DE10307423A1 - Quality control of strongly ionized crystals, whereby high energy radiation is used to generated electron-hole pairs in the crystal and the corresponding absorption spectrum measured - Google Patents

Abstract

Quality control method, especially for strongly ionized crystals, in which a crystal (14) is irradiated with electromagnetic radiation (13) and reflected radiation (15) within a given wavelength bandwidth is detected. The bandwidth includes an absorption range in which the radiation is absorbed to form electron-hole pairs, with a resultant broad absorption peak detected in the spectrum of the reflected radiation. The width of the peak indicates the quality of the crystal.

Description

The invention relates to a method for quality determination of, especially strongly ionic, crystals and the use such certain crystals.

For the imaging properties of the crystals used in optics are common Defects and dislocations in the crystal are important. In particular for the Optics for the high-energy short-wave radiation in the far ultraviolet, like for example for microlithography is used, these are imperfections and Dislocations, i.e. all deviations from the perfect lattice periodicity, are special Importance. For this short-wave electromagnetic radiation with a wavelength of, for example 193 nm or 157 nm or even less are only a few materials for optics suitable. A currently common The material used is calcium fluoride. The quality of the crystals available is now so good that crystals with thicknesses a few centimeters practically no absorption in the above wavelength can be determined. however has been shown to be electromagnetic Radiations of such short wavelengths still damage (laser damage) in the material, which increases the absorption.

In WO 01/86032 there is a multi-stage Quality determination procedure described by fluoride crystals, the Pb, Ce and Na as impurities contain. In addition to that caused by lead absorption Luminescence also through the orientation of small-angle grain boundaries Diffraction determined by synchrotron radiation.

The basis of the invention The problem is to specify a method that can be used to improve the quality of crystals can also be determined quantitatively when absorption is practically not is detectable.

To solve the problem, a method of the type mentioned is specified in which electromagnetic radiation is radiated onto a crystal and the absorption or change of this radiation in the crystal is determined in reflection in a predetermined wavelength range of λ1-λ2. The method according to the invention is now characterized in that the predetermined wavelength range encompasses that region at the lower edge of the band edge in which the radiation is absorbed by excitation in the crystal and the wavelength-dependent reflectivity R = (I ^Refl (λ)): ( I is detected ⁱⁿ (λ)). The wavelength dependence of the reflectivity is used as a measure of the quality of the crystal. The position of the minimum and maximum, in particular in relation to one another, and the slope in between have been shown to be useful features for determining the quality. Preferably, however, a complex dielectric function ε is determined in the absorption region and the imaginary part ε is determined therefrom. The peak width serves in particular the peak half width of the imaginary part in the absorption area, ie in the area of exciton formation as a measure of the quality of the crystal.

The method according to the invention is based on the knowledge that even with almost perfect crystals, high-energy electromagnetic radiation can produce so-called excitons. Such an exciton occurs when an electron is lifted from a valence band of the crystal into a conduction band of the crystal and thereby creates a hole, that is, a point in the valence band from which negative electrical charge is missing. These two interact with each other 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 that is approximately in the range of the lattice constant. These excitons are scattered at missing parts or transfers. The scatter of local impurities shortens the exciton lifetime τ ^-1 = τ ^-1 _ph + τ ^-1 _sc , where ph means phonons and sc scattering. If electromagnetic radiation is then successively generated for several wavelengths, irradiated onto the crystal and the intensity of the reflected radiation is measured, the wavelength-dependent complex dielectric function can be determined from this. It has been shown 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 certain peak width. The peak width of this exciton peak is small enough that this peak, in particular the peak width, can be determined quite clearly. It has been shown that the lifetime 1 / half-width of the exciton is a sensitive measure of the number of defects and dislocations in the crystal, especially at low temperatures.

Particularly well suited for quality determination the half-width of the exciton peak. The full width at half maximum of the exciton peak depends with the lifetime of the exciton. In particular, the Half width of the exciton peak inversely proportional to the lifetime of the exciton.

The more defects and dislocations there are in the crystal, the faster the exciton disintegrates and the shorter the lifespan of the exciton. The half-width of the exciton peak is therefore a measure of disorder, that is to say Defects and dislocations in the material, ie the larger the disorder in the crystal, the greater the half-width.

In another training of Invention is high energy electromagnetic radiation Radiation, especially synchrotron radiation. By means of this high energy Radiation can be the quality of the crystal particularly efficiently. A preferred high energy Radiation is synchrotron radiation that is of high quality and high intensity available is.

It is also an advantage if the given wavelengths can be adjusted using a monochromator. This monochromator allows it, a narrow wavelength range gradually to select successively. This enables good and reproducible results to be achieved. In particular, this enables a step-by-step scan.

In one embodiment of the invention the radiation at a slit surface, in particular the (111) Surface, reflected. Such gap areas can be in high quality generate so that unwanted errors in quality determination of the crystal can be excluded. In particular the (111) area let yourself generate 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 further development of the invention is characterized in that the wavelength associated with the maximum value and / or the half-value 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 share of the excitations over the band gap,
λ is the wavelength
out of function

where R (λ) is the wavelength-dependent reflection signal,
ε (λ) the complex dielectric function,
λ is the wavelength
is determined using 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. The sum of the squares of the deviations is then formed. The result is the parameters for which there is a minimum of the sum of the squares of these deviations. This least-square algorithm can, for example, be carried out on a conventional computer. Standard fit routine from the gnu C ⁺⁺ libraries as implemented, for example, in the "gnuplot" program (available at www.gnuplot.info/).

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

Although the determination according to the invention also in a normal atmosphere (Pressure, air, etc.) feasible , it is preferably in a vacuum, especially in an ultra-high vacuum carried out. This allows the influences exclude contamination from the ambient air. In particular, when the electromagnetic radiation reflects on a slit surface should be thus ensuring a clean and reproducible gap area.

In another training of At least the crystal is invented during the quality determination stabilized to a, especially 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 experienced to reduce. Ideally, only those are shown at T = 0 Kelvin Scattering of impurities (impurities, Dislocations) that limit the lifespan of an exciton. Usual measuring temperatures are 4 or 4.2 K to 400 K, preferably 75 or 77 K to 300 K. Have been particularly useful temperatures between 150 in particular 170 K and room temperature proved. In a particularly preferred embodiment, the one to be determined has Crystal during of the entire measurement process the entire volume has a uniform temperature.

The method with the features of the invention let yourself advantageous for quality determination of strongly ionic crystals. It is particularly suitable for quality determination of calcium fluoride, magnesium fluoride, barium fluoride and strontium fluoride and mixed crystals as well as corundum crystals such as sapphire.

In the following an embodiment of the Invention with reference to the figures explained. Show it:

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

2 a reflectivity measured with synchrotron radiation, plotted against the wavelength, and

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

1 shows a schematic representation of an apparatus for performing the method with the features of the invention. A radiation source is shown 10 to generate electromagnetic radiation 11 , The radiation source 10 can for example be a synchrotron 10 for generating synchrotron radiation 11 his. The synchrotron 10 outgoing synchrotron radiation 11 passes through a monochromator 12 to generate 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 a control for the monochromator is shown 12 and the crystal 14 , Still not in the 1 Evaluation means, such as a computer, are shown for recording and evaluating those from the detector 16 measured intensity. The control, not shown in the figure, is used to set the monochromator 12 transmitted wavelength range and for possibly controlling the parameters of the crystal 14 , Such parameters can be, for example, the angle of the crystal 14 to the monochromatic radiation 13 as well as the temperature of the crystal 14 his.

Means for adjusting the temperature of the crystal are also not shown in the figure 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. The reflectivity determined with a synchrotron radiation is plotted on the ordinate against the wavelength in nm on the abscissa. The reflectivity R is an absolute dimensionless quantity between 0 and 1 normalized to the radiated intensity:

where I (λ) is from that of the detector 16 determined intensity of the reflected radiation 15 and I ₀ (λ) the intensity of the monochromatic radiation 13 is. The following equation applies to the reflection signal R:

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

where ω = c / λ,
n _{0 is} the static refractive index of the crystal,
τ the
Exciton excitation energy is
ω ₀ corresponds to the exciton excitation energy,
ε _{band is} the share of the excitations over the band gap, and
λ is the wavelength
the complex dielectric function can be determined using a suitable algorithm. 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. The result of the leastsquare algorithm is the parameter set with which this sum of the squares of the deviations takes 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. The real part or the imaginary part of the dielectric function is plotted on the ordinate against the wavelength in nm on the abscissa. The real part ε ^| (λ) is shown in the figure with a solid line. The imaginary part ε ^|| (λ) is shown in the figure with a dotted line. As can be seen from the figure, there is a maximum of the imaginary part ε ^|| in the region of a wavelength of 112 nm to see (λ).

This maximum can be generated so-called excitons in the calcium fluoride crystal used assign.

The peak width assigned to the exciton peak is characteristic of the density of the contamination or dislocation at which the exciton is scattered. The exciton peak at CaF _{2 is} at a wavelength of 112 nm.

The width of this exciton peak is the Lifetime τ des Excitons are inversely proportional. Entered in the figure is so-called half-width H, at which the intensity on their half value has subsided. As a measure of the width, however other definitions of width can also be used, such as the 1 / e width at which the intensity declined to a value 1 / e is.

ist die Breite, nämlich die Halbwertsbreite H, ein Maß für die Unordnung im Kristall. Die Lebensdauer τ eines Exzitons ist nämlich umso kleiner, je mehr durch chemische Verunreinigungen oder Versetzungen hervorgerufene Abweichungen von der perfekten Gitterperiodizität es in dem Kristall gibt. Auf diese Weise kann somit mittels Bestimmen der Breite H sowohl die Dichte der Verunreinigungen als auch gleichzeitig die Dichte von Kristallstörungen, wie Versetzungen etc., in einem Kristall bestimmt werden.Since the relationship applies:

is the width, namely the half width H, a measure of the disorder in the crystal. The lifespan τ of an exciton is in fact shorter, 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, both the density of the impurities and, at the same time, the density of crystal defects, such as dislocations, etc., can be determined 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 particularly strongly ionic crystals, in which an electromagnetic radiation ( 13 ) radiated onto a crystal and reflected ( 15 ) this radiation in the crystal ( 14 ) is determined in a wavelength range λ ₁ -λ ₂ , characterized in that the wavelength range comprises an absorption range in which the radiation is absorbed with the formation of excitons, whereby a generated peak having a width is detected by this absorption and the quality from the peak width 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. A method according to claim 1 or 2, characterized in that 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 the predetermined wavelengths by means of a monochromator ( 12 ) can be set. Method according to one of the preceding claims, characterized in that the radiation ( 13 ) is reflected on a slit 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-value width (H) 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 _tied the portion of the excitations over the band gap, λ is the wavelength, from the function

where R (λ) the wavelength-dependent reflection signal, ε (λ) the complex dielectric function, λ the wavelength, is determined using a least-square algorithm. Method according to one of the preceding claims, characterized characterized it is carried out in a vacuum, in particular in an ultra-high vacuum. Method according to one of the preceding claims, characterized in that at least the crystal ( 14 ) is stabilized to a temperature of 4 K to 400 K during the quality determination. Use of the method according to one of the previous claims obtained crystal, for the production of lenses, prisms, light guide rods, optical Windows and optical components for DUV photolithography, Steppers, excimer lasers, wafers, computer chips, as well as integrated Circuits and electronic devices containing such circuits and contain chips.