Method for determining crystal defect concentrations below 10 ppm in semiconductor materials based on photomodulated reflectance measurements.

Abstract

In the case of semiconductor samples, the method makes it possible to determine the charge carrier lifetime and the concentration of crystal defects due to recombination defect centers present in the material, based on photomodulated reflectance (PMR) measurements working in the quasi-static modulation frequency range. The defect centers present in essentially monocrystalline semiconductor samples (M1) can be of intrinsic or extrinsic origin and are typically low-mass -H + , He + - electrically active defect sites caused by the implantation of high energy ions or impurity atoms, e.g. metal contaminants introduced during other technological steps. The method can be used in all cases where the crystal defect concentration is typically in the ppb-ppm range, its depth distribution is approximately uniform, and the size of the excitation / analysis laser spot in the PMR measurement is significantly smaller than the thickness of the zone containing the crystal defects. The total lifetime τ tot from which, knowing the recombination lifetimes of other charge carriers and the time constants of diffusion processes, the lifetimes and concentrations assigned to intrinsic or extrinsic defects can be determined and correlated with the implantation parameters or other technological parameters.

Description

[Technical field]

[0001] The present invention relates to a method for deriving charge carrier lifetimes and defect site concentrations from photomodulated reflectance measurements when the defect concentrations in semiconductors are low, on the order of ppm to ppb, and more specifically to a method for determining crystal defect concentrations of less than 10 ppm in semiconductor materials based on photomodulated reflectance measurements. [Background technology]

[0002] Photomodulated reflectance (abbreviated PMR) is a non-destructive, non-contact testing technique widely used in semiconductor technology, which allows samples to be inspected based on optical principles after one technological step at a time, for example immediately after ion implantation and before a subsequent heat treatment step.

[0003] From previous studies, for example, the study by F. Ujhelyi, A. Pongracz, A. Kun, J. Szivos, B. Bartal, B. Fodor, A. Bolcskei-Molnar, Gy. Nadudvari, J. Byrnes, and LM Rubin, “Mid-low energy implantation tilt angle monitoring with photomodulated reflectance measurement” (Proc. 30th Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC), Saratoga Springs, NY, USA, May 6-9, 2019, pp. 1-4) and the study by A. Pongracz, J. Szivos, F. Ujhelyi, Zs Zolnai, O. Sepsi, A. Kun, Gy. Nadudvari, J. Byrnes, LM Rubin, and ED Moore, “Tilt angle and dose rate monitoring of low energy ion implantation processes with photomodulated reflectance measurement” (Proc. 31st Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC), Saratoga Springs, NY, USA, August 24-26, 2020, pp. 1-4) that the measured PMR signal shows high sensitivity to the ion implantation dose, and furthermore, from the study by Z. Zolnai, F. Korsos, A. Pongracz, V. Samu, Z. Kiss, B. Fodor, J. Szivos, L. Rubin, E. Moore, and J. Byrnes, "Room temperature micro-photoluminescence measurements for monitoring defects in low-energy high-dose As and B implanted silicon" (Proc.From the 32nd Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC), Saratoga Springs, NY, USA, May 10-12, 2021, pp. 1-4), it is known that the measured PMR signal shows high sensitivity to the current density of the ion implantation, the energy and mass of the implanted ions, as well as to the tilt angle of the sample in case of implantation in the channel direction.

[0004] Moreover, due to the small sampling area of ​​a few mm2, PMR is also suitable for high-resolution sample mapping and for testing the homogeneity of samples after applied technological steps. Therefore, the technical and theoretical development of this method is considered to be important for semiconductor technology and materials science.

[0005] The PMR technique basically measures the change in the reflection of the sample under optical excitation, but this parameter is also related to and informs on many other physical properties of the material under test. For example, for shallow and ultra-shallow pn transitions, the exact depth of the transition can be determined, which is usually within the range of less than 100 nm, as is known from the work by F. Dortu, T. Clarysse, R. Loo and W. Vandervorst, "Extracting active dopant profile information from carrier illumination power curves," J. Vac. Sci. Technol., B 24, 375 pages, 2006. The theoretical background of the PMR method, i.e. the method of calculating the PMR signal in differently doped p-type and n-type semiconductors, has been reviewed in detail in the literature, for example in the work "Progress in the physical modeling of carrier illumination" by F. Dortu, T. Clarysse, R. Loo, B. Pawlak, R. Delhougne and W. Van-dervorst (J. Vac. Sci. Technol., B 24, 1131 p., 2006) or in the work "Low frequency modulated optical reflectance for the one-dimensional characterization of ultra-shallow junctions" by F. Dortu (PhD thesis, IMEC, Leuven, Belgium, 2009). In these works, values ​​of material parameters relevant for the PMR effect are also reported for single crystal Si samples.Methods for deriving the total charge carrier lifetime from the PMR signal have also been described for Si, but also when investigating the dynamics of free charge carriers in, for example, InGaN / GaN quantum valley structures, e.g., in the work by A. Salnick, A. Mandelis, A. Othonos, and C. Christofides, “Noncontact lifetime reconstruction in countinuously inhomogeneous semiconductors: generalized theory and experimental phototermal result for ion-implanted Si,” in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 16, edited by D O. Thompson and D E Chimenti, Plenum Press, New York, 1997, pp. 371-378, or in the work by X. Lei, B. Li, Q. Sun, J. Wang, and C. Gao, “Electronic transport characterization of B+ ion-implanted silicon wafers with nonlinear photocarrier See the study by M. P. Halsall, I. F. Crowe, J. Mullins, R. A. O. Liver, M. J. Kappers, and C. J. Humphreys, “Photomodulated Reflectivity Measurement of Free-Carrier Dynamics in InGaN / GaN Quantum Wells” (ACS Photonics 5:4437-4446, 2018).

[0006] However, in the ion-implanted Si samples examined, where the PMR effect in the damage layer is dominated by thermo-optical rather than electro-optical effects, the defect density is typically in the high range of 0.1-1% or even higher, and the defect concentration is very non-uniform with respect to depth. On the other hand, ion-implanted and subsequently heat-treated Si samples have been studied, but in this case the defect structure and defect concentration profile that emerges are less well known, and in addition to residual complex array defects, end-of-range (EOR) defects may also be present in the sample. In another study, in the case of InGaN / GaN, it was assumed that the sample has a single crystal structure for a given doping level and does not contain structural defect sites that may be generated as a result of ion implantation, or unwanted contaminants, e.g. metallic impurities that enter the sample during the manufacturing or post-processing steps of the raw materials used. Again, the presence of such defects was not taken into account when evaluating the PMR signal.

[0007] Furthermore, from the point of view of semiconductor technology, it is often important to know the amount of structural defects at low concentrations, such as ppm or even ppb, and the possible defect sites connected to impurity atoms, and their influence on the electrical properties (charge carrier lifetime).

[0008] Herein, a step forward is presented compared to previous methods, which, when evaluating the PMR signal, takes into account the effects of structural defect sites or contaminating atoms, which are present almost uniformly in low concentrations in essentially single-crystalline samples, while using appropriate reference measurements. In such cases, the PMR effect is dominated by electro-optical effects, and a significant excess charge carrier concentration can be maintained in the sample. This approach allows obtaining information about the influence of the typically deep levels that defect sites create in the forbidden band on the charge carrier lifetime and its concentration. Using this method, the lifetime of point defects present in the crystal lattice can be derived from the lifetime value of the total charge carriers, after separating from the total useful lifetime other lifetime contributions such as the contributions of Shockley-Read-Hall recombination, Auger recombination, and the characteristic time constant due to diffusion of charge carriers.

[0009] The defect concentrations and specific lifetime values ​​thus obtained are important parameters both from a technological and a material science point of view.

[0010] The earliest publications related to the outlined measurement method are older and can be found in the late 80's in US Patent 4,579,463 or JP 2-89335. Photomodulated reflectance can be found under this name and other names such as Therma-Wave, Modulated Optical Reflectance (MOR), etc. US Patent 6,489,801 (B1) lists all the physical properties that can affect the measured reflected signal but does not include a qualitative discussion of them.

[0011] Several well-known documents discuss manufacturing technology solutions used during ion implantation procedures and mainly their monitoring: WO 99 / 08307 A1 describes the calibration of an ion implanter against a previously measured dose; US Patent No. 6,812,717 (B2) discloses the correspondence of measurements with "parameters used to generate the measurements", e.g. ion implantation control parameters, or the conclusion about lateral diffusion by comparing the distribution of measurements with a specific design geometry and the application of the "accept-reject" criteria during manufacturing on this basis.

[0012] JP 1-134240 A proposes a solution for determining the change in depth distribution of lattice defects with respect to polishing at various depths without a quantitative determination.

[0013] US Patent No. 8,120,776 (B1) describes the determination of the properties of ultrashallow pn transitions using the DC component of photomodulation reflectance measurements, where the lattice defect concentration is determined based on a comparison with the DC signal obtained on a preliminary reference sample.

[0014] In the previously mentioned "therma-wave" (TW) technology, the correlation between the TW signal and the implanted dose has been studied for a long time. For example, S. Hahn et al. 13 ~10 15 cm -2 ) and 100keV Si+ (dose 10 14 ~10 15 cm -2 We also report defect concentrations measured by deep level transient spectroscopy (DLTS) and TW signals in heat-treated samples after quasi-amorphization / amorphization implantation of ZnO. The defect densities in the heat-treated samples were in the ppb range. Although a qualitative correlation was established, the defect densities could not be obtained from the TW signal.

[0015] M. Anjum et al. reported that the TW method was used to measure the energy of 0.5 to 3 MeV (10 12 ~10 14 cm -2 ) high energy P + The effect of implantation was investigated (see Nucl. Instrum. Methods Phys. Res. B 55 (1991) 266-268). For channel-directed implants with an energy of 2 MeV, correlations were found between dose and TW signal and between tilt angle and TW signal, but defect concentration estimation was not addressed.

[0016] W. Kiepert et al. + (Dose 10 11 ~10 15 cm -2 ) implanted Si samples were investigated by laser modulated optical reflectivity (Surface and Coatings Technology 116-119 (1999) 410-418). In this, low energy implants only affect the top 1 mm of the sample, and the resulting defect concentrations are in the range of 0.1-1% ppm, which is high in terms of the method. The authors do not consider the role of defect concentration on the charge carrier lifetime when modelling the measured signal.

[0017] In their study "Review of Progress in Quantitative Nondestructive Evaluation" (Vol. 16, DO Thompson and DE Chimenti, eds., Plenum Press, New York, 1997, pp. 371-378), A. Salnick et al. + (Dose 10 13 cm -2 ) implanted Si samples were investigated by photothermal reflectance (PTR) before and after thermal treatment. The researchers' aim was to evaluate the charge carrier lifetime and diffusion coefficient in a depth-dependent manner. The intensity and phase of the measured PTR signal were adjusted by computer simulation as a function of the frequency of modulation. In the implanted samples investigated, the defect density is quite high, typically 0.1-1%, and the defect concentration is very inhomogeneous with respect to depth. On the other hand, the defect structure and defect concentration profile occurring in the thermally treated samples are less well known, which means that in addition to the residual composite block defects, end-of-range (EOR) defects may also be present. The authors later showed that the defect concentration profile was significantly higher in the implanted samples than in the untreated samples, with a wide dose range (10 9 ~10 15 cm -2 ) at 100 keV B + , P + , As + The analysis is repeated for implantation of 1000 .mu.m. See A. Salnick and J. Opsal, Journal of Applied Physics 91, 2874, 2002. The shallow defect structure is qualitatively different from that of the samples we have examined. The authors did not evaluate the useful lifetime of the defect sites.

[0018] X. Lei et al. + Injection (dose 10 11 ~10 16 cm -2) Si samples and heat-treated Si samples were measured by photogenerated charge carrier radiometry (PCR) and evaluated as a function of modulation frequency with the same purpose as the aforementioned Salnick work (Journal of Applied Physics 127,035701(2020)). Information on the lifetime of the entire charge carriers was obtained, but the lifetime of the defect sites was not evaluated. In similar tests, the very inhomogeneous sample structure, e.g., shallow defect profiles, diffusion during heat treatment, the presence of end-of-range (EOR) defects after heat treatment, etc., make the evaluation more complex and uncertain than in the case of the method according to the present invention for studying non-heat-treated defect structures with a nearly uniform distribution extending to considerable depths.

[0019] MPHalsall et al. investigated unimplanted single-crystal InGaN / GaN structures using the PMR technique and evaluated the charge carrier lifetime as a function of the power of the generated laser, taking into account SRH, Auger, and radiative processes (see ACS Photonics 5:4437-4446 (2018)). The presence of structural defects was not taken into account. Summary of the Invention [Problem to be solved by the invention]

[0020] The aim of the present invention is to enable the determination of the lifetime of charge carriers, which is overlooked in the above examples. [Means for solving the problem]

[0021] The present invention is based on the recognition that the crystal defect concentration, which has been largely ignored up until now, plays an important role in the lifetime of the charge carriers, and therefore, when determining this lifetime, low crystal defect concentrations of the order of ppm to ppb are naturally taken into account, which is advantageous for light modulation reflectometry, and when carried out, can give highly reliable results.

[0022] The set problem is solved by a method for deriving charge carrier lifetimes and defect site concentrations in semiconductors from light modulation reflectance measurements in the case of low defect concentrations of the order of ppm to ppb according to the features of claim 1. Some advantageous implementations of the method are recited in the dependent claims.

[0023] Monitoring of implantation dose and charge carrier lifetime in a highly accurate and non-destructive manner based on defect concentration is a key element in the manufacturing process. The method according to the invention based on PMR analysis can be used very well for this. In the case of C-MOS based imaging electronics, it is equally important to monitor the presence of metallic impurities (Fe, Cr, etc.) that impair the stable operation of the devices and their influence on the lifetime of charge carriers in the starting semiconductor base wafer. The described PMR based method can also be used here within certain contaminant concentration ranges.

[0024] The invention will now be described in more detail by way of example with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0025] [Figure 1] 1 is a flow chart of a possible implementation of the proposed method for ion implantation specimens. [Diagram 2] FIG. 1 shows examples of DR / R0 values ​​calculated for lightly doped (about 10-15 cm-3) Si samples containing various uniform concentrations of excess defect sites. [Figure 3a-3b] FIG. 1 shows the concentration of vacancy centers produced by 1.5 MeV hydrogen ion implantation in a single crystal Si sample as a function of depth. [Figure 4] FIG. 4 shows the PMR signal measured on a Si sample implanted under the conditions shown in FIG. 3, together with the value of a reference measurement. [Diagram 5] FIG. 1 shows the charge carrier lifetime contribution and effective diffusion time constant obtained from PMR measurements by this method as a function of implanted dose. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] A brief description of PMR technology The working principle of the PMR technique is based on the fact that the complex refractive index of a sample changes as a result of optical excitation, which can also be optically detected - through a change in reflectance.

[0027] In the case of PMR, one single mode laser is used for excitation and for measuring the resulting reflectivity change. In the case shown, the wavelength of the excitation laser is 808 nm, while the wavelength of the measurement laser is 980 nm. These lasers are attached to a common optical fiber and focused to a common spot on the sample with a diameter of about 3 μm, so that excellent spatial resolution can be achieved with this technique. Due to the use of near-infrared wavelengths, the measurement is not only non-contact but also non-destructive.

[0028] To detect the change in PMR (ΔR), the intensity modulation of the excitation laser incident on the sample is strictly sinusoidal, in our case at 2 kHz, while the intensity of the incident measurement laser is kept constant. Using the measurement technique "lock-in", we look for the Fourier amplitude corresponding to the 2 kHz modulation frequency at the reflected intensity of the measurement laser. The "raw" PMR signal RawPMR is defined as the quotient of the Fourier amplitude obtained from the reflected signal of the measurement laser - this is the alternating current, or AC component - and the direct current, or DC component of this reflected signal, which is in fact the relative reflectivity change: RawPMR = I refl AC / I refl DC =ΔR / R.

[0029] For semiconductor materials, the change in reflectivity is due to the generation of excess charge carriers (electrons and holes) during photoexcitation, which creates a temperature gradient.

[0030] When studying ion-implanted semiconductor samples, the PMR signal is also affected by the crystal lattice damage and the change in charge carrier concentration caused by the ion implantation. Therefore, the PMR technique is sensitive to all parameters of the implantation process, such as the ion mass, the ion dose, the ion energy, the direction of the ion beam and the tilt angle of one of the main crystal axes of the sample and the rotation angle of the crystal plane perpendicular to the crystal axes, as well as the magnitude of the implanted ion current density. Since the PMR signal usually shows a nonlinear dependence, the sensitivity is different for different parameters and for different ranges.

[0031] In the method according to the invention, the dose dependence of the PMR signal is followed for high energy hydrogen ion implantation of 1.5 MeV. Although not described in detail here, the state of the art required for the implementation of the method is known to those skilled in the art.

[0032] FIG. 1 shows a flow chart of a possible implementation of the proposed method for an ion-implanted sample M1.

[0033] Conditions, approximations and parameters required for carrying out the procedure For a semiconductor sample M1 that satisfies the following conditions, charge carrier lifetimes and concentrations, as well as contaminant atom concentrations, that can be assigned to defect locations are derived from the PMR signal measured in step S1: (i) Sample M1 is considered to have an essentially single crystal structure, which contains electrically active defect sites at low ppm-ppb concentrations. The defect sites can be defect centers created during implantation of ions with energies of about 1-10 MeV, e.g. in the case of Si these are typically defect centers created by vacancies, divacancies, dangling bonds, or impurity atoms, e.g. metal impurities, atoms such as Fe, Cr, Ni, etc., located at substitutional or interstitial lattice sites. The defect concentration N def is the maximum penetration depth R of the implanted ions from the sample surface p The capture (recombination) cross section of a defect site for free charge carriers is S def It is. (ii) Defect concentrations are typically 1013 ~10 16 cm -3 It is assumed that, since the PMR effect is so low that the crystal lattice essentially retains the physical properties characteristic of an undamaged single crystal, the excess of defect sites only causes local disturbances, essentially affecting the lifetime of the charge carriers. For this reason, in the following, for the material parameters influencing the PMR effect, we shall use values ​​valid for single crystal materials and assume that they are known with sufficient accuracy. (iii) The transverse ambipolar and thermal diffusion models defined in the described procedure, i.e., the characteristic diffusion times are las is the thickness of the area containing the defect, and in the case of ion implantation, the maximum ion penetration depth R p is significantly smaller than R las ≪R p It can be used for the geometry where (iv) Modulation frequency of the pump laser, f mod Since f is low in the presented case mod = 2 kHz, and it is assumed that the changes induced by successive modulation periods in the sample M1 do not overlap in time between adjacent modulation periods. The effect of the modulation is quasi-static, and the time constant of the processes occurring in the sample is 1 / f mod It is shorter, and thus the sample M1 has time to follow the effects of the periodically varying pump laser power. It should be noted that this condition is met in the kHz modulation range used, but may be considered less applicable, for example, in the MHz range.

[0034] The material parameters of the sample M1 used in the process, together with their names, are given in the following list. Since the procedure is presented hereafter with silicon, the corresponding material parameters of Si are also listed here: R0 = 0.317 is the reflectivity of the sample M1 at the wavelength of the sampling laser, n0 = 3.58 is the refractive index of the sample M1 at the wavelength of the sampling laser, α bba=945cm -1 is the optical absorption coefficient of the sample M1 at the wavelength of the excitation laser, β=-1.2×10 -22 cm -3 is the electro-optic coefficient at the wavelength of the sampling laser, δ T =2.9×10 -4 K -1 is the thermo-optic coefficient at the wavelength of the sampling laser, m e * =0.286m e is the effective mass of the electron, m h * =0.36m e is the effective mass of the hole, m e =9.1×10 -31 kg is the mass of an electron, Da=10cm 2 s -1 is the ambipolar diffusion coefficient of the excess charge carriers, D t =κ / ρC=0.91cm 2 s -1 is the thermal diffusion coefficient of sample M1, κ=1.5Wcm -1 K -1 is the thermal conductivity of sample M1 (at 300 K), ρ=2.32gcm -3 is the material density of sample M1, C=0.71Jg -1 K -1 is the specific heat of sample M1 (at 300 K), A n =2.8×10 -31 cm 6 s -1 is the Auger recombination coefficient of electrons, A p =9.9×10 -32 cm 6 s -1 is the Auger recombination coefficient of holes, U Aug (cm -3 s-1 )=A n (PN 2 -NN ie 2 )+A p (NP 2 -PN ie 2 ) is the Auger recombination value, U SRH (cm -3 s -1 )=(PN-N ie 2 ) / (τ P (N+N ie )+τ N (P+N ie ) is the value of Shockley-Read-Hall (SRH) recombination, τ N = τ 0 N / (1+(N a +N d ) / P SRH ), τ P = τ 0 P / (1+(N a +N d ) / N SRH ), τ 0 N =2×10 -3 s is the SRH material parameter; τ 0 P =2×10 -4 s is the SRH material parameter; N SRH =P SRH =5×10 16 cm -3 is the SRH material parameter, N ie =10 10 cm -3 is the intrinsic charge carrier concentration of sample M1; P0(cm -3 )=[(N a -N d )+((N a -N d ) 2 +4N ie2 ) 1 / 2 ] / 2 is the equilibrium hole concentration of sample M1; N a (cm -3 ) is the acceptor doping element concentration of sample M1; N d (cm -3 ) is the donor-dopant concentration of sample M1, N0(cm -3 )=N ie 2 / P0 is the equilibrium electron concentration of sample M1; ΔN(cm -3 ) is the excess electron concentration, ΔP(cm -3 ) is the excess hole concentration, N=N0+ΔN is the total electron concentration, P=P0+ΔP is the total hole concentration, σ def (cm 2 ) is the electron capture cross section of the dominant defect type in sample M1, N def (cm -3 ) is the density of the dominant defect type in sample M1, v th =(3k B T / m e * ) 1 / 2 =2.09×10 7 cm s -1 is the thermoelectron velocity in sample M1 (at a temperature of 300 K), The plane xy is the plane of the sample surface. The z direction is the normal to the surface of sample M1 (depth within sample M1), i.e., the direction of the laser beam.

[0035] The technical parameters of the PMR required to apply this procedure are as follows, with example current values ​​given below: I pump (Wcm -2 ) is the power density of the pump laser, R las= 1.5 µm is the radius of the excitation and sampling laser spots, f mod = 2kHz is the excitation laser modulation frequency, λ pump = 808 nm is the excitation laser wavelength, λ probe = 980 nm is the sampling laser wavelength.

[0036] Analysis of PMR signals The periodically varying pump laser power (AC excitation component) periodically creates excess charge carriers, electrons and holes, in the sample M1 with maximum concentrations ΔN and ΔP. This causes a periodic change in the refractive index and reflectance of the sample M1 (its decrease to ΔN) with maxima |Δn| and |ΔR|. Furthermore, the sample temperature also periodically changes (its increase to ΔN) with a maximum value ΔT. The PMR signal, i.e. the relative change in reflectance of the sample M1, ΔR / R0, can be calculated as follows (see the already mentioned work "Progress in the physical modeling of carrier illumination" by F. Dortu, T. Clarysse, R. Loo, B. Pawlak, R. Delhougne, and W. Vandervorst): ΔR / R0=[4 / (1-n0 2 )]{β(ΔN / m e * +ΔP / m h * )+δ T ΔT} +[4 / (1-n0 2 )]{β∫0 ∞ cos(4πn0z / λ probe )[(dΔN / dz) / m e * +(dΔP / dz) / m h * ]dz +δ T ∫0 ∞ cos(4πn0z / λ probe )(dΔT / dz)dz} (1) n0, R0, β, and δ Tis the wavelength of the sampling laser, λ probe are the refractive index, reflection coefficient, electro-optic coefficient, and thermo-optic coefficient of the sample M1 at m e * and m h * are the effective masses of the electron and hole. These material parameters are known with high accuracy for commonly used laser wavelengths for single crystal Si, e.g., λ probe For 980 nm, the above parameters are: n = 3.58, R0 = 0.317, β = -1.2 × 10 -22 , and β T =2.9×10 -4 K -1 (See F. Dortu, T. Clarysse, R. Loo, B. Pawlak, R. Delhougne, and W. Vandervorst: “Progress in the physical modeling of carrier illumination”, J. Vac. Sci. Technol., B 24, 1131 (2006)), and e * = 0.286, and m h * =0.36.

[0037] The second and third lines of equation (1) contain the gradients of quantities ΔN, ΔP, and ΔT in the z direction perpendicular to the plane of the sample M1, and the intensities of the sampling laser beam components reflected from the z depth due to the refractive index gradient are summed up taking into account their phase. In what follows, we will show that in this case the values ​​of the terms containing the two integrals are negligible compared to the first term.

[0038] Knowing ΔN, ΔP and ΔT, the value of the measured PMR signal, i.e. ΔR / R0, can be calculated based on the first term of equation (1). Due to the high power density of the excitation laser, ΔN=ΔP, and in this case it is assumed that the generated excess charge carrier concentration is much higher than the basic doping of the semiconductor sample. In the examples presented later, this condition is fulfilled. (i) The defect concentration is assumed to be constant with depth on the wavelength scale of the sampling laser. (ii) For initially depth-dependent profiles ΔN(z) and ΔP(z), the intensity I of the excitation laser increases with depth. pump (z)=I pump (0)exp(-α bba z) decreases, resulting in a decrease in the total effective charge carrier lifetime τ tot But (D a τ tot ) 1 / 2 ≪R p Since the distance is relatively short, the charge diffusion in the vertical direction (z direction) can be neglected. Here, D a is the ambipolar diffusion coefficient of charge carriers, whose value is D a Approximately 10cm 2 s -1 In the above formula, R p is the maximum penetration depth of the ion. (iii) Similarly, for an initially depth-dependent temperature profile T(z), the effective lateral thermal diffusion time constant τ tot But (D t τ t ) 1 / 2 ≪R p Since the distance is relatively short, the thermal diffusion in the vertical direction (z direction) can be neglected. Here, D t Approximately 1cm 2 s -1 is the lateral thermal diffusivity, where D t = κ / ρC, where κ = 1.5Wcm -1 K -1 , ρ=2.32gcm -3 , and C = 0.71 Jg -1 K -1 are the thermal conductivity, density, and specific heat of the silicon single crystal.

[0039] Figure 2 shows the results of a low-doping (approximately 10 -15 cm -3)Si sample. Also shown is the ΔR / R value for a defect-free reference Si sample M2. The ΔR / R value for the defect-free reference Si sample M2 is shown by the thick horizontal line V1. The zero value reflectance change is shown by the dashed line V2. The calculations are performed with an excitation laser wavelength λ pump = 808 nm, excitation laser power P las = 40 mW, and a circular laser spot of 3 μm diameter is referenced. The electron capture cross section of the defect site is σ def =3×10 -15 cm 2 The calculations were carried out based on equations (14) and (15) with the material parameters given in the conditions necessary for carrying out the procedure. Since even at a defect concentration of 1 ppb there is a visible difference compared to the reference sample M2, where the reflectance change is significant in the ppb-ppm range, the PMR method can be successfully used to determine the defect concentration and its assigned lifetime via measurements on a suitable reference sample M2. It should be noted that at defect concentrations below about 0.1 ppm, electro-optical effects dominate over thermo-optical effects, in which case it is possible to maintain a significant excess charge carrier concentration in the sample M1, and the PMR signal shows negative values.

[0040] Figure 3a shows the results of the various doses (10 11 ~10 15 cm -2 ) at 1.5 MeV H + Simulations of the vacancy concentration as a function of depth for ion-implanted Si sample M1 are shown. The simulations were performed using the popular computer program SRIM (Stopping and Range of Ions in Matter, see www.srim.org) with conventionally fixed material parameters for Si: atomic displacement threshold energy 15 eV, density 2.32 g cm -3 The vacancy profile was determined by the implantation of light H +To take into account the intensive vacancy recombination processes occurring in rare collision cascades induced by ions, a correction with a survival probability of Cacc = 0.1 was made. It can be seen that the defect concentration varies very little as a function of depth and can therefore be considered as uniform in the evaluation procedure applied in the PMR analysis. The vacancy concentration increases linearly with the implant dose and varies approximately in the range of 1 ppb to 10 ppm. 10 14 cm -2 The implanted hydrogen concentration profile for the dose is shown by line V3. The ion penetration depth is Rp ≫ 30 mm, and hydrogen is R p are concentrated in the vicinity of

[0041] Figure 3b shows the results of the various doses (10 11 ~10 15 cm -2 ) at 1.5 MeV B + ions and As + SRIM simulations of vacancy concentration as a function of depth for ion-implanted Si sample M1. The ion penetration depth is much smaller than for hydrogen irradiation, and the vacancy concentration is two and five orders of magnitude higher for boron and arsenic irradiation, respectively, than for hydrogen implantation at comparable doses, as shown by line V4.

[0042] Figure 4 shows the 1.5 MeV H + Ions were administered at five different doses (10 11 ~10 15 cm -2 ) implanted at low B doping (approximately 10 15 cm -3 3 shows the measured PMR signal of the p-type Si sample M1 that was subjected to the annealing treatment. The signal magnitude is: PMR signal=10 6 ×ΔR / R0. The measurement parameters are: excitation red laser wavelength λ pump = 808 nm, excitation red laser output P pump = 40mW, modulation frequency f mod = 2kHz, sampling infrared laser wavelength and output λ probe = 980 nm, P probe= 20 mW. The diameter of the laser spot is 3 μm. Zero reflectance change is indicated by dashed line V5. The PMR signal is very sensitive within the defect concentration range of ppb to ppm estimated from the SRIM simulation, and varies almost linearly on the log dose scale, with a range of 10 14 cm -2 The experimental values ​​of ΔR / R0 show good agreement with the values ​​calculated according to the procedure presented in Fig. 1, but the slope of the measured curve is almost constant and smaller than the calculated slope. Possible reasons for this will be discussed in connection with Fig. 5.

[0043] Figure 5 shows the 1.5 MeV H + Ions were administered at five different doses (10 11 ~10 15 cm -2 ) for the Si sample M1 implanted with 1000 .mu.m, which was evaluated using the method described from the PMR measurements shown in FIG. 4. Triangles 10 show the values ​​for the reference unimplanted Si sample M2. The figure shows the charge carrier lifetime τ tot , Auger recombination lifetime τ Aug , and the recombination lifetime τ at the defect site caused by the implantation determined in step S4. def as a function of dose. a and τ t denotes the characteristic time constant of ambipolar charge carrier diffusion and thermal diffusion. It can be seen that at lower doses the entire useful lifetime is dominated by ambipolar diffusion, while the role of Auger recombination is relatively small over the dose scale. As dose and defect concentration increase, the recombination lifetime τ def gradually plays a decisive role because at the lowest doses, the lifetime τ def is roughly on the scale of μs, but at intermediate doses the line τ a , and is almost an order of magnitude smaller at the maximum dose. Here, the total useful lifetime is essentially the lifetime value τ def The slope of dashed line V6 is -1 / 2, so τ def shows a semi-proportional square-root dependence on dose, i.e., the effective defect concentration (N def) depends on the square root of the dose. This means that N def The results suggest a quasi-linear dose dependence of τ. One of the reasons may be the dynamic heat treatment and the recombination of Si vacancies and interstitials generated during implantation, which becomes more significant with increasing defect concentration. Meanwhile, the diffusion of implanted hydrogen atoms promoted by implantation also leads to the generation of hydrogen-defect site complexes and the passivation effect of hydrogen atoms bound to defect sites, resulting in a large τ def In some cases the dose dependence of τ can be quasi-linear. Therefore, PMR measurements can also provide information about in situ defect recombination processes occurring during dynamic heat treatment and implantation. In the defect concentration range of ppb-ppm, there are few available measurement methods that provide similar quantitative information. Moreover, the advantage of PMR is that it is a non-destructive and non-contact method. The τ by the described method can be calculated by the following method: def and N def The reliability of the evaluation is based on the 1.5 MeV H + This is supported by other researchers finding a similar square-root relationship between dose and effective defect concentration based on microwave photoconductivity transient (MW-PCD) measurements, see for example E. Gaubas et al., "In situ analysis of the carrier lifetime in silicon during implantation of 1.5 MeV protons," Lithuanian Journal of Physics, 50(4):427-433, 2010.

[0044] Electro-optic effect, generation of additional charge carriers Light frequency ν pump and has a Gaussian intensity distribution profile in the transverse direction (r) at a power density I pump The excess charge generation rate of a pumping laser irradiating a sample M1 with can be determined as a function of the z-depth of the sample M1 according to the following equation: G pump (z)=(I pump / hν pump )exp(-r 2 / Rlas 2 )(1-R0)α bba exp(-α bba z) (2) In the above formula, R las is the characteristic radius of the laser spot, α bba is the absorption coefficient belonging to the interband electronic transition of sample M1, and its value is α bba = α for 808 nm bba =945cm -1 R las and α bba If we know G pump can be calculated, and examples can be found in the work of DE Aspnes and AA Studna (Phys. Rev. B 27:985-1009 (1983)).

[0045] The time derivative of the excess charge carrier concentration, ΔN, is: dΔN / dt=G pump -ΔN(t) / τ tot (3) The solution of equation (3) is: ΔN(t)=G pump τ tot (1-exp(-t / τ tot )) (4) Here, τ tot is the total effective characteristic lifetime of the excess charge carriers, including the effects of recombination and charge carrier diffusion, and refers to the characteristic time until they disappear due to recombination processes or diffusion laterally, i.e. in the xy plane in the area below the monitoring laser spot. As is evident, in the investigated case, τ tot is usually about 10 -8 ~10 -9 Within the range of τ tot ≪1 / f mod Therefore, equation (4) can be further simplified: ΔN(τ tot )=G pump τ tot (5) According to this, ΔN is G pumpIn other words, it can satisfy the condition of being quasi-static. tot can be calculated using the following formula: τ tot =(τ SRH -1 +τ Aug -1 +τ def -1 +τ a -1 ) -1 (6) In the above equation, τ SRH , τ Aug , and τ def are the lifetimes of Shockley-Read-Hall (SRH) recombination, Auger recombination, and charge carrier recombination at the defect site, and τ a is the characteristic time constant of lateral ambipolar charge carrier diffusion, which is the generation rate ΔG(x,y)~exp(-(x 2 +y 2 ) / R las 2 )=exp(-(r 2 ) / R las 2 ) induced by the charge package, characterizes the lateral spread in time ΔN(x,y) with a two-dimensional Gaussian characteristic. Its value is τ a =(eR las ) 2 / D a and can be designated by evaluating the measured value against a reference sample, i.e., an uninjected or impurity-free sample M2 that does not contain the substitutionally added element being tested as a recombination center.

[0046] One of the key points of the method according to the present invention is the expression of equation (6), τ tot τ introduced in the calculation of def and τ a This term has not, to the inventors' knowledge, been included in this form in previous studies of PMR signal interpretation.

[0047] Returning to the integration of equation (1) with the gradient dΔN / dz, based on equation (5), we find that: dΔN / dz=τ tot (dG pump / dz)=-τ tot α bba G0exp(-α bba z) (7) Here, τ tot is usually about 10 -8 seconds (see FIG. 4), and G0 is the maximum value of the charge carrier generation rate at the surface of the sample M1. By substituting equation (7) into the corresponding integral term in equation (1), the integrated value ΔN is about 10 15 cm -3 This is the first term of equation (1) (usually ΔN about 10 18 cm -3 ), and therefore for PMR signals the gradient term can be omitted in the estimation.

[0048] The charge carrier lifetime τ belonging to a given recombination channel j and the recombination coefficient U assigned to the same channel j Relationship between: ΔN / U j = τ j (8) U j The values ​​of can be calculated by well-known methods for the Auger and SRH processes and can be found in several places in the referenced literature, and these components have already been detailed in the description of the conditions necessary for the operation of the procedure. Aug and U SRH It is important to note that both depend on ΔN and ΔP. It is emphasized that under the conditions during the PMR measurements (relatively high ΔN, ΔP values), SRH recombination is negligible compared to Auger recombination.

[0049] For the defect center to be examined, ΔN / U def = τ def In the above equation, U def = σ def N def ΔNv thwhere σ calculated in steps S5 and S6 def and N def are the recombination cross section and the density of defect centers, and v th is the thermal velocity of the charge carriers at room temperature. Therefore, τ def Once known, the characteristic path length L that can be assigned to defect recombination is def =(σ def N def ) -1 We can obtain σ def If is known, in step S7, N def The value of σ can also be obtained. def Data on the values ​​of can be found in the literature, for example in the work of M.-L. David, E. Oliviero, C. Blanchard and J.F. Barbot (Nucl. Instr. Meth. Phys. Res. B 186:309-312, 2002), for Si and σ for divacancy. def =1-5×10 -15 cm 2 and for the center connected to the vacancy, σ def =1-11×10 -15 cm 2 For interstitial metal impurities in Si, the electron capture cross section is σ def =5×10 -14 cm 2 , σ in Cr def =2.3×10 -13 cm 2 , and σ in V def =5×10 -14 cm 2 This is known from the work of D. Macdonald and L. J. Geerligs (Appl. Phys. Lett. 85(18):4061, 2004). def A useful overview of values ​​can be found in the work of FE Rougieux, C. Sun, and D Macdonald (Solar Energy Materials and Solar Cells, 187:263-272 (2018)).

[0050] Thermo-optical effect, temperature rise of sample M1 The excess free electrons generated by the pump laser move from the valence band to the conduction band and then - pump =1.53 eV) is the forbidden band of Si (E gap = 1.12 eV) - the extra differential energy is supplied to the lattice via phonons, which reduce their energy from the excited state to the level corresponding to the conduction band minimum. This relaxation takes place over a period of 10 -12 This occurs on a very fast time scale of seconds, resulting in rapid heat release (H hc , a heat source term of "hot electrons" or "hot holes") and a rise in temperature. -Due to the indirect band gap of Si-The relaxation of excess charge carriers from the conduction band minimum via the recombination of electron-hole pairs releases almost all of the energy corresponding to the band gap in the form of heat (H rec , recombination heat source term). Recombination can occur via the SRH and Auger processes or via defects. This further increases the temperature of the Si crystal. The higher the temperature, the higher the refractive index due to the thermo-optic effect, which results in an effect opposite to the electro-optic effect, which decreases the refractive index. Heat source member H hc and H rec , and the temperature rise ΔT is calculated as follows: H hc =G pump (hν pump -E gap ) (9) H rec =(U Aug +U SRH +U def )E gap (10) ΔT = (H hc +H rec ) τ t / ρC (11) where τ t is the characteristic time constant of lateral thermal diffusion, which is the temperature profile ΔT(x,y)~exp(-(x 2 +y 2 ) / R las 2) characterizes the lateral spread over time of the sigma-based ... t =(eR las ) 2 / D t can be estimated based on and specified by evaluating the measured value against a reference sample, i.e., an uninjected or uncontaminated sample M2 that does not contain the substitutionally added element to be tested as a recombination center. def The values ​​of all parameters other than can be assumed to be known, and the value of ΔT can be calculated as U def For the reference (undamaged or uncontaminated) sample M2, U def =0.

[0051] Returning to the integration of equation (1) involving the dΔT / dz gradient, we obtain: dU Aug / dz=(dU Aug / dΔN)(dΔN / dz) ≒ 3(A n +A p )ΔN 2 (dΔN / dz) (12) dU def / dz=(dU def / dΔN)(dΔN / dz)=(σ def N def v th )(dΔN / dz) (13) Taking into account the already described forms dΔN / dz and dG pump Using / dz, this integral can be calculated. Its value is about 0.003 to 0.2 °C in the range of defect concentrations from ppb to ppm. This is the same as for similar N def This is negligible compared to the value of the main term ΔT, which determines the thermo-optic effect and is usually within a range of about 1 to 10°C.

[0052] Procedure for assessing PMR signals Using the results of the above analysis, the PMR signal of the reference sample M2 without defect centers can be calculated using the following equation: ΔR / R0| ref=|4 / (1-n0 2 )|{βΔN ref (1 / m e * +1 / m h * )+δ T (G pump (hν pump -E gap )+(U SRH,ref +U Aug,ref )E gap ) τ t / ρC} (14) Here, U SRH,ref and U Aug,ref depends on the first and third powers of ΔN, and ΔR / R0 can be calculated for all values ​​of ΔN. The experimentally determined value ΔR / R0| ref Then, in step S2, ΔN ref The value of U can then be determined from this result. SRH,ref and U Aug,ref The value of can be determined.

[0053] The PMR signal in the implanted sample M1, which in this example contains a defect center, can be calculated using the following equation: ΔR / R0| imp = |4 / (1-n0 2 )|{βΔN imp (1 / m e * +1 / m h * )+δ T (G pump (hν pump -E gap )+(U SRH,imp +U Aug,imp +U def )E gap ) τ t / ρC} (15) ΔR / R0|, experimentally determined from equation (15) in step S3 for the damaged (implanted) sample M1 imp From the value of ΔN imp Additional consideration is required to obtain the value of ΔN ref =G pump τref In the above equation, τ ref is the total effective lifetime of the charge carriers. At the same time, in the damaged (injected) specimen M1, ΔN imp =G pump τ imp In the above equation, τ imp is the total useful life measured on the implanted sample M1. G pump Since the value of is the same for the undamaged sample M2 and the damaged sample M1 based on the conditions described in the description of the conditions necessary for the operation of the procedure, ΔN ref / τ ref = ΔN imp / τ imp and the recombination coefficient can be assigned to the defects present in the implanted sample M1 and is found to be: U def =(U Aug,ref -U Aug,imp )+(U SRH,ref -U SRH,imp )+(ΔN ref -ΔN imp ) / τ a (16) Here, U of the reference sample M2 Aug,ref , U SRH,ref , ΔN ref The value of is already known from equation (14). ΔR / R0| imp The measured value of is known, and U from equation (16) def Substituting this into equation (15), the ΔN of test sample M1 is imp The value of σ can then be obtained. def N def and σ def If we know, N def It is noted that under the measurement conditions used, SRH recombination can generally be neglected, which leads to simplified forms of equations (14), (15) and (16).

[0054] The method according to the invention uses H of MeV energy. + , He +It can be advantageously used in the case of implantation. In semiconductor technology, high energy hydrogen ion implantation steps, roughly MeV, are often used. Due to their small mass, hydrogen ions penetrate much deeper into the sample (e.g. silicon) than the larger donor ions (e.g. phosphorus, arsenic) or acceptor ions (e.g. boron) that have been used traditionally. Furthermore, hydrogen ion implantation results in orders of magnitude smaller defect concentrations than implantation of heavier ions of comparable dose and energy. High energy hydrogen implantation makes it possible to control the conduction properties in deep zones of the Si substrate, even tens of micrometers below the surface of the sample. High energy, low dose hydrogen implantation allows tuning the charge carrier lifetime and improving the switching properties of various power electronic devices, examples of which can be found in the work of P. Hazdra, K. Brand, J. Rubes, and J. Vobecky, "Local lifetime control by light ion irradiation: impact on blocking capability of power PiN diodes," Microelectron. J. 32(5):449-456, 2001, or A. Hallen, M. Bakowski, and M. Lundqvist, "Multiple proton energy irradiation for improved GTO thyristors," Solid-State Electronics, 36 / 2:133-141, 1993. Hydrogen implantation in the moderate dose range allows the formation of donor centers and, as a result, buried n-type regions in complex semiconductor structures. See, for example, the work of Y. Zohta, Y. Ohmura, and M. Kanazawa, "Shallow donor state produced by proton bombardment of silicon," JJ Appl. Phys. 10(4):532, 1971. High-energy hydrogen implantation is a step frequently used in the design of electronic imaging devices such as C-MOS cameras, which allows 11 ~10 16cm -2 Within the applied dose range, small concentrations of defects in the ppb to ppm range are formed, typically in the upper 10-100 mm of the sample thickness range.

[0055] The method according to the invention can also be advantageously used for other high energy low dose implants and for channel oriented low dose deep implants, where the method can also be used to check the correctness of the sample orientation and to precisely determine the cut surface of the sample, since channel oriented implants can be used to significantly increase the penetration depth of the implanted ions and significantly reduce the defect concentration caused by the implanted ions, see for example the work of M. Posselt, B. Schmidt, C.S. Murthy, T. Feudel and K. Suzuki, "Modeling of damage accumulation during ion implantation into single-crystalline silicon", J. Electrochem. Soc. 144:1495, 1997. The direction of the well-collimated ion beam with low divergence is parallel to one of the crystallographic axes of the semiconductor crystal, for example parallel to the crystallographic directions of Si

[0100] or Si

[0110] . The implanted ions then undergo a transverse oscillatory motion perpendicular to their direction of travel between the parallel atomic rows and planes of the crystal, which reduces the probability of direct ion-atom collisions and also the nuclear and electronic damping forces acting on the ions. The channel effect plays an important role below a low defect concentration range, typically 0.1-1%, at which point it is inhibited by the emergent defect centers. On the other hand, the measurement of the channel effect is also very sensitive to the precise orientation of the sample, where a typical tilt of the ion beam of about 0.1-1° with respect to the crystallographic direction inhibits the effect. The resulting defect concentration is therefore strongly dose- and implantation-direction-dependent. The method is suitable for monitoring defect concentrations and charge carrier lifetimes at a fixed dose with varying tilt angles, or at a fixed tilt angle with variable dose, typically in the defect concentration range of ppb-ppm. The described procedure is also suitable for precisely determining the cutting plane of the base slice, i.e., for monitoring with high precision the inclination angle of the sample surface and a given crystallographic direction that differs from 90° by about 0.1-1°.

[0056] Treatment within the range of small defect concentrations is achieved by high-energy, low-concentration implants (H + , He + ) and for higher concentration injections (B + , P + , As + ), it can be considered an advantage that it may be useful to monitor the dynamic thermal process during implantation as a function of dose, which allows more precise planning of implantation techniques used in the semiconductor industry.

[0057] The proposed method can be advantageously used when measuring the concentrations of uniform O, C contamination, oxygen-crystal defect complexes, or uniform metallic contamination and when estimating the associated lifetimes.

[0058] Another advantage is that the method can be applied to other semiconductor materials (e.g., silicon carbide (SiC), germanium (Ge), etc.) if the physical material parameters discussed above are known and appropriate laser wavelength, laser power, and modulation frequency are used for the PMR method.

Claims

1. 1. A method for determining a crystal defect concentration of less than 10 ppm in a semiconductor material based on photomodulation reflectance measurements, comprising: Injecting (S1) excess charge carriers into a sample (M1) of semiconductor material using irradiation that is periodically modulated in time, characterizing the optical reflection modulation (ΔR) caused by the change in excess charge carriers over time by the amount of modulation caused in the reflection (R) of a test beam having a constant power over time; forming a ratio (ΔR / R) of the optical reflection modulation (ΔR) to the measured reflection (R); deriving from the obtained ratio the concentration of the excess charge carriers formed during irradiation; Total charge carrier lifetime (τ ｔｏｔ ) based on the concentration of excess charge carriers; The total charge carrier lifetime (τ ｔｏｔ ) that can be assigned to the crystal defect sites. ｄｅｆ ) and Based on this, the crystal defect concentration is judged (S7). To characterize the A method comprising:

2. 2. The method according to claim 1, characterized in that the semiconductor sample (M1) implanted with low-mass ions is measured by optical modulation reflectometry.

3. 2. The method according to claim 1, characterized in that a semiconductor sample (M1) implanted with hydrogen or helium ions is measured by light modulation reflectometry.

4. 2. A method according to claim 1, characterized in that it comprises measuring a semiconductor sample (M1) implanted with low-mass ions by optical modulation reflectometry, the implantation energy being chosen to be greater than 300 keV.

5. Measuring a semiconductor sample (M1) implanted with low-mass ions by optical modulation reflectometry, the implant dose being between 1e10 and 1e17 1 / cm ２ 2. The method of claim 1, further comprising: determining whether the measured value is greater than or equal to the measured value.

6. 6. The method according to claim 1, wherein the portion of the formed crystal defect concentration that is greater is located at a depth of 100 micrometers from the surface of the sample (M1).

7. 7. The method according to claim 1, characterized in that a semiconductor sample (M1) containing a concentration of crystal defects caused by metallic impurities in the semiconductor crystal is measured by light modulation reflectometry.

8. 7. The method according to claim 1, characterized in that a semiconductor sample (M1) containing a concentration of crystal defects caused by oxygen impurity complexes in the semiconductor crystal is measured by photomodulation reflectometry.

9. Measuring a semiconductor sample (M1) implanted with non-low mass ions by optical modulation reflectometry, the following conditions being met: R ｌａｓ ２ <<R ｐ ２ and Here, R ｌａｓ is the laser spot radius of the pumping and sampling PMR, R ｐ 9. The method according to claim 1, wherein the condition is satisfied: ##EQU1## where .lambda..times ...

10. 9. The method according to claim 1 , characterized in that a semiconductor sample (M1) implanted with non-low mass ions is measured by optical modulation reflectometry, the semiconductor sample having a low defect concentration formed as a result of channel effects due to the implantation conditions used.

11. 9. The method according to claim 1, further comprising measuring by optical modulation reflectometry a semiconductor sample (M1) implanted with non-low mass ions, the semiconductor sample (M1) having a low defect concentration formed as a result of channel effects due to the implantation conditions used, wherein a ratio ΔR / R for said measurement shows a detectable dependence on the tilt angle between the direction of the ion beam and one of the main crystal axes of the sample (M1).

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