Optics: measuring and testing – Refraction testing – Schlieren effect
Reexamination Certificate
1999-04-14
2001-01-30
Rosenberger, Richard A. (Department: 2877)
Optics: measuring and testing
Refraction testing
Schlieren effect
C324S754120
Reexamination Certificate
active
06181416
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to methods and apparatus for imaging the carrier density and temperature of semiconductor circuits.
BACKGROUND OF THE INVENTION
Schlieren Imagery
Schlieren imagery is an imaging process whereby changes in the angular deviation of an optical beam are transformed into changes in the intensity of the Schlieren image. A Schlieren imaging apparatus contains two image planes, a source image plane, where an image of the optical source is produced, and an object image plane, where an image of the object illuminated by the optical source is produced. Refractive index gradients in the object produce angular deviations in the optical beam. These angular deviations are transformed by the Schlieren optics into deviations in the position of the optical source image. A filter, e.g. a knife-edge, placed in the plane of the source image causes the angular deviations to produce intensity shifts in the object image.
There are many variations in the basic Schlieren concept. For example, dark field microscopy is a form of Schlieren imagery. However, all Schlieren apparatus utilize a finite size source with some preset geometry and a mask (typically at the source image plane) which causes amplitude variations to appear in the object image as a result of refractive index gradients in the object. For the following discussion, a knife-edge type Schlieren system as described in
Schlieren Methods,
L. A. Vasil'ev, pages 86-149 is assumed. For small angular deviations, it can be shown that the change in object image intensity is linearly related to the refractive index gradient in the illuminated object by
Δ
I
=
kI
0
∫
∂
n
∂
x
ⅆ
z
,
(
1
)
where k is a constant relating to the source size, object transmission and reflection parameters, and focal powers of the imaging system, I
0
is the illumination intensity, n is the refractive index of the object, z is in the propagation direction of the optical beam, and x is the direction perpendicular to the knife-edge and z.
Semiconductor Imagery
The refractive index of semiconductors is known to be affected by the internal properties of the semiconductor. Specifically, the electric field, temperature, and carrier density will all cause changes in the refractive index. Table 1 contains theoretical estimates for the magnitude of these effects in terms of small signal variations for GaAs (gallium arsenide). The effects of electric field, E, temperature, T, and electron density, N
e
, on refractive index, n, are shown. The effect of hole density is similar to electron density. Other semiconductor materials, such as silicon will show similar behaviors.
TABLE 1
Semiconductor Property
Refractive Index
Electric Field
δn
δE
=
3
×
10
-
9
(
cm
/
V
)
Temperature
δn
δT
=
3
×
10
-
4
(
1
/
K
)
Carrier Density
δn
δN
e
=
4
×
10
-
21
(
cm
3
)
Electric fields only affect the refractive index of semiconductors which are noncentrosymmetric. For example strong electro-optic effects occur in GaAs but not in silicon. Techniques for obtaining electro-optic images in noncentrosymmetric semiconductors, specifically GaAs are described in “Electro-Optic Imagery of High-Voltage GaAs Photoconductive Switches,” R. A Falk, J. C. Adams, C. D. Capps, S. G. Ferrier, and J. A Krinsky, IEEE Trans. Electron Devices 42, 43-9 (1995), and “Electro-Optic Imaging of Internal Fields in (111) GaAs Photoconductors,” J. C. Adams, R. A. Falk, S. G. Ferrier, and C. D. Capps, IEEE Trans. Elect. Devices 42, 1081-85, (1995). These techniques involve analyzing the polarization rotation of light passing through the GaAs sample, whose wavelength is well below the absorption bandedge. In order to compensate for the multi-valued nature of the polarization rotation, specialized algorithms were utilized to process the images. Although a remarkable measurement, the techniques employed will not work in semiconductors such as silicon and are only useful for electric fields, i.e. they are not applicable to temperature or carrier density measurements.
Heinrich et al. and Goldstein et al. have demonstrated optical, high-speed sampling of carrier density and thermal effects in semiconductors at a single spatial point. Electric field could be sensed indirectly through the change in carrier density, which occurs in the depletion region of reversed biased junctions. The work of the first group is described in “Noninvasive Sheet Charge Density Probe for Integrated Silicon Devices,” H. K. Heinrich, D. M. Bloom, and B. R Hemenway, Appl. Phys. Lett. 48, 1066-8, (1986). The work of the second group is described in “Heterodyne Interferometer for the Detection of Electric and Thermal Signals in Integrated Circuits through the Substrate,” M Goldstein, G. Solkner, and E. Gornik, Rev. Sci. Instrum. 64, 3009-13 (1993). Both of those optical arrangements utilized interferometric means to extract a signal from the changes in refractive index caused by the two effects. In both cases, a pair of optical beams is brought in through the backside of the semiconductor device. One beam, used as a reference, is reflected off of a convenient point on the upper surface of the device and brought back into the optical detector. The second beam is positioned onto the point of interest, reflected off of the upper surface and combined with the reference beam to form the interferometric signal. In the case of Heinrich, et al., a modified Nomarski interference microscope was utilized as the interferometric system. Goldstein, et al. utilized a variant on a heterodyne, interference microscope.
The detection schemes of Heinrich, et al. and Goldstein, et al. were performed at a single point. An extension of their work could be to scan the optical beam(s) in order to assemble an image of the target. An imaging system may one-day be devised that utilizes a point-by-point sequential scanning method in which an image of an entire object may be created by accumulating several images of different optical spots on the object. While effective for some circumstances, there are, however, situations in which sequential scanning may still be impractical. Specifically, the timing of the scanning should preferably correspond to the timing of changes in the refractive index of the object. If, for example, a “single shot” event occurs in which the refractive index change only occurs for a small, fixed period of time, then the optical spot may not be present at the point of the refractive index change when it occurs. In that case, the image obtained would not properly reflect the change in the refractive index.
An adequate solution to the above problems has eluded those skilled in the art. More specifically, a need exists for a method or apparatus for imaging the internal characteristics of a semiconductor circuit, including temperature and carrier density, independent of the timing of the circuit.
SUMMARY OF THE INVENTION
In accordance with this invention, a method and apparatus for imaging the carrier density and temperature in a semiconductor circuit or device is provided. An imaging system in accordance to this invention includes an optical source combined with a first knife-edge. The optical beam from this combination is collimated and passed through a semiconductor device. An image of the combination is then formed at the position of a second knife edge. In addition, an image of the semiconductor device is formed at some distance behind the second knife-edge. The arrangement of the optical system is such that angular deviations in the optical beam caused by refractive index gradients in the semiconductor device are transformed into intensity variations in the image of the semiconductor device. The refractive index gradients result from carrier density or temperature variations inside the semiconductor device. Thus, an image of the carrier density or temperature gradients in the semiconductor device is obtained.
In addition to the optical system described above, the invention includes means t
Black Lowe & Graham PLLC
Optometrix Inc.
Rosenberger Richard A.
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