Spectroscopy on Vertical Microcavities for the Mid-Infrared

Spectroscopy on Vertical Microcavities for the Mid-Infrared

W. Heiss1), T. Schwarzl, and G. Springholz

Institut fur Halbleiter- und Festkorperphysik, Universitat Linz,Altenbergerstraße 69, A-4040 Linz, Austria

(Received May 13, 2001; in revised form July 3, 2001; accepted July 4, 2001)

Subject classification: 42.55.Sa; 78.30.Hv; 78.67.Hc; S8.12; S8.13

Mid-infrared microcavities from IV–VI semiconductors (lead salts) are investigated by infraredtransmission measurements. Epitaxial Pb1––xEuxTe/EuTe multilayers with an refractive index con-trast of more than 80% are used as Bragg interference mirrors with a very large mirror stop bandwidth. Therefore, the polarization splitting of cavity modes which are strongly detuned in respectto the center of the mirror stop band can by studied. It is found to show a quadratic dependenceas function of the detuning energy. Furthermore, by inspecting the ratio between the width andthe height of cavity resonances, the absorption edge of ordered, self-organized PbSe quantum dotsis clearly detected.

1. Introduction

Microcavities consisting of high reflectivity Bragg mirrors have attracted tremendousinterest during the last few years due to their unique physical properties like the appear-ance of cavity polaritons and the “vacuum field Rabi splitting” [1]. Furthermore, micro-cavites are used to suppress competing modes in resonant cavity light emitting diodesand vertical cavity surface emitting lasers with the aim to achieve light sources with highefficiencies and thresholdless laser operation (for an overview see, e.g., [2]). While mostmicrocavity devices are fabricated by the use of III–V semiconductor compounds withband gap energies equivalent to wavelengths in the near-infrared [2], in this work weinvestigate microcavities for the mid-infrared, operating at wavelengths between 3 and6 mm. Our devices are based on narrow-gap IV–VI semiconductors (lead salts), whichare well suited for opto-electronic devices, caused by their favorable band structure andlow Auger recombination rates. Lead salts have been used to fabricate mid-infraredlasers, which can be applied for high resolution and high sensitivity chemical gas analysis[3] and atmospheric pollution monitoring [4]. The advantages of lead salt lasers as com-pared to other mid-infrared laser diodes is that they allow to access the longest emissionwavelength of 30 mm [4] and the highest operation temperature of 223 K in cw [5] andof 60 �C in pulsed mode [6]. Apart from the conventional edge emitting lasers, veryrecently, surface emitting lead-salt mid-infrared microcavity lasers were demonstrated[7–9]. In these devices, by optically pumping with 100 fs pulses laser emission from PbTequantum wells has been obtained up to a temperature of 65 �C [10].

In this work, we report on linear optical properties of IV–VI microcavities, consistingof EuTe/Pb1––xEuxTe Bragg mirrors. These microcavities benefit from a large stop bandwidth and a high finesse, resulting from the high refractive index contrast of over 80%for the material combination used for the Bragg mirrors [11]. Therefore, they can be

phys. stat. sol. (a) 188, No. 3, 929–935 (2001)

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1) Corresponding author; Tel.: ++43 732 2469 9643; Fax: ++43 732 2468 9696;e-mail: [email protected]

used to study optical transitions of nanostructures with small absorption cross sections. Inparticular, this is demonstrated on multilayers of ordered, self-organized PbSe quantumdots embedded between the cavity mirrors. Due to the large width of the Bragg mirrors,Fabry-Perot resonances are sustained which are strongly detuned with respect to thestop band center wavelength. For these resonances, a pronounced splitting between theTE and TM polarized mode is observed, much larger than in III–V microcavities.

2. Sample Growth and Experimental Details

We discuss the properties of Bragg mirrors and microcavities based on IV–VI semi-conductors. The samples were grown by molecular beam epitaxy (MBE) onto (111)oriented BaF2 substrates using compound effusion cells for PbSe and PbTe, and elementalsources for Eu and Te. The epitaxial growth of the Pb0.95Eu0.05Te(PbTe) and EuTelayers used as material combination for the Bragg mirrors was carried out at 260 �Csubstrate temperatures and the growth rates of EuTe and PbTe were around 1 mm/h.One sample contains a superlattice of correlated, self organized PbSe quantum dots.These are formed during heteroepitaxial growth of PbSe on Pb1––xEuxTe (111) due tothe 5.4% lattice-mismatch [12]. Due to the strong increase of the Pb1––xEuxTe energyband gap with Eu content (DEg/DxEu = 4.48 eV at 4 K), a quantum confinement of thefree carriers in the PbSe dots is achieved already for Eu concentrations of a few per-cent. We have chosen xEu = 5%, which corresponds to a Pb1––xEuxTe band gap of422 meV as compared to 145 meV for PbSe at 4 K. To obtain PbSe dots with an arealdot density of about 5 � 1010 cm––2, an average dot height of 120 �A, a width of 300 �A,and a size dispersion of typically around �15%, five monolayers PbSe were depositedat a substrate temperature of 360 �C.

The samples were characterized by Fourier transform infrared (FTIR) transmission-and reflectivity measurements using an Al mirror as reference. The angular dependenttransmission experiments were done by the use of a rotation stage allowing to turn thesample with a precision of a tenth of a degree. The accuracy of the angle dependence,however, is delimited to about one degree, due to the convergence of the incidencelight beam.

The experimental results are compared to theoretical transmission and reflectionspectra computed by the transfer matrix method [13]. In order to determine the exactvalues of the dispersion of the refractive indices of the layer materials, transmissionmeasurements were performed for single reference layers. The measured data werethen fitted to calculations using a model for the dielectric function of lead salts [14],which gives an analytic Kramers-Kronig conform expression of the optical constantsincluding the non-parabolicity of the band structure near the energy gap and the many-valley band structure of the lead salt compounds. To describe the cavity sample contain-ing a superlattice of correlated, self organized PbSe quantum dots, the dielectric func-tion was modified in order to take into account the two-dimensional and zero-dimen-sional joint density of states present in the wetting layers and the quantum dots.

3. Bragg Mirrors

The high efficiency of our Bragg mirrors is demonstrated in Fig. 1 by the reflectivityspectrum of a stack of seven PbTe(321 nm)/EuTe(776 nm) layer pairs. The broad mir-ror stop band of high reflectivity centered at an energy of 1360 cm––1 (7.3 mm) is clearly

930 W. Heiss et al.: Spectrocopy on Vertical Microcavities for the Mid-Infrared

visible. Outside of the stop-band region the Fabry-Perot fringes of the total mirrorthickness appear. The solid line depicts the calculated reflectivity, which is in goodagreement with the measured data. In the center of the stop band the theoretical reflec-tivity amounts 99.97% assuming no absorption in the layers. Experimentally, the reflec-tivity R can not be obtained with a precision better than 2% for this spectral range dueto the lack of well characterized reference mirrors. From transmission measurementsprobing T = 1––R we obtain values smaller than 0.3%, confirming the very high mirrorreflectivity.

One outstanding feature of the mirror reflectivity presented in Fig. 1 is the large widthof the mirror stop band, ranging from 980 cm––1 (10.2 mm) to 1700 cm––1 (5.87 mm). Thislarge width results from the very high refractive index contrast of about 80% for thematerial combination PbTe with nPbTe = 5.39 and EuTe with nEuTe = 2.3. For comparisonwith other Bragg mirrors it is useful to relate the stop band width to the center wave-length, giving a value of 59%. This value represents, to the best of our knowledge, thehighest relative stop band width ever obtained for MBE grown Bragg reflectors. It is byfar higher, than the relative width typically obtained by the use of combinations of

phys. stat. sol. (a) 188, No. 3 (2001) 931

Fig. 1. Reflectivity spectrum of a7 period PbTe/EuTe Bragg inter-ference mirror. The solid line, cal-culated by the transfer matrixmethod, is in good agreementwith the experimental data

Fig. 2. Relative width of the Braggmirror stop band for various mate-rial combination as function oftarget wavelength. Data are takenfrom Refs. [15–17]

III–V [15] and II–VI [16] semiconductors used in the visible spectral range and at awavelength of 1.5 mm, as demonstrated in Fig. 2. The stop band width is even largerthan that of Bragg mirrors using combinations of wide band gap fluorides as lowrefractive index materials with GaAs [17] or Pb1––xSrxSe [18] as high index materials.

4. Microcavities Containing Correlated Quantum Dots

In this section absorption measurements on a superlattice of self-assembled PbSeStranski-Krastanow islands embedded in lattice-mismatched Pb0.95Eu0.05Te barriers arepresented. In self-assembled quantum dot superlattices, the elastic interactions betweenthe growing dots on the surface and those buried within the previous layers often leadto the formation of long range correlations within the dot ensembles [19]. In lead saltquantum dot superlattices, dot correlations inclined to the growth direction are observed,dependent on the superlattice period. This leads to a unique fcc-like ABCABC . . .vertical dot stacking sequence and a nearly perfect lateral ordering within the growthplane, corresponding to the formation of self-organized trigonal 3D lattices of dots[12].

While the ordering mechanism and the topography of the correlated PbSe quantumdot superlattices have been clarified [12, 19, 20], there are almost no optical studies onPbSe quantum dots reported. Up to now, absorption measurements did not give conclu-sive results, due to the small optical density of the dots, and due to the fact, that ab-sorption spectra of lead salt films are dominated by strong interference fringes. To over-come these problems, we have embedded a 140 period superlattice of 5 ML PbSe dotsalternating with 48 nm Pb0.95Eu0.05Te spacer layers on top of a 3 mm thick buffer be-tween two Bragg mirrors, forming a vertical cavity. Due to the large cavity length of10.3 mm, within the stop band region of the Bragg mirrors 16 cavity resonances aresupported with an energy distance of 88 cm––1. The FTIR transmission spectrum of thecavity stop band region is shown in the inset of Fig. 3. At 300 K the absorption edge ofthe quantum dots is expected to be well above the cavity stop band. Thus the wholestructure represents an unfilled optical cavity, which is also evidenced by the mirrorsymmetric distribution of the resonance peak heights. As the temperature is lowered,


Fig. 3. Ratio between resonance widthand height of the resonances of a cavitycontaining a superlattice with ordered,self-organized PbSe quantum dots. Theshoulder at 2600 cm––1 corresponds to theabsorption of the dots. Inset: Transmis-sion spectrum of the same microcavity forthe Bragg mirror stop band region

the dot absorption shifts into the stop band region due to the decreasing PbSe bandgap. As a result the higher cavity modes become strongly damped, leading to a decreaseof their amplitude and a broadening of their width. Therefore, from the ratio betweenthe width and the amplitude (W/H) of the damped modes, the quantum dot absorptioncan be measured. As shown in Fig. 3, at a temperature of 50 K W/H gives small valuesup to an energy of 2400 cm––1, whereas at higher energies W/H strongly increases.In addition to the strong increase of W/H as function of energy, a shoulder is clearlyobserved at 2600 cm––1. From a comparison to our model calculations described abovethis shoulder can be assigned to the absorption from the oblique valleys of the PbSequantum dots. Therefore, the strong absorption above the shoulder has to be attributedto the wetting layer whereas the small increase of W/H at 1800 cm––1 corresponds toabsorption from the longitudinal valley.

5. Polarization Splitting of Strongly Detuned Cavity Modes

Due to the polarization dependence of the reflection and transmission coefficients de-scribed by the Fresnel equations the cavity resonances split into TE and TM modes bytilting the incident light away from the surface normal direction. From analytic calcula-tions of the resonance energies given in [20] this splitting DE is proposed to be directproportional to the difference between the energy of the cavity mode and that of thecenter of the mirror stop band ED. Therefore, large polarization splittings are expectedfor our IV–VI microcavities where cavity resonances quite far from the stop band cen-ter can be obtained. In particular, we have used a 4l microcavity supporting five cavityresonances, as shown in the inset of Fig. 4a) by the transmission spectrum of the cavityin the stop band region. The energy of the most detuned resonances with order m = 6and m = 10 is about 450 cm––1 off from the mirror center. The m = 9 and m = 10

resonances are strongly damped by ab-sorption from 4 PbTe quantum wellsinserted at the antinode positions inthe cavity. Figure 4a) shows the polari-zation splitting of the m = 6 mode at1860 cm––1. At an internal angle ofonly 10.3� (64� external) it amounts18 cm––1 yielding a relative splitting of1%. In comparison, in GaAs/AlAscavities the detuning of the resonances

phys. stat. sol. (a) 188, No. 3 (2001) 933

Fig. 4. a) FTIR transmission of the m = 6resonance of a 4l microcavity for TE andTM polarization at an internal angle of10.3�. Inset: Transmission spectrum of thestop band region of the microcavity. b) An-gle dependent dispersion of the m = 6 modefor TE and TM polarization

is limited by the small stop band widths resulting in a polarization splitting of only0.1% at an external angle of 60� [22]. For the TE mode we observe, in addition, aconsiderable larger finesse than for the TM mode, which appears much higher andbroader in the transmission spectrum. The difference of the finesse is due to a lowerreflectivity for the TM polarization as predicted by the Fresnel formulas. The angulardispersion of the polarization modes of the m = 6 resonance is shown in Fig. 4b). Bothdispersions are fitted with the same dispersion relation for the angle dependent reso-

nance energy (EðQÞ ¼ Eð0Þ=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 � ðsin Q=neffÞ2

q[22]) by using different values for the

effective refractive index (3.55 and 4.25 for TM and TE mode, respectively).By measuring the angle dispersion of all five cavity modes (m = 6 to m = 10), we

find a quadratic dependence of the polarization splitting on the detuning energy ED, incontrast to the proposed dependence from the analytical calculations. Therefore, wesuggest to use the numerical transfer matrix method [13] for the design and calculationof high quality microcavities instead of using analytical calculations, where only approx-imate results can be obtained.

6. Summary

High quality lead salt microcavities for the mid-infrared have been investigated byFTIR transmission experiments. Due to the high refractive index contrast of thePb1––xEuxTe/EuTe multilayers used for the Bragg interference mirrors, very large widthsof the mirror stop bands are achieved. We have made use of these wide stop bands, tostudy the absorption of ordered, self-organized PbSe quantum dots with small opticaldensity. In particular, the absorption edge of the quantum dots can be clearly detectedby inspecting the ratio between the width and the hight of the cavity resonances.Furthermore, the polarization splitting of cavity modes which are strongly detuned inrespect to the center of the mirror stop band is demonstrated. It is found to show aquadratic dependence as function of the detuning energy in contradiction to theoreticalpredictions.

Acknowledgements This work was supported by the Fonds zur Forderung der wis-senschaftlichen Forschung, the Gesellschaft fur Mikroelektronik, and the AustrianAcademy of Sciences.

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Spectroscopy on Vertical Microcavities for the Mid-Infrared