Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
  • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
  • G01N21/55—Specular reflectivity
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
  • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
  • G01N21/1717—Systems in which incident light is modified in accordance with the properties of the material investigated with a modulation of one or more physical properties of the sample during the optical investigation, e.g. electro-reflectance
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
  • G01N21/84—Systems specially adapted for particular applications
  • G01N21/88—Investigating the presence of flaws or contamination
  • G01N21/95—Investigating the presence of flaws or contamination characterised by the material or shape of the object to be examined
  • G01N21/9501—Semiconductor wafers

Definitions

• the invention relates to the field of characterisation of doped semiconductors. More particularly, the present invention relates to non-destructive optical measurement techniques for determining the active doping concentration profile of a semiconductor region.
• the ITRS roadmap highlights the precise characterisation of ultra-shallow junctions, formed by shallow doping of semiconductor regions, as one of the top challenges for sub-32 nm Si-CMOS technologies.
• Such a junction is typically characterized by a maximum active doping level N and a junction depth X j and an abruptness S.
• Photomodulated Optical Reflectance is a widely used non-destructive and contactless technique to characterize in a qualitative way the doping profile of such a doped semiconductor region. It is a fully optical, hence non-contact, pump-probe technique.
• a modulated-power pump laser is directed towards the doped semiconductor region to modify the refractive index profile thereof.
• This refractive index profile can be modified through generation of excess carriers in the sample, also known as the Drude effect, and/or by temperature effects of the sample under study.
• a probe laser is directed to this doped semiconductor region where it will be reflected depending on the refractive index profile.
• the reflected probe laser signal By coupling the reflected probe laser signal to a lock-in amplifier, only the variations in the reflectivity of the doped semiconductor sample induced by the modulated pump laser are measured.
• the probe laser thus measures, via reflection, the changes in refractive index induced by the pump laser.
• PMOR is commonly used for monitoring implant dose in as-implanted (i.e. unannealed) silicon wafers, and hence has been the subject of much investigation in this field.
• the variation in refractive index is due to the large increase in the temperature in the illuminated sample (dominant thermal component).
• This technique has also been studied extensively on box-like active doping profiles as obtained by Chemical Vapor Deposition (CVD), where the measured signals are due mostly to the pump-generated excess carriers with only a weak contribution due to a mild increase in temperature (dominant plasma component).
• PMOR technique is the Therma-Probe® technique (TP) described in "Non-destructive analysis of ultra shallow junctions using thermal wave technology" by Lena Nicolaides et al. in Review of Scientific Instruments, volume 74, number 1, January 2003.
• the TP technique is a high-modulation-frequency implementation of the PMOR technique.
• a complete active doping profile can be determined or reconstructed from an optical measurement on the doping profile.
• the active doping profile may be any arbitrary doping profile.
• PMOR can in embodiments according to the present invention be used for determining activated implantation profiles whereby PMOR signals are due to a subtle balance between the plasma and thermal components.
• the combined information contained in the PMOR offset curves, wherein the PMOR signal is measured as a function of pump-probe beam separation, and in the time-independent (DC) reflectance is combined and is sufficient to reconstruct the underlying free carrier profile.
• carrier profiles in ultra shallow junctions can be determined non-destructively, i.e. without sample preparation.
• doping incorporation may be monitored at key points in the process flow and thus leading to an enhanced product quality.
• a method for determining the active dopant profile may be applied in-line, i.e. in the production process environment. It is an advantage of embodiments of the present invention that a unique solution may be determined for the active doping profile based on an optical measurement of the active doping profile.
• photomodulated optical measurement techniques for determining the active doping concentration profile of a semiconductor region are provided, as well as devices and software for carrying out the techniques.
• the present invention relates to a method for optically determining a substantially fully activated doping profile, the substantially fully activated doping profile being characterized by a set of physical parameters, the method comprising - obtaining a sample comprising a fully activated doping profile and a reference obtaining photomodulated reflectance (PMOR) offset curve measurement data and DC reflectance measurement data for said sample comprising the fully activated doping profile and for said reference, and
• PMOR photomodulated reflectance
• Obtaining photomodulated reflectance offset curve measurement data and DC reflectance measurement data may be done by performing a photomodulated reflectance offset curve measurement and by performing a DC reflectance measurement.
• DC reflectance measurement there is meant a time-independent reflectance measurement or reflectance measurement allowing determination of the overall reflectance of the sample.
• Obtaining photomodulated reflectance offset curve measurement data and DC reflectance measurement data may be obtaining data recorded using the same measurement setup.
• Obtaining photomodulated reflectance offset curve measurement data and DC reflectance measurement data may be obtaining data recorded substantially simultaneous or simultaneous.
• the method typically also comprises selecting a predetermined profile shape for fully activated doping profile defined by the set of physical parameters, whereby determining values for the set of physical parameters comprises determining values for the set of physical parameters defining the predetermined profile shape.
• Determining the set of physical parameters of the doping profile may comprise determining a surface excess carrier concentration AN SU b and excess temperature ATsurf from the photomodulated reflectance offset curve measurement data obtained for the reference and determining a reflectance R 0 from the DC measurement data obtained for the reference.
• Determining the set of physical parameters of the doping profile may comprise determining from the photomodulated reflectance offset curve measurement data on the sample and from the DC reflectance measurement on the sample one, more or preferably all of a junction depth X j , an active doping concentration N ac t and a profile abruptness or backside slope S act .
• the present invention relates to an optical measurement method for determining a substantially fully activated doping profile, the substantially fully activated doping profile being characterized by a set of physical parameters, the method comprising
• the sample measurement com prising o determining sample parameters from a photomodulated reflectance measurement on the sample
• the reference measurement comprising o determining substrate parameters from a photomodulated reflectance measurement on the reference;
• the reference (which is free of dopants) will also undergo a pre-amorphization implant and a subsequent annealing step with the same parameters as used for the sample.
• a sample may be provided comprising a doped part (the doped part comprising the substantially fully activated doping profile).
• the sample may comprise also the reference, whereby the reference may be an undoped part, i.e. free of dopants.
• the substantially fully active doping profile may be characterized by a set of physical parameters.
• the set of physical parameters may comprise a junction depth X j , an active doping concentration N act , a profile backside slope S act , a surface active doping concentration N sur f-
• a doping profile may be characterized by an arbitrary functional dopant (X j , N act , S act , N surf , ).
• n in put gathered in addition to the photomodulated reflectance (PMOR) measurement, see later, the number of physical parameters that can be determined is at least 1 + n in put-
• N 0 and W two physical parameters need to be determined and therefore one independent measurement (for example a PMOR DC measurement) is needed on top of the basic PMOR measurement, see later.
• two physical parameters need to be determined (N 0 and W) and therefore one independent measurement (for example a PMOR DC measurement) is needed on top of the basic PMOR measurement (see later).
• a doping concentration profile may for example be characterized by a Complementary Error function.
• two physical parameters need to be determined (N 0 and W) and therefore one independent measurement (for example a PMOR DC measurement) is needed on top of the basic PMOR measurement (see later).
• the doping concentration profile of the sample is not limited to the function profiles mentioned above, but may be any arbitrary function profile D(X j , N ac t, S ac t, With substantially fully activated doping profile is meant that more than 50%, more preferably more than 60% of the total amount of dopants is activated. Dopant activation may be defined as the percentage of the active dose to the as-implanted dose (as determined for example by Hall measurements).
• Determining substrate parameters from a photomodulated reflectance measurement on the reference comprises :
• Determining sample parameters from a photomodulated reflectance measurement on the sample using the substrate parameters comprises :
• the physical parameters may for example be X j and N act , or for the specific case of a Gaussian profile with N 0 and W. Determining at least two of the physical parameters is done based on AN SUb and AT surf from the reference PMOR measurement. Additionally at least another sample parameter may be determined before the step of extracting the set of physical parameters from the reference parameters and substrate parameters. For example a sheet resistance (R s ) measurement may be performed after the PMOR offset curve measurement and the DC measurement on the sample, there from determining in general one additional physical parameter, for example, S act (or for example ⁇ in the case of a generalized Gaussian).
• R s sheet resistance
• a PMOR power curve may be measured there from determining in general one additional physical parameter (which is needed for a reconstruction of the doping profile).
• the set of physical parameters may be extracted from the reference parameters and substrate parameters.
• the step of performing the sample measurement may be done prior to the step of performing the reference measurement or vice versa.
• a reconstruction of the dopant profile is performed based on the combination of PMOR offset curve measurements, DC reflectance measurements and - depending on the number of physical parameters that have to be determined - a number of additional physical measurements such as for example sheet resistance measurements, PMOR power curve measurements, SIMS measurements, electrical AFM measurements (e.g. SSRM), ....
• the reconstruction step may be performed prior to the calibration step or vice versa.
• a new fast, non-destructive and highly local ( ⁇ 1 ⁇ measurement spot) carrier-profiling technique is based on the combined measurement of the PMOR offset curves and of the DC reflectance of a probe laser.
• the technique has been tested on a variety of B-implanted layers with and without GE PAI.
• the extracted carrier profiles follow the expected qualitative trends when it comes to annealing temperature and PAI conditions.
• the profiles also prove to be in good agreement with other profiling techniques such as SIMS or SSRM, with an average accuracy of about 3 nm.
• the present invention also relates to a system for optically determining a substantially fully activated doping profile, the substantially fully activated doping profile being characterized by a set of physical parameters, the system comprising a PMOR measurement system comprising a pump laser and a probe laser for obtaining photomodulated reflectance (PMOR) offset curve measurement data and for obtaining DC reflectance measurement data of the probe laser and a processing system for receiving photomodulated reflectance (PMOR) offset curve measurement data and for obtaining DC reflectance measurement data of the probe laser for a sample and a reference and for determining, based on the measurement data values for the set of physical parameters of the doping profile.
• a PMOR measurement system comprising a pump laser and a probe laser for obtaining photomodulated reflectance (PMOR) offset curve measurement data and for obtaining DC reflectance measurement data of the probe laser
• a processing system for receiving photomodulated reflectance (PMOR) offset curve measurement data and for obtaining DC reflectance measurement data of the probe laser for a sample and a reference and for determining,
• the present invention also relates to a computer program product for determining a substantially fully activated doping profile, the substantially fully activated doping profile being characterized by a set of physical parameters, wherein the computer program product is adapted for receiving photomodulated reflectance (PMOR) offset curve measurement data and for receiving DC reflectance measurement data of the probe laser for a sample and a reference and for determining, based on the measurement data values for the set of physical parameters of the doping profile.
• the present invention also relates to a machine readable data carrier storing the computer program product as described above or to the transmission of such a computer program product over a network.
• FIG. 1 illustrates the determination of a profile model to an active dopant profile using R dc and R AC measurements, according to an embodiment of the present invention.
• FIG. 2 illustrates an exemplary method for determining an active dopant profile according to a particular embodiment of the present invention.
• FIG. 3 illustrates a comparison between the SIMS profile (total doping), SSRM profile (free carriers) and PMOR (free carriers) of a sample implanted with B (0.5 keV, 10 15 cm “2 ) after Ge preamorphisation (5 keV, 5xl0 14 cm “2 ) and annealed at 1300°C, illustrating advantages of embodiments of the present invention.
• FIG. 4 illustrates a comparison between the peak concentration of the PMOR profile and the peak concentration of the active SIMS profile of 8 selected layers.
• Diamond symbols represent the peak SIMS active doping concentration using mobility model I and the stars using mobility model II.
• the full line represents the 1-1 correlation.
• FIG. 5 illustrates a comparison between the depths of the PMOR and SIMS profiles at a concentration of 5el9cm "3 of 8 selected layers.
• the full line represents the 1-1 correlation and the dotted line represents the case of a PMOR profile 25% deeper than the SIMS profile.
• FIG. 6 illustrates a comparison between the abruptness of the PMOR and SIMS profiles of 8 selected layers.
• the full line represents the 1-1 correlation and the dotted line represents the case of a PMOR profile lnm/dec steeper than the SIMS profile.
• FIG. 7 illustrates principles as can be used in embodiments of the present invention.
• a comparison of a profile of infinite slope, i.e. a box like profile, with a profile of a finite slope is shown (a)
• subsequent excess carrier profiles when the substrate carrier concentration is of 10 17 cm “3 (interrupted lines) and 10 18 cm “3 (full lines) for both the profile with finite slope and the profile with infinite slope are shown (b) and the behavior of the integrand in the equation for R AC for arbitrary profiles is shown (c).
• FIG. 8 illustrates offset curves, i.e. curves as function of the laser beam separation, as can be used in embodiments of the present invention, indicating the amplitude of the
• AC reflectance AR TM file (a) the phase of the AC reflectance AR? r ° file (b), the amplitude of the difference ( r )] ( c ) and the phase of the difference [ARj ⁇ ? ⁇ (r)— A ? ⁇ " 's'iraie (r)].
• Measurements are illustrated for five samples implanted on the same substrate with B (0.5 keV, 10 15 cm “2 ) after a Ge preamorphization implant (5 keV, 5 x 10 14 cm “2 ) and laser annealed at 1150°C, 1200°C, 1225°C, 1250°C and 1300°C.
• the arrows show the trend observed when increasing the annealing temperatures.
• the behavior of the phase and wavelength of the plasma wave are recognized in (d) for the four highest annealing temperatures, which ensures that the technique can safely be used on these samples.
• FIG. 9 illustrates fitting curves of experimental data indicating features of
• FIG. 9 (e) illustrates a comparison of the TP profiles (interrupted lines) with the SIMS profiles (full lines) measured on the samples.
• the SSRM profile of one of the samples is also shown.
• the active SIMS doping concentrations are respectively 1.71xl0 20 cm “3 , 1.80xl0 20 cm “3 and 1.80xl0 20 cm “3 .
• FIG. 10 illustrates measurement probability distributions as obtained from Monte- Carlo simulations of the three profile parameters used in an exemplary embodiment of the present invention, i.e. (a) the peak active doping concentration N 0 , (b) the depth X cst at which the profile strarts to decay and (c) the abruptness A.
• the narrow peaks show that the developed technique determines all three fitting parameters with good precision.
• FIG. 11 illustrates the TP versus SIMS profile characteristics and their sensitivity to modeling errors.
• FIG. 11(a) illustrates a comparison of the peak active doping concentration N 0 with the SIMS peak doping concentration obtained from sheet resistance measurements.
• FIG. 11(b) illustrates a comparison of the depths
• FIG. 11 c) illustrates a comparison of the TP and SIMS profile abruptnesses A and at a 10 19 cm "3 concentration.
• Model II assumes a 30% greater electrorefractive effect
• model III assumes a doubled modulated irradiance of the pump laser
• FIG. 12 illustrates a comparison of the TP profiles as obtained from the fitting of the experimental data measured on three samples assuming a profile decaying exponentially (full lines) or a profile following a complementary error function (interrupted lines). While the depth and abruptness are unique, the peak active doping concentration depends upon the profile shape.
• the present invention relates to a method for optically determining a substantially fully activated doping profile.
• the substantially fully activated doping profile is characterized by a set of physical parameters, e.g. by a predetermined profile characterized by a set of physical parameters.
• a predetermined profile may be any type of profile, such as for example a Gaussian profile, a Lorentzian profile, a box or box-like profile embodiments of the present invention not being limited thereto.
• the method comprises obtaining a sample comprising a fully activated doping profile and a reference, whereby the reference may be part of the same sample.
• the method also comprises obtaining photomodulated reflectance (PMOR) offset curve measurement data and DC reflectance measurement data for said sample comprising the fully activated doping profile and for said reference.
• the measurement data is advantageously obtained using the same measurement setup, e.g. using a PMOR recording system.
• the DC reflectance measurement data may be DC reflectance measurement data for DC reflectance of the probe laser used in the PMOR recording system. It is an advantageous that, for obtaining a substantially fully activated dopant profile can be obtained using a relatively simple setup, without the need for measurement equipment different from the PMOR setup.
• the measurement data may be advantageously obtained simultaneously.
• the method also comprises determining values for the set of physical parameters of the doping profile based on both the photomodulated reflectance offset curve measurements and the DC reflectance measurements.
• Embodiments of the present invention advantageously make use of DC reflectivity which is linear sensitive to active doping concentration, for obtaining information regarding the doping concentration, and of AC reflectivity obtained through PMOR which is sensitive for lower doping concentrations for determining depth and optionally also abruptness of the active doping profiles.
• the latter is illustrated in FIG. 1, indicating a profile for the active doping profile, whereby the DC reflectivity measurement data especially contributes for determination of the active doping concentration and wherein the PMOR measurement data especially contributes to the depth and abruptness of the active doping profile.
• the active doping profile may be described using a predetermined profile characterized with parameters determined using the PMOR and the DC reflectivity measurement data. Such a predetermined profile can also provide further information for such regions where no measurement data were recorded.
• the exemplary method 200 comprises in a first step measuring 210 a DC reflectance and PMOR offset curves in a region free of dopants. Such measurements allow determining 220 model parameters for the model that will be used for determining the active doping profile to be determined.
• Determining model parameters 220 may for example in one particular embodiment be determining 222 the DC reflectance of the undoped semiconductor based on the DC reflectance measurement and obtaining 224 the excess carrier concentration and excess temperature generated by the pump laser, although embodiments of the present invention are not limited thereto and, depending on the model used, also other model parameters may be derived from the measurements in a region free of dopants.
• the DC reflectance and PMOR offset curves are measured 230 in the region comprising the active doping profile. Based on the measurements obtained in step 230 and on the model parameters determined in step 220, the measurement results are fitted to the model selected for the active doping profile and the active doping profile is thus determined. This is illustrated in step 240.
• determining the active doping profile may comprise or may be determining the parameters further defining the model for the active doping profile.
• parameters in one example may be the surface peak free carrier concentration, the depth at which the carrier concentration starts to decay and the abruptness of the profile.
• TP630XP tool TP
• PMOR ThermaProbe TP630XP tool
• the PMOR signal is a measure of the change AR in reflectance of the probe laser due to the injection by the pump laser of excess carriers and heat (resulting in surface excess temperature AT sur face)
• Nact(z) z representing depth
• m e (respectively rri ) is the effective mass of electrons (respectively holes) in silicon.
• R 0 is the DC reflectance of undoped Si
• n 0 is the refractive index of undoped Si
• ⁇ is the Drude coefficient
• S dn / dT s the temperature coefficient of the refractive index in Si, all four taken at wavelength OROBE .
• the above equation shows that the PMOR signal can be understood as the coherent sum (interference) of the reflections occurring at all depths of the excess carrier profile (including a thermal component at the surface expressed by the last component between the brackets).
• the link between the excess carrier distribution AN[N act (z), AN sub (x)] and the (equilibrium) free carrier profile N ACT (z) is known by the person skilled in the art.
• the PMOR signal as given by the equation above is measured as a function of the distance x between the probe and the pump beams (with a maximum distance of 4 ⁇ ).
• the DC reflectance R of the probe laser is also influenced by the (equilibrium) free carrier profile.
• the variation in DC reflectance AR DC at wavelength ⁇ ,-obe due to a hole profile N act (z) is given by
• R DC is easily understood as the coherent sum of the reflections occurring at all depths of the (equilibrium) free carrier profile.
• the DC reflectance is a direct image of N act (z)
• the PMOR signal is an indirect image of N ACT (z)[via ⁇ ] .
• the combination of the PMOR offset curves with the DC reflectance is very promising.
• PMOR offset curves have been shown to be essentially sensitive to the depth of the profile.
• the change in DC reflectance is directly proportional to the peak carrier concentration, as can be seen from the above formula. In other words, the combination of both measured parameters gives access to the depth of the profile (mostly via the PMOR offset curve) and to the carrier concentration of the profile (mostly via the DC reflectance).
• the measurement and fitting procedure is divided into two phases. Both phases involve a measurement and the fitting of the obtained data.
• the fitting algorithms in the exemplary study discussed is based on a Levenberg-Marquardt optimization algorithm, embodiments of the present invention not being limited thereto.
• a first phase I also referred to as the calibration phase
• the three parameters appearing in the equations above which are not linked to the free carrier profile, i.e. AN sub ⁇ x), T sul f (x), R 0 were fixed. These three parameters were then used in
• Phase II the DC reflectance and the PMOR offset curve on a region free of dopants was measured.
• the three-dimensional linear ambipolar diffusion equation and heat equation were solved. This determined AN sub [x) and AT su ⁇ ⁇ x), i.e. the excess carrier concentration and excess temperature generated by the pump laser in the Si substrate.
• AN sub ⁇ x) and AT su ⁇ ⁇ x) are influenced by any possible damage of the substrate, as is the case in preamorphized layers.
• the calibration phase therefore advantageously was measured on a site free of any dopant, but having undergone the same preamorphisation implant PAI (and anneal) as the considered doped sample. For this reason, during the processing of each ultra-shallow profile, a lithographic step was performed in order to keep a region free of dopants. Except for this additional step, the dopant free regions followed the same process as the doped regions, making them ideal candidates for the calibration of AN sub ⁇ x) and AT su ⁇ ⁇ x) . It thereby was assumed that the B implant induces negligible extra damage to the sample.
• a second phase II also referred to as a reconstruction phase
• the PMOR offset curves and the DC reflectance on the considered active doping profile were measured.
• the data were then fitted with a carefully parameterized profile.
• restriction was performed to two-parameter or three-parameter profiles (box, Gaussian, Lorentzian, .7) whereby below the example of box profiles with an exponential tail (three parameters) is discussed.
• box, Gaussian, Lorentzian, .13 the fitting profiles used in the present exemplary study can be written
• N 0 is the surface (peak) free carrier concentration
• X is the depth at which the carrier concentration starts to decay
• a is the abruptness of the profile.
• the fitting algorithm optimizes N 0 , X and a based on the above equations and using the values of or R 0 , ⁇ sub (x), AT , (x) determined in the calibration phase.
• the PMOR signal is sensitive to the free carrier profile only via the plasma component of the above formula.
• the plasma component therefore advantageously should dominate the thermal component.
• the latter is obtained by using high activation in the layer and low (end-of-range) defect concentrations.
• PAI preamorphization implant
• SIMS measures the total (i.e. electrically active and inactive) doping profile
• SSRM measures the resistivity profile. It has been shown that it is possible to extract the carrier profile from a SIMS measurement if the sheet resistance and carrier mobility are available.
• carrier profiles can be deduced from SSRM measurements only if the carrier mobility is known. For instance, the SSRM profile in FIG. 3 assumes a hole mobility of 100 cm 2 .V _1 .s 1 in the doped layer. In other words, whether using SIMS or SSRM, mobility is always needed if one wants to extract carrier profiles.
• Sheet resistance has been measured using a Four- Point Probe (FPP).
• FPP Four- Point Probe
• two different mobility models are used, respectively setting upper and lower limits to the mobility range (hence defining respectively lower and upper limits of the active doping concentration range). Both mobility values are obtained using Klaassen's model.
• a first model considered only the carrier scattering upon active dopants (no scattering on inactive dopants). This is also referred to as model I. It is, however, well-known that this assumption tends to overestimate the mobility in a ultra-shallow junction USJ. As a consequence, the obtained carrier concentration will be underestimated.
• FIG. 4 shows the correlation between the peak concentration N 0 of the extracted PMOR profile and the peak concentration of the active SIMS profiles.
• two mobility models are used for determining mobility for use in the SIMS measurements giving two peak active SIMS doping concentration for comparison.
• FIG. 5 compares the depth of the PMOR and SIMS profiles at a concentration of 5el9 cm "3 . It can be observed that PMOR almost systematically overestimates the depth of the profile, as given by SIMS. This could actually also be observed in FIG. 3 and can be explained by the probable overestimation of AN sub (x) ⁇ due to calibration). Finally, FIG. 6 compares the abruptness of the PMOR and SIMS profiles. The agreement here also was very good though PMOR profiles are systematically slightly steeper (typically lnm/dec).
• AR AC can be written as ) + SAT 1 (r)
• AR AC can be understood as the coherent sum of two reflections.
• the second reflection is occurring at each depth of the excess carrier profile.
• FIG. 7 illustrates the analogy. More particularly, it shows two active doping profiles with different slopes (FIG. 7a illustrating a profile of infinite slope 702 and a profile of a finite slope 704)) and the subsequent excess carrier profiles for two different excess carrier concentrations in the substrate for 10 17 cm “3 and 10 18 cm “3 (FIG.
• the integrand of the above equation reduces to a peak at the junction, i.e. the interface reflection is composed of one single large reflection. Furthermore, the position of this peak is independent from the substrate injection. On the other hand, when the slope of the profile is finite, the multiple reflections at the interface broaden the peak. The position of the maximum of this peak, i.e.
• the maximum interface reflection can be understood as the depth to which AR ac is sensitive.
• the maximum interface reflection moves according to the substrate injection. Mathematically, this can be understood as follows : Neglecting the cosine envelope of the integrand, the position z max of the maximum interface reflection can be defined as the position at which the excess carrier profile is the steepest, i.e. an approximate value of z max can be found by solving the following implicit equation 3 2 ⁇ # ⁇ ( ⁇ )
• the maximum interface reflection comes from the depth where the doping concentration is 1.57 x AN SUb - From this result, it is correct to extrapolate that the maximum interface reflection always originates from a depth where the doping is commensurate with the substrate injection, independently from the profile itself. Note that the particular value obtained in the above equation, however, cannot be generalized for all profiles since the profile derivatives are involved.
• AR AC is sensitive to the depth at which the active doping profile reaches a concentration of the order of the substrate injection. This has two important implications. First it means that, in the measurements performed, AR AC is only sensitive to the moderately doped region of the profile. Second if the injection level can somehow be changed, the position of the maximum interface peak is shifted accordingly, i.e. part of the profile is scanned. This explains the sensitivity of offset curves to the abruptness of the profiles, as a direct consequence of the lower carrier injection when moving away from the pump beam. Concerning the DC reflectance R dC , contrary to AR AC , it is known that it is mostly sensitive to the highly doped region of the profile.
• R dc fixes the peak doping concentration based on the depth and abruptness determined by AR AC in the moderately doped region of the profile, as is also illustrated and described above with reference to FIG. 1, illustrating features of the principle of the technique of embodiments of the present invention. It is to be noticed that since R AC is blind to the region of the profile situated above a 10 19 cm "3 doping concentration, the peak concentration determined by R dC depends on the assumed shape of the profile in that particular region. The corresponding uniqueness problem is solved by selecting a good profile shape for the active dopant profile. In the present exemplary study, a method as described above with reference to FIG. 2 was used for determining the active dopant concentration. Further features of the exemplary method are described below.
• the method comprises measuring DC reflectance and PMOR offset curve in a region free of dopants.
• a substrate or reference measurement is run, i.e. a measurement on a sample presenting no doped layer but having undergone the same process flow as the sample under investigation.
• the substrate measurement is run on a region of the sample which has received no dopant implant but has been preamorphized (if relevant) and annealed exactly like the doped sample under investigation.
• the method also comprises determining model parameters for a model to be used for determining the active doping profile.
• the DC reflectance R 0 can be derived from the ⁇ substrate re f
• the index subO refers to the time independent mode, whereas the index subl refers to the time dependent mode.
• the method also comprises measuring DC reflectance and PMOR offset curve in a region comprising the active doping profile.
• a profile measurement is run on the sample to be characterized. This yields AR ⁇ ° ⁇ le offset curves and r> profile
• the method further comprises fitting of the measurement results using the model for the active doping profile and the obtained model parameters thus determining the active doping profile.
• the model for AC and DC reflectances on non-homogeneous samples therefore typically is fitted to the experimental AR ⁇ lle offset curves, using the previously determined AN subQ ⁇ r), AN subl (r) and AT ⁇ r) and to the
• the profile shape may be determined by two or three parameter fittings.
• box-like profiles with an exponential tail were used and seemed to provide appropriate results, i.e.
• N 0 is the peak active doping concentration of the profile
• X cst is the depth at which the profile starts to decay and A is its abruptness (nanometer/decade).
• the fitting algorithm determines N 0 , X cst , and A.
• the fitting in the present example is based on a Levenberg-Marquardt algorithm (minimization of the least-square error).
• the technique in the present example relies on the substrate measurement for the determination of the substrate plasma and thermal components. As a consequence, the substrate measurement advantageously is carefully monitored.
• a verification procedure can be used to make sure that the substrate measurement meets the requirement, i.e. AN sub0 (r), AN subl ⁇ r) and AT ⁇ r) are the same in the substrate and profile measurements.
• One method for verifying this may be subtracting the substrate measurement R ⁇ bstrate from the profile measurement AR ⁇ . ° ⁇ lle measured on the unknown doped profile.
• the phase and wavelength of the plasma wave should be recognized. This is illustrated in FIG. 8.
• the plasma phase and wavelength can be identified in FIG. 8(d) for all layers except the lowest annealing temperature, underlying the thermally dominated behavior of the latter. The latter also shows that the impact of the boron-implantation-induced damage on the plasma and thermal components is negligible (after anneal).
• the fitted curves are shown in FIG. 9 (a) and (b) for the substrate measurement and (c) and (d) for the profile measurement. It is clearly observed that the theoretical curves nicely fit the experimental data.
• the so-called TP profiles obtained from the fitted data are shown in FIG. 9(e) together with the SIMS profiles measured on the three samples.
• the SSRM profile measured on one of the samples has also been added (assumed mobility is 100 cmVV 1 ).
• the TP profiles have been obtained in less than 30 minutes (20-minute measurement and less than 10 minutes fitting).
• the quantitative agreement between the TP and active SIMS (and SSRM) profiles is acceptable since the average deviation on the derived depths at a doping of 10 19 cm "3 is of 3 nm.
• the average deviation on the peak active doping concentration is of 5 x l0 18 cm ⁇ 3 .
• TP profiles in the present example are deeper than the SIMS profiles. TP and SIMS are also in contradiction when it comes to the relative depths of the three profiles.
• N 0 , X cst and A are defined as the standard deviations of their respective distributions. It can be observed that all three parameters are determined with very high precision. It can also be noted that the peaks of X cst in FIG. 10 (b) are clearly separated. As a conclusion, random errors cannot explain the discrepancy between the TP and SIMS profiles observed in FIG. 9(e).
• FIG. 11(a) shows the comparison of peak active doping concentration N 0 obtained from our measurement technique with the peak active doping concentration
• FIG. 11(b) shows the comparison of the depths X jP and X s a lMS at which respectively the TP and SIMS profiles reach a concentration of 10 19 cm "3 .
• FIG. 11(c) compares the abruptnesses A and of respectively the TP and SIMS profiles (value taken around a 10 19 cm "3 concentration).
• Different models are used to indicate the effect of variation of parameters.
• Model II shows an impact of a 30% greater electrorefractive effect, to counteract the observed underestimation of this effect.
• Model III assumes a double modulated irradiance of the pump laser to account for the underestimated excess carrier concentration in the substrate.
• model IV reduces the layer injection, to counteract the overestimated sensitivity to the active doping concentration in the layer.
• the latter model assumes that the constant mode of the excess carrier concentration in the substrate AN sub0 is equal to 2
• the values used for each of these models can give a good feeling of the impact of the different modeling errors.
• FIG. 11(b) compares the depths of the TP and SIMS profiles at a 10 19 cm "3 concentration. As already observed in FIG. 9(e), the TP profiles are always deeper than the SIMS profiles. Further, the depths of the SIMS measures it shallower. It can be seen in FIG. 11(b) that, though the depths of the TP profiles vary according to the used model, none of the modified models explains the anti-correlation. The error is therefore seems not correlated to the modeling errors discussed above.
• the anti-correlation could be due to an additional modeling error lying in the substrate measurement fitting.
• the evolution of AR in FIG. 9(c) seems to indicate an evolution of the junction depth in agreement with the SIMS profiles.
• the trend observed in these data is also partly due to the decrease in the substrate plasma component, as can be observed in FIG. 9(a) and as expected when increasing the Ge PAI dose or energy (increased damage).
• the error may be due to a less accurate discrimination between both effects (reduction in substrate plasma component and deeper profile). This may indicate that the variations in AN subl and ⁇ ) with the energy and dose of the Ge implant are not properly accounted for.
• the assumed homogeneous ambipolar diffusivity and recombination lifetime have to be blamed.
• N 0 is very sensitive to the modeling error. This can easily be explained by the fact that N Q is very sensitive to the modeling error . This can easily be explained by the fact that N 0 is fixed by R dc after the depth and abruptness have been determined by R ac . Furthermore, the values of N 0 are quite difficult to compare with the
• N gjM s values since the latter assumes crystalline mobility.
• the impact of modeling error on N 0 is complex and in advantageous embodiments can be taken into account when determining depth accuracy.
• FIG. 12 compares the obtained TP profiles for all three samples. While the obtained depths and abruptnesses in the moderately doped regions are independent from the assumed shape, the peak active doping concentrations are significantly impacted by the profile shape.
• the fast non-destructive profile characterization technique based on the combined measurement of R ac offset curves and R dC according to embodiments of the present invention.
• the technique has a high precision and is in acceptable agreement with SIMS and SSRM. In advantageous embodiments, modeling errors could be taken into account. Further, the depth and abruptness of the profiles obtained using this technique are unique but the obtained peak active doping concentration depends on the assumed profile shape. A higher pump irradiance alternatively could directly solve this uniqueness problem.
• the present invention also relates to computer-implemented methods for performing at least part of the methods for optically determining a substantially fully activated dopant profile.
• Embodiments of the present invention also relate to corresponding computer program products.
• the methods may be implemented in a computing system. They may be implemented as software, as hardware or as a combination thereof. Such methods may be adapted for being performed on computer in an automated and/or automatic way. In case of implementation or partly implementation as software, such software may be adapted to run on suitable computer or computer platform, based on one or more processors.
• the software may be adapted for use with any suitable operating system such as for example a Windows operating system or Linux operating system.
• the computing means may comprise a processing means or processor for processing data.
• the computing system furthermore may comprise a memory system including for example ROM or RAM, an output system such as for example a CD-rom or DVD drive or means for outputting information over a network.
• a memory system including for example ROM or RAM
• an output system such as for example a CD-rom or DVD drive or means for outputting information over a network.
• Conventional computer components such as for example a keybord, display, pointing device, input and output ports, etc also may be included.
• Data transport may be provided based on data busses.
• the memory of the computing system may comprise a set of instructions, which, when implemented on the computing system, result in implementation of part or all of the standard steps of the methods as set out above and optionally of the optional steps as set out above.
• the obtained results may be outputted through an output means such as for example a plotter, printer, display or as output data in electronic format.
• inventions of the present invention encompass computer program products embodied in a carrier medium carrying machine readable code for execution on a computing device, the computer program products as such as well as the data carrier such as dvd or cd-rom or memory device. Aspects of embodiments furthermore encompass the transmitting of a computer program product over a network, such as for example a local network or a wide area network, as well as the transmission signals corresponding therewith.

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