DE10307423B4 - Method for determining the quality of crystals - Google Patents

Abstract

Method for determining the quality of in particular strongly ionic crystals, in which an electromagnetic radiation (13) is irradiated onto a crystal and the reflection (15) of this radiation in the crystal (14) is determined in a wavelength range λ ₁ to λ ₂ , characterized in that Wavelength range includes an absorption region in which the radiation is absorbed to form excitons, this absorption generates a width-having peak, a peak width determined and from the peak width, the quality of the crystal is determined.

Description

The The invention relates to a method for determining the quality of, in particular strongly ionic, crystals and the use of such specific crystals.

For the picture properties The crystals used in optics are often flaws and dislocations important in the crystal. Especially for the optics for the high-energy Short-wave radiation in the far ultraviolet, as for example for the Microlithography, these are defects and dislocations, So all deviations from the perfect lattice periodicity, of particular Importance. For this short-wave electromagnetic radiation having a wavelength of, for example 193 nm or 157 nm or even less are only a few materials for optics suitable. One currently common used material is calcium fluoride. The quality of the available crystals is now so good that on crystals with thicknesses a few centimeters practically no absorption in the mentioned wavelength determine. however has been shown that electromagnetic Radiations of such short wavelengths nevertheless a damage (Laserdamage) in the material, which increases the absorption.

In WO 01/86032 is a multi-step method for quality determination of fluoride crystals containing Pb, Ce and Na as impurities contain. This is in addition to the induced by lead absorption Luminescence also the orientation of small angle grain boundaries Diffraction of synchrotron radiation determined.

The underlying problem of the invention is to provide a method with the quality of crystals even then can be determined quantitatively, though absorption is virtually undetectable.

To solve the problem, a method of the type mentioned is given, in which an electromagnetic radiation is irradiated to a crystal and the absorption or change of this radiation in the crystal in reflection in a predetermined wavelength range of λ1-λ2 is determined. The method according to the invention is characterized in that the predetermined wavelength range encompasses the region at the lower edge of the band edge in which the radiation is absorbed by excitons in the crystal and wherein the wavelength-dependent reflectivity R = (I ^Refl (λ)): ( I ^In (λ)) is detected. The wavelength dependence of the reflectivity is used as a measure of the quality of the crystal. As expedient features for determining the quality, the position of the minimum and the maximum in particular to each other and the intermediate slope have shown. Preferably, however, a complex dielectric function ε is determined in the absorption region and from this the imaginary part ε "is determined. The peak width in particular serves the peak half-width of the imaginary part in the absorption region, ie in the region of the exciton formation as a measure of the quality of the crystal.

The method according to the invention is based on the finding that energy-rich electromagnetic radiation can produce so-called excitons even in the case of nearly perfect crystals. Such an exciton arises when an electron is raised from a valence band of the crystal into a conduction band of the same, thereby creating a hole, that is, a position in the valence band that lacks negative electrical charge. These two interact and the resulting electron-hole pair is called an exciton. The excitation energy for such an exciton corresponds to the band gap between the valence band and the conduction band, reduced by the binding energy of the exciton. In particular, so-called free excitons arise with an electron-hole distance which is approximately in the range of the lattice constant. These excitons are scattered at defects or dislocations. The scattering of local impurities shortens the exciton lifetime τ ^-1 = τ ^-1 _ph + τ ^-1 _sc , where ph signifies phonons and sc scattering. If electromagnetic radiation is successively generated in succession for several wavelengths, irradiated onto the crystal and the intensity of the reflected radiation is measured, this can be used to determine the wavelength-dependent complex dielectric function. It has been found that the imaginary part of the dielectric function describes a peak that can be assigned to an exciton. This peak contains a maximum value and a specific peak width. The peak width of this exciton peak is small enough so that this peak, in particular, the peak width can be determined quite clearly. It has been found that the lifetime 1 / half width of the exciton, especially at low temperatures, is a sensitive measure of the number of defects and dislocations in the crystal.

Especially good for the quality determination is suitable the half-width of the exciton peak. The half width of the exciton peak hangs together with the lifetime of the exciton. In particular, the Halfwidth of the exciton peak inversely proportional to the lifetime the exciton.

ever there are more defects and dislocations in the crystal, the faster decays the exciton again and the shorter is thus the lifetime of the exciton. The half width of the Thus, exciton peaks are a measure of disorder, ie defects and dislocations in the material, i. the half width is all the more bigger, ever bigger the Clutter in the crystal is.

at Another embodiment of the invention is the electromagnetic Radiation high energy radiation, especially synchrotron radiation. By means of this high-energy radiation, the quality of the crystal can be determine particularly efficiently. A preferred high energy Radiation is synchrotron radiation, which is high quality and high intensity available is.

It is also advantageous if the given wavelengths by means of a monochromator be set. This monochromator allows a narrow wavelength range gradually to select sequentially. As a result, good and reproducible results can be achieved. In particular, this makes a stepwise scan possible.

at an embodiment The invention relates to the radiation at a gap surface, in particular the (111) surface, reflected. Such cleavage surfaces can be in high quality generate, so that unwanted errors in the quality determination of the crystal can be excluded. In particular, the (111) area let yourself produce quickly and easily.

wobei ω = c/λ
n₀ der statische Brechungsindex des Kristalls ist,
τ die Exzitonenlebensdauer ist,
ω₀ der Exzitonenanregungsenergie entspricht,
ε_band der Anteil der Anregungen über die Bandlücke ist,
λ die Wellenlänge ist,
aus der Funktion

wobei R (λ) das wellenlängenabhängie Reflexionssignal,
ε (λ) die komplexe dielektrische Funktion,
λ die Wellenlänge ist,
mittels eines least-square Algorithmus ermittelt wird. Bei diesem sogenannten least-square Algorithmus werden die einzelnen Parameter variiert und zu jeder Wellenlänge die Abweichung des berechneten Intensitätswertes von dem gemessenen Intensitätswert bestimmt. Anschließend wird die Summe der Quadrate der Abweichungen gebildet. Als Ergebnis erhält man die Parameter, für die sich ein Minimum der Summe der Quadrate dieser Abweichungen ergibt. Dieser least-square Algorithmus kann beispielsweise auf einem konventionellen Computer durchgeführt werden. Standard fit routine aus dem gnu C⁺⁺ libraries wie es beispielsweise in dem Programm "gnuplot" implementiert ist (erhältlich unter www.gnuplot.info/).A development of the invention is characterized in that the wavelength associated with the maximum value and / or the half-width with one approach

where ω = c / λ
n _{0 is} the static refractive index of the crystal,
τ is the exciton lifetime,
ω ₀ corresponds to the exciton excitation energy,
ε _{band is} the fraction of excitations across the band gap,
λ is the wavelength,
from the function

where R (λ) is the wavelength-dependent reflection signal,
ε (λ) the complex dielectric function,
λ is the wavelength,
is determined by means of a least-square algorithm. In this so-called least-square algorithm, the individual parameters are varied and the deviation of the calculated intensity value from the measured intensity value is determined for each wavelength. Subsequently, the sum of the squares of the deviations is formed. As a result one obtains the parameters for which a minimum of the sum of the squares of these deviations results. For example, this least-square algorithm can be performed on a conventional computer. Standard fit routine from the gnu C ⁺⁺ libraries as implemented for example in the program "gnuplot" (available at www.gnuplot.info/).

in principle is the inventive method detectable at a reflection signal at any angle, however it is preferable that the reflection signal as close to as possible as vertical as possible To determine radiation incidence. This means that the radiation incidence and the measured reflection signal as possible at right angles to the surface of the Crystal should stand. Preferred deviations are maximum 15 degrees, in particular a maximum of 10 degrees, with a maximum of 5 degrees or maximum 2 degrees is very particularly preferred.

Even though the determination of the invention also under normal atmosphere (Pressure, air, etc.) feasible is, it is preferably in vacuum, especially in ultra-high vacuum carried out. This allows the influences exclude from contamination by the ambient air. Especially, when the electromagnetic radiation is reflected at a cleavage surface should be, can be to ensure a clean and reproducible gap.

at Another embodiment of the invention is at least the crystal while the quality determination stabilized to one, in particular low temperature. Through this stabilized as homogeneous as possible Crystal temperature will be better comparability of each intensity data guaranteed. At a low temperature, thermal effects can also be achieved to reduce. Ideally, at T = 0 Kelvin only the Scattering of impurities (impurities, Dislocations), which limit the life of an exciton. Usual measuring temperatures are 4 or 4.2 K to 400 K, preferably 75 or 77 K to 300 K. To be particularly useful Temperatures between 150 in particular 170 K and room temperature proved. In a particularly preferred embodiment, the to be determined Crystal while of the entire measurement process the entire volume on a uniform temperature.

The Method with the features of the invention can be advantageous for quality determination use of strongly ionic crystals. In particular, it is suitable for quality determination of calcium fluoride, magnesium fluoride, barium fluoride and strontium fluoride and mixed crystals and of corundum crystals such as sapphire.

in the The following will be an embodiment of Invention with reference to the figures explained. Show it:

1 a schematic representation for carrying out the method with the invention features,

2 a reflectance measured with synchrotron radiation, plotted versus wavelength, and

3 a from the measurement in 2 derived diagram of the real part and the imaginary part of the dielectric function, plotted over the wavelength.

1 shows a schematic representation of an apparatus for performing the method with the features of the invention. Shown is a radiation source 10 for generating electromagnetic radiation 11 , The radiation source 10 for example, a synchrotron 10 for generating synchrotron radiation 11 be. The of the synchrotron 10 outgoing synchrotron radiation 11 goes through a monochromator 12 for generating a monochromatic radiation 13 , The monochromatic radiation 13 meets a crystal 14 and is reflected on this. The reflected radiation 15 gets from the crystal 14 to a detector 16 where the intensity of the reflected radiation 15 is measured. Not in the 1 shown is a control for the monochromator 12 and the crystal 14 , Wieterhin not in the 1 illustrated are evaluation means, such as a computer, for receiving and evaluating the detector 16 measured intensity. The controller, not shown in the figure, is for adjusting that of the monochromator 12 transmitted wavelength range and for the eventual control of the parameters of the crystal 14 , Such parameters can, for example, the angle of the crystal 14 to the monochromatic radiation 13 as well as the temperature of the crystal 14 be.

Also not shown in the figure are means for adjusting the temperature of the crystal 14 ,

wobei I (λ) die von dem Detektor 16 ermittelte Intensität der reflektierten Strahlung 15 und I₀ (λ) die Intensität der monochromatischen Strahlung 13 ist. Für das Reflexionssignal R gilt die folgende Gleichung:

wobei ε (λ) die komplexe dielektrische Funktion und λ die Wellenlänge ist. Mit einem Ansatz:

wobei ω = c/λ,
n₀ der statische Brechungsindex des Kristalls ist,
τ die Exzitonenanregungsenergie ist,
ω₀ der Exzitonenanregungsenergie entspricht,
ε_band der Anteil der Anregungen über die Bandlücke ist, und
λ die Wellenlänge ist,
läßt sich mit Hilfe eines geeigneten Algorithmus die komplexe dielektrische Funktion bestimmen. Dazu können beispielsweise die einzelnen Parameter mittels eines sogenannten least-square Algorithmus variiert werden und zu jedem Satz Parameter die Abweichung des so ermittelten Reflexionssignales von dem gemessenen Reflexionssignal bestimmt werden. Es wird dann für alle Wellenlängen die Summe der Quadrate der Abweichungen bestimmt. Als Ergebnis des leastsquare Algorithmus erhält man den Parametersatz mit dem diese Summe der Quadrate der Abweichungen den kleinsten Wert annimmt. Die komplexe dielektrische Funktion läßt sich dabei aufteilen: ε(λ) = ε'(λ) + ε''(λ) 2 shows a diagram of reflectivity. Plotted is the reflectivity determined with a synchrotron radiation on the ordinate against the wavelength in nm on the abscissa. The reflectivity R is given as an absolute dimensionless variable between 0 and 1 normalized to the radiated intensity:

where I (λ) is the one from the detector 16 determined intensity of the reflected radiation 15 and I ₀ (λ) the intensity of the monochromatic radiation 13 is. For the reflection signal R, the following equation holds:

where ε (λ) is the complex dielectric function and λ is the wavelength. With an approach:

where ω = c / λ,
n _{0 is} the static refractive index of the crystal,
τ is the exciton excitation energy,
ω ₀ corresponds to the exciton excitation energy,
ε _{band is} the fraction of excitations over the band gap, and
λ is the wavelength,
can be determined using a suitable algorithm, the complex dielectric function. For this purpose, for example, the individual parameters can be varied by means of a so-called least-square algorithm, and the deviation of the reflection signal thus determined from the measured reflection signal can be determined for each set of parameters. The sum of the squares of the deviations is then determined for all wavelengths. As a result of the leastsquare algorithm, one obtains the parameter set with which this sum of the squares of the deviations assumes the smallest value. The complex dielectric function can be divided: ε (λ) = ε '(λ) + ε''(λ)

Where ε ^| (λ) the real part and ε ^|| (λ) the imaginary part of the complex dielectric function ε λ).

3 shows a diagram of the dielectric function plotted against the wavelength. Plotted is the real part or the imaginary part of the dielectric function on the ordinate versus the wavelength in nm on the abscissa. The real part ε ^| (λ) is represented by a solid line in the figure. The imaginary part ε ^|| (λ) is shown in the figure with a dotted line. As the figure is in the range of a wavelength of 112 nm, a maximum of the imaginary part ε ^|| (λ).

This Maximum can be the generation of a so-called exciton in the calcium fluoride crystal used assign.

The peak width associated with the exciton peak is indicative of the density of the impurity at which the exciton is scattered. The exciton peak is at CaF ₂ at a wavelength of 112 nm.

Further is the width of this exciton peak of the lifetime τ of the exciton inversely proportional. Entered in the figure is the so-called half-width H, at the intensity has subsided to its half value. As a measure of the width but can also other definitions of width are used, such as the 1 / e width at which the intensity subsided to a value 1 / e is.

Since the relationship applies: Hα1 / τ is the width, namely the half width H, a measure of the disorder in the crystal. The lifetime τ of an exciton is the smaller, the more deviations from the perfect lattice periodicity caused by chemical impurities or dislocations exist in the crystal. In this way, by determining the width H, it is thus possible to determine both the density of the impurities and, at the same time, the density of crystal defects, such as dislocations etc., in a crystal.

10

synchrotron

11

synchrotron

12

monochromator

13

monochromatic radiation

14

crystal

15

reflected radiation

16

detector

Claims (10)

Method for determining the quality of in particular strongly ionic crystals, in which an electromagnetic radiation ( 13 ) is irradiated on a crystal and the reflection ( 15 ) of this radiation in the crystal ( 14 ) is determined in a wavelength range λ ₁ to λ ₂ , characterized in that the wavelength range comprises an absorption region in which the radiation is absorbed to form excitons, this absorption producing a peak having a width, determining a peak width, and from Peak width the quality of the crystal is determined. Method according to Claim 1, characterized in that a complex dielectric function ε is determined in the absorption region and the imaginary part (ε ^|| ) is determined therefrom, and the quality of the crystal is determined from the peak width of the imaginary part. Method according to claim 1 or 2, characterized that as Peak width the half width (H) is used. Method according to one of the preceding claims, in which the electromagnetic radiation is high energy, in particular synchrotron radiation ( 11 ) is. Method according to one of the preceding claims, characterized in that predetermined wavelengths are measured by means of a monochromator ( 12 ). Method according to one of the preceding claims, characterized in that the radiation ( 13 ) is reflected at a gap surface, in particular the (111) surface. Method according to one of the preceding claims, characterized in that the wavelength associated with the maximum value and / or the half-width (H) with the projection

where ω = c / λ, n _{0 is} the static refractive index of the crystal, τ is the exciton lifetime, ω _{0 is} the exciton excitation energy, ε _{band is} the proportion of excitations across the band gap, λ is the wavelength, from the function

where R (λ) is the wavelength-dependent reflection signal, ε (λ) is the complex dielectric function, λ is the wavelength, using a least-square algorithm. Method according to one of the preceding claims, characterized characterized in that it in a vacuum, in particular in ultra-high vacuum, is performed. Method according to one of the preceding claims, characterized in that at least the crystal ( 14 ) is stabilized during the quality determination to a temperature of 4 K to 400 K. Use of with the method of one of previous claims obtained crystal for the production of lenses, prisms, Lichtleitstäben, optical Windows and optical components for DUV photolithography, steppers, excimer lasers, Computer chips, and integrated circuits and electronic devices contain such circuits and chips.