Microreflectance difference spectrometer based on a charge coupled device camera: surface distribution of polishing-related linear defect density in GaAs (001) L. F. Lastras-Martínez,* R. Castro-García, R. E. Balderas-Navarro, and A. Lastras-Martínez Instituto de Investigación en Comunicación Óptica, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, San Luis Potosí, México *Corresponding author:
[email protected] Received 3 August 2009; revised 2 October 2009; accepted 4 October 2009; posted 6 October 2009 (Doc. ID 115034); published 20 October 2009
We describe a microreflectance difference (μRD) spectrometer based on a charge coupled device (CCD), in contrast to most common RD spectrometers that are based on a photomultiplier or a photodiode as a light detector. The advantage of our instrument over others is the possibility to isolate the RD spectrum of specific areas of the sample; thus topographic maps of the surface can be obtained. In our setup we have a maximum spatial resolution of approximately 2:50 μm × 2:50 μm and a spectral range from 1.2 to 5:5 eV. To illustrate the performance of the spectrometer, we have measured strains in mechanically polished GaAs ð001Þ single crystals. © 2009 Optical Society of America OCIS codes: 120.2130, 120.6200, 300.6470, 110.0180.
1. Introduction
Besides providing information on optical absorption and reflection, polarized light spectroscopy takes advantage of the anisotropy of the optical properties of noncubic materials, to reveal information about structure and composition that is valuable for both characterization and diagnostic purposes in in situ and ex situ applications. Reflectance difference (RD) spectroscopy [1,2] is a polarized light technique that has been shown to be useful for the characterization of cubic semiconductors and metal surface states [3]. RD spectra comprise components of different physical origins, such as linear defects [4–7], surface electric fields [8], surface strains associated with reconstructions in vacuum [9], and piezo-optical properties [10–12]. Concerning the surface electric field as a source of an 0003-6935/09/305713-05$15.00/0 © 2009 Optical Society of America
optical anisotropy through a piezoelectric effect, it has been used for the determination of doping levels of GaAs ð001Þ on a quantitative basis [13]. The development of theoretical models to understand the physical origin, through the modeling of the line shapes of the RD spectra, has increased its power and utility, suggesting that the extension of the RD spectroscopy to a microscopic scale could further increase the potential of the technique. It has been proved that the extension of some spectroscopies to a microscopic scale increases their usefulness. That is the case of the micro Raman spectroscopy [14–16], the microphotoluminescence [17,18], and the micro RD (μRD) spectrometer based on a Ti:sapphire laser [19]. In another application, the residual stress in GaAs wafers has been investigated by using an infrared polariscope [20] and a photoelastic homodyne technique (PHT) [21]. In the PHT setup a linear polarized laser beam of 1:3 μm wavelength is passing through the wafer, and due to the birefringence induced by 20 October 2009 / Vol. 48, No. 30 / APPLIED OPTICS
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dislocations, the transmitted light splits into ordinary and extraordinary beams, which are related to the principal stress components. To generate a stress image, the wafer is mounted on either an XY or a rotary stage. The spectrometers described above, nevertheless, have limited use in in situ applications, due to either requirement of low temperatures or of having the sample mounted on an XY stage. To overcome this problem, in this paper we report on a μRD spectrometer that can be used in either ex situ or in situ applications. The instrument is based on a setup reported for us previously [22] and uses a charge coupled device (CCD) camera as a light detector. Our setup has several advantages over the Ti:sapphire laser based system: (i) the energy range is broader, (ii) shifting between spectroscopy ranges does not require a change of optics, (iii) RD spectra for each region can be obtained with no mechanical movements, and (iv) μRD spectra can be used to characterize and study the spatial distribution of surface defects, surface electric fields, and surface strains in both ex situ and in situ conditions and during the growth process of semiconductors or devices. To illustrate the performance of the spectrometer, we have measured the distribution of linear defects on the surface ð001Þ of GaAs. We choose this sample considering that (i) the distribution of defects can be easily generated by a mechanical polish of the surface of the crystal and (ii) we have a physical model that describes the line shape of the RD spectra induced by the defects. The outline of this paper is as follows. In Section 2 we describe the setup used to measure the μRD spectra. In Section 3 the line shape of the μRD spectra induced by linear defects is discussed. In Section 4 we discuss the experimental results. Finally we give conclusions in Section 5. 2. Experimental Setup
The experimental setup is schematically shown in Fig. 1. The light coming from a xenon (75 W) or a tungsten (100 W) lamp is focused by the spherical
mirrors M1 and M2 at the entrance slit of a 0:5 m monochromator (SPEX HR460). However, for measurements, we have selected the tungsten lamp, as it leads to lower noise spectra. An arrangement of two 457:2 mm focal length spherical mirrors (M3 and M4) directs the light beam at the output of the monochromator through a polarizer prism (quartz Rochon) and a photoelastic moduIator (Hinds Instruments, model PEM-90) in tandem and focuses it on the surface of the sample (spot area 5:0 mm×5:0 mm), with an angle of incidence of ∼7°. The photoelastic modulator (PEM) is operated with a λ=2 retardation during the whole wavelength range. To reduce as much as possible the astigmatism of the light beam emerging from the monochromator, the spherical mirrors M3 and M4 were vertically tilted þ10° and −10°, respectively. Upon reflection, the light beam is focused with the help of a 5× objective and a quartz lens of 75 mm of focal length on the CCD area. The CCD is a front illuminated device (Princeton Instruments, VersArray) with a resolution of 512 × 512 pixels. The controller of the CCD (ST-133A) is equipped with a 16 bit analog to digital (A/D) converter. Our system has a spatial resolution of approximately 2:50 μm × 2:50 μm and can be used in the spectral range from 1:1 eV to 5:5 eV. The Rochon prism is oriented at þ45°, and the polarization of the light incident on the sample is oriented along the ½110 direction. When the PEM is turned on, the phase of the component of the polarization perpendicular to the incidence plane switches between 0° (light polarized along ½110) and 90° (light at a frequency of 50 kHz. Conpolarized along ½110) sidering that the CCD exposure time of 0:01 s is three orders of magnitude larger that the period of the modulation of the PEM, when the PEM is turned on, we may assume that the sample is illuminated with unpolarized light. The difference in reflectivity is obtained by the numerical subtraction of two reflectivity spectra: the spectrum R½110 measured with the PEM turned off (light polarized along ½110), and the spectrum ðR½110 þ R½110 Þ=2 measured with the PEM turned on (unpolarized light). We define the reflectivity R as the numerical addition of these two reflectivity spectra. Thus the μRD signal is given by ΔR 1 R½110 − R½110 ¼ ; R½110 R 4
Fig. 1. Optical agreement of the μRD spectrometer used in this work. The polarized and unpolarized spectra are taken by turning the PEM off and on, respectively. The RD signal is obtained by subtracting numerically both spectra. The working spectral range is 1:1–5:5 eV. 5714
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ð1Þ
where we have assumed that R½110 ∼ R½110 in the denominator of Eq. (1). The PEM is operated so as to accomplish a λ=2 retardation during the whole wavelength range to maintain the relationship given by Eq. (1). Our RD configuration can also be applicable in real time spectroscopic mode. In such a mode, one can account for the voltage driving the PEM in order to obtain the correct λ=2 retardation for each measured energy [23].
3. Line Shape of the μRD Spectrum Induced by Linear Defects
A. Reflective Difference Spectra Obtained by Using a CCD and a Photomultiplier Based System
The line shape of the μRD spectra induced by the spatial distribution of defects is given by [4,5,7]
Figure 2 shows the RD spectra for our GaAs sample around E1 and E1 þ Δ1 optical transitions. Open squares show the spectrum measured with a photomultiplier-based spectrometer. In this system the electric output of the photomultiplier is analyzed by a lock-in amplifier. Open circles show the spectrum obtained by taking the numerical difference of the two reflectivity spectra obtained with the CCD, as explained in Section 2. In this case, the spectrum was obtained by taking the average of all pixels of the CCD. We have taken the average of six spectra, each measured with an exposure time of 0.01 s at each wavelength before stepping the monochromator to the next point. The RD spectrum was corrected for parasitic signals by the subtraction of RD spectra taken with the sample rotated at the azimuth angles of 0° and 45° according to the procedure detailed in
ΔR 1 dr 2 μ Δε ; ¼ 2l pρRe R nr dn
ð2Þ
where ρ is the density of the induced defects, l is the length of the linear defect, p is equal either to l or to the light penetration depth K −1 , whichever is smaller, and n and r are the complex refractive index and reflectivity, respectively. Δε is the change in dielectric function induced by the linear defects, defined as Δε ¼ ε½110 − ε½110 for a beam of light incident on the ð001Þ surface. For E1 and E1 þ Δ1 interband transitions of symmetry Λ (transitions occurring along the h111i direction in the Brillouin zone), linear defects with cores along ½110 induce a change in the complex dielectric function dominated by components proportional to the dielectric function ε and to its first energy derivative according to Refs. [4–6]. The change is written as Δε ¼
D5 4D5 dε pffiffiffi he22 iε þ p1ffiffiffi he22 i ; dE Δ1 6 2 2
ð3Þ
where Δ1 is the spin orbit splitting energy, D51 is the interband orthorhombic deformation potential, and D5 is the orthorhombic deformation potential for the valence band. The parameters are for transitions of symmetry Λ in the Brillouin zone. The parameter he22 i in Eq. (3) is the mean value of the strain corresponding to the tensor component perpendicular to the dislocation core and parallel to the surface [5]. The mean value is performed by averaging the component e22 over the area of the spot of the incident light. Assuming that the average area scans the strain field of several dislocations, we interpret the spatial dependence of the μRD amplitude as the spatial distribution of the dislocation density ρ in Eq. (2). 4. Experimental Results
To characterize the performance of the CCD-based spectrometer we performed μRD measurements on a zinc doped p-type GaAs ð001Þ sample with a carrier concentration of 1:0 × 1017 cm−3. To generate a spatial strain distribution, we lightly rubbed the sample against a cloth wet with 1:0 μm diamond abrasive compound. The rubbing movements were kept along the ½110 crystal direction, in such a way to generate dislocations preferentially aligned. The rubbing increases the strength of the RD amplitude due to the strain induced by the defects [4,5]. The spatial distribution of defects along the GaAs sample surface could then be probed by our μRD spectrometer that will respond to the average strain induced by dislocations present in the illuminated spot.
Fig. 2. RD spectra obtained by using a CCD- and PM-based spectrometers. The CCD spectrum was multiplied by pffiffiffi4 according to Eq. (1). The PM spectrum was multiplied by 2 2 to obtain the peak to peak amplitude of the signal. The solid line is the best fit obtained by using Eqs. (2) and (3). Note that although the CCD spectrum is noisier, both spectrometers measure essentially the same line shape and amplitude. 20 October 2009 / Vol. 48, No. 30 / APPLIED OPTICS
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A 1.8 [110]
∆R
R
Fig. 3. (Color online) Spacial distribution of the defects density on the surface of GaAs ð001Þ after a mechanical polishing along the ½110 direction. The surface was generated after a linear interpolation of the points obtained by fitting the amplitude of 4096 (64 × 64) spectra. Note the symmetry of the distribution oriented along the linear defects. The spatial resolution is ∼20 μm. The grid is spaced 90 μm. The performance of the instrument is excellent. 5716
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0.7
B
1.4
1.2
B. Spatial Distribution of Linear Defects
As we mentioned above, one of the advantages of the use of a CCD as a light detector is the possibility to measure the spectrum of a group of pixels, which corresponds to a specific area of the semiconductor surface under analysis. For each such spectrum the amplitude l2 phe22 iρ is obtained by following the approach described in Subsection 4.A. Assuming that the product l2 phe22 i has a constant value for any point on the surface, the spatial distribution of the RD spectrum amplitudes must be proportional to the dislocation density ρ. Figure 3 shows the spatial dependence of density on the surface of the sample. The spatial resolution is ∼20 μm, and the spacing of the grid is ∼90 μm. The
1.6
1.6
Amplitude
Ref. [24]. Note that the RD spectra obtained with both spectrometers have essentially the same line shape and amplitude, the spectrum measured with the CCD being noisier. Spectra shown in Fig. 2, including zero position, are typical of RD spectra in uniaxial strained GaAs crystals [4,5,12]. The zero position is, however, not important for our application, as our method relies on the difference amplitude between E1 and E1 þ Δ1 transitions. The solid line of Fig. 2 is the fit obtained by using Eqs. (2) and (3) and the parameters D5 ¼ −5:0 eV, D51 ¼ 8:8 eV, and Δ1 ¼ 0:22 eV [12]. The detailed fitting procedure is described elsewhere [10,12]. To fit the amplitude, we have used a least square algorithm. A value of l2 phe22 iρ ¼ 1:42 × 10−3 was obtained from the fit of the amplitude of the spectrum.
1.0
A
B 90 µm
0.8
Displacement Fig. 4. (Color online) Inset: Image of the right bottom square indicated in Fig. 3 amplified by a factor of 2. The spatial resolution is ∼10 μm, and the grid spacing is ∼45 μm. The profile obtained along the diagonal line is indicated in the inset, from point A to point B. The amplitude is normalized to the amplitude obtained in the spectrum of Fig. 3.
image was generated by performing a linear interpolation among neighboring points. The topography of the surface shows grooves with the symmetry of the defects (lines along the ½110 direction) and yields the spatial dependence of the density ρ. Brown and yellow colors indicate maximum and minimum amplitudes, respectively. To obtain a more detailed image of ρ, we have increased the resolution by a factor of 2. The inset of Fig. 4 shows the right bottom area indicated by a square in Fig. 3. The points in Fig. 4 are the profile of ρ obtained from point A to point B of the line in dicated in the inset (direction ½110). The amplitude is normalized to the amplitude of the spectrum of Fig. 2. The profile shows the changes of ρ around the unit amplitude indicated by the dashed line in Fig. 4. The results illustrate that the spectrometer can be used as a very sensitive tool for the determination of the density of defects in semiconductors or metals. 5.
Conclusions
We describe a μRDS spectrometer based on a CCD as a light detector. The performance of the instrument
was tested by measuring the μRD spectra of a zinc doped p-type GaAs ð001Þ sample with a carrier concentration of 1:0 × 1017 cm−3 slightly rubbed along the ½110 direction against a cloth wet with 1:0 μm diamond abrasive compound. The rubbing procedure generates a distribution of linear defects on the surface. As is well known, the linear defects produce a strain field that induces an optical anisotropy that can be measured using RD. The sensibility of the μRD spectrometer is good enough to resolve the differences in amplitude of the spectra among different region within the area of the spot of the light incident on the sample. The system presented in this paper would be a valuable tool for the diagnostic of anisotropic structures because it operates in reflection mode, in contrast to polarimeters suited for transmission mode, a drawback for growth environments such as in molecular beam epitaxy and metalorganic chemical vapor deposition reactors. More precisely, the μRD spectrometer constitutes a promising tool for the study and characterization of the distribution of the strain fields, surface electric fields, and roughness of the surface of semiconductors and metals. We would like to thank E. Ontiveros and G. Rodríguez-Pedroza for technical assistance. This work was supported by Consejo Nacional de Ciencia y Tecnología through grants 23962 and 79635. References 1. D. E. Aspnes and A. A. Studna, “Anisotropies in the aboveband-gap optical spectra of cubic semiconductors,” Phys. Rev. Lett. 54, 1956–1959 (1985). 2. P. Weightman, D. S. Martin, R. J. Cole, and T. Farrell, “Reflection anisotropy spectroscopy,” Rep. Prog. Phys. 68, 1251–1341 (2005). 3. G. E. Isted, P. D. Lane, and R. J. Cole, “Effect of thermally induced surface defects on the optical anisotropy of Agð110Þ,” Phys. Rev. B 79, 205424 (2009). 4. L. F. Lastras-Martínez and A. Lastras-Martínez, “Dislocationinduced effects in the reflectance-difference spectrum of semiinsulating GaAs ð100Þ,” Solid State Commun. 98, 479–483 (1996). 5. L. F. Lastras-Martínez and A. Lastras-Martínez, “Reflectance anisotropy of GaAsð100Þ: Dislocation-induced piezo-optic effects,” Phys. Rev. B 54, 10726–10735 (1996). 6. Y. H. Chen, Z. G. Wang, J. J. Qian, and Z. Yang, “Polishingrelated optical anisotropy of semi-insulating GaAs studied by reflectance difference spectroscopy,” J. Appl. Phys. 88, 1695–1697 (2000). 7. L. F. Lastras-Martínez and A. Lastras-Martínez, “Reflectancedifference spectroscopy of semi-insulating GaAs ð110Þ around the fundamental gap,” Phys. Rev. B 64, 085309 (2001). 8. A. Lastras-Martínez, R. E. Balderas-Navarro, and L. F. Lastras-Martínez, “Linear electro-optic reflectance modulated spectra of GaAs ð001Þ around E1 and E1 þ Δ1 ,” Thin Solid Films 373, 207–210 (2000). 9. L. F. Lastras-Martínez, J. M. Flores-Camacho, R. E. BalderasNavarro, M. Chavira-Rodríguez, A. Lastras-Martínez, and M. Cardona, “Effect of reconstruction-induced strain on the
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