Comparative study of SiO2, Si3N4 and TiO2 thin ... - OSA Publishing

Vol. 24, No. 21 | 17 Oct 2016 | OPTICS EXPRESS 24032

Comparative study of SiO2, Si3N4 and TiO2 thin films as passivation layers for quantum cascade lasers S IMON F ERRÉ , 1,2,3,* A LBA P EINADO, 4 E NRIC G ARCIA -C AUREL , 4 VIRGINIE TRINITÉ ,5 MATHIEU CARRAS, 2 AND ROBSON FERREIRA 3 Research & Technology, Route Départementale 128, 91767 Palaiseau, France Centre d’intégration NanoINNOV, 8 avenue de la Vauve, F-91120 Palaiseau, France 3 Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France 4 LPICM, CNRS, Ecole Polytechnique, Université Paris-Saclay, 91128 Palaiseau, France 5 III-V Lab, 1 Avenue Augustin Fresnel, 91767 Palaiseau, France 1 Thales

2 MirSense,

* [email protected]

Abstract: The aim of this article is to determine the best dielectric between SiO2, S i 3N4 and TiO2 for quantum cascade laser (QCL) passivation layers depending on the operation wavelength. It relies on both Mueller ellipsometry measurement to accurately determine the optical constants (the refractive index n and the extinction coefficient k) of the three dielectrics, and optical simulations to determine the mode overlap with the dielectric and furthermore the modal losses in the passivation layer. The impact of dielectric thermal conductivities are taken into account and shown to be not critical on the laser performances. c 2016 Optical Society of America OCIS codes: (140.5965) Semiconductor lasers, quantum cascade; (120.2130) Ellipsometry and polarimetry;(160.2750) Glass and other amorphous materials.

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#272647 Journal © 2016

http://dx.doi.org/10.1364/OE.24.024032 Received 29 Jul 2016; revised 29 Sep 2016; accepted 29 Sep 2016; published 7 Oct 2016


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1.

Introduction

Quantum Cascade Lasers (QCLs) have been one of the flagships of mid-infrared sources in the past ten years. In fact, they have shown to be reliable [1, 2], easily integrable [3] and powerful devices [4, 5] from 4 µm to 9 µm. Wavelength limitations are relentlessly pushed to a broader range either on the shorter wavelengths side, down to 2.6 µm [6] or towards the far infrared (FIR) range [7–9], up to 26 µm, and even up to the terahertz [10, 11]. Whether it be for achieving higher power or better efficiency in the usual spectral range, or to improve the general performances of still-limited devices out of this range, a better understanding and a careful design of the QCL structure are needed. Two main structures are used for QCLs fabrication: the passivated ridge (PR), shown in Fig. 1, and the buried heterostructure (BH). The differences between both rely mainly on the material used for lateral light confinement and the electric insulation of the ridge. For PR devices, the ridge is insulated with a dielectric film that is opened on top of the ridge to allow electrical contact. Regarding BH devices, the ridge is surrounded with an insulating crystalline material. For most applications, such as spectroscopy, PR are sufficient. In particular, when thermal issues are not too stringent, such as for pulsed operation or continuous wave operation with limited electrical power, it is not necessary to add


a second growth step, which is both costly and introduces some yield uncertainties. Moreover, in the case of spectroscopy, chemical etching of the active region is often mandatory to have a reasonable regrowth performance which introduces effective index variation in the laser and thus wavelength uncertainties. The dielectric material plays a key role in the device performance. In fact, to design it, a trade-off needs to be found in between its three purposes: manage the generated heat, efficiently confine the light in the active region and allow electrical insulation. This paper aims to choose the dielectric best suited for each operation wavelength and to identify dielectrics suitable for future devices. To do so, a figure of merit (FOM) is defined taking into account the optical losses in the dielectric and the thermal resistance of the device. A schematic cross-section of a PR QCL is shown in Fig. 1. The gain region is vertically sandwiched between two cladding layers, made of different sublayers for an optimum vertical confinement. A thin (from 300 nm to 1 µm) dielectric film is deposited on top of the ridge and a via is etched through it to allow electric contact. In the case of PR devices, the dielectric material acts as a buffer layer that strongly confines the light, avoids undesirable optical absorption by the free carriers within the metal contacts, and electrically insulates the ridge.

Fig. 1. Typical structure of a PR device. The laser ridge consists of an active region (red) sandwiched in between two cladding layers (green) providing vertical confinement. It is covered with a passivation layer (blue) etched on top of the ridge for the metal contact (yellow) to insure current injection. The other metal contact is deposited on the bottom of the substrate (grey).

Nevertheless, it induces optical losses and reduces thermal dissipation efficiency, as it usually has a poor thermal conductivity. As a matter of fact, the dielectric layer has to be carefully engineered in order to find a trade off between good electrical insulation, lateral optical confinent, sufficient heat dissipation, as well as, low optical losses. The degrees of freedom that we have on the dielectric design are: the material choice, the material quality (through the deposition process) and the dielectric layer geometry. In addition, material constants of the deposited dielectric have to be measured as they are dependent on the deposition process and the wavelength. In particular, the refractive index and the extinction coefficient, later denoted as n and k respectively, are crucial in the optical modes simulation, and therefore in the optical losses estimation. SiO2 has been currently used for laser operation at short wavelength devices and Si3 N4 at longer wavelength devices, the separation between both regions being typically in the 6 to 7 µm range. For wavelengths longer than 9 µm, the choice of the dielectric is still under investigation. Organic dielectrics such as photoresist [12], as well as, Si3 N4 [13, 14] and SiO2 [15] have been used. First, we will define a figure of merit to compare the different dielectric materials, SiO2 , Si3 N4 and TiO2 . Both optical and thermal properties of the materials will be taken into account in the FOM. Second, we will describe the Mueller ellipsometry setup used for modeling the dielectric films in the range from 3 µm to 11.1 µm, and determining the optical parameters n


and k. Then, thermal and optical simulations will be reported, with the experimental values previously found for the optical parameters, and the FOM will be evaluated. Finally, we will discuss which material is the best for a specific wavelength. 2.

Definition of the figure of merit

A relevant figure of merit for QCL is the threshold current density. It is strongly related with the losses and can be expressed as [16]: TZ A (1) j th = j0 exp T0 where j0 and T0 are constants depending on the laser performances. TZ A is the temperature in the active region of the laser. We have TZ A = Tpel + Rth U Id where Tpel is the temperature of the Peltier module regulating the temperature of the device, Rth is its thermal resistance, U is the voltage drop across the device, I the current running through it and d is the duty cycle of the power supply. Hence, j0 is representing the temperature independent part of the threshold current density. To estimate it, we refer to another expression of the threshold current density [16]: α˜ p +α˜ m + n2therm gc (2) j th = e τe f f where e is the electron charge, gc ∝ ΓZλA is the gain cross section of the active region, n2therm represents the thermally-activated back-scattering of the lower lasing state and τe f f is the electron effective lifetime. The losses stem from different parts, α˜ m stands for the front mirror loss, whereas α˜p represents the propagation losses coming from the fact that the optical mode is overlaping not only with the gain region but also with the surrounding materials. Therefore, we can decompose the propagation losses α˜ p = x Γx α x = Γdiel α diel + Γclad α clad + Γmet α met into, respectively, the losses in the passivation dielectric, the cladding layers and the free carrier absorption in the metal. Γx is the overlap of the mode with a given part of the device and α x its associated absorption coefficient. As the thermal dependence is fully taken into account in the exponential part of Eq. (1), j0 is estimated from Eq. (2) by neglecting the thermal depending term n2therm . Therefore, by bringing Eqs. (1) and (2) together, we obtain: j th

λ ∝ ΓZ A

⎛ ⎞ ⎜⎜⎜ ⎟⎟ Tpel + Rth U Id ⎜⎜⎝α˜ m + α x Γx ⎟⎟⎟⎠ exp T0 x

(3)

Furthermore, the FOM aims to distinguish the best dielectric for a given wavelength. Thus, we set aside in Eqs. (1) and (2) all the terms that do not depend on the dielectric. We simplify Eq. (3) considering that the relative variation with the dielectric of the mode overlap with the active region (ΔΓZ A /ΓZ A < 2%) and the propagation losses other than the losses in the dielectric are weak. In fact, the losses at the facets and in the cladding are unchanged. The passivation layer is chosen thick enough to keep the free carrier absorption in the metal surrounding the ridge lower than in the dielectric. Finally, given those assumptions, we define the following figure of merit: Rth U Id (4) FOM = α diel Γdiel exp T0

In pulsed mode (PW), the exponential part becomes negligible (exp R thTUId ≈ 1) and the 0 FOM reduces to α diel Γdiel leaving aside the thermal effects. Furthermore, the electric properties of the dielectric materials are to be examined, as one of


their main functions is to insure electrical insulation. In fact, several leakage paths are possible in QCLs. First, within the active region, the electrons can flow through the energy states without undergoing radiative transition. In fact, they can be thermally excited to states higher than the upper lasing state, which reduces the population inversion, and even to states of the continuum, which decreases the effective density of carriers. This leakage source is independent of the dielectric chosen for the passivation layer. Thereby, it is not taken into account. The other principle path of leakage current stems from the material surrounding the laser ridge. In the case of BH devices, the Fe-doped InP used to bury the structure is semi-insulating and important current leakages can be observed, favored by regrowth issues, such as interface defects and insufficient or non-uniform doping. With regard to PR devices, the passivation layer is very thick and its resistivity is high. Then, the current that could flow through the dielectric film is assumed to be negligible. In addition, as opposed to p-n-based bipolar devices, QCLs are n-n unipolar devices. Therefore, it is considered that current leakage related with surface recombination occurring at the mesa-sidewall interface between the semiconductor and the dielectric layer are negligible. As a consequence, the electrical parameters of the dielectric thin films are not taken into account in the FOM. On the one hand, we perform optical simulations to evaluate the mode overlap with the dielectric passivation layer of QCLs. For the simulation to be as accurate as possible, we use n and k of SiO2 , Si3 N4 and TiO2 obtained from Mueller ellipsometry measurements of single layers of those materials deposited on a InP substrate as will be discussed in section 2 (see Fig. 2). Moreover, the evaluation of the thermal resistance of the structure is performed taking into account the thermal conductivity of the considered dielectric material. From Eq. (4), we see that the thermal resistance has to be taken into account for devices operating in continuous mode (CW) or quasi-continuous mode (QCW). In PW, the thermal load is negligible and the role of the optical losses is predominant. Finally, we combine both simulated dielectric losses and thermal resistance in the general FOM written in Eq. (4) in order to discriminate the best dielectric depending on the operation wavelength. 3.

Measurement of the optical constants (n,k) by Mueller ellipsometry

In this section we describe the experimental set-up and data analysis methodology carried out concerning the infrared (IR) Mueller ellipsometry measurements. A Mueller ellipsometer is an optical instrument that measures the Mueller matrix of a sample. The Mueller matrix is a 4x4 matrix that describes how polarization of an incident beam is transformed after being reflected, transmitted or scattered by the sample [17]. The IR Mueller ellipsometer used in this work is sketched in Fig. 2. This instrument consists of a Fourier Transform infrared (FTIR) spectrometer equipped with a thermal Globar source, two arms controlling the incident and exiting polarization with respect to the sample (Polarization States Generator and Analyzer, respectively, PSG and PSA) and finally a nitrogen cooled MCT detector. Both PSG and PSA consist of a holographic grid linear polarizer and a rotating double Fresnel rhomb which provides a quasi-achromatic retardation within the measured spectral range (from 2 to 11 µm). The sample is illuminated with a focused beam with an angle of incidence equal to 60◦ and an ellipsoidal spot size about 2x3 mm. Thanks to the optimized conditions set for the IR Mueller ellipsometer, it is possible to provide polarimetric measurements that are accurate to 0.5% at the best. More details about the optical design, operation and calibration of the Mueller ellipsometer can be found in [18, 19]. The Mueller matrix of isotropic samples, like the ones that have been used for the purposes


Fig. 2. Sketch of the IR Mueller ellipsometer showing the entry and the exit arm as well as the position of the sample. The optical elements used to build the PSG and the PSA are also shown: a linear polarizer (LP) and a double Fresnel rhomb (FP). The mirrors used to focus and to collimate the light beam along the optical path are also indicated (flat mirrors, fM, and off-axis parabolic mirrors, pM) as well as some circular diaphragms (D).

of this study, are block-diagonal and show the following characteristics [17, 20, 21]: ⎡ ⎢⎢⎢ 1 ⎢⎢ I M = ⎢⎢⎢⎢ c p ⎢⎢⎣ 0 0

Ic p 1 0 0

0 0 Ic −Is

⎤ 0 ⎥⎥ ⎥ 0 ⎥⎥⎥⎥ ⎥ Is ⎥⎥⎦⎥ Ic

(5)

with ⎧ ⎪ Ic p = cos(2Ψ) ⎪ ⎪ ⎪ ⎨ = sin(2Ψ) cos(Δ) I ⎪ c ⎪ ⎪ ⎪ ⎩ I = sin(2Ψ) sin(Δ) s

(6)

The coefficients Ψ and Δ are the standard ellipsometric angles, which are defined from the fundamental ellipsometric equation [20]: ρ=

rp = tan (Ψ) exp (iΔ) rs

(7)

where the values r p and r s correspond to the complex Fresnel reflection coefficients of the sample for a polarization of light parallel, “p”, and perpendicular, “s”, respectively, to the plane of incidence of the light beam in respect to the sample. Here, tan(Ψ) corresponds to the amplitude ratio between the “p” and “s” components of the polarization after reflection, and Δ is the phase shift of the “p” in respect to the “s” component. Data analysis in ellipsometry is an indirect process. In general, the experimental data is compared to data simulated using a parametric model that represents the physical structure and the optical properties of the sample under study. The optical model depends on a few


parameters, like the thickness of thin films, or their respective refractive indexes. The parameters of the model are varied until the difference between the experimental and the simulated data is minimized. The quality of the fit is commonly evaluated with a figure of merit, which is used during the fitting process to guide the numerical algorithm during the search of the optimal values for the parameters of the optical model. In this work, the following figure of merit has been assumed [22]: ⎡ ⎤ ⎢⎢⎢ (IsT − IsE ) 2 (IcT − IcE ) 2 (IcTp − IcEp ) 2 ⎥⎥⎥ 1 k k k k k k 2 ⎢ ⎥⎥⎥ ⎢ (8) + + χ = ⎦ N − M − 1 ⎣⎢ k σ 2I s σ 2Ic σ 2Ic p where N refers to the number of data points, M is the total number of fitted parameters and Is , Ic and Ic p correspond to the non-null Mueller matrix elements defined in Eq. (6). The superscripts, T and E, denote model and experimental data respectively. The sigmas represent the noise level, around 1%. We used the Mueller matrix elements to perform data fits, instead of Ψ and Δ, because they are the natural magnitudes measured by the Mueller ellipsometer, and also because being bounded between -1 and 1, the fitting procedure is numerically more stable than if Ψ and Δ were used. All numerical simulations and models have been performed with the DeltaPsi2 software (by Horiba Scientific). The dielectric function at IR frequencies of the materials studied in this work can be modeled by the following expression which is the sum of three contributions: ∗PS = ∞ +

ω2p −ω2 + iΓD ω

+

L

f k ωk2

k=1

(ω2 − ωk2 ) + iγk ω

(9)

The first term, ∞ , is an adjustable parameter and represents the dielectric permittivity at high frequencies. The second term, the Drude formula, accounts for the contribution of free charge carriers. It has two adjustable terms, ω p , the plasma frequency, and ΓD , the damping frequency. Finally, the third term corresponds to a series of classical Lorentz oscillators. The triplet (f, ω and γ) represents respectively (weight, frequency and width) for each oscillator. Lorentz oscillators account for resonant phonon modes found at long IR frequencies [22]. SiO2 , Si3 N4 and TiO2 are deposited onto quarters of n-doped InP 2 inches wafer (1 in. = 2.54 cm). A quarter is kept to be measured separately and to determine the spectroscopic dependence of the n, and k values of the substrate. SiO2 and Si3 N4 are deposited by PECVD with a Nextral ND200, SiH4 being the precursor gas as well as N2 O for SiO2 and NH3 for Si3 N4 . The stoichiometry of the thin films deposited by PECVD is not measured directly. Nevertheless, an ellipsometer is used to measure their n and k in the visible range to check the stability of the process. The processes have been calibrated to realize close to stoichiometry SiO2 and Si3 N4 thin films. TiO2 has been deposited by IBAD with a DENTON Infinity equipment. Target layer thicknesses are 1200 nm, 1000 nm and 900 nm respectively for the SiO2 , Si3 N4 and TiO2 films. Bare wafer was measured by Mueller ellipsometry and modeled with ∞ and a Drude formula. Table 1 shows the fitted parameters ∞ , ω p and ΓD . SiO2 , Si3 N4 and TiO2 samples were modeled by using a semi-infinite InP substrate, whose dielectric function corresponded to the one previously determined (i.e., we used ω p and ΓD values of Table 1) , and a thin layer of the dielectric material under study. The fitted parameters were the respective thin film thickness, and the parameters corresponding to the Lorentz oscillators of the dielectric function of the dielectric materials. In particular, SiO2 , Si3 N4 and TiO2 were respectively modeled with four, three and two Lorentz oscillators. The number and parameters of the oscillators have been chosen without taking into account any a priori knowledge on the absorbing mecanisms and materials. In this way, we follow the same procedure as Kischkat [23] in order to have the best description of our material as regards the optical constants. On the one hand, the fit thickness of the thin films was


Fig. 3. Measured (solid lines) and fitted (dashed and dotted lines) Is , Ic , Ic p for the InP wafer (blue) and SiO2 (black), Si3 N4 (red) and TiO2 (green) thin films.

found to be 1141 nm, 996 nm and 894 nm for SiO2 , Si3 N4 and TiO2 , respectively, which are very close to the target values. On the other hand, the fitted optical parameters are listed in Table 1. Figure 3 shows the experimental and best-fitted ellipsometric data Is , Ic , and Ic for the four analyzed samples. All parametric models present an excellent fit quality which yield a good χ2 factor, detailed in Table 1, in accordance with other Mueller ellipsometry experiments [24, 25]. From the parametric models, we have extracted the refractive index n and the extinction coefficient k of the thin films. The absorption coefficient of each dielectric is deduced from the extinction coefficient by α = 4π λ k. Figure 4 shows the spectral dependence of n and k for the three analyzed dielectric materials. In the spectra of n and α, absorption bands feature as peaks for α and as inflections for n. Even if we fitted the data without assuming a given number of oscillators as a starting point, we can relate the absorption peaks that we found to vibrational absorptions referenced in the literature. In Fig. 4, both SiO2 and Si3 N4 present an absorption peak respectively at 4.45 µm and 4.66 µm that can be attributed to the longitudinal stretching mode of the Si-H bonds [26, 27]. Indeed, hydrogenation of the dielectric film happens during the deposition process as SiH4 is used as a precursor. This absorption peak does not appear for SiO2 and Si3 N4 films deposited with other techniques, such as RF sputtering [23]. PECVD deposition is preferable for QCL fabrication since it realizes conformal films whereas sputtering is more directional. In order to have enough dielectric material on the ridge sidewalls, sputtering compels to deposit thicker layers which leads to a more complex fabrication. In a similar fashion, TiO2 presents an absorption peak at 3 µm. This is attributed to adsorbtion of water [28,29]. The wider and stronger absorption region located at higher wavelength (8.8 µm and 9.8 µm for SiO2 and 12 µm for Si3 N4 ) is assigned to the main resonances of the material (respectively, Si-O symmetric and antisymmetric stretching vibrations, and Si-N stretching vibrations [26]).


Table 1. Model parameters for InP substrate, SiO2 , Si3 N4 and TiO2 ∞

Mat.

InP

SiO2

Si3 N4

TiO2

2.43

5.01

4.75

Thick.

parameters

(nm)

ω p (eV)

ΓD (eV)

0.265

0.00801

f

ω (eV)

γ (eV)

0.421

0.110

0.011

0.455

0.126

0.00953

0.0749

0.141

0.00923

0.00330

0.278

0.0108

f

ω (eV)

γ (eV)

1.284

0.103

0.00754

0.398

0.116

0.0155

0.0219

0.266

0.016

f

ω (eV)

γ (eV)

6.26

0.0722

0.0127

0.0220

0.415

0.373

χ2

N.A.

1.1

1141

12.7

996

3.29

894

5.03

SiO2 Si3N4 TiO2

n

4,5 4 3,5 3 2,5 2 1,5 1 0,5 2

9.89

Model

3

4

5

6

7

8

9

10

11

12

13

10

11

12

13

Wavelength (μm) -1

α (cm )

10000 1000 100 2

3

4

5

6

7

8

9

Wavelength (μm) Fig. 4. Refractive index (top figure) and absorption coefficients (bottom figure) of SiO2 , Si3 N4 and TiO2 .


4. 4.1.

Results Simulation of the propagation losses and thermal resistance

The simulation of thermal and optical responses of the laser structure has been performed with an in-house script that combines COMSOL and MATLAB software engines. The definition of the simulated device structure mimics the real fabrication steps. First we choose a wafer type, and input the active region and cladding layers information. Then we define the process steps, being either material deposition or regrowth (specifying the material itself as well as its thickness) or etching (giving the etching depth and mask and if the etching is wet or dry). Finally, a submount and a mounting procedure is given. After this device structure definition, the COMSOL engine is called to numerically solve Maxwell’s and Fourier’s equations and data are post-processed with MATLAB. Typically, for optical mode simulations, the overlap on each part of the device can be extracted. The flexibility of such a framework allows us to study systematically the influence of a given parameter, such as an element of the device geometry (dielectric thickness, laser width, ...) or a material property (refractive index, thermal conductivity, ...). We simulate PR structures, such as presented in Fig. 1. The cladding layers are n-doped InP, and their refractive index is described by a Drude model. For the sake of comparison, the dielectric thickness has been taken constant, equal to 500 nm regardless of the wavelength, and the top cladding layer has been choosen thicker than for a real devices (8 µm instead of 2 to 4 µm) in order to strike off the losses in the top metal contact from the study. A thinner cladding layer would change the vertical mode overlap. Nevertheless, the horizontal distribution of the mode is similar. The simulation framework was used to study devices with ridge width (W) such as the width to wavelength ratio equals to W λ = 1.2. Indeed, it is a rule of thumb so that the ridge should not be too large to avoid higher order tranverse modes but large enough to maximize the mode overlap with the active region. In order to evaluate the FOM defined in equation 4, we numerically solved Maxwell’s equations and heat conduction Fourier’s law equation to get the mode overlap with the dielectric, Γdiel , and the thermal resistance, Rth . First, we simulate the mode overlap with the dielectric, Γdiel , with the dielectric refractive index by taking into account the fitted values from the Mueller ellipsometry measurements. As shown in Fig. 5, it appears that the best confinement is provided by SiO2 below 9 µm, because of its low refractive index. On the other hand, for those wavelengths, Si3 N4 and TiO2 show less confinement efficiency than SiO2 because they have a higher refractive index. Above 10 µm, Si3 N4 refractive index also increases because of a vibrational resonance, increasing the mode overlap with the dielectric whereas TiO2 keeps a good confining efficiency. From those overlaps, we can deduce the modal losses in the dielectric by multiplying it by the absorption coefficients α diel shown in Fig. 4. Second, we calculate the thermal resistance of devices with ridge widths corresponding to the studied wavelength range. To do so, a 8 µm-thick cladding is not a realistic assumption anymore. We used a 2.7 µm-thick top cladding layer for wavelengths shorter than 7 µm and 3.5 µm above 7 µm. A 5 µm-thick gold layer on top of the ridge is used for the simulation. Thermal conductivities for PECVD-deposited SiO2 and Si3 N4 of 1.3 W/mK, and 10 W/mK have been chosen [30]. As few studies have been led as regards to TiO2 thin films thermal conductivity and because the deposition process is not as mature as for SiO2 and Si3 N4 , we took a thermal conductivity of 8.5 W/mK [31], the value reported in the literature ranging from 1.6 W/mK [32] to 14.4 W/mK. The calculated thermal resistances are plotted on the inset of Fig. 5, the lines for Si3 N4 and TiO2 overlap because of their close thermal conductivity.Furthermore, we also plot in orange color the thermal resistance of equivalent BH-QCL in the figure inset. Their thermal resistance appears to be better than SiO2 -passivated devices, but similar to structures passivated with a high thermal conductivity. In fact, in the case of PR device with a poor thermal conductor such


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Overlap with dielectric (%)

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Wavelength (μm) Fig. 5. Overlap with the passivation film for SiO2 (black), Si3 N4 (red), TiO2 (green). The thermal resistance Rt h is plotted in the inset. The thermal resistance of Si3 N4 and TiO2 are overlapping due to their close thermal conductivities. For the sake of comparison, we also represent the thermal resistance of buried devices of equivalent width.

as SiO2 , the heat can only be dissipated vertically, through the metal contact opening. When the thermal conductivity of the dielectric material increases, the heat load can be also laterally extracted through the dielectric sidewalls to the metal which acts like a very efficient heat sink. The thermal conductivities used in the simulations are 250 W/mK for gold and 62 W/mK for Fe:InP. Better thermal performances for PR against BH devices have already been demonstrated in the case of devices mounted epilayer-up [33]. 4.2.

Calculation of the FOM

In addition to the previously simulated mode propagation losses and thermal resistances, to estimate the FOM (Eq. (4)), we take typical high power QCL values: T0 = 200K, U = 15V, I = jW L where j = 5kA/cm2 , L = 5mm, d = 3% in PW and W = 1.2λ. This ratio between the ridge width and wavelength has been chosen in order to maximize the output power while keeping high quality beam profile. Indeed, the ridge needs to be large enough to maximize the mode overlap with the active region, and thus the modal gain. Nevertheless, if the ratio is increased, higher order transverse cavity modes appear leading to a critically degraded far-field emission pattern. In addition, the impact of the dielectric becomes less significant. Figure 6 shows the FOM, where two regions can be distinguished in both PW and CW modes. On the one hand, at shorter wavelengths, SiO2 is the best candidate whereas at longer wavelengths its FOM critically increases, making it a worse dielectric than either TiO2 or Si3 N4 . Between those two zones there is a transition region in which the spectral range is weakly dependant on the thermal conductivity of the passivation layer. According to the results shown in Fig. 6, TiO2 appears to be more convenient than Si3 N4 or SiO2 to be used as passivation layer above 8.3 µm, if TiO2 is available as process material. The FOM gap of TiO2 with its challenger, Si3 N4 , increases quickly with wavelength and is higher than one order of magnitude at 11 µm. Another noteworthy fact is that the FOM is roughly constant for TiO2 over the range


Fig. 6. Evolution of the FOM vs λ for SiO2 (black), Si3 N4 (red) and TiO2 (green). Dashed lines stands for CW mode (d= 1), dashed lines for PW mode (d=3%). Below the graph we show the best dielectric according to the wavelength in CW and PW mode. For each CW and PW, we represent on the first row the case if TiO2 is available and on the second row, the case it is not available.

8 µm to 11 µm, even more in PW. As an example, it could allow to study evolution of the losses of other parts of the QCL with wavelength, independently of the dielectric losses. If TiO2 is not an option, Si3 N4 becomes more interesting than SiO2 above 8.4 µm in CW mode and above 8.5 µm in PW mode. Furthermore, it is to note that, as TiO2 does not show the typical Si-H absorption line of SiO2 and Si3 N4 , it presents the best FOM in the window 4.36 µm - 4.55 µm, with a FOM twice as good as the one of SiO2 . Thus, it makes it an appealing choice for high power applications, such as infrared countermeasures, often targeting this spectral range. 5.

Conclusion

In summary, the dielectric with the best performances as a passivation layer, among SiO2 , Si3 N4 and TiO2 , is identified according to a defined figure of merit. It takes into consideration both optical and thermal properties of the dielectric material. The optical constant n and k of SiO2 , Si3 N4 and TiO2 were modeled in the range 3 to 11.1 µm by fitting experimental results obtained by Mueller ellipsometry. Mueller ellipsometry provided an accurate knowledge of the spectroscopic optical properties of the materials under study. The optical mode overlap and propagation losses in the dielectric passivation film of QCL structures were obtained, performing optical simulations relying on the modeled n and k. Similarly, the thermal resistances of those structures were also numerically computed. From this figure of merit, evaluated for each material based on the results of those simulations, two regions for the choice of the dielectric material were identified. SiO2 is the best dielectric for shorter wavelength and TiO2 (or Si3 N4 if TiO2 is not available) above 8.3 µm (8.5 µm). Moreover, the choice of the material depends little on its thermal conductivity. Thus, the same dielectric material can be chosen in PW and CW mode. Our study also highlights the impact of hydrogenation of the dielectric in the case of PECVD deposition. Study and optimization of the deposition process is needed in order to reduce the absorption peak around 4.55 µm for SiO2


and Si3 N4 . Otherwise, TiO2 is also a good candidate for applications at 4.4 µm - 4.5 µm. Our study was focusing on the design of dielectric thin films for QCL. Nevertheless our experimental results, and especially the models of n and k, for PECVD-deposited SiO2 and Si3 N4 , and TiO2 can be useful for a wide range of devices and applications. Acknowledgments The authors thank Yannick Robert from Thales Research and Technologies for TiO2 deposition and Ferenc Borondics from SMIS beamline at SOLEIL synchrotron for hosting the IR ellipsometry experiment.