ISSN 10637850, Technical Physics Letters, 2013, Vol. 39, No. 12, pp. 1071–1073. © Pleiades Publishing, Ltd., 2013. Original Russian Text © D.D. Firsov, O.S. Komkov, 2013, published in Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 2013, Vol. 39, No. 23, pp. 87–94.

Photomodulation Fourier Transform Infrared Spectroscopy of Semiconductor Structures: Features of Phase Correction and Application of Method D. D. Firsov and O. S. Komkov St. Petersburg Electrotechnical University “LETI”, St. Petersburg, 197376 Russia email: [email protected], [email protected] Received July 11, 2013

Abstract—A method for measuring photoreflectance (PR) by using a Fourier transform infrared (FTIR) spectrometer has been implemented. Features of application of the phasecorrection method necessary for storing information on the sign of the spectrum were revealed. The method was applied for measuring the energy spectrum of charge carriers in In xGa 1 – xAs/GaAs single quantum wells in the nearinfrared range. A good agreement with the results obtained by means of a diffraction spectrometer for the same samples in the same wavelength range is observed. Application of the developed photomodulation FTIR spectroscopy method for measuring photoreflectance in InSb epitaxial layers in the wavelength range of 2–10 μm has been demonstrated. DOI: 10.1134/S1063785013120079

Modulation spectroscopy is one of the most power ful optical methods in studying the band structure of bulk semiconductors and energy levels in lowdimen sional structures. However, classical modulation methods using monochromators for spectral disper sion of light do not have sufficient sensitivity in the midinfrared (IR) range of the spectrum and are hardly used for wavelengths greater than 4 μm. Their deficiencies are caused by ineffective use of the light flux in the “slit—diffraction grating (or prism)” sys tem, along with a relatively small brightness of the sources of radiation and low sensitivity of the photo detectors in the midIR range. The development of effective modulationspec troscopy methods in the longwave range is important due to the continuing interest in narrowband semi conductor structures that are used in creating high frequency transistors, night vision devices, gas sensors, and systems of wireless communication. In [1], a new method for measuring photomodulated reflection and transmission was proposed based on the use of a Mich elson interferometer. A series of photoreflectance (phototransmittance) spectra in the wavelength range of 1–9 μm were obtained. Similar systems for measur ing photomodulation spectra using Fourier transform infrared (FTIR) spectrometers were later developed in works of other groups [2, 3], with a maximum wave length of 20 μm in the photoreflectance spectrum [4]. However, in such measurements, the problem of the signal’s sign preservation arises when obtaining the modulated spectrum. This is due to the fact that information on the sign of the signal is

eliminated during the procedure of phase correc tion when we use conventional FTIR spectroscopy algorithms [5, 6]. In [1], measures were obviously taken to restore the sign of resultant spectra, but there is no description of them. Meanwhile, this problem was not attended to in [2, 4], which may have resulted in distorted photoreflectance spec tra. In our work, the experimental setup used for mea suring modulation spectra is based on a VERTEX 80 (Bruker Optics) commercial FTIR spectrometer that supports stepscan mode of the interferometer’s mir ror movement. The recording system of our device was modified, which allowed us to obtain an amplified sig nal at the output of the photodetector. The signal was fed to an SR830 lockin amplifier and then returned to an analog to digital converter of the spectrometer for further processing. In the spectral range from 0.8 to 1.1 μm, FTIR photoreflectance measurements were performed using a silicon photodiode, a fluorite (CaF2) beamsplitter, and an incandescent lamp. A HeNe laser (λ = 632 nm) with a power of 2 mW was used to modulate the reflectance of the sample. A laser beam modulated at a frequency of 800 Hz was directed onto the same place of the sample where the reflec tance was measured. For the measurements in the midIR range (up to 16 μm), a CdHgTe photovoltaic detector, a KBr beamsplitter, and a SiC globar were used. In this case, the sample was exposed to radiation of a semiconductor laser diode (809 nm) with a power up to 400 mW. The spectral resolution for these mea surements was set to 32 cm–1 (4 meV, or 3.2 nm at

1071

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FIRSOV, KOMKOV FKOs

QW excitonic transitions

0

ΔR, a. u. ΔR, a. u.

10 8 1.0

Grating spectrometer

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FTIR: Power spectrum

0 (c)

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Eg InSb (120 K) 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 Energy, eV

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Fig. 1. Photoreflectance spectra of In0.225Ga0.775As/GaAs single quantum well of 15 nm width obtained using (a) a diffraction spectrometer, and a Fourier transform infrared spectrometer with different phase correction: (b) by Eq. (2), (c) by the conventional Mertz method, and (d) by the Mertz method with a stored phase.

Fig. 2. Photoreflectance spectrum of InSb epitaxial layer measured with an FTIR spectrometer. The spectrum is normalized to the spectrum of reflection. The phase cor rection was carried out by the Mertz method with a stored phase.

λ = 1 μm). This allowed us to perform measurements in the stepscan mode in a relatively short time.

by value ϕ(σ) of the phase error, where σ ~ 1/λ is the wavenumber [6]:

Testing of the setup developed for the photomodu lation FTIR spectroscopy was performed on a struc ture with an In0.225Ga0.775As/GaAs single quantum well having a thickness of 15 nm. Earlier, an intense electroreflectance signal in the range of 0.8–1.1 μm was observed for this structure at room temperature [7]. This allowed us to compare the FTIR results with the photoreflectance spectra from this structure that were obtained using a classical setup with a grating spectrometer [8]. Considering the problem of restor ing the sign of the signal, this comparison was neces sary in developing the appropriate phasecorrection method. Figure 1a shows nonnormalized photoreflection spectrum ΔR obtained using a classical setup with an IKS31 diffraction spectrometer. In the spectrum, we can see the Franz–Keldysh oscillations (FKOs) corre sponding to 110nmthick GaAs cap layer, and some spectral features due to exciton transitions in the single quantum well [9] (shown by arrows). With an FTIR spectrometer, the interferogram of radiation is mea sured directly, and the according spectrum is calcu lated. The use of the phase correction is necessary, since a real interferogram I(σ) is not absolutely sym metric relative to point of zero optical path difference of the rays δ = 0 [5, 6]. Complex spectrum B(σ) is a result of inverse Fourier transform of such interfero gram, and it differs from realintensity spectrum B0(σ)

∞

∫

B ( σ ) = const [ I ( δ ) – I ( ∞ ) ]e

– i2πσδ

dδ

(1)

–∞

= B 0 ( σ )e

iϕ ( σ )

.

The procedure of exclusion of the phase error from B(σ) when obtaining a real spectrum is conventionally called phase correction [10]. Figure 1b shows results obtained by a very simple method of phase correction. In this case, the com plex spectrum B(σ) is transformed into a real spec trum by calculating the square root of the “power spectrum” [10]: Bp ( σ ) = =

B ( σ )B* ( σ )

2

(2)

2

Re [ B ( σ ) ] + Im [ B ( σ ) ] .

This approach allows one to determine the ampli tude of the useful signal, but information on its sign is lost, which makes it unsuitable for processing the results of modulation spectroscopy. Figure 1c shows the spectrum for which the phase correction is per formed by the multiplicative Mertz method [11]. This method and the mathematically equivalent method of Forman’s convolution [12] are most widely used in modern Fourier transform infrared spectroscopy. The phase error in these methods is determined from the

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complex spectrum with low resolution B'(σ) by the formula [5]: [ B' ( σ )] . ϕ' ( σ ) = arctan Im  (3) Re [ B' ( σ ) ] Since in practice the phase error is a slowly varying function of the wavenumber [5], the condition ϕ'(σ) ≈ ϕ(σ) takes place. Correspondingly, a real spectrum can be obtained when compensating the phase error [11]: – iϕ' ( σ )

B R ( σ ) = Re [ B ( σ )e ]. (4) In the standard methods by Mertz and Forman, when calculating the phase error, it is assumed that B0(σ) > 0 at all frequencies. However, processing of the modulation spectra in this case leads to an erroneous result, since the spectra include the extrema with dif ferent signs (Fig. 1a). This follows from the equality iϕ

i(ϕ + π)

(5) ( – B 0 )e = B 0 e . Consequently, phase correction by the Mertz method leads to a positive sign for the majority of extrema, as can be seen in Fig. 1c. Negative domains next to the most intense extrema represent artifacts described in [13]. Uncertainty caused by (5) does not signify when search for the phase error is based on the spectrum of the signal which is a priori positive. Since the phase error depends foremost on the interferometer [5], it can be found from separate measurements of unmod ulated reflected radiation R provided that the step movement of the mirror is well reproduced. In this case, the complex reflectance spectrum R(σ) is substi tuted into (3) and the phase correction of the spectrum for required modulation signal ΔR(σ) is carried out by (4). The thusobtained spectrum in Fig. 1d shows a very good agreement with the results of standard photore flectance measurements (Fig. 1a). The small differ ence in the Franz–Keldysh oscillation period is due to a partial straightening of the surface bending of the energy bands that is caused by the light of the interfer ometer leading to a decrease in the buildin electric field. Application of the developed method for obtaining modulation spectra is of greatest interest in the mid IR range. The structure with an undoped InSb epitax ial layer obtained by molecularbeam epitaxy on an InSb substrate was chosen as the test object. Figure 2 shows the photoreflectance spectrum of this structure when placed in a nitrogen cryostat at a temperature of ~120 K. As far as we know, this result is the first exper imental measurement of photoreflectance from bulk InSb. To analyze the spectrum, we used the modified threepoint method [14]. This allowed us to determine the energy of critical point E = 0.222 ± 0.002 eV and a parameter of spectral broadening Γ = 0.063 eV. The obtained value of E is close to the band gap width of InSb which equals 0.226 eV at 120 K [15]. Moreover, it is worth noting the presence of additional heating TECHNICAL PHYSICS LETTERS

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caused by the probing beam and the modulation laser beam. Successful measurements allow us to conclude that the photomodulationspectroscopy method based on an FTIR spectrometer is applicable in the midIR range. The high sensitivity of the method, along with the correct determination of the signal sign, makes it an effective tool for the study of narrowgap semicon ductor materials and structures based on them. Acknowledgments. The authors thank the molecu larbeam epitaxy group at the Ioffe Physical Technical Institute under the direction of S.V. Ivanov for growing InSb structures. This work was partially supported by the Ministry of Education and Science of the Russian Federation (federal targeted program “Scientific and Scientific Pedagogical Personnel of the Innovative Russia,” con tract no. 14.V37.21.0338). RERERENCES 1. T. J. C. Hosea, M. Merrick, and B. N. Murdin, Phys. Status Solidi (a)202 (7), 1233–1243 (2005). 2. Jun Shao, Wei Lu, Fangyu Yue, Xiang Lu, Wei Huang, Zhifeng Li, Shaoling Guo, and Junhao Chu, Rev. Sci. Instrum. 78 (1), 01311 (2007). 3. M. Motyka, G. Sek, J. Misiewicz, A. Bauer, M. Dall ner, and S. Hofling, Appl. Phys. Express 2, 126505 (2009). 4. Jun Shao, Lu Chen, Xiang Lu, Wei Lu, Li He, Shaoling Guo, and Junhao Chu, Appl. Phys. Lett. 95 (1), 041908 (2009). 5. P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry (Wiley & Sons, Hoboken, New Jersey, 2007). 6. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972). 7. A. N. Pikhtin, O. S. Komkov, and F. Bugge, Phys. Sta tus Solidi (a) 202 (7), 1270 (2005). 8. O. S. Komkov, A. N. Pikhtin, and Yu. V. Zhilyaev, Izv. Vyssh. Uchebn. Zaved., Mater. Elektr. Tekhn. 53 (1), 45 (2011) [Russ. Microelectron. 41 (8), 508 (2012)]. 9. A. N. Pikhtin, O. S. Komkov, and K. V. Bazarov, Semi conductors 40 (5), 592 (2006). 10. J. Gronholz and W. Herres, Instrum. Comput. 3, 10– 16 (1985). 11. L. Mertz, Transformation in Optics (John Wiley and Sons, New York, 1965). 12. M. L. Forman, W. H. Steel, and G. A. Vanasee, J. Opt. Soc. Am. 56 (1), 59 (1966). 13. S. M. Hutson and M. S. Braiman, Appl. Spectrosc. 52 (7), 974–984 (1998). 14. T. J. C. Hosea, Phys. Status Solidi (b) 189 (2), 531–542 (1995). 15. C. L. Littler and D. G. Seller, Appl. Phys. Lett. 46 (1), 986–988 (1985).

Translated by G. Dedkov 2013