameter zis directly proportional to the eigenvalues k�e;p�n , the retrievingenergy values E �e;p�

n and the effective mass of the carriers. Theeffective mass for electrons or electron holes in a solid m�

�e;p� isstated in units of the rest mass of an electron, and it is usually inthe range of (0.01–10) me (me—rest mass of the electron invacuum). The energy offset by the confinement is given bythe solutions of the intersection point z of the transcendentequations for the states of electrons and the states for theholes [11]:

f 1�z� � tan�z� and f 2�z� �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiσ2 − z2

z2

r; (1)

with σ � Lwell2ℏ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m�

e;pE0

qand z � Lwell

2ℏ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m�

e;pE�e;p�n

q;

(2)

where z is a dimensionless parameter, E0 defines the energy ofthe finite barrier for the electrons, ℏ is the reduced Planck con-stant, Lwell corresponds to the layer thickness of the quantumwell, n depicts the number of the energy level, the indices �e; p�refer to the electrons and holes, respectively, and m�

�e;p� displaysthe effective mass. The total optical gap is given by the additionof the optical gap of the high refractive index material the en-ergy value of electronic states E �e�

n as well as the energy value ofthe hole states E �p�

n . It has to be mentioned that the effectivemasses are fit parameters in the approach, because the effectivemass is linked to the periodic structure of a crystalline solid. Foramorphous materials, the bands are not clearly defined, and theeffective mass gains an empirical character. In addition, theelectrons tunnel into specific regions of the barriers consideringan exponential decay e−γx with

γ � 2

Lwell�σ − z� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m�

e;p�E0 − E�e;p�n �

ℏ2

s; (3)

whereby x defines the position, and z and σ are the presentedparameters of Eqs. (1) and (2), respectively. The tunneling

into the barriers broadens the quantum well Lwell byLeff � Lwell � 2∕γ.

All presented dielectric nanolaminates are manufactured byapplying an IBS process. Because the process parameters arevery reproducible, layers smaller than 2 nm are produced byvarying the time. Thicker layers are controlled with an opti-mized broadband optical monitoring system (BBM) [1].Samples are characterized applying high resolution spectromet-ric transmittance and reflectance measurements (PerkinElmer—Lambda1050) close to the normal angle of incidence(AOI). On the basis of the obtained absorption coefficientα�ω�, a Tauc approximation is applied to determine the opticalgap. In detail, by plotting the square root of the product of theabsorption coefficient α�ω� and the frequency of light ω versusthe photon energy, the optical gap is defined as the intersectionpoint with the photon energy at an absorption coefficient ofzero [12]. Additionally, the layer structures of nanolaminatesare analyzed by applying TEM (Tecnai G2 F20 TMP).Mass-thickness contrast in brightfield TEM imaging is appliedto analyze the thickness of the layer. For further investigations,the samples are tested with respect to their LIDT according toISO 21254 [13]. Under an AOI of 6°, the samples are irradi-ated at p-polarized laser pulses, characterized by a central wave-length of λz � 775 nm, with a pulse duration of τP � 130 fs,a repetition rate of 1 kHz, and an effective beam diameter ofd beam � 97 μm. The LIDT value at the threshold of 0% isdepicted after the sample is irradiated by 10,000 pulses.

Table 1 summarizes the properties of manufactured nano-laminates. Five different Tantala and silica stacks �LH�nL aremanufactured by varying the layer thickness of the high refrac-tive index material down to 0.5 nm and keeping the thicknessof the low refractive index barriers with 20 nm, as well as thetotal design thickness of the samples with �382� 10� nm con-stant in every sample. The thickness is selected to about 3QWOT at λc � 800 nm to ensure a precise calculation ofthe refractive indices (�1%) by applying Sellmeier formalism.The nanolaminate sequences can be considered as single layers.Coating stacks containing nanolaminate wells that are 8-nmthick causes optical gap values comparable to single high refrac-tive index materials of Tantala of 4.30 eV [14]. A clear changein the optical gap is obvious for manufactured samples withindex quantum wells smaller than 4 nm. For instance, a blueshift of the optical gap up to 123% is observed for 0.5-nmTa2O5 wells with respect to single Ta2O5 films. These shiftsindicate a change in the electron confinement for Tantala layerssmaller than 4 nm (insets in Fig. 2). A maximum change of theindex of refraction Δnref � 0.18 is reached with respect to avarying optical gap.

Fig. 1. Schematic principle of the designed nanolaminates. n definesthe number of layer pairs.

Table 1. Properties of Manufactured Nanolaminatesa

Well[nm] Design

Optical Gap [eV]for H � Ta5O2

Refractive Indexat 800 nm

8 �LH�13L 4.31� 0.05 1.654 �LH�15L 4.35� 0.05 1.572 �LH�16L 4.50� 0.05 1.521 �LH�17L 4.65� 0.05 1.490.5 �LH�18L 5.30� 0.05 1.47

aEach well thickness measurement was performed with Tantala, respectively.Every barrier of L � SiO2 remained constant at 20 nm.

Letter Vol. 42, No. 21 / November 1 2017 / Optics Letters 4503

The increase of the optical gap of the high refractive indexmaterial is calculated by applying Schrödinger formalism[Eq. (1)], depending on the length Lwell of the quantum welland the effective mass of the electrons. In a simplified model,the effective mass is inversely proportional to the optical gap.With respect to the effective electron mass, the effective massof the electron holes is expected to be one order of magnitudehigher and is kept constant in the calculations. The barrier ofSiO2 is set to 7.5 eV [15]. A good correlation between the pre-dicted and determined optical gap values of the manufacturedsamples is reached. The effective electron mass of Tantala canbe approximated in between (0.7–0.9) me (Fig. 2).

In the following, three main conditions are considered tovalidate the electronic quantization in amorphous Ta2O5-SiO2

nanolaminates. First, a blue shift caused by higher silica contenthas to be excluded. The total thickness of the presentedsamples in Table 1 is kept constant, while the content of silicais increased for shorter quantum wells, in correlation withvarying Tantala content. Three additional nanolaminateswith an absolute constant thickness of �33� 1� nm ofTantala are compared (Fig. 3). The barrier layers areselected to reach a constant total physical design thickness

of d phy � �377� 5� nm. The blue shift is similar to a decreas-ing quantum well thickness of Tantala, with respect to the sam-ples presented in Fig. 3.

Second, the electrons tunnel into the barriers approximatingan exponential decay and broaden the wells by Leff according toEq. (3). For the following study, an effective electron mass of0.8me , a well thickness of Lwell � 1 nm, and a barrier limitof E0 � 7.5 eV were assumed. This results in an effective wellof Leff ≈ 1.16 nm. The electron confinement is expected tostay constant by lowering the barriers above the calculated ef-fective well. Four additional samples are compared and charac-terized. The barriers are lowered from 20 nm down to 1 nm,while the wells are kept constant with 1 nm (Table 2). The totaldesign thickness is kept constant for samples with barriers of20, 10, and 5 nm. As a crosscheck, the absolute content of34-nm Ta2O5 is equal for the sample applying 1 nm and10 nm barriers. The optical gap remains constant accordingto the theoretical predictions. The index of refraction couldbe improved by Δnref � 0.3 for decreasing silica content withrespect to the 20 nm and 1 nm barriers. The tunable index ofrefraction in combination with a constant optical gap depicts amajor advantage compared to ternary composites. The compo-sition ratio of the sputtered materials determines both theindex of refraction and the optical gap [14].

The third condition requires a strict amorphous layer struc-ture with steep interfaces. The possible formation of ternarycomposites at the barriers and wells must be prevented. Aclassical high-low stack of Ta2O5 and SiO2 was manufacturedwith various sequences of nanolaminates and then prepared forTEM inspection (Fig. 4). The thicknesses determined by TEMof the Ta2O5 and SiO2 layers was �1.3� 0.5� nm and�20� 0.5� nm, respectively, and matched the designed layerdimensions. A clear Ta2O5 layer structure is visible, indicatingthe good quality of the interfaces.

Fig. 2. Determined optical gap values are correlated to calcula-tions applying different effective masses m�

e as fit parameters.Transmittances of the nanolaminates are shown in the insets.

Fig. 3. Transmittance measurement of different samples with aconstant thickness of Tantala. Silica is used as low refractive indexmaterial. d phy depicts the total physical design thickness.

Fig. 4. Brightfield TEM cross-section image of a dielectric nano-laminate showing the alternating layer structure of Ta2O5 (brightcontrast areas) and SiO2 (dark contrast areas).

Table 2. Variation of Barriers with Constant Wells of1 nm

Barrier[nm] Design

Optical Gap [eV]for H�Ta5O2

Refractive Indexat 800 nm

20 �LH�17L 4.65� 0.05 1.4910 �LH�34L 4.62� 0.05 1.555 �LH�61L 4.60� 0.05 1.581 �LH�34L 4.67� 0.05 1.79

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A promising application can result in the implied changeof the electron confinement in dielectric nanolaminates. Thepower compatibility of optical components can be increasedby substituting high refractive index layers affected by high fieldintensities with a certain stack of nanolaminates, comparable torefractive index steps down (RISED) concept applied for ter-nary composites [16]. In the following, 10,000 LIDT tests forthe nanolaminate samples (Table 1) were performed and com-pared to a single Tantala layer. The LIDT values were de-coupled from the possible different intensity distributions jE j2in the films and normalized to the maximum LIDT value andsummarized as relative LIDT (Fig. 5). A clear increase of thedamage threshold can be observed for shorter well thicknesses,corresponding to higher optical gaps. A similar increase of thethreshold fluence results with respect to ternary composites[6,14,17–19]. In future studies, nanolaminate structures willbe implemented in designs for complex optical components re-quired for ultra-short pulse applications to improve the LIDTin the fs regime. A detailed comparison between ternary com-posites and nanolaminates has to be included with respect tothe evolution of the optical gap and index of refraction as wellas the LIDT. In practical applications, nanolaminates offer thepossibility to tune the optical gap without applying a complexzone target system in the coating machine. Empirical studiesin the fs regime indicate that plenty of interlayers are not influ-encing the LIDT for high quality coating processes [4]. In ternarycomposites, the index of refraction and optical gap are determinedby the selected composition of the sputtered target materials,which depends on the position of the zone target assembly, es-pecially the deposition of complex optics, like chirped mirrors,which require several switches of the zone target. Small posi-tioning errors for ternary composites have huge impacts on thesensitive target parameters of the group delay dispersion.

In conclusion, a novel approach is presented to generateamorphous dielectric materials with adjustable optical

properties required for the precise production of high qualityoptical components. Binary layer structures are created by em-bedding a high refractive index material (quantum well) in amatrix of a low refractive index material (barrier). A quantiza-tion resulting in a new electric and optical confinement couldbe observed by selecting the thickness of the well material to besmaller than 4 nm. In good correlation with theoretical models,the quantized nanolaminates offer a method to determine theeffective electron mass of the quantum well material itself. Theobserved increase of the LIDT of the manufactured Tantalasamples illustrates the high potential of quantized nanolami-nates in high power coatings.

Funding. Deutsche Forschungsgemeinschaft (DFG)(Cluster of Excellence 201 Quest); Volkswagen Foundation(Hymnos (ZN3061)).

Acknowledgment. The authors thank the LNQE forTEM.

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