SU1659792A1 - Interference technique for measuring index of refraction and index of absorption - Google Patents

Abstract

The invention relates to technical physics, in particular to non-destructive methods of quality control of semiconductor structures in microelectronics. The purpose of the invention is the extension of the class of plane-parallel plates under study to plates with a smaller thickness while simplifying the determination of the indices of refraction and absorption of a plane-parallel plate. The interference transmission or reflection spectrum is measured at an angle of incidence of radiation of 6-70 ° C. and, using an iterative method, solve a system of equations relating these indicators to the calculated and experimental data. As the calculated and experimental data, the ratios of the intensities and coordinates of successive reflections on the calculated interferogram and on the experimental interferogram obtained by the complex Fourier transform of a fragment of the interference transmission or reflection spectrum in the studied range are used, regardless of the degree of absorption in this range. 2 Il. (Ls

Description

The invention relates to optics, technical physics, mainly to non-destructive methods for studying materials, in particular, to microelectronics.

The aim of the invention is to expand the class of plane-parallel plates under study to plates with a smaller thickness while simplifying the measurement process.

Fig. 1 shows a scheme for measuring reflection and transmission spectra; Fig. 2 is a view of the module of the complex Fourier transform of the experimental and calculated interferograms;

A device for implementing the method contains a source of light 1, mirror lenses 2 and 3, rotating mirrors 4, 5 and 6, a monochromator 7 connected to a receiving-amplifier unit 8, the output of which is connected to a computer complex 9. The sample 10 can be located in an attachment in two positions ensuring the registration of the spectrum in the transmitted and reflected radiation. In figure 2 - curve 11 corresponds

VI

yu yu

curve, and curve 12 - the experimental values of the interferogram.

The method is carried out as follows.

The transmission spectrum, for example, a 500 μm thick silicon wafer, is measured on an IKS-25 quasi-two-beam infrared vacuum spectrometer. The spectral range is 839.5-1044.0, the spectral width of the target is 0.5 cm, the recording step is 0.05 (10 samples per width of the slit), the signal-to-noise ratio is 100, the angle of incidence of the radiation is selected in the range from 6 to 70 °, moreover, its lower limit is determined by the parameters of the attachment, and the upper one by the value of the Brewster angle for the material under study.

The resulting spectral curve is processed in fragments of 4096 points. Since the main integral of the Fourier transform must be calculated in infinite limits, and the spectrum measurement range is finite, an apodization operation (multiplication by a weight function) is performed to suppress the resulting side maxima of the interferogram.

Each fragment is apodized using the Gauss apodization function with a half-width of 8 cm centered around the center of the fragment, after which a complex Fourier-representation is performed (dimensionality is 4096 points). In a hollow interferogram, the program automatically determines the values of the ratio Z3 of the intensity of the first reflection AI to the intensity of zero AO (central maximum)

 Ai

Z. - -

AO

and the distance-Ae between these reflexes with coordinates Xi and Ho De Xi - Ho,

The expression for calculating the theoretical transmission spectrum is the ratio of the square of the magnitude of the transmitted light to the square of the amplitude of the incident light.

The complex amplitude of transmitted light is obtained by summing an infinite number of contributions corresponding to multiple reflection of a light wave in a layered structure. At the same time, the amplitude reflection and transmission coefficients are calculated using the Fresnel formulas for absorption media, taking into account the complex nature of the parameters of the phase shift,

The initial calculated transmittance spectrum is calculated by the formula

T (H6 (L) (Un)

, (4-n | 4k "l (((V-k4W; i" cos (4lUntJ) + BkO-TAk) .5; n (4V) n, J),

where T is the transmission of the studied material;

V is the wave number, cm;

d is the material thickness

n, k are the refractive indices and absorption indices, respectively.

The refractive indices and absorption indices were given by the following initial values of n no 3.0, k ko 0. The calculated spectrum was processed similarly to the experimental one, obtaining Zp and dr. Then the system of equations that are nonlinear with respect to n and k was solved iteratively.

Zp Z3 Dr De

The iteration process is terminated when the values of n and k found ensure that the left and right sides of the equations of the system coincide with a given accuracy.

With the above initial parameters, the iteration process was completed in 7 cycles. The calculated values obtained correspond to the characteristics of the sample. The method is demonstrated on a single-layer structure, but its application is most effective for multilayer structures.

Using the method in the electronics industry as a non-destructive method of quality control of semiconductor structures at the initial stages of the technological process of their creation will significantly increase the percentage of usable products.

Claims (1)

The invention The interference method for determining the refractive index and absorption index, including the direction of the sample, made in the form of a plane-parallel plate, the luminous flux, recording its interference spectrum and determining the refractive index and absorption indices by solving the parameters with the calculated and registered interference spectra, characterized in that, with the aim of expanding the class of test planes ial, plates on the plate with a smaller thickness in simplifying the measurement process, the light flux is directed at an angle plate studied on. satisfying the relation yuschim 6 ° and arctg n max where Pmax is the maximum value of the measured refractive index, the interference spectrum of the plate is recorded in the past or reflected spectrum, The ratio of the intensities and the difference in coordinates of consecutive reflections on the obtained and calculated interferograms are measured. obtained by the complex Fourier transform of the calculated and recorded interference spectra, and the refractive indices and plate absorption is determined by solving an iterative method of a system of equations relating these indicators with the ratio of intensities and the difference in coordinates of consecutive reflexes on interferograms. Yu Have 9 Fig 1 7.5