Abstract:
This invention is a device for measuring of absolute distances by means of low coherence optical interferometry. The proposed apparatus eliminates thermal of the conventional fiber optic interferometers caused by variation of the refractive index of the optical fiber material to change of the temperature.

Description:
BACKGROUND OF THE INVENTION 
   The low coherence optical interferometry has been proven to be an effective tool for characterization of thin and ultra-thin semiconductor wafers and other materials. It is particularly valuable for the measurement of the thickness of wafers thinner than 150 μm, or wafers mounted on dielectrics materials such as tapes or sapphire plates. For these applications, standard well-established non-contact thickness gauges, such as air pressure or capacitance gauges do not provide direct physical results which meet industry process windows or require introduction of additional experimental parameters. While the bulk of effort was concentrated in the area of metrology for manufacturing of ultra thin Silicon wafers, other very promising areas include metrology of III-V materials mainly for opto-electronics and microwave applications and metrology of micro electro mechanical (MEM) structures. 
   It has been recognized that low coherence optical interferometry can be used to measure absolute distances between a probe and a wafer. The accurate distance ranging measurements are necessary when measuring physical characteristics of the wafer such as bow and warp. In practice, the absolute distance ranging measurements were not very accurate due to thermal drift of the optical elements of the system. The present invention reduces this effect, and in particular eliminates the influence of the thermal drift of the fiber optic components on performance of the low coherence optical interferometer. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
       FIG. 1  represents a conventional low coherence interferometer. 
       FIG. 2  represents a low coherence interferometer with a probe head, without a reflective base element, including ray paths. 
       FIG. 3  represents a low coherence interferometer with a probe head, with a reflective base element in collinear configuration including ray paths. 
       FIGS. 4 and 5  represent a low coherence interferometer with a probe head, with a reflective base element in non-collinear configurations, including ray paths. 
       FIG. 6  depicts an interferogram of light reflected from a reflective and nontransparent sample. 
       FIG. 7  is an example of an interferogram (expanded scale). 
       FIG. 8  depicts a temperature drift of the measured distance using the system shown in  FIG. 1 . 
       FIG. 9  depicts an interferogram of light reflected from reflective and nontransparent sample showing a probe with a reflective base element. 
       FIG. 10  represents a Michelson interferometer as shown in  FIG. 1 , in which a reflective base element is added, and the two reflections as shown in  FIG. 9 , are caused by the light, reflected from the reflective base element, and from the specimen, respectively. 
       FIG. 11  represents two Michelson interferometers, as shown in  FIG. 5 , one having its probe head in proximity to one surface of the specimen, the other having its probe head in proximity to the other surface of the specimen. 
   

   DESCRIPTION OF THE INVENTION 
   The apparatus used in the measurements is a fiber optics interferometer shown in  FIG. 1 , which represents a low coherence Michelson interferometer. Light emitted by a low coherence source is split, by means of  a  beam-splitter, into two beams: the first beam is called the reference beam, which propagates in the reference arm of the interferometer; the second portion of the beam is called the signal beam, which propagates in the signal arm. The polarization of the reference beam is controlled by means of polarization controller, and is collimated by means of lens on a reflective element, made of a reflective material, such as  a  mirror, optical flat, partially reflective optical flat, semi and transparent materials or corner cube retro reflector. The mirror resides on  a  delay stage such that the length of the optical path of the reference beam is controlled by means of an optical delay stage. The reference beam is reflected from the reference movable mirror, passes again through the polarization controller and is partially transmitted by a beam-splitter and directed to a detector. The signal beam is collimated by a lens and impinges  a  sample. The reflected portion of the signal beam is directed by means of a beam splitter cube towards a detector. 
   The intensity of the optical beam impinging  the  detector surface I d  is given by:
 
 I   d =½( I   r   +I   s )+ Re               E   r *( t +τ)· E ( t )           (1)
 
where I s  and I r  are signal and reference beams, τ is delay equal to difference of the optical paths of the signal and reference beams, t is time, E r  and E s  are electric fields of reference and signal beams respectively, and angle           . . .           bracket means averaging over t.

   When the optical paths of the signal and reference beams differ by much more than the coherence length of the source, the intensity detected by a detector is simply equal to the first τ independent term in the Equation (1); however when the paths of the reference and signal beams differ within the coherence length, then the second term becomes comparable to the first term. This phenomenon is well known and was applied in the past for distance ranging, since the optical delay time is related to the difference in length Δl between the reference and signal beams, by  a  simple formula:
 
τ=2· n·Δl   (2)
 
where n is the refractive index of the medium. Equation 2 implicitly assumes that the medium is non-dispersive within the bandwidth of the light source.
 
   An example of the interferogram of light reflected from the surface of a reflective (and nontransparent) sample is shown in  FIG. 6  and  FIG. 7 . 
   In principle, the position of the center burst can be used directly for distance ranging. The results of such a measurement are presented in  FIG. 8 . The result presented in  FIG. 8  reveals a significant drift. Experiments in which various elements of the low coherence interferometer shown in  FIG. 1  were heated, indicated that change of the optical path of the signal arm contributes the most to thermal drift, observed in  FIG. 8 . The temperature coefficient of  the  refractive index of glass is 20 ppm/° C. 
   This means that in the case of a 2 m optical fiber change of the optical length of the fiber is of the order of 40 microns/°C. The change of the physical length of the fiber due to physical thermal expansion is less significant. The coefficient of thermal expansion is several times smaller than the temperature coefficient of refractive index. 
   An insertion of one more light reflecting element (reflective base element), into the signal arm of the interferometer and placing it slightly closer to the optical fiber, connecting the probe head and the interferometer, than to the specimen to be measured, can provide one more reference point, which is independent of the thermal effect mentioned above. The distance between the new reference point and the wafer&#39;s surface can be measured instead of the wafer&#39;s surface absolute position. In the case of the thermal expansion of the fiber mentioned above, the positions of the both reflections, measured by the interferometer, will be changing synchronously and the measured distance will remain the same. 
   In  FIG. 1  light emitted by a low coherence source  501  is split by means of a beam-splitter  503  into two beams: the first beam, called a reference beam, propagates in the reference arm of the interferometer  508 , and the second beam called  a  signal beam propagates in the signal arm  505 . The polarization of the reference beam is controlled by means of  a  polarization controller  509 , and is collimated by means of  a  lens  510  on  a  reference arm movable mirror  511 . The reference arm movable mirror  511  resides on  a  delay stage such that the length of the optical path of the reference beam is controlled by means of an optical delay stage  511 . The reference beam is reflected from the reference arm movable mirror, passes again through a polarization controller  509  is partially transmitted by a beam-splitter  503  and directed to a detector  502 . The signal beam  505  is collimated by a lens  506  and impinges a sample  507 . The reflected portion of the signal beam is directed by means of  a  beam splitter cube  503  towards a detector  502 . 
   In  FIG. 2  a low coherence interferometer  5  has a external probe head  3 , placed in proximity to the specimen  1 , is connected to the interferometer by a optical fiber  4 . The light  2 , outgoing from the interferometer probe head  3 , is reflected from the specimen  1  and collected back by the probe head  3 . The electrical signal is them transferred to the computer  7  through an electrical cable  6 . 
   In  FIG. 3  the interferometer probe head  3  of the low coherence interferometer  5 , in addition has a semi-transparent reflective base element  8  placed between the specimen  1  and the probe head  3 . The portion of the light  2  outgoing from the interferometer probe head  3 , is reflected from the semi-transparent interface  8 , while the other portion is reflected from the specimen  1 . The light is collected back by the probe head  3  and transmitted to the interferometer through an optical fiber  4 . The electrical signal is them transferred to the computer  7  through an electrical cable  6 . 
   In  FIG. 4  the probe head  3  of the low coherence interferometer  5 , in addition, has a flat beam splitter  9 , placed between the specimen  1  and the probe head  3 , and a reflective surface  8 , placed on a side of the probe head  3 . The portion of the light  2  outgoing from the probe head  3 , is split by the flat beam splitter  9 , reflected from the reflective surface  8 , while the other portion is reflected from the specimen  1 . The total distance from the point of the probe head from which the light emanates, to the reflective surface  8 , is less, than that to the specimen  1 . The light is collected back by the probe head  3  and transmitted to the interferometer through an optical fiber  4 . The electrical signal is them transferred to the computer  7  through an electrical cable  6 . 
     FIG. 5  repeats the embodiment shown at  FIG. 4 , but a cubic beam splitter  9  is used instead of a flat one. 
   In  FIG. 6  an example is shown of the interferogram of light reflected from the surface of reflective (and nontransparent). When optical paths of the signal and reference beams are approximately equal strong interference feature is observed. This feature is referred to sometimes in Fourier transform interferometry as “center burst”. 
   In  FIG. 7  details of the center burst oscillations are revealed, which are spaced by approximately half of the wavelength of incident radiation λ/2, as shown in  FIG. 7 , representing an expanded interferogram. 
   In  FIG. 8  the result of the distance ranging measurement, using the system in  FIG. 1 , is shown. The result reveals large thermal drift of the system. 
   In  FIG. 9  an interferogram of light is shown reflected from a reflective and nontransparent sample using a probe with a reflective base element as described in  FIG. 4 . The interferogram reveals two features. The left feature corresponds to reflection from a reflective base element, while the right feature represents reflection from a reflection from the specimen. 
     FIG. 10  shows the low coherence interferometer already shown in  FIG. 1 , where a beam splitter  514  and a reflective base element  515 , are added to the probe head  516 . The reflective base element  515  is located closer to the beam splitter  514 , than the specimen  507 . When the reference mirror  511  moves from the right to the left (as shown in the Figure), the interferometer first comes to the condition when the optical path in the reference arm  508  becomes equal to the path to the reflective base element  515 , and one can see the first interference peak  512  on a light detector  502 , then it comes to the condition when the optical path in the reference arm  508  becomes equal to the path to the specimen  507 , and one can see the second interference peak  513  on a light detector  503 . By measuring the distance between the two said positions of the reference mirror  511 , the position of the specimen surface, relative to the position of the reflective base element, is measured. The peaks  512 ,  513  structure is same as shown in FIGS.  6 , 7 , and  9 . Peaks  512 ,  513  are shown as a light intensity vs the position of the reference mirror  511 . 
     FIG. 11  shows two Michelson interferometers  5 , as shown in  FIG. 5 , one having its probe head  3 , in proximity to one surface of the specimen  1 , the other having its probe head in proximity to the other surface of the specimen. 
   In order to eliminate the influence of the thermal drift of the length of the optical path in fiber, the optical head is redesigned in such way as to introduce the additional reflective base element residing in the signal arm of the interferometer as discussed in  FIGS. 2 ,  3 ,  4 , and  5 . The interferometer in this configuration is measuring the interference features resulting from the reflection from the reflective base element and reflections from the surface of the sample. A typical interferogram for such a measurement (in this particular case we used the configuration shown in  FIG. 5 ) is shown in  FIG. 9 . The interferogram reveals two features, one corresponding to reflection from the reflective base element and a second feature corresponding to the reflection from the sample surface. The absolute position of each of these two features is subject to thermal drift due to changes of the refractive index in the optical fibers. The difference between the positions of these two features does not depend on drift of the optical path in fibers; both features suffer the same drift. The measurements using this configuration demonstrated that thermal drift was reduced to below 0.6 μm in 10 minutes interval.