Abstract:
In a measuring apparatus for a semiconductor multiple layer structure, a spectrometer disperses light from a sample for measurement of the photoluminescence spectrum or disperses probe light to irradiate the sample for the measurement of the reflection spectrum. A controller makes a guide member guide the white light to the spectrometer and acquire electric signals from a first detector for the measurement of the reflection spectrum, and makes the guide member guide the light from the spectrometer to a second detector to acquire electric signals for the measurement of the photoluminescence spectrum.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     The present invention relates to quality evaluation and control of semiconductor multiple layer structures.  
         [0003]     2. Background Art  
         [0004]     An epitaxial wafer having a multiple layer structure is used for fabricating semiconductor devices, and the quality evaluation and control therefor are necessary in order to decrease the number of defectives and to reduce the fabrication cost. Items assessed for quality on an epitaxial wafer include thicknesses and compositions of the multiple layers. The thickness is mainly measured with a technique such as infrared-ray or X-ray interference by using interference of electromagnetic waves, or. ellipsometry (polarization analysis) by using change in the degree of polarization between incident and reflecting lights. On the other hand, the compositions of the layers in an epitaxial wafer are evaluated with band gap energies obtained by spectrum measurement of photoluminescence generated by irradiation of excitation light such as laser beams (for example, Masashi Ozaki, Semiconductor Evaluation Technique, Ch. 7 [in Japanese], ed. Takashi Katouda, Sangyo Tosho, Tokyo, 1989).  
         [0005]     There are many items assessed on an epitaxial wafer besides the above-mentioned thickness and composition. One of them is the internal electric field strength, known to depend on the doping concentration and the state at the surface/interface in an epitaxial wafer. Further, the internal electric field strength was recently reported to have a correlation with current gain in a heterojunction bipolar transistor. Therefore, the internal electric field strength is regarded as an important item in quality evaluation on an epitaxial wafer.  
         [0006]     The internal electric field strength can be measured with a technique called as light modulated reflection spectroscopy or photoreflectance (hereinafter referred also to PR) spectroscopy. In this method, change in reflectance, ΔR/R, caused by irradiating external modulated light such as laser light called as pumping light to a sample, is measured with light called as probe light (detection light). The change in reflectance, ΔR/R, is recorded as a function of wavelength or photon energy of the probe light. In a sample having an internal electric field, the change in reflectance, ΔR/R, exhibits an oscillatory profile called as Franz-Keldysh oscillations (for example, refer to “Franz-Keldysh Oscillations in Modulation Spectroscopy”, H. Shen and M. Dutta, Journal of Applied Physics, vol. 78, pp. 2151-2176 (1995)). The period of the oscillation is determined by the internal electric field strength. Therefore, the internal electric field can be investigated by analyzing the period of the Franz-Keldysh oscillations. Further, Japanese Patent laid open Publication 11-51856/1999 shows that the photoreflectance from a sample can be detected only with the integrated intensity thereof, without a spectrometer.  
         [0007]     The above-mentioned three items, thickness, band gap energy and internal electric field, are measured with techniques different from each other in the evaluation of the quality of the epitaxial wafer. Therefore, much time and work are needed in order to measure all the three items. Further, the cost is high for providing apparatuses for the three measuring techniques. This leads to a barrier for strict quality control.  
       SUMMARY OF THE INVENTION  
       [0008]     An object of the invention is to simply evaluate internal electric field strength, thickness and band gap energy in a semiconductor multiple layer structure.  
         [0009]     In one aspect of the invention, in a measuring apparatus for a semiconductor multiple layer structure, a first light source generates light for exciting a sample of the semiconductor multiple layer film to measure photoluminescence spectra and generates external modulated light to the sample for measurement of reflection spectra. A second light source generates white light for probe light to measure the reflection spectra. A spectrometer disperses light from the sample for the measurement of the photoluminescence spectra or disperses light from the first light source to irradiate the sample for the measurement of the reflection spectra. A first detector for the measurement of the photoluminescence spectra detects light emitted from the spectrometer and converts it to an electrical signal, while a second detector for the measurement of the reflection spectra detects light reflected from the sample irradiated with the probe light dispersed by the spectrometer. A guide member guides the light from the spectrometer to the first detector or guides the white light from the second light source to the second detector. A controller makes the guide member guide the white light from the second light source to the first detector and acquire electric signals from the first detector for the measurement of the reflection spectra and makes the changer guide the light from the spectrometer to the second detector and acquire electric signals from the second detector for the measurement of the photoluminescence spectra.  
         [0010]     In another aspect of the invention, in a measuring method for a semiconductor multiple layer structure, a sample of semiconductor multiple layer structure is irradiated with excitation light, and photoluminescence from the sample after transmitting a spectrometer is detected while the spectrometer is swept, and the detected light intensity is recorded as a function of photon energy. White light is entered to the spectrometer to irradiate the sample with monochromatic light emitted from the spectrometer, and the spectrometer is swept while the sample is irradiated with the external modulated light to detect reflection light from the sample, and the detected reflection spectra are recorded as a function of photon energy.  
         [0011]     An advantage of the present invention is that the internal electric field strength, the thickness and the band gap energy in a semiconductor multiple layer structure can be measured with one apparatus.  
         [0012]     Another advantage of the present invention is that the internal electric field strength, the thickness and the band gap energy in a semiconductor multiple layer structure can be measured nondestructively by measuring both photoreflectance and photoluminescence spectra of the semiconductor multiple layer structure.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0013]     These and other objects and features of the present invention will become clear from the following description taken in conjunction with the preferred embodiments thereof with reference to the accompanying drawings, and in which:  
         [0014]      FIG. 1  is a diagram of reflecting light in a semiconductor multiple layer film consisting of N layers;  
         [0015]      FIG. 2  is a graph of Franz-Keldysh oscillations of a heterojunction structure of Al 0.3 Ga 0.7 As (thickness d nm)/GaAs;  
         [0016]      FIG. 3  is a diagram of an optical measurement system in a PL/PR measuring apparatus;  
         [0017]      FIG. 4  is a diagram of a signal processing system in the PL/PR measuring apparatus;  
         [0018]      FIG. 5  is a graph of a typical PL spectrum observed with the optical measuring system shown in  FIG. 3 ;  
         [0019]      FIG. 6  is a graph of a typical PR spectrum observed with the optical measuring system shown in  FIG. 3 ; and  
         [0020]      FIG. 7  is a graph of the plot of the extremum positions of energy of Franz-Keldysh oscillations as a function of its index. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0021]     Referring now to the drawings, embodiments of the invention are described below. Previously, the thickness, the band gap energy and the internal electric field in a semiconductor multiple layer structure prepared as an epitaxial wafer or the like were measured with different techniques. Then, it is desirable to measure them nondestructively, simultaneously, precisely and simply. In order to solve this problem, it would be necessary to develop a technique/principle for evaluating two or more quality items based on data obtained by one measuring technique and to provide an apparatus which can evaluate two or more items.  
         [0022]     Then, the light modulated reflection (photoreflectance (PR)) spectroscopy used for the evaluation of the internal electric field and the photoluminescence (PL) spectroscopy used for evaluating the band gap energy are paid attention. They belong to technical field of spectroscopy and have common components for measurement. Therefore, it may be possible to provide a single apparatus for measuring light modulated reflection spectra or photoluminescence spectra, or PR and PL spectra may be measured by the single apparatus.  
         [0023]     Next, evaluation of thickness is paid attention. Many techniques of prior art evaluation for thickness is performed by analyzing spectra affected by interference due to multiple layer structure. Especially, the line shape of reflection/transmission spectra is sensitive to interference. The above-mentioned PR spectroscopy used for evaluating the internal electric field is one of the light-reflection techniques, and it may also be used for evaluating thickness. However, it is not yet known how to analyze the line shape of PR spectra affected by interference in a multiple layer film, and it is not yet used to evaluate thicknesses in a multiple layer structure.  
         [0024]     The invention proposes a spectroscopic measurement method for the internal electric field strength and thickness on the basis of PR spectroscopy in order to achieve simple and simultaneous evaluation of the internal electric field strength, thickness and band gap energy in a semiconductor multiple layer structure in an epitaxial wafer. In this method, the internal electric field strength and the thickness are obtained simultaneously from Franz-Keldysh oscillations of the semiconductor multiple layer structure. Further, a spectrum measuring apparatus is proposed to obtain both PR and PL spectra for precise evaluation based on the spectroscopic technologies. In the evaluation of the internal electric field strength and thickness from PR spectra, it is necessary to use band gap energy as a parameter. Then, as will be described below, the spectrum measuring apparatus uses the same spectrometer. Thus, the band gap energy obtained from PR spectra has no relative error to that obtained from PL spectra principally. Then, the apparatus is very advantageous for precise evaluation of thickness based on PR spectra.  
         [0025]     First, a process is explained for evaluating the internal electric field strength and thickness at the same time based on Franz-Keldysh oscillations of a semiconductor multiple layer film.  FIG. 1  shows the reflected light from a semiconductor multiple layer structure consisting of N layers, where A 0  is incident light, and A n  (n≠0) is light reflected from an interface between n-th layer L n  and (n+1)-th layer L n+1 , where n is a natural number between 0 and N. The complex amplitude reflectance r of such a multiple layer structure is represented as follows.  
               r   =       r   0     +       (     1   -     R   0       )     ⁢       ∑     n   =   1     N     ⁢       C   n     ⁢     r     n   ,     n   +   1         ⁢     ⅇ     ⅈ   ⁢           ⁢     δ   n                   ,           (   1   )             
 
 where r 0  is complex amplitude reflectance and R 0  (≡|r 0 | 2 ) is energy reflectance at the surface of the multiple layer structure, r n,n+1  is complex amplitude reflectance at L n /L n+1  interface, and C n  is a proportion constant related to transmittance. In Eq. (1), δ n  represents a quantity called as phase delay, given as follows.  
                 δ   n     =       ∑     j   =   1     n     ⁢     2   ⁢     k   j     ⁢     d   j     ⁢   cos   ⁢           ⁢     θ   j           ,           (   2   )             
 
 where j is a natural number, and k j  and d j  are wave number of light and thickness of j-th layer in the multiple layer structure, respectively. Further, θ j  is reflection angle at the j-th layer, and it can be calculated based on the incident angle to the sample and the known index of refraction of the sample. 
 
         [0026]     The energy reflectance R of the entire semiconductor multiple layer structure is given by a square |r| 2  of absolute value of the complex amplitude reflectance.  
             R   ≡     rr   *     ≈       R   0     +     2   ⁢     (     1   -     R   0       )     ⁢       ∑     n   =   1     N     ⁢       C   n     ⁢           ⁢     Re   ⁡     [       r   0     ⁢     r   n       ]       ⁢       ⅇ     ⅈ   ⁢           ⁢     δ   n         .                     (   3   )             
 
 A relationship that |r| 2 =r·r* is used here where r* is a complex conjugate of r. Further, it is assumed that the complex amplitude reflectance at the surface of the multiple layer structure is sufficiently larger than those at the interfaces therein. In a visible light region, r 0  can be taken generally as a real number. Then, the modulated reflectance ΔR n  at interface L n /L n+1  between the n-th layer L n  and the (n+1)-th layer L +1  is represented as follows.
 
Δ R   n =2 r   0 (1− R   0 ) C   n   Re[Δr   n,n+1   e   iδn ].  (4)
 
 In Eq. (4), Δr n, n+1  is proportional to modulated component δε PR   n+1  of dielectric function. That is,
 
Δ r   n,n+1   =B   n δε PR   n+1 ,  (5)
 
 where B n  is a proportion constant. In the case where δ n →0, that is, for a bulk crystal having no overlayers except the surface, Eq. (4) follows Eq. (6) on PR signals derived by Serafin et al.
 
Δ R/R=αRe[ε   PR   ]+βIm[δε   PR ].  (6)
 
         [0027]     Eq. (6) shows that the real and imaginary parts of the proportion constant B n  in Eq. (4) correspond to Serafin coefficients α and β. In the visible light region, α is generally much larger than β. Therefore, B n  can also be approximated as a real number. As a result, Eq. (4) is expressed as follows.  
               Δ   ⁢           ⁢     R   n       ∝       Re   ⁡     [     δ   ⁢           ⁢     ɛ     n   +   1     PR     ⁢     ⅇ     ⅈ   ⁢           ⁢     δ   n           ]       .             (   7   )                     δ   ⁢           ⁢       ɛ   n   PR     ⁡     (     ℏ   ⁢           ⁢   ω     )         ≡       ɛ   n   on     -     ɛ   n   off         ⁢     
     ⁢           =         -   2     ⁢           ⁢     ik   n     ⁢       ∫   0       W   n     -     Δ   ⁢           ⁢     W   n           ⁢       ⅇ     2   ⁢   ⅈ   ⁢           ⁢     k   n     ⁢   z       ⁢   Δ   ⁢           ⁢       ɛ   n     ⁡     (       ℏ   ⁢           ⁢   ω     ,       F   n   on     ⁡     (   z   )         )       ⁢     ⅆ   z           +     
     ⁢           ⁢     2   ⁢           ⁢     ik   n     ⁢       ∫   0     W   n       ⁢       ⅇ     2   ⁢           ⁢   ⅈ   ⁢           ⁢     k   n     ⁢   z       ⁢   Δ   ⁢           ⁢       ɛ   n     ⁡     (       ℏ   ⁢           ⁢   ω     ,       F   n   off     ⁡     (   z   )         )       ⁢     ⅆ   z               ,           (     8   ⁢   a     )             and                             Δ   ⁢           ⁢       ɛ   n     ⁡     (       ℏ   ⁢           ⁢   ω     ,     F   n       )         =         ɛ   n     ⁡     (       ℏ   ⁢           ⁢   ω     ,     F   n       )       -       ɛ   n     ⁡     (       ℏ   ⁢           ⁢   ω     ,   0     )           ,           (     8   ⁢   b     )             
 
 where ε n (hω/2π, F n ) is a dielectric function perturbed by electric field F n , where h is Planck constant, h is h/2π and (hω/2π) represents photon energy. F n   on (z) and F n   off (z) are strengths of electric field under the irradiation of pumping light and under no irradiation, respectively, and they are given as follows.  
                 F   n   off     ⁡     (   z   )       =         F   n     ⁡     (   z   )       ≡         F     0   ,   n         W   n       ⁢     (       W   n     -   z     )                 (     9   ⁢   a     )             and                               F   n   on     ⁡     (   z   )       =           F     0   ,   n         W   n       ⁢     (       W   n     -     Δ   ⁢           ⁢     W   n       -   z     )       =       F   n     ⁡     (     z   +     Δ   ⁢           ⁢     W   n         )           ,           (     9   ⁢   b     )             
 
 where W n  is thickness of a depletion layer, ΔW n  is change in W n  due to carriers generated by the irradiation of pumping light, and F o,n  represents electric field strength at the interface when not irradiated with the pumping light. 
 
         [0028]     Then, it is apparent that W n  and ΔW n  have a following relationship with F n  and ΔF n .
 
Δ W   n   /W   n   =ΔF   n   /F   0,n .  (10)
 
 If it is assumed that ΔE n &lt;&lt;F o,n  and k n ΔW n &lt;&lt;1, Eq. (8a) is represented as follows.
 
δε n   PR ( h ω)≈2 ik   n ∫ 0   W     n   Φ n ( z ) dz− 2 ik   n {∫ 0   W     n   Φ n ( z+ΔW   n ) z −Φ n ( W   n   +ΔW   n )Δ W   n }  (11a)
 
 where
 
Φ n ( z )≡ e   2il     n     z Δε n ( hω,F   n ( z )).  (11b)
 
 Further, by approximating
 
Φ n ( z+ΔW   n )−Φ n ( z )=( dΦ   n ( z )/ dz )Δ W   n ,
 
 and by neglecting terms higher than (ΔW n ) 2 , δε PR   n  is represented as follows.
 
δε n   PR ( hω )=2 ik   n Δε n ( hω,F   0,n )Δ W   n   (12)
 
         [0029]     At M o  singularity, Δε(hω/2π, F) is is represented as follows.  
                 Δ   ⁢           ⁢     ɛ   ⁡     (       ℏ   ⁢           ⁢   ω     ,   F     )         ∝           (     ℏ   ⁢           ⁢   Θ     )       1   /   2           (     ℏ   ⁢           ⁢   ω     )     2       ⁢     (       g   ⁡     (     -   η     )       +     if   ⁡     (     -   η     )         )         ,           (     13   ⁢   a     )             where                         η   ≡           ℏ   ⁢           ⁢   ω     -     E   0         ℏ   ⁢           ⁢   Θ       .             (     13   ⁢   b     )             
 
 In Eq. (13a), g(−η) and f(−ƒ) are functions called as electro-optic functions, and asymptotic solutions thereof at higher energy region above the band gap energy are represented as follows.  
                   g   ^     ⁡     (     -   η     )       =       1   4     ⁢     η     -   1       ⁢           ⁢     sin   ⁡     (       4   3     ⁢     η     3   /   2         )           ,           (     14   ⁢   a     )             and                             f   ^     ⁡     (     -   η     )       ≈       -     1   4       ⁢     η     -   1       ⁢       cos   ⁡     (       4   3     ⁢     η     3   /   2         )       .               (     14   ⁢   b     )             
 
 It is assumed here that the effect of the life time of electrons/holes on the electro-optic function can be neglected. 
 
         [0030]     By using the asymptotic solutions, ΔR n (hω/2π) or Franz-Keldysh oscillations are represented as follows.  
                 Δ   ⁢           ⁢       R   n     ⁡     (     ℏ   ⁢           ⁢   ω     )         ∝       1   4     ⁢       (         ℏ   ⁢           ⁢   ω     -     E     0   ,     n   +   1             ℏ   ⁢           ⁢     Θ     n   +   1           )       -   1       ⁢           ⁢     cos   ⁡     (         4   3     ⁢       (         ℏ   ⁢           ⁢   ω     -     E     0   ,     n   +   1             ℏ   ⁢           ⁢     Θ     n   +   1           )       3   /   2         +     δ   n       )           ,           (   15   )             
 
 where E o,n+1  is band gap energy of (n+1)-th layer. Further, (h/2π)Θ n+1  is a physical quantity called as electro-optic energy, and it is represented by a following Equation.  
                   (     ℏ   ⁢           ⁢     Θ     n   +   1         )     3     ≡         ⅇ   2     ⁢     ℏ   2     ⁢     F     n   +   1     2         2   ⁢     μ     n   +   1             ,           (   16   )             
 
 where e and μ n+1  are elementary charge and reduced mass of electron and hole, respectively. 
 
         [0031]      FIG. 2  shows spectra (solid line) of Franz-Keldysh oscillations measured on a two-layer sample with Al 0.3 Ga 0.7 As (having thickness of d nm)/GaAs heterojunction structure and another spectra (dashed line) of Franz-Keldysh oscillations obtained with numerical calculation with Eq. (15). The Franz-Keldysh oscillations shown in  FIG. 2  are normalized. In  FIG. 2 , “×5” means data displayed with a scale of five times on the axis of ordinates. By comparing the solid and dashed lines, it is apparent that the phase of the Franz-Keldysh oscillations obtained by the numerical calculation agrees with that obtained experimentally though many approximations and assumptions are involved in the calculation. Therefore, the photon energies, at which Franz-Keldysh oscillations have maxima or minima, agree with the counterparts at which Eq. (15) has maxima or minima. In Eq. (15), the photon energy of the m-th extremum of the Franz-Keldysh oscillations from the band gap energy E 0,n  follows Eq. (17).  
                 4     3   ⁢   π       ⁢       (       E   m     -     E     0   ,   n         )       3   /   2         =         (     ℏ   ⁢           ⁢     Θ     n   +   1         )     3     ⁢       (     m   -       δ   n     /   π       )     .               (   17   )               
 The plot of the extrema of the Franz-Keldysh oscillations according to Eq. (17) has a linear form. Then, the slope of the line gives the electro-optic energy (h/2π)Θ n+1 , and the electric field strength F 0, n+1  can be calculated from this value based on Eq. (16). On the other hand, an intercept at the axis of ordinates gives phase delay δ n . The phase delay is determined by performing this plot for the Franz-Keldysh oscillations arising from each interface. According to the definition of δ n  (Eq. (2)), a difference between δ n  and δ n−1  has a following relationship.
 δ n −δ n−1 =2 k   n   d   n cosθ n .  (18) 
         [0032]     The thickness d n  of n-th layer can be derived from this Equation. Thus, the internal electric field strength and the thickness in the layers of a semiconductor multiple layer structure can be evaluated at the same time from the Franz-Keldysh oscillations.  
         [0033]     It is known that the electric field strength can be obtained from the electro-optic energy by plotting the extrema of the Franz-Keldysh oscillations; however, the physical background on the intercept was not understood. The plot proposed here has a characteristic that the phase delay is obtained from the intercept at the axis of ordinates and that the thickness is obtained therefrom.  
         [0034]     FIGS.  3  and 4 show an apparatus to measure PR and PL spectra based on the above-mentioned principle.  FIG. 3  schematically shows an optical measuring system, and  FIG. 4  shows a signal processing system in the apparatus. In the signal processing system shown in  FIG. 4 , PR and PL signals detected by the optical measuring system are processed.  
         [0035]     As shown in  FIG. 3 , an optical path is changed with a mirror  14  in order to measure PR or PL spectra. In each case of the measurement of PR or PL spectra, the measurement data obtained by the optical measuring system is processed by the signal processing system shown in  FIG. 4 .  
         [0036]     In the optical system provided in the measuring apparatus, a light source  1  of white light is used to provide probe light, and it is, for example, a lamp. When PR spectra are measured, the mirror  14  reflects the light from the light source  1  toward a spectrometer  3 . A condenser lens  2  guides the light to the spectrometer  3  in order to generate the probe light. The spectrometer  3  generates monochromatic light from the lamp light and supplies the probe light to detect the reflectance R and modulated reflectance ΔR. The condenser lens  4  focuses the probe light generated by the spectrometer  3  onto the surface of a sample  5 .  
         [0037]     Further, a light source  9  for excitation light, such as a laser device, generates the external modulated light when PR spectra are measured. A power stabilizer  10  stabilizes the power of the light source  9 . A filter  11  for the light source such as a neutral density filter is provided for controlling the intensity of the excitation light. A modulator  12  such as an optical chopper converts the continuous wave form of the light to a square wave form. A condenser lens  13  focuses the external modulated light onto a region irradiated with the probe light in a surface of the sample.  
         [0038]     The excitation light source  9  such as a laser device generates the excitation light for PL spectrum measurement and/or the external modulated light for PR spectrum measurement. The spectrometer  3  generates the monochromatic light used as the probe light from the light emitted by the light source  1  in order to detect reflectance R and modulated reflectance ΔR. Further, the spectrometer  3  is used to disperse the light from a sample when PL spectra are measured.  
         [0039]     The condenser lens  6  guides the probe light reflected from the sample  5  to a detector  8  for PR measurement. A long path filter  7  removes the external modulated light scattered at the sample  5 . The detector  8  converts the light signals reflected from the sample  5  to electrical signals.  
         [0040]     When PL spectra are measured, the light source  9  generates excitation light for the sample  5 . The lens  4  condenses the light emitted from the sample  5 , as shown with dashed line, to the spectrometer  3 . The spectrometer  3  disperses the light emitted from the sample  5 , and the condenser lens  2  sends the photoluminescence to a detector  15 . At this time, the direction of the mirror  14  is changed so that the as-received photoluminescence is sent to the detector  15 .  
         [0041]      FIG. 4  schematically shows the signal processor for signals detected by the measuring system shown in  FIG. 3 . In the signal processor, a current-to-voltage converter  21  converts a current signal received from the detector  8  or  15  to a voltage signal. A band-path filter  22  is a frequency filter for separating the ac (corresponding to ΔR) and dc signals (signal R) from the overall signal. A dc voltmeter  23  is a device for measuring the dc component. A lock-in amplifier  24  is a device used for phase detection of the ac components or lock-in detection. A reference frequency signal for the lock-in amplifier  24  is provided from a modulator  12  of the optical measuring system. When the pumping light is intermittent light, the signal from the detector  15  is measured by the lock-in amplifier, while when it is a continuous light, the signal is measured by the dc voltmeter  23 . A computer  25  controls the above-mentioned components for the measurement, acquires all the signals, and calculates on the basis of the acquired signals. The computer  25  controls the spectrometer  3  and records input signals from the dc voltmeter  23  or the lock-in amplifier  24 . For example, for the modulated reflection spectra, the change in reflectance ΔR/R is calculated and recorded based on the signals from the detector  15  as a function of photon energy (hω/2π). Thus, the change in reflectance ΔR/R can be recorded as a function of photon energy (hω/2π). Then, by deriving and plotting the above-mentioned Franz-Keldysh oscillations of the semiconductor multiple layer structure, the internal electric field strength and the thickness are evaluated simultaneously based on the Franz-Keldysh oscillations.  
         [0042]     Next, steps for a measurement with the spectrum measuring apparatus is explained.  
         [0043]     (A) In order to measure PL spectra of an epitaxial wafer (sample  5 ), the direction of the mirror  14  is changed so that the light from the sample  5  enters the detector  15 . When the PL spectra are measured, it is desirable to deactivate the unnecessary light source  1  of white light.  
         [0044]     (B) The excitation light such as laser light irradiates the sample  5 . The excitation light may be intermittent light generated by the modulator  12  or continuous light without using the modulator  12 . However, if the light from the sample is very weak, in order to improve signal-to-noise ratio, the combination of the modulator  12  and the lock-in amplifier  24  is used, where the lock-in amplifier  24  is used to detect the light in synchronization with the phase of the intermittent light. In this case, the phase of the lock-in amplifier is matched with that of the intermittent light as follows. First, the excitation light scattered by the sample  5  is collected by the condenser lens  4  to the spectrometer  3 . Then, the detector  15  detects the light transmitting the spectrometer  3 , and the phase of the lock-in amplifier  24  is matched with the detected signal.  
         [0045]     (C) The light from the sample  5  transmits through the lens  4  to a slit of the spectrometer  3 .  
         [0046]     (D) The light outgoing from the spectrometer  3  is focused by the lens  2  onto the detector  15  which converts the optical signal to an electrical signal.  
         [0047]     (E) The signal obtained by the detector  15  is measured with the lock-in amplifier  24  when the pumping light is intermittent light, or with the dc voltmeter  23  when it is continuous light.  
         [0048]     (F) Light intensity is recorded, by sweeping the spectrometer  3 , as a function of wavelength λ or photon energy (hω/2π) as shown in  FIG. 5 .  
         [0049]     (G) The band gap energy is determined based on peaks of the observed photoluminescence spectra. The positions of the peaks correspond to band gap energy of each layer.  
         [0050]     (H) Next, the direction of the mirror  14  is changed in order to measure PR spectra of the epitaxial wafer, so that the light of the white light source  1  (such as a lamp) enters the spectrometer  3 . In this state, the light outgoing from the spectrometer  3  is probe light.  
         [0051]     (I) External modulated light such as a laser beam from the light source  9  is irradiated onto the sample  5 .  
         [0052]     (J) By removing the long path filter  7 , the external modulated light scattered by the sample  5  enters the detector  8 . In this state, the phase of the lock-in amplifier  24  is matched with the detected signal as a reference signal.  
         [0053]     (K) The long path filter  7  is inserted so that the external modulated light is prevented from entering the detector  8 .  
         [0054]     (L) The spectrometer  3  is swept, and the probe light is detected by the detector  8 .  
         [0055]     (M) The detected signal is transmitted through the band path filter  22  to separate the dc component corresponding to reflectance R from ac components corresponding to modulated reflectance ΔR.  
         [0056]     (N) The dc and ac components are measured with the dc voltmeter  23  and the lock-in amplifier  24 , respectively.  
         [0057]     ( 0 ) The computer  25  calculates ΔR/R to obtain PR signals.  
         [0058]     (P) By repeating the above-mentioned steps K to O, the PR spectra ΔR/R is recorded as a function of wavelength λ or photon energy (hω/2π).  
         [0059]     (Q) Numbering is performed on the extrema appearing in the Franz-Keldysh oscillations in the PR spectra, in the order from E 0  to higher energy, as shown in  FIG. 6 . The numbers (m=1, 2, 3, . . . ) shown in  FIG. 6  represent indices for the extrema of the Franz-Keldysh oscillations in the photoreflectance (PR) spectrum, and an arrow shows the position of band gap energy E o . It is noted in  FIG. 6  that the scale of the axis of ordinates is displayed in five times for indices equal to or larger than 6.  
         [0060]     (R) The obtained extrema are plotted according to Eq. (17). As shown in an example in  FIG. 7 , ζ is proportional to index m.  
         [0061]     (S) Fitting is performed with parameters (h/2π)Θ n  and δ n  in Eq. (17).  
         [0062]     (T) The electric field strength is obtained from (h/2π)Θ n  according to Eq. (16), and the thickness is determined from δ n  according to Eq. (18).  
         [0063]     Although the present invention has been fully described in connection with the preferred embodiments thereof with reference to the accompanying drawings, it is to be noted that various changes and modifications are apparent to those skilled in the art. Such changes and modifications are to be understood as included within the scope of the present invention as defined by the appended claims unless they depart therefrom.