Schematic of photomodulated infrared spectroscopic set-up. The M 1 − M 4 mirrors are for PR measurement. For PT, the M 1 − M 4 mirrors are removed, and the sample is rotated by 90° to perpendicular to the probe beam. 

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... PR is one type of photomodulated spectroscopy. It is a powerful nondestructive tool for optical characterization of semiconductor electronic band structures. A conventional PR experimental system is based on a disper- sive monochromator. Generally, it consists of a monochromator, a combination of pump ͑ normally a laser ͒ and probe ͑ wavelength tuned monochromatic light ͒ beams, and a phase-sensitive detection ͓ lock-in amplifier ͑ LIA ͒ and mechanical chopper ͔ set. Modulation of the electric field in the sample is realized by photoexcited electron-hole pairs cre- ated by the pump beam, which is modulated at a frequency by the chopper. The derivative nature of a PR spectrum sup- presses unwanted background effects and emphasizes the structures located in the energy range of interband transitions and other weak features that may not be seen in a normal 1 optical reflectivity spectrum. Therefore, PR spectroscopy has found wide applications in characterizing materials’ band 2–5 structures in the last decades. It is noteworthy, however, that up to now the studies have been mostly limited to the wide-band materials in visible and near infrared spectral regions with a wavelength shorter than 4 ␮ m. 6,7 This limitation is due mainly to the facts that ͑ i ͒ the source in the mid-to far-infrared spectral region produces far fewer photons than the tungsten filament lamps, and ͑ ii ͒ the long-wavelength photodetector, e.g., HgCdTe, is inherently less sensitive than the Si- or InGaAs-based visible-region one. The joint effect of the source and the detector makes the inefficiency of grat- ing spectroscopy increasingly important. Thus the band structures of narrow-gap materials have not been well stud- ied, making engineering their properties difficult, although the narrow-gap materials play crucial roles in optoelectronic applications. Recently, an attempt of extending photomodulated measurements to longer wavelength by a technique based on a slow-scan Fourier transform infrared ͑ FTIR ͒ spectrometer 8 was reported. The results illustrated the possibility of apply- ing PR measurements to the mid- and even far-infrared spectral regions. However, the technique was rather tricky and complicated, as it demanded special considerations of the FTIR spectrometer on both hardware and software aspects. The spectrum obtained was not normalized and therefore contained not only the material-related photomodulation information but also the system response determined by the probe beam, the detector, and possibly the environmental disturbance introduced to the optical path. The signal-to- noise ratio and spectral resolution were miserable and unre- 8 liable to some degree for quantitative analysis. In fact, similar problems of signal-to-noise ratio and spectral resolution also occurred in the double-modulated infrared photoluminescence ͑ PL ͒ technique based on a slow-scan FTIR 9 spectrometer. A key issue involved was that the scanner of the Michelson interferometer in a slow-scan FTIR spectrometer moved continuously and modulated the probe beam with so-called Fourier frequencies. As a principle, these frequencies should be well separated from the external modulation frequency applied to the pump beam by the chopper. It se- verely limited the selection of the LIA’s time constant and hence drastically reduced the achievable spectral resolution and signal-to-noise ratio. In this letter, new progress in implementing photomodulated spectroscopy with a commercial step-scan FTIR spectrometer is reported. The experimental setup is introduced briefly, and PR and/or phototransmittance ͑ PT ͒ spectra are given in the mid- and far-infrared spectral regions to verify the performance of the technique. The preliminary line-shape analysis indicates that the PR spectrum can be well described by the third-derivative line-shape function, which can serve as a proof of the derivative nature of the spectrum. The ad- vantage of the technique is foreseen in the study of the narrow-gap semiconductor’s electronic band structures. In contrast to the slow scan, a most distinct feature of the step scan is that the scanner of the interferometer steps to a position of fixed optical path difference by using the internal He–Ne control signal and can remain perfectly still at that position while data acquisition takes place. This means that the probe beam is internally modulated at a Fourier frequency of 0 Hz from the point of view of the data acquisition. The problem of separating the external modulation frequency from the internal Fourier frequency hence no longer 10,11 exists. This fully relaxes the restriction on the selection of the LIA’s time constant and the pump-beam modulation frequency and makes sufficient space for significantly im- proving the attainable spectral resolution and signal-to-noise ratio. Figure 1 schematically illustrates the experimental setup of photomodulated spectroscopy in the long-wavelength spectral region. A FTIR spectrometer ͑ Bruker IFS 66v/S ͒ , which runs in the step-scan mode, is used to realize three purposes of ͑ i ͒ producing a probe beam with a Globar lamp and a KBr beam splitter, ͑ ii ͒ detecting signals with its liquid– nitrogen cooled HgCdTe detector, and ͑ iii ͒ calculating ⌬ R and R ͑ or ⌬ T and T ͒ spectra by its electronic controller and Fourier transform computing device. An Ar + -ion laser oper- ates at a 514.5 nm spectral line. Its output is chopped by a mechanical chopper to form a pump beam, and is then fo- cused onto the sample surface to cover the area being illu- minated by the probe beam. The reference output of the chopper is used to lock the LIA to the chopper frequency ␻ . The ac and dc outputs of the detector are coupled to the LIA and an electrical low-pass filter ͑ LPF ͒ , respectively. The outputs of the LIA and the LPF are then fed into the electronic controller for data acquisition. After Fourier transformation, the ⌬ R - and R - ͑ or ⌬ T - and T - ͒ related spectra, B ac LIA and B dc , are obtained simultaneously. It should be explicitly pointed out that for such a system, the restriction on the LIA’s time constant is fully removed, and hence a sufficient long time constant, e.g., 10 1 – 10 3 ms rather than ഛ 1 ms, can be as- signed to the LIA for filtering noise out. This is beneficial to the signal-to-noise ratio of the PR ͑ or PT ͒ spectrum. 10 For PR measurements, the M 1 – M 4 mirrors ͑ in dashes ͒ are employed. For PT measurements, all the M mirrors are removed, and the sample is rotated by 90° to keep it perpendicular to the probe beam. The final normalized PR or PT spectrum, namely, ⌬ R / R or ⌬ T / T , is determined by ...

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... 20 January 2007; accepted 22 January 2007; published online 16 February 2007 DOI: 10.1063/1.2696984 ͔ In the original published paper Appl. Phys. Lett. 89 , 182121 2006 Fig. 1 contained an error. The orientation of the FTIRs beam splitter was falsely illustrated. The correct version of Fig. 1 is shown below. We apologize for this ...

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... 20 January 2007; accepted 22 January 2007; published online 16 February 2007 DOI: 10.1063/1.2696984 ͔ In the original published paper Appl. Phys. Lett. 89 , 182121 2006 Fig. 1 contained an error. The orientation of the FTIRs beam splitter was falsely illustrated. The correct version of Fig. 1 is shown below. We apologize for this ...