WO2005114232A2

WO2005114232A2 - Method and apparatus for the determination of the concentration of impurities in a wafer

Info

Publication number: WO2005114232A2
Application number: PCT/EP2005/052225
Authority: WO
Inventors: Hans Richter; Vladimir D. Akhmetov; Oleksandr Lysytskiy
Original assignee: Ihp Gmbh - Innovations For High Performance Microelectronics / Institut Für Innovative Mikroelektronik
Priority date: 2004-05-14
Filing date: 2005-05-13
Publication date: 2005-12-01
Also published as: WO2005114232A3

Abstract

The invention relates to a method for the determination of the concentration of an impurity in a wafer. The method comprises repeatedly changing the position of the plate during the period of the registration trecording by displacing the plate along its plane of the surface, such that the light beam of the infrared spectrometer alternately passes through one of the samples at a time, thus recording partial spectra from both samples, accumulating recorded spectral information in the time intervals between the position changes of the plate, dividing the obtained spectral information into two sets of spectral information corresponding to the first sample and to the reference sample, and performing averaging and statistical analysis for each set of spectral information, in order to determine an average differential spectrum and its statistical error.

Description

Method and Apparatus for the Determination ofthe Concentration of Impurities in a Wafer

Field of the Invention

The invention concerns a method for the determination of the concentration of impurities in wafers by means of differential infrared spectroscopy, including a step of recording infrared spectra of a first sample of the wafer to be analyzed and a reference sample from a reference wafer. The invention further concems a spectroscopic apparatus for performing the mentioned method.

Background of the Invention

Adding impurities to wafers, for instance nitrogen to a silicon wafer, leads to drastic changes of some properties of the wafer materials as well as of the atomic processes under heat treatment of the wafer.

In the case of nitrogen, two methods are commonly used for the detection of nitrogen: secondary ion mass spectrometry (SIMS) and Fourier transform infrared spectroscopy (FTIR). The latter seems to be of particular interest, because it is nondestructive, faster, relatively low-cost and able to provide additional information about the atomic state of a given impurity such as interstitial, substitutional, in point complexes and in the silicon nitride precipitates. However, the relatively weak intensity of the nitrogen related absorption bands did not allow to perform measurements on standard silicon wafers so far. Special samples with a thickness of approximately 10 mm are usually used for nitrogen determination by infrared spectroscopy, cf. K. Tanahashi, H. Yamada-Kaneta, N. inoue, Jap. J. Appl. Phys., 43, L436(2004). This approach is not suitable for monitoring the concentration of nitrogen and its state in the silicon lattice for wafers before and during semiconductor processing. Consequently, the development of analytical methods for the determination of nitrogen in silicon wafers is very important.

Fig. 1 shows a diagram illustrating a method for determination of the concentration of an impurity in a wafer according to the prior art.

According to the method illustrated in Fig. 1 , an infrared spectrum Ei is recorded during a time span t-ι-t₂ from a reference sample, which is known to have a particularly low concentration of an impurity of interest, such as nitrogen in silicon. The time span tι-t₂ is chosen long enough to provide a sufficient signal-to-noise ratio. The time span may for instance be 4.5 hours.

During a second time span t,₂-t₃, a spectrum E₂ of a sample of interest is recorded, for which the impurity concentration shall be determined. The length of time span t₂-t₃ is equal to that of time span tι-t₂- For switching from the reference sample to the sample of interest a sample holder containing both the reference sample and the sample of interest may be switched from a first to a second position. Alternatively, the reference sample may be replaced by the sample of interest on the sample holder.

From the two collected spectra Ei and E₂, a differential transmittance spectrum is obtained by calculating the spectral dependence of the quotient E^IE₂ and is shown in Fig. 1 by a full line 10. The true spectrum is shown for comparison by a dashed line 12. As can be seen, the obtained differential transmittance spectrum T suffers from distortions mainly caused by noise and instabilities of the signal recorded in the spectrometer.

Therefore, current spectroscopic methods lack photometric quality of the recorded spectra, preventing a determination of the impurity concentration with high accuracy and a low detection limit, both criteria being required in order to make use of such methods in commercial wafer production.

It is an object of the invention to provide a spectroscopic method and a spectroscopic apparatus for the determination of an impurity concentration in a sample with high a definitely known precision and with an improved detection limit.

Summary of the Invention

According to a first aspect of the invention, a method is provided for the determination of the concentration of an impurity in a wafer including a step of recording infrared spectra of a first sample of the wafer to be analysed and a reference sample from a reference wafer during a period t r_ecor_din_g of spectrum registration ,

wherein the infrared spectra are taken in a spectral range comprising at least one spectroscopic absorption feature caused by the presence of the impurity in the wafer and for the determination of the concentration of the impurity the following steps are performed:

- cutting both samples either from the wafers or using the whole wafers as the samples, mounting both samples prior to the recording step in a plane on a surface of a moveable plate, the plate containing two windows allowing a light beam of the infrared spectrometer to pass through one of the samples at a time, recording the infrared spectra under Brewster's angle of light incidence using p- polarised incident light, repeatedly changing the position of the plate during the period of the registration t recor_ding by displacing the plate along its plane of the surface, such that the light beam of the infrared spectrometer alternately passes through one of the samples at a time, thus recording partial spectra from both samples, preferably in equal number, accumulating recorded spectral information in the time intervals between the position changes of the plate,

- dividing the obtained spectral information into two sets corresponding to the first sample and to the reference sample, performing averaging and statistical analysis for each set of spectral information, in order to determine an average differential spectrum and its statistical error,

- determining the absorption coefficient of the at least one spectroscopic absorption feature using the average differential spectrum and the known thickness of the sample determining the impurity concentration in the first sample using a calibration factor.

It should be noted that the term "wafer" is used herein to describe the shape of the samples to be analyzed, which may also be described as a disc or a slice. The term "wafer" shall not be understood as restricting the use of the invention to the field of semiconductors or even to silicon wafers only, even if the primary field of use of the method of the invention may currently lie in this technology area. Further, the period of registration t_reCor_din_g is the time span between the beginning of the recording of the first infrared spectrum and the end of the recording of the last infrared spectrum of the complete set of infrared spectra.

The term partial spectrum is used to refer to one infrared spectrum, which according to the method of the invention forms a part of the multiple number of infrared spectra recorded during the period of registration or in_g from each sample. It does not imply any limitation as to the spectral range covered.

It should be noted that the registration of a spectrum, as used herein, is in the art also referred to as the recording of the spectrum.

The invention is based on the perception that two factors limit the sensitivity of infrared measurements of impurities in wafers, such as nitrogen in silicon wafers:

1) strong interference effects in the wafer

2) noise and instabilities of the signal in the spectroscopic equipment.

The method of the invention achieves an improvement of the photometric accuracy of the average differential spectrum obtained after recording multiple spectra from the sample of interest and from the reference sample. The method of the invention achieves this advantage without having to increase the total time of measurement in comparison with prior-art spectroscopic methods as described with reference to Fig. 1. In fact, the total time used for recordation of infrared spectra should be kept equal or even shorter in comparison to prior-art methods.

The detection limit for nitrogen in the standard wafers reached with the present method of the invention is as low as 3 x 10¹⁴ cm^"3 for a period of registration (tr_eoor_ding) of 2 hours.

According to the method of the invention, the interference problem is drastically suppressed by using Brewster's angle of incidence, approx. 73°, and p-polarised light, instead of conventionally used normal incidence and unpolarised light. Moreover, the Brewster-angle geometry allows one to perform in one embodiment of the invention spectroscopic measurements not only on a single thin sample, but on a stack of samples, too. This enhances the intensity of the bands in a transmission spectrum and, thus, the sensitivity of the measurements.

It is noted however, that in principle the method of the invention can also be performed without making use of Brewster's angle of incidence. In that case, both samples should be prepared with the same thickness and with high quality polished two surfaces which should be parallel one to another, , and must remain in exactly the same spatial position during the complete period of spectrum registration t r_ecor_dmg- The geometrical quality of modem semiconductor wafers satisfies the mentioned strong geometrical requirements. However, such high geometrical quality seems to be difficult to achieve with laboratory-scale abrasive equipment. Therefore, the use of Brewster's angle of incidence in conjunction with wafers is currently a part the most preferred embodiment of the invention.

In the following, preferred embodiments of the method of the invention will be described.

In one embodiment, the method comprises guiding a light beam illuminating the sample currently measured through a diaphragm having a fixed aperture. The diaphragm is positioned closely to the measured sample. Preferably, the extensions of the opening of the diaphragm are smaller than the size of windows transmitted by the light beam on the sample holder. This way parasitic modulation of the signal by the windows of the sample holder is prevented.

According to another embodiment, the first sample is formed by a number of samples, in particular, by a first stack of samples or whole wafers to be analyzed, wherein the reference sample is formed by a second stack of reference samples or reference wafers, the first and second stacks containing equal numbers of samples or wafers. The use of multiple samples or wafers increases the depth of an absorbance (or transmittance) feature to be analyzed and can thus be helpful in the case of a particularly low impurity concentration. Displacing the plate may comprise a linear movement of the plate, a rotation of the plate, or a superposition of a linear movement and a rotation of the plate.

In a preferred embodiment of the method of the invention, a recording time span t_singie between the starting times of two subsequent partial spectra is longer than two times a dead time span tjβa_d between completing the recording of the one spectrum and starting the recording of the subsequent spectrum.. The recording time span tsm_gie which is herein also reffered to as the recording time of a partial spectrum, is preferably as short as possible, given the above the limitation. The dead time span t_dea is typically formed by the sum of the time span needed for the displacement of the plate between its two end positions and for making the spectroscopic apparatus ready for recording the next spectrum. The degree of improvement of the photometric quality of spectra measured according the method of the invention saturates or even degrades if the sum of the recording time span tsingi_e and the dead time span t_dea_d is shorter than twice the dead time span. For in this case, more than 50 % of the complete period of registration trecor_ding is spent for technical manipulations and not for the acquisition of spectral information.

One of the important advantages of the method of the invention is its ability to provide a determination of the reliability of the recorded spectra. In a preferred embodiment of the invention, at least four infrared spectra are recorded from each sample and, accordingly, four differential spectra are obtained. If the number of spectra from each sample were chosen smaller than 4, the improvement of photometric quality according to the invention becomes relatively weak, because both drift and low-frequency noise of the system could still provide a significant contribution to the recorded signal. Furthermore, it would be impossible to apply statistical analysis to the obtained set of spectra in order to determine the confidence interval, and the photometric accuracy of the resulting differential spectrum.

The maximum number of partial spectra recorded from each sample does preferably not exceed the ratio between a preselected time span forming the period of registration tr_βC0r_ding and four times the dead time span t_dΘad. This embodiment combines the advantages of the two embodiments described last. A further embodiment of the method of the invention comprises a step of monitoring the position of the sample, which is currently illuminated with the light beam of the infrared spectrometer, with reference to the incident light beam. This can for instance be done by comparing images of the light reflected from the surfaces of the samples. During such comparison, the stage should be periodically shifted.

In this embodiment, a step of fine-positioning the moveable plate for placing the currently illuminated sample in an identical or close-to identical position with reference to the incident light beam before recording a next infrared spectrum of the sample is preferably performed to avoid the occurrence of errors due to uncontrolled motion of the sample relative to the respective window.

In order to avoid recording spectra of samples with contaminated surfaces, which typically comprise unwanted absorption features, a step of cleaning surfaces of both samples is performed before mounting same on a movable plate. For example, cleaning in organic solvents followed by a refresh of the Si samples/wafers in HF acid is desirable before mounting them on the moving stage in order to remove organic traces as well as native oxide layers.

In order to further minimize differences in absorption features from native oxide layers and/or adsorubates, the cleaning of the surfaces of the first sample and of the reference sample is performed simultaneously using the same cleaning method and, preferably, the same cleaning process if possible.

In one embodiment of the method of the invention, the averaging step comprises arithmetically adding all infrared spectra recorded from the first sample to form a first averaged spectrum, and arithmetically adding all infrared spectra recorded from the reference sample to form an averaged reference spectrum. Subsequently, a final differential transmission spectrum is calculated by dividing an averaged spectrum of the sample of interest by an averaged spectrum of the reference sample.

According to another embodiment, the method comprises a step of ascertaining differential spectra T|^* by calculating quotients Ti^* = si/ n of each pair Si, n of infrared spectra formed by an infrared spectrum Si of the first sample and of an infrared spectrum η of the reference sample taken immediately before or after S|, wherein i denotes an index of a respective pair of spectra between 1 and k, and where k is 0.5 times the number of recorded spectra. The method of this embodiment preferably further comprises a step of calculating a first average differential spectrum T* of the differential spectra T_s ^*.

In an embodiment comprising a alternative and preferred averaging method, the averaging step comprises dividing the two sets of obtained spectral information into at least four different groups of spectral information, each group thus consisting of two subsets of spectral information, one subset corresponding to the first sample and the other subset to the reference sample,

- performing averaging for each subset of spectral information, thus obtaining at least four averaged infrared spectra from the first sample and at least four averaged infrared spectra from the reference sample, - calculating respective differential spectra Ti from the at least four pairs of obtained averaged spectra, thus obtaining at least four differential average spectra, and

- calculating a second average differential spectrum T from the obtained at least four differential average spectra.

The purpose for the grouping of the sets of pairs of spectra is to obtain more exactly the spectrum of differential transmittance T from the whole set of measured spectra.

The solution of the present embodiment is based on the perception that the limit of the mean value of the Ti does not tend to the true value of T when i tends to infinity. This is due to a nonlinear contribution of noises contained in the recorded partial spectra η of the reference sample to the mean value of Tj, and is caused by the arithmetical operation of dividing performed in calculating the differential spectrum. The limit of the mean of the differential spectra Tj always exceeds the true differential spectrum by a factor of (1 + δ), where δ is in the order of σ², and σ is the relative dispersion of η.

The issue of this error can be demonstrated in the simple modelling case where both the true mean values of the partial spectra Si obtained from the sample of interest and π obtained from the reference sample are exactly equal to 1, and assuming that noises for Si and η are represented by only two discrete levels, +σ and -σ. Such two- level distribution function is the simplest approximation of a real symmetrical distribution function of noises. In such a model case, the experimentally obtained set of Ti will be represented by 4 values, (1+σ)/(1+σ), (1+σ)/(1-σ), (1-σ)/(1+σ), and (1- σ)/(1-σ). The probabilities of measuring each of 4 values are equal due to uncorrelated noises in Sj and n. Therefore, the mean of Ti will tend to the average of (1+σ)/(1+σ), (1+σ)/(1-σ), (1-σ)/(1+σ), and (1-σ)/(1-σ) when i tends to infinity. It is easy to calculate this average value, which is equal to 1/(1 - ϋ.25*^). Taking into account that the expression 1/(1-x) is approximately equal to 1 + x, if x « 1, the limit of average Ti is equal to 1 + 0.25 σ² instead true value 1.

On the other hand, a differential transmission calculated according to the previous embodiment as T = (average of Sj)/(average of n) exactly tends to true value of T when i tends to infinity. However, no information can be derived about the confidence interval from such averaging treatment of the set of measured spectra.

Therefore, the present embodiment provides what can be named an intermediate averaging procedure, by first grouping certain subsets of partial spectra of the set of spectra, in order to simultaneously derive both, differential transmission with considerably suppressed nonlinear effect of noises and a value of the confidence interval.

Nevertheless, the calculation of the individual T = Sj/n seems to be effective for the filtration, if needed, of partial spectra Si.n, with anomalous high noises.

The method preferably further comprises a step of calculating an average differential spectrum T of the differential spectra Ti. The step of performing statistical analysis preferably comprises evaluating spectral dependence of a confidence interval Eps according to the formula

Again, Tj and T are functions of spectral position.

According to a second aspect of the invention, a spectroscopic apparatus is provided for determining the concentration of an impurity in a sample by means of infrared spectroscopy, comprising an infrared (IR) spectrometer and a sample holder, wherein

- the sample holder comprises a moveable plate providing a plane on its surface for mounting at least one first sample and at least one reference sample, the plate containing at least two windows allowing a light beam of the infrared spectrometer to pass through either the at least one first sample or the at least one reference sample at a time

- the spectroscopic apparatus comprises means for repeatedly moving the plate between two end positions with a predetermined velocity and at a predetermined rate during the period of the data acquisition, a first end position allowing a spectrum to be taken through at least one first window, and a second end position allowing a spectrum to be taken through at least one second window, the spectroscopic apparatus comprises a light source and polarization means for sending p-polarised incident light onto either the at least one first sample or the at least one second sample at a time the sample holder and the light source are arranged with respect to each other such that infrared spectra are recorded under Brewster angle of p-polarised light incidence onto the respective sample.

The spectroscopic apparatus of the invention serves to perform the method of the invention. Its particular use is in the field of semiconductor technology. The spectroscopic apparatus of the invention can be integrated into production lines for semiconductor wafers and semiconductor devices and allows to obtain reliable information on impurity concentration in a wafer within a short time. Further advantages of the spectroscopic apparatus of the invention directly correspond to those explained in the context of the method of the first aspect of the invention.

It is noted that the use of the spectroscopic apparatus of the invention is not restricted to an application in infrared spectroscopy. It can also be used in other spectral ranges, such as in the visible optical spectrum or in the ultraviolet spectral range, by employing a spectrometer, which is appropriate for the respective spectral range. It is also possible to apply the principle of the moving sample holder to other spectroscopic techniques, where low-frequency noise and instabilities of the signal in the spectroscopic equipment may have a negative impact on the spectroscopic accuracy, such as luminescence spectroscopy or luminescence excitation spectroscopy.

In the following, preferred embodiments of the spectroscopic apparatus of the second aspect of the invention will be described.

A preferred embodiment of the spectroscopic apparatus of the invention comprises an evaluation unit adapted to group the obtained spectra into certain sets corresponding to the first sample and to the reference sample and to perform averaging for each set of spectra, in order to determine an average differential spectrum T as well as the auxiliary spectra T| and their statistical error.

In a further embodiment of the spectroscopic apparatus the evaluation unit is adapted to determine the absorption coefficient of at least one spectroscopic absorption feature using the average differential spectrum T and the thickness of the sample.

In a preferred embodiment of the spectroscopic apparatus the evaluation unit is adapted to determine the impurity concentration in the first sample using a preset calibration factor.

The spectroscopic apparatus of the invention can be combined with any known prior art spectroscopic apparatus for infrared spectroscopy. In particular, the spectroscopic apparatus of the invention can be implemented in the form of a dispersive spectrometer (based on monochromators with scanning or on polychromators with focal plane detector arrays) or in the form of a Fourier Transform Infrared (FTIR) spectrometer. In Fourier spectrometry, both conventional rapid-scan FTIR spectrometers and step-scan spectrometers can be used. A FTIR spectrometer preferably comprises the sample holder and the light source. In the case of scanning dispersive spectrometers, the inventiv method should be applied to each step of scanned transmission spectrum. In the case of step-scan FTIR spectrometer, the invented method should be applied to each step of mirror position of the interferometer.

in a preferred embodiment of the spectroscopic apparatus of the invention, the means for repeatedly moving the plate between two end positions comprise an actuator unit connected to the moveable plate, which is arranged and adapted to move the plate in a plane between the first and second end positions. Preferably, a control unit is provided, which is connected to the actuator and adapted to provide to the actuator control signals starting and for stopping a periodic motion of the plate, one motion period comprising motion of the plate back and forth once between the first and second end positions. Indicating a current destination position of movement, which corresponds to an end position of the plate.

A further embodiment of the spectroscopic apparatus of the invention comprises a detector unit, the detector unit being arranged and adapted to detect infrared light transmitted through one of the windows of the plate and to provide electric signals indicative of an intensity of light incident on the detector unit as a function of either time or wavelength of transmitted light or both. As is well-known, FTIR spectra are obtained from the time dependence of detected intensity during a modulation of infrared radiation caused by moving mirror within the interferometer forming the FTIR spectrometer. In contrast grating spectrometers are preferably operated in a mode where the whole spectrum of light transmitted by the sample is recorded as a function of wavelength. This is typically done by using a Charge-Coupled-Device (CCD) detector behind the sample and a dispersive spectrometer. Other types of detectors can be used as well.

In a further embodiment, the control unit is adapted to provide control signals to the detector unit instructing the detector unit to start or stop recording an infrared spectrum.

In another embodiment, the control unit is adapted to select the duration of a recording time span ts_ingie between beginning and stopping the recording of one infrared spectrum longer than two times a second time span t _ead between beginning the motion of the plate and beginning the recording of the next infrared spectrum.

Preferably, the control unit is further adapted to control the number of recorded spectra from each sample to be smaller than or equal to the ratio between a preselected time span of the period of registration tr_ΘCOr_din_g and four times the dead time span t ead-

The period of registration trecor_ding can in one embodiment be provided by an operator of the spectroscopic apparatus via providing an input value to an input unit connected to the control unit and adapted to receive and forward to the control unit.

In a further embodiment, the evaluation unit is adapted to ascertain differential spectra Ti by calculating quotients Ti = (average Si)/(average π) of each chosen n groups of S|, η of infrared spectra formed by an infrared spectrum S| of the first sample and of an infrared spectrum η of the reference sample taken immediately before or after Si, wherein i denotes an index of a respective pair of spectra between 1 and k, which is 0.5 times the number of recorded spectra. ln further embodiment, the evaluation unit is adapted to perform statistical analysis by evaluating a spectral dependence of a confidence interval Eps according to the formula

Another embodiment of the spectroscopic apparatus of the invention has a diaphragm, which is arranged, as seen in the direction of incident light, in front of the surface plane for mounting the samples on the moveable plate, the diaphragm being arranged to reduce the extension of the light beam impinging on the currently irradiated sample to a size smaller than the windows on the moveable plate.

Preferably, the sample holder of this embodiment comprises fixing elements, which are adapted and arranged to exert identical forces on the samples in holding them in their respective position relative to the respective windows.

In another embodiment the sample holder comprises two wings, each providing a plane on its surface for mounting at least one first sample and at least one reference sample, and each having one first window and one second window arranged to let an incident light beam sequentially pass samples mounted on the first or second window of both wings, the wings being arranged a mutual angle forcing light beam incident under Brewster's angle on a first or reference sample mounted on one wing to also impinge on the first or reference sample mounted on the other wing under Brewster's angle.

In a further embodiment of the spectroscopic apparatus of the invention, a plane mirror is positioned behind the sample, as seen in the direction of the incident light beam, such that the transmitted light beam is reflected back onto the sample under Brewster's angle of incidence. This embodiment allows letting the light beam pass through the same sample twice. In this embodiment, a beam splitter is preferably arranged in front of the sample, the beam splitter being adapted to transmit the light beam incident on the sample and to reflect the light beam transmitted by the sample after being reflected from the plane mirror.

In order to hold a stack of samples, an embodiment of the spectroscopic apparatus has a holder containing a sample fixing arrangement, which is adapted to fix a stack of samples in front of each window.

Short Description of the Figures

Fig. 2 shows a diagram illustrating an embodiment of the method for the determination of the concentration of an impurity in a wafer according to the invention.

Fig. 3 shows a Fourier transform infrared spectroscopic apparatus forming an embodiment of the invention.

Fig. 4 shows transmittance spectra of silicon wafers containing nitrogen, as obtained by a prior-art method and a method of the invention.

Fig. 5 shows differential transmission spectra taken from reference samples according to a prior-art method and according to the method of the invention as well as 100 %-lines according to the prior-art method and according to the method of the invention.

Fig. 6 shows lines 100% obtained over a wide, diagnostically important IR spectral range using the prior-art method according to Fig. 1 and the method of the invention.

Fig. 7 shows an enlarged region marked VII in the spectrum of Fig. 6. Fig. 8 shows an alternative embodiment of a sample holder for use in the spectroscopic apparatus of Fig. 3.

Fig. 9 shows a further embodiment of a spectroscopic apparatus forming an alternative setup compare to Fig. 3.

Detailed Description of Preferred Embodiments

Fig. 2 shows a diagram illustrating an embodiment of the method for the determination of the concentration of an impurity in a wafer according to the invention. The concept of the diagram on the left-hand side of Fig. 2 corresponds to that on the left-hand side of Fig. 1. The position of the sample holder is schematically drawn as a function of time.

As can be seen, the period of registration formed by the time span trfe is identical to that used in the method according to the prior art shown in Fig. 1. However, the position of the sample holder is switched much more frequently. In fact, the number of position changes shown in Fig. 2 is much lower than the actual number, which is typically used and can range even up to more than 10000.

Thus, two groups of spectra are obtained. A first set of spectra, referred to as "odd spectra" in Fig. 2, is recorded from the reference sample. In alternating order with the odd spectra, a set of "even spectra" is recorded from the sample to be analyzed. In total, 2k records of raw spectra are obtained. A raw spectrum lists transmitted intensity values as a function of wave number. The number of even and odd spectra is identical. Thus, while the prior art-method of Fig. 1 first obtains all measurements on the reference sample and then, after changing the sample, obtains all measurements from the studied sample, the method of the invention provides a fast alternation of samples, for which the spectra are recorded.

According to the method of the invention, the resulting differential transmission spectrum is calculated as the ratio of the sum of all even spectra to the sum of all odd spectra. The shorter interval between two adjacent measurements in the multiple procedure of the invention leads to a decisive reduction of the influence of drift and low-frequency noise in the resulting differential transmittance spectrum.

Fig. 3 shows a schematic diagram of a Fourier transform infrared spectroscopic apparatus forming an embodiment of the invention. The spectroscopic apparatus 300 of Fig. 3 is based on a well-known FTIR spectrometer. It comprises a Michelson interferometer 302. In the Michelson interferometer, a light source 304 irradiates a concave mirror 306. Due to the position of light source 304 in the focal point of concave mirror 306, a parallel beam is directed to a beam splitter 308.

A first fraction of the light incident on beam splitter 308 is reflected to a fixed plane mirror 310 and redirected through beam splitter 308. A fraction of the light reflected from fixed mirror 310 is transmitted through beam splitter 308 and directed onto sample holder 312. A second fraction of the light coming from concave mirror 306 is transmitted through beam splitter 308 and directed onto moveable plane mirror 314. The light reflected from movable plane mirror 314 is redirected onto beam splitter 308. A fraction of the light reflected from moveable plan mirror 314 is directed to sample holder 312 and superimposes with the light, which has been directed through the first branch of the Michelson interferometer described earlier.

Sample holder 312 comprises a plate 315 forming a plane surface 316 for mounting two samples, only one of which is shown by reference number 318. A mounting mechanism is indicated by angular elements 320 and 322. Sample holder 312 has a diaphragm 324 on its side 326 facing beam splitter 308. Light incident on sample holder 312 is transmitted through the diaphragm 324, window 328, and through sample 318. Sample holder 312 contains two windows, diaphragms and two sets of mounting elements two allow switching between sample 318 and a second sample by moving sample holder 312 back and forth in a direction peφendicular to the paper plane. The second sample cannot be shown in the view of Fig. 3 because it is not located in the plane of the paper.

Sample holder 312 is movable in a plane perpendicular to the paper plane, as indicated by symbol 330. The displacement of sample holder 312 is effected by an actuator, which is schematically indicated at reference number 332. Light transmitted through sample 318 is focussed onto detector 334 by concave mirror 336.

Operation of the spectroscopic apparatus is controlled by control unit 338. Control unit 328 particularly controls the operation of actuator 340, which moves plane mirror 314, and of actuator 332, which moves sample holder 312. Furthermore, control unit 338 controls the operation of detector 334 in collecting and outputting measured intensity data during a scan. It is noted that control unit 338 may contain several separate units. Control unit 338 may also be implemented in the form of a software running on a standard personal computer. Input of control parameters is enabled by an interface to an external input unit such as a computer keyboard 342.

Data collected by detector 324 are stored in a data base 344. Operation of data base 344 is also controlled by control unit 338. Every scan taken is stored in a separate file in data base 344. The file structure or the organisation of data base 344 allows to differentiate between scans taken from sample 318 and scans taken from a reference sample on sample holder 312.

Data base 344 is connected to an evaluation unit 346, which is adapted to perform a fast Fourier transform algorithm and an averaging algorithm on each set of spectra obtained from the sample of interest 318 and from the reference sample.

Evaluation unit 346 has access to k pairs of partial spectra, si, r-i, s₂, r₂,...Sj, n,..., Sk-ι, r_k_ι, s_k, r_k are obtained after finishing the whole procedure. Spectra named s belong to analyzed sample of interest, spectra named r belong to the reference sample. For calculation of the final differential spectrum as well as a confidence interval, evaluation unit 346 divides the set of pairs of spectra into n groups, where 4 ≤ n ≤ k.

The whole temporal sequence of the pairs of partial spectra, from s^nd r-i to s_k and r_k is thus divided into n equally long groups, according to n periods obtained by dividing the whole period of registration trecor_din_g into n equally long subperiods. The k and n are preferably chosen by such that the ratio m = k/n is integer. If it is not valid for the desired n, the value k is substituted by k¹ = [k/n]-n, and the restricted set of partial spectra with indexes from 1 to k¹ instead of k is considered.

Each group contains m pairs of partial spectra. Thus, the first group consists of spectra with indexes from 1 to m, the second one consists of spectra with indexes from m+1 to 2m, and the last group consists of spectra with indexes from (n-1)»m +1 to k (= n*m). The maximum value of n is k. The maximum n implies that each group consists from only pair of partial spectra Sj and η. The minimal value of n should not be less than 4, because an application of statistical analysis to a small number of groups becomes very problematic.

After dividing the spectra into the groups, each of the group of spectra is considered independently, as a whole set of measured spectra, according the above mentioned procedure.

The s-type and r-type spectra are averaged within each of the groups. Let us refer to the calculated averaged spectra with large letters, from S1, R1, to Sn, Rn. The averaged spectra S and R are calculated within each of the groups.

Then, evaluation unit 348 calculates "partial" differential average spectra Ti = Si/Ri, i = 1 to n. Again, the term "partial" refers to the fact that there is a multiple number of differential average spectra at this point. Thus, differential average transmission spectra Ti to T_n are obtained corresponding to n groups. The resulting "total" differential spectrum T is calculated according to T = average of Ti.

Statistics unit 348 is connected with evaluation unit 346 and data base 344 and adapted to perform a statistical analysis of the spectra by evaluating a spectral dependence of a confidence interval Eps according to the formula

It is noted that if n = k, one obtains the procedure without grouping. The value of n should be chosen in dependence of what type of information is more important, T or noises. A sequence of data processing can be performed with different values of n to obtain both types of information. We recommend the n = 4 for routine measurements and n = k for the testing of an experimental equipment (after change of light source, photodetector, scanning mechanism, as well as after appearance of indications on degradation of photometric quality etc).

The data provided by evaluation unit 346 and statistics unit 348 are provided as output, for instance to a computer monitor, and to data base 344.

The spectra shown in the diagram of Fig. 4 provide the transmittance of various samples as a function of the wave number of the transmitted light in the spectral range between 900 and 1040 cm^"3. The transmittance is shown on the ordinate in the range between 0,9990 and 1 ,0008. A total of four spectra A to D is shown.

Spectrum A is a transmittance spectrum taken from a sample of a silicon wafer of 200 mm diameter and 730 μm thickness having one side polished. Spectrum B was taken from the same wafer. The difference between spectrum A and spectrum B is that spectrum A was taken using a prior-art FTIR method and apparatus while spectrum B was taken using the method of the invention and an apparatus according to Fig. 3.

Spectrum C shows the transmittance spectrum of a stack of two samples, both having a thickness of 730 μm. Both samples were taken from the same wafer.

Spectrum D shows the transmittance of a sample of 780 μm thickness measured according to prior-art FTIR method, the same as used for spectrum B. The wafer used in this case had a diameter of 300 mm and was polished on both sides.

All spectra are differential spectra obtained after division by the spectrum of a respective reference sample. The spectra exhibit absoφtion features characteristic for the presence of nitrogen in the samples. A first nitrogen-related absoφtion feature is observed at 963 cm^"1 and attributed to interstitial nitrogen pairs (NN). A second absoφtion feature at 995 cm^"1 approximately coincides with the known absorption at 996 cm^"1 of a nitrogen- nitrogen-oxygen (NNO) complex. The observed shift of 1 cm^"1 is attributed to an interference with an absoφtion feature of thermal donors, which is known to be located at 990 cm^"1. A third absoφtion feature at 1013 cm^"1 corresponds to another known absorption band of thermal donors.

It can be clearly seen that spectrum A, obtained by the prior-art recording method, looks distorted in comparison with spectrum B, which was obtained from the same sample using the multiple recording method of the invention.

Spectrum C differs from spectrum B only by the fact that a stack of samples was measured. In fact, the absorption features detected have an amplitude, which is approximately a factor of 2 larger than in spectrum B. The fact that the doubling is not exact for the absoφtion feature at 995 cm^"1 is probably coursed by a scattering of the intensities of this band in different places of the wafers used for the two stacked samples.

Spectrum D, which was taken from a wafer polished on both sides using the prior-art FTIR method also used for spectrum A, shows that the drift observed in the spectrum is not caused by possible instabilities of the optical properties of the grinded surface of the sample used for spectrum A.

Fig. 5 shows spectral data demonstrating the superior photometric quality of the spectra shown in Fig. 4 and taken according to the invention. Spectra E and F show differential transmittance spectra obtained from two reference samples, that is, samples known to have no measurable concentration of nitrogen. Spectrum E was taken using the method of the invention, while spectrum F was taken using the prior- art method shown in Fig. 1. A comparison of spectra E and F clearly shows that the transmittance spectrum remains close to the value of 1.0000, while spectrum F deviates from the expected behaviour and exhibits broad artificial spectral features, which can be attributed to low-frequency noise and drift. Another demonstration of the superiority of the method of the invention is visible by a comparison of spectra G and H, which represent measured 100%-lines measured using the method of the invention and the prior-art method of Fig. 1. 100%-lines were measured by using the same measurement conditions without placing samples on the sample holder. The comparison of spectra G and H shows that the traditional method generates a considerable drift of the 100%-line, deviating from the value of 1.000 by up to more than 0.0004. In contrast, the 100%-line measured according to the invention deviates within an interval of less than 0.00005.

It is noted that the total error measured in the transmittance of a differential spectrum may even exceed the error of the 100%-line because of possible additional errors connected with the process of changing the samples during differential measurements in the prior-art method. Such additional errors can be due to non- equivalent spatial positions of two samples, including some variation of the angle of incidence.

The method of the invention allows to detect the presence of nitrogen in the samples with a detection limit of approximately 3 x 10¹⁴ cm^"3, using a time span of data accumulation of approximately 2 hours.

Figs. 6 and 7 show three different sets of two 100% lines measured over a wide spectral range, one 100%-line obtained by a prior-art method (dotted lines 602a to c) and one obtained by the method of our invention (full lines 604a to c). Each of the methods was applied for a long recording time, nearly 9 hours, and was repeated three times, in order to derive the reproducibility of the photometric advantage of the inventive method. Fig. 7 shows an enlarged view of the transmittance range between the values of 0,99997 and 1.00003, which is marked by "VII" in Fig. 6, in order to consider quantitatively the achieved quality of 100%- line according to the invention..

The spectral range shown in Figs. 6 and 7 is frequently used in wafer diagnostics during wafer processing and covers the main vibrational bands of different states of oxygen O and nitrogen N in the silicon lattice as well as O, N, carbon C, and fluorine F in silicon dioxide based insulating layers on the wafers. The spectra were recorded using a FTIR spectrometer BOM EM DA8 and a spectrometer of the same type, which was modified to form a spectroscopic apparatus according to the invention. A MCT detector cooled with liquid nitrogen, a Ge/KBr beamsplitter, and a spectral resolution of 1 cm^"1 were employed. All 5 measurements were done in a vacuum of 1 to 3 Torr in a fully automated regime, in a temperature stabilised closed room.

All spectra 602a to c and 604 a to c were obtained using a period of registration _recordi_ng of approximately 9 hours. One pair of spectra was recorded following the prior-art method of Fig. 1 during the period of registration to obtain spectra 602 ao to c, and a total number of 708 partial spectra were recorded during an identical period of registration for the method of the invention to obtain spectra 604 a to c. The ratio of dead time t_dead to the time t_Sj_ngι_Θ of recording a single partial spectrum was approximately 0.3 for spectra 604 a to c. Further, the 100%-lines 604 a to c were calculated as the ratio between averaged odd and even spectra. 5 The spectra shown were obtained after dividing the data by a straight line obtained as a linear approximation to the 100%-line recorded in the spectral region between 700cm^"1 and 1300cm ¹. The comparison of the deviation of 100%- lines allows one to estimate, visually and in a direct manner, the achieved photometric improvement as a result of using the invention. The accuracy of the0 method of the invention is improved by a factor of 30 as compared to the prior-art method.

Fig. 8 shows an alternative embodiment of a sample holder for use in the spectroscopic apparatus of Fig. 3. Sample holder 800 shown in Fig. 8 comprises two wings 802 and 804 of basically identical construction, which corresponds to the5 construction of sample holder 312 shown in Fig. 3. A plate 806 is formed to have two wings 806.1 and 806.2 enclosing an angle α. The angle α is chosen such that an incoming light beam, which is incident on a first sample 810, mounted on section 806.1 at Brewster's angle, will also hit a second sample 812 mounted on the second section 806.2, after being transmitted by the first sample 810 under Brewster's angle. A first diaphragm 814 is provided to limit the extension of the incident light beam passing through window 816 and first sample 810. A second diaphragm 818 is provided to limit the extension of the light beam after passing through second sample 812 and second window 820. Sample holder 800 is constructed to contain a total of four samples, two of which form reference samples, arranged in the same manner as samples 810 and 812. The sample holder 800 thus allows increasing the sample thickness traversed by the light beam without deviating from Brewster's angle of incidence for the second sample. This way, an enhanced absoφtion contrast can be obtained especially in the case of very weak absoφtion features, which are observed at low concentration levels of nitrogen.

Fig. 9 shows a further embodiment of a spectroscopic apparatus forming an alternative setup of that shown in Fig. 3. The setup of Fig. 9 serves to increase the sensitivity by guiding the light beam through the same sample twice. This is achieved by placing a fixed plane mirror 900 behind sample holder 312, which is placed at Brewster's angle with reference to incident light beam 902. The transmitted light beam 904 is reflected by mirror 900, and the reflected beam 906 is directed onto sample 903 at Brewster's angle. The transmitted beam 908 is reflected by a beam splitter 910 and directed to a detector.

The embodiments described above made use of FTIR spectroscopic methods. However, the invention is not limited to one spectroscopic method. For instance the method of the invention can also implemented using a dispersive spectrometer.

Claims

1. A method for the determination of the concentration of an impurity in a wafer including a step of recording infrared spectra of a first sample of the wafer to be analysed and a reference sample from a reference wafer during a period of spectrum registration tr_ecor_ding. wherein the infrared spectra are taken in a spectral range comprising at least one spectroscopic absorption feature caused by the presence of the impurity in the wafer and for the determination of the concentration of the impurity the following steps are performed: - cutting both samples either from the wafers or using the whole wafers as the samples,

- mounting both samples prior to the recording step in a plane on a surface of a moveable plate, the plate containing two windows allowing a light beam of the infrared spectrometer to pass through one of the samples at a time, - recording the infrared spectra under Brewster's angle of light incidence using p-polarised incident light,

- repeatedly changing the position of the plate during the period of the registration trecor ing by displacing the plate along its plane of the surface, such that the light beam of the infrared spectrometer alternately passes through one of the samples at a time, thus recording partial spectra from both samples,

- accumulating recorded spectral information in the time intervals between the position changes of the plate,

- dividing the obtained spectral information into two sets of spectral information corresponding to the first sample and to the reference sample, - performing averaging and statistical analysis for each set of spectral information, in order to determine an average differential spectrum and its statistical error, determining the absorption coefficient of the at least one spectroscopic absoφtion feature using the average differential spectrum and the known thickness ofthe sample determining the impurity concentration in the first sample using a calibration factor.

2. The method of claim 1 , wherein the first sample is formed by a first stack of samples or whole wafers to be analysed, wherein the reference sample is formed by a second stack of reference samples or reference wafers, the first and second stacks containing equal numbers of samples or wafers.

3. The method of claim 1 or 2, wherein displacing the plate comprises a linear movement of the plate, a rotation of the plate, or a superposition of a linear movement and a rotation of the plate.

4. The method of one of the preceding claims, wherein a recording time span tsingi_e between the starting times of two subsequent partial spectra is longer than two times a dead time span t^a_d between completing the recording of the one spectrum and starting the recording of the subsequent spectrum.

5. The method of one of the preceding claims, wherein at least four infrared spectra are recorded from each sample.

6. The method of one of the preceding claims, wherein no more spectra are recorded from each sample than the ratio between a preselected time span forming the period of registration _or ing and four times the dead time span tdead-

7. The method of one of the preceding claims, comprising a step of monitoring the position of the sample currently illuminated by the light beam of the infrared spectrometer with reference to the incident light beam.

8. The method of claim 7, comprising a step of fine-positioning the moveable plate for placing the currently illuminated sample in an identical or close to identical position with reference to the incident light beam before recording a next infrared spectrum of the sample.

9. The method of one of the preceding claims, comprising a step of cleaning surfaces both samples before mounting them on the moveable plate.

10. The method of claim 9, wherein the cleaning of the surfaces of the first sample and the reference sample is performed simultaneously using the same cleaning conditions.

11. The method of one of the preceding claims, wherein the averaging step comprises adding all infrared spectra recorded from the first sample to form a first averaged spectrum and adding all infrared spectra recorded from the reference sample to form an averaged reference spectrum.

12. The method of one of the preceding claims, comprising a step of ascertaining differential spectra Ti^* by calculating quotients Tj^* = Sj/ η of each pair Si, η of infrared spectra formed by an infrared spectrum Si of the first sample and of an infrared spectrum n. of the reference sample taken immediately before or after Si, wherein i denotes an index of a respective pair of spectra between 1 and k, and where k is 0.5 times the number of recorded spectra.

13. The method of claim 12, comprising a step of calculating a first average differential spectrum T* of the differential spectra T .

14. The method of one of the claims 1 to 10, wherein the averaging step comprises dividing the two sets of obtained spectral information into at least four different groups of spectral information, each group thus consisting of two subsets of spectral information, one subset corresponding to the first sample and the other subset to the reference sample, - performing averaging for each subset of spectral information, thus obtaining at least four averaged infrared spectra from the first sample and at least four averaged infrared spectra from the reference sample, calculating respective differential average spectra T from the at least four pairs of obtained averaged spectra, thus obtaining at least four differential average spectra, and

15. The method of claim 13, wherein the step of performing statistical analysis comprises evaluating spectral dependence of a confidence interval Eps according to the formula

wherein n is the total number of differential average spectra.

16. Spectroscopic apparatus for detemnining the concentration of an impurity in a sample by means of infrared spectroscopy, comprising an infrared, IR, spectrometer and a sample holder, wherein

- the spectroscopic apparatus comprises means for repeatedly moving the plate between two end positions with a predetermined velocity and at a predetermined rate during the period of the registration, a first end position allowing a spectrum to be taken through at least one first window, and a second end position allowing a spectrum to be taken through at least one second window,

- the spectroscopic apparatus comprises a light source and polarization means for sending p-polarised incident light onto either the at least one first sample or the at least one second sample at a time

- the sample holder and the light source are arranged with respect to each other such that infrared spectra are recorded under Brewster angle of p- polarised light incidence onto the respective sample.

17. The spectroscopic apparatus of claim 16, wherein the IR spectrometer is a Fourier Transform Infrared (FTIR) spectrometer.

18. The spectroscopic apparatus of claim 17, wherein the FTIR spectrometer comprises the sample holder and the light source.

19. The spectroscopic apparatus of one of the claims 16 to 18, wherein the FTIR spectrometer is adapted to operate in a step-scan mode.

20. The spectroscopic apparatus of one of the claims 16 to 19, wherein the means for repeatedly moving the plate between two end positions comprise an actuator unit connected to the moveable plate, which is arranged and adapted to move the plate in a plane between the first and second end positions.

21. The spectroscopic apparatus of claim 20, comprising a control unit, which is connected to the actuator and adapted to provide to the actuator control signals starting and for stopping a periodic motion of the plate, one motion period comprising motion of the plate back and forth once between the first and second end positions.

22. The spectroscopic apparatus of claim 21 , further comprising a detector unit, the detector unit being arranged and adapted to detect infrared light transmitted through one of the windows of the plate and to provide electric signals indicative of an intensity of light incident on the detector unit as a function of either time or wavelength of transmitted light or both.

23. The spectroscopic apparatus of claim 22, wherein the control unit is adapted to provide control signals to the detector unit instructing the detector unit to start or stop recording an infrared spectrum.

24. The spectroscopic apparatus of one of the claims 20 to 23, wherein the control unit is adapted to select the duration of a recording time span

between the starting times of two subsequent partial spectra to be longer than two times a dead time span trj_ead between completing the recording of the one spectrum and starting the recording of the subsequent spectrum.

25. The spectroscopic apparatus of one of the claims 20 to 24, wherein the control unit is further adapted to control the number of recorded spectra from each sample to be smaller than or equal to the ratio between a preselected time span of the period of registration or_din_g and four times the dead time span

26. The spectroscopic apparatus of claim 25, comprising an input unit connected to the control unit and adapted to receive and forward to the control unit an input value of the period of registration or in_g.

27. The spectroscopic apparatus of one of the claims 16 to 26, further comprising an evaluation unit adapted to group the obtained spectra into two sets corresponding to the first sample and to the reference sample and to perform averaging and statistical analysis for each set of spectra, in order to determine an average differential spectrum T and its statistical error.

28. The spectroscopic apparatus of claim 27, wherein the evaluation unit is adapted to ascertain differential spectra Ti by calculating quotients T|^* = S|/ η of each pair S|, η of infrared spectra formed by an infrared spectrum S| of the first sample and of an infrared spectrum η of the reference sample taken immediately before or after si, wherein i denotes an index of a respective pair of spectra between 1 and k, and where k is 0.5 times the number of recorded spectra.

29. The spectroscopic apparatus of claim 28, wherein the evaluation unit is adapted to calculate a first average differential spectrum T^* from the differential spectra T|.

30. The spectroscopic apparatus of claim 27, wherein the evaluation unit is adapted to - divide the two sets of obtained spectral information into at least four different groups of spectral information, each group thus consisting of two subsets of spectral information, one subset corresponding to the first sample and the other subset to the reference sample, perform averaging for each subset of spectral information, thus obtaining at least four averaged infrared spectra from the first sample and at least four averaged infrared spectra from the reference sample, calculate respective differential average spectra Ti from the at least four pairs of obtained averaged spectra, thus obtaining at least four differential average spectra, and - calculate a second average differential spectrum T from the obtained at least four differential average spectra.

31. The spectroscopic apparatus of claim 30, wherein the evaluation unit is adapted to perform statistical analysis by evaluating a spectral dependence of a confidence interval Eps according to the formula

32. The spectroscopic apparatus of one of the claims 27 to 31 , wherein the evaluation unit is adapted to determine the absoφtion coefficient of at least one spectroscopic absoφtion feature using the average differential spectrum T and the thickness of the sample.

33. The spectroscopic apparatus of claim 32, wherein the evaluation unit is adapted to determine the impurity concentration in the first sample using a preset calibration factor.

34. The spectroscopic apparatus of one of the claims 16 to 34, having a diaphragm, which is arranged, as seen in the direction of incident light, in front of the surface plane for mounting the samples on the moveable plate, the diaphragm being arranged to reduce the extension of the light beam impinging on the currently irradiated sample to a size smaller than the windows on the moveable plate.

35. The spectroscopic apparatus of one of the claims 16 to 34, wherein the sample holder comprises fixing elements, which are adapted and arranged to exert identical forces on the samples in holding them in their respective position relative to the respective windows.

36. The spectroscopic apparatus of one of the claims 16 to 35, wherein the sample holder comprises two wings, each providing a plane on its surface for mounting at least one first sample and at least one reference sample, and each having one first window and one second window arranged to let an incident light beam sequentially pass samples mounted on the first or second window of both wings, the wings being arranged a mutual angle forcing light beam incident under Brewster's angle on a first or reference sample mounted on one wing to also impinge on the first or reference sample mounted on the other wing under Brewster's angle.

37. The spectroscopic apparatus of one of the claims 16 to 35, wherein a plane mirror is positioned behind the sample, as seen in the direction of the incident light beam, such that the transmitted light beam is reflected back onto the sample under Brewster's angle of incidence.

38. The spectroscopic apparatus of claim 37, wherein a beam splitter is arranged in front of the sample, the beam splitter being adapted to transmit the light beam incident on the sample and to reflect the light beam transmitted by the sample after being reflected from the plane mirror.

39. The spectroscopic apparatus of one of the claims 16 to 38, wherein the sample holder contains a sample fixing arrangement, which is adapted to fix a stack of samples in front of each window.

40 The spectroscopic apparatus of claim 20 or 21, wherein the actuator unit is adapted to linearly move the plate or to rotate the plate or to effect a superposition of a linear movement and a rotation of the plate.