Designation: F 95 89 (Reapproved 2000) Stard Test Method for Thickness of Lightly Doped Silicon Epitaxial Layers on Heavily Doped Silicon Substrates Using an Infrared Dispersive Spectrophotometer 1 This stard is issued under the fixed designation F 95; the number immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript epsilon (e) indicates an editorial change since the last revision or reapproval. INTRODUCTION In editions of this test method published through 1987, the title scope of the method required that the epitaxial layer substrate be of the same conductivity type. This requirement was dropped, allowing the epitaxial layer substrate to be of opposite conductivity type in the revision first published in 1988, subject to the continuing requirements of minimum allowed resistivity of the epitaxial layer maximum allowed resistivity of the substrate. This same revision changed specifications on dispersive instruments from wavelength values to wave number values, where appropriate. A brief description of the theory of this test method is given in Appendix X1. Automated test systems, utilizing Fourier-Transform Infrared Spectrophotometry (FT-IR) are widely used for epitaxial layer thickness measurements. Because such instruments are normally supplied with proprietary software for measurement analysis, detailed procedures for the use of such instruments are not included in this test method. However, for information purposes, estimates of single instrument repeatability multiinstrument reproducibility, based on a 1986/1987 multilaboratory comparison of FT-IR instrument measurements are given in Note 6 Appendix X2. Automated test systems, utilizing Fourier-Transform Infrared Spectrophotometry (FT-IR) are widely used for epitaxial layer thickness. Because such instruments are normally supplied with proprietary software, detailed procedures for the use of such instruments are not included in this test method. 1. Scope 1.1 This test method 2 provides a technique for the measurement of the thickness of epitaxial layers of silicon deposited on silicon substrates. A dispersive infrared spectrophotometer is used. For this measurement, the resistivity of the substrate must be less than 0.02 V cm at 23 C the resistivity of the layer must be greater than 0.1 V cm at 23 C. 1.2 This technique is capable of measuring the thickness of both n- p-type layers greater than 2 µm thick. With reduced precision, the technique may also be applied to both n- p-type layers from 0.5 to 2 µm thick. 1.3 This test method is suitable for referee measurements. 1.4 This stard does not purport to address all of the 1 This test method is under the jurisdiction of ASTM Committee F01 on Electronics is the direct responsibility of Subcommittee F01.06 on Silicon Materials Process Control. Current edition approved Aug. 25, 1989. Published October 1989. Originally published as F 95 68 T. Last previous edition F 95 88a. 2 DIN 50437 is an equivalent method. It is the responsibility of DIN Committee NMP 221, with which Committee F-1 maintains close technical liaison. DIN 50437. Testing of Inorganic Semiconductor Materials: Measurement of the Thickness of Silicon Epitaxial Layers by the Infrared Interference Method, is available from Beuth Verlag GmbH Burggrafenstrasse 4-10, D-1000 Berlin 30, Federal Republic of Germany Vol 10.05. safety concerns, if any, associated with its use. It is the responsibility of the user of this stard to establish appropriate safety health practices determine the applicability of regulatory limitations prior to use. 2. Referenced Documents 2.1 ASTM Stards: E 177 Practice for Use of the Terms Precision Bias in ASTM Test Methods 3 E 932 Practice for Describing Measuring Performance of Dispersive Infrared Spectrophotometers 4 F 84 Test Method for Measuring Resistivity of Silicon Slices with an In-Line Four-Point Probe 5 3. Terminology 3.1 Definitions: 3.1.1 epitaxial layer in semiconductor technology, a layer of semiconductor material having the same crystalline spacing as the host substrate on which it is grown. 3 Annual Book of ASTM Stards, Vol 14.02. 4 Annual Book of ASTM Stards, Vol 03.06. 5 Annual Book of ASTM Stards, Vol 10.05. Copyright ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States. 1
3.1.2 index of refraction the relative index of refraction is defined by Snell s law as the ratio of the sine of the angle of incidence to the sine of the angle of refraction. The angles are measured between the surface normal the infrared beam. The value of this index for the wavelength range from 6 to 40 µm is 3.42 relative to air for silicon having resistivity greater than 0.1 V cm. 3.1.3 interface the boundary between the substrate the epitaxial layer as determined by this technique. 3.1.4 substrate in semiconductor technology, a wafer that is the basis for subsequent processing operations in the fabrication of semiconductor devices or circuits. 3.1.4.1 Discussion The devices or circuits may be fabricated directly in the substrate or in a film of the same or another material grown or deposited on the substrate. 4. Summary of Test Method 4.1 The reflectance of the specimen is measured as a function of wave number using an infrared spectrophotometer. The reflectance spectrum of a suitable specimen exhibits successive maxima minima characteristic of optical interference phenomena. The thickness of the epitaxially deposited layer is calculated using the wave numbers of the extrema in the reflectance spectrum, the optical constants of the layer the substrate, the angle of incidence of the infrared beam upon the specimen. 5. Apparatus 5.1 Double-Beam Infrared Spectrophotometer This apparatus shall utilize monochromatic infrared light of known variable wave numbers. This light shall be reflected from the specimen the reflectivity shall be recorded as a function of wave number. It is essential that the wave numbers indicated by the apparatus be carefully calibrated. Calibration accuracy shall be determined in accordance with Practice E 932, using polystyrene lines at 1601.6 648.9 cm 1. The calibration accuracy shall be 0.05 µm. The useful range of wave number is 1670 to 250 cm 1. The precision thickness capabilities stated in Section 11 were established using data in the range 900 to 300 cm 1. In general, thinner specimens require a broader wavelength range than thicker ones. 5.2 Specimen Holder The specimen holder shall be so constructed that no damage can be inflicted by the holder on the epitaxial layer. 5.3 Masking Aperture The size of the masking aperture shall be such as to restrict the illuminated area on the specimen surface to a value sufficiently small to eliminate the effect of thickness fluctuations, without impairing detection of the reflected light. The masking aperture shall be constructed from a nonreflecting material such as matte-surface graphite. 6. Test Specimen 6.1 The specimen surface shall be highly reflective, free from large-area imperfections, free of passivating layers except native oxides. The specimen surface may be cleaned prior to measurement by any technique which does not affect the specimen polish or the layer thickness. 7. Preparation of Apparatus 7.1 Establish the maximum allowable scan speed as follows: 7.1.1 Choose a specimen with a substrate resistivity between 0.008 0.02 V cm, (see Scope) an epitaxial layer of such thickness that an observable minimum occurs at a wave number less than 400 cm 1. 7.1.2 Choose a suitable masking aperture. 7.1.3 Place the specimen on the instrument record the spectrum of a minimum wave number less than 400 cm 1 using the slowest scan speed available. 7.1.4 Record the position of the minimum. 7.1.5 Increase the scan speed in steps record the position of the minimum for each scan speed. 7.1.6 Allowable scan speeds are those which show a shift of the minimum of less than 61 cm 1 relative to the position of the minimum as determined at the slowest scan speed. 8. Procedure 8.1 Hle the specimen carefully to avoid surface damage to the thin epitaxial layer. 8.2 Place the specimen over the aperture mask to expose the desired location to the beam. 8.3 Obtain a reflection spectrum similar to that shown in Fig. 1. Do not attempt a calculation of layer thickness if the peak amplitude to noise amplitude ratio is less than five. NOTE 1 The interference pattern may be obscured or illegible if the thickness of the epitaxial layer varies by more than 4 % over the masking aperture, or if the interface impurity concentration profile does not approximate a step function. 8.4 Determine the wave number of each extremum in the reflection spectrum by averaging the intercepts of the reflection spectrum a horizontal line 3 % of full scale below a FIG. 1 Typical Reflection Spectrum for n-type Specimen 2
TABLE 1 Phase (Shifts (f/2p) for n -Type Silicon Wavelength, Resistivity, V cm µm 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.012 0.014 0.016 0.018 0.20 2 0.033 0.029 0.028 0.027 0.027 0.026 0.025 0.024 0.023 0.022 0.020 0.019 0.017 0.016 0.021 4 0.061 0.050 0.047 0.046 0.045 0.043 0.041 0.039 0.038 0.036 0.034 0.031 0.029 0.027 0.025 6 0.105 0.072 0.064 0.062 0.060 0.057 0.055 0.052 0.050 0.048 0.044 0.042 0.039 0.036 0.033 8 0.182 0.099 0.083 0.078 0.075 0.071 0.067 0.064 0.016 0.059 0.054 0.051 0.047 0.043 0.040 10 0.247 0.137 0.105 0.095 0.090 0.084 0.079 0.075 0.071 0.069 0.063 0.059 0.055 0.051 0.047 12 0.289 0.183 0.132 0.115 0.106 0.098 0.091 0.084 0.081 0.078 0.072 0.067 0.062 0.057 0.053 14 0.318 0.225 0.164 0.137 0.124 0.113 0.104 0.097 0.092 0.087 0.080 0.074 0.069 0.064 0.059 16 0.339 0.258 0.197 0.163 0.144 0.129 0.117 0.109 0.102 0.097 0.088 0.082 0.075 0.070 0.065 18 0.355 0.283 0.226 0.189 0.166 0.146 0.131 0.121 0.113 0.107 0.096 0.089 0.082 0.076 0.070 20 0.368 0.303 0.251 0.214 0.188 0.165 0.147 0.134 0.124 0.117 0.105 0.096 0.088 0.081 0.075 22 0.378 0.319 0.272 0.236 0.209 0.183 0.163 0.148 0.136 0.127 0.113 0.104 0.095 0.087 0.081 24 0.387 0.333 0.289 0.255 0.229 0.202 0.179 0.162 0.148 0.138 0.122 0.111 0.101 0.093 0.086 26 0.394 0.344 0.303 0.272 0.246 0.219 0.196 0.177 0.161 0.150 0.131 0.119 0.108 0.099 0.091 28 0.401 0.353 0.316 0.286 0.261 0.235 0.211 0.191 0.175 0.161 0.141 0.127 0.115 0.104 0.096 30 0.406 0.362 0.326 0.298 0.275 0.250 0.226 0.206 0.188 0.173 0.150 0.135 0.121 0.110 0.101 32 0.411 0.369 0.336 0.309 0.287 0.263 0.240 0.219 0.210 0.185 0.160 0.143 0.128 0.116 0.106 34 0.415 0.375 0.344 0.319 0.297 0.274 0.252 0.232 0.213 0.197 0.170 0.151 0.135 0.122 0.112 36 0.419 0.381 0.351 0.327 0.307 0.285 0.263 0.243 0.225 0.209 0.180 0.160 0.143 0.129 0.117 38 0.422 0.386 0.357 0.335 0.315 0.294 0.273 0.254 0.236 0.220 0.191 0.167 0.150 0.135 0.123 40 0.425 0.391 0.363 0.341 0.323 0.302 0.283 0.264 0.246 0.230 0.200 0.178 0.158 0.141 0.128 maximum or above a minimum. This procedure reduces the ambiguity encountered when the extrema are broad. NOTE 2 A more correct procedure for locating the position of the extrema on layers less than 2 µm thick is to draw the tangent envelops to the spectrum determine the intersection of the envelopes with the interference spectrum. 6 However, this procedure is apparently more difficult to perform since its use in a round-robin test (see 11.3) resulted in reduced rather than improved precision. 8.5 Measure the resistivity of the substrate in the area of the thickness measurement on the side opposite the epitaxial layer using the four-probe method of Test Method F 84. 9. Calculation 9.1 Determine the orders for the maxima minima 6 Schumann, P. A., The Infrared Interference Method of Measuring Epitaxial Layer Thickness, Journal Electrochemical Society, Vol 116, 1969, p. 410. observed using the following equation: P 2 5 ml 1 /~l 1 2l 2! 1 1/2 2 ~f 2 l 1 2f 22 l 2!/2p~l 1 2l 2! (1) P 2 = order of the extremum associated with l 2, l 1 = 10 000/y 1, l 2 = 10 000/y 2, m = difference in the orders of the extrema considered, f 21 f 22 are the phase shifts suffered by the ray reflected at the interface for l 1 l 2 respectively. 9.1.1 Obtain the phase shifts f 21 f 22 from Table 1 or Table 2. Round off the calculated order, P 2, to an integer for a maximum a half integer for a minimum. After calculating one order, assign the orders to the remaining extrema in descending order with increasing wavelength as shown in Fig. 1. 9.2 Calculate the thickness using the following equation: TABLE 2 Phase Shifts (f/2p) for p -Type Silicon Wavelength, Resistivity, V cm µm 0.001 0.0015 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.012 0.014 0.016 0.018 0.020 2 0.036 0.034 0.033 0.033 0.033 0.034 0.034 0.033 0.032 0.031 0.030 0.028 0.027 0.025 0.024 0.024 4 0.067 0.060 0.057 0.055 0.055 0.055 0.055 0.054 0.052 0.050 0.049 0.045 0.043 0.040 0.038 0.037 6 0.119 0.091 0.082 0.076 0.074 0.073 0.072 0.071 0.068 0.066 0.064 0.059 0.056 0.053 0.050 0.049 8 0.200 0.140 0.114 0.099 0.094 0.091 0.089 0.086 0.083 0.080 0.077 0.072 0.067 0.064 0.060 0.059 10 0.261 0.199 0.158 0.127 0.115 0.110 0.105 0.102 0.097 0.093 0.089 0.083 0.078 0.073 0.070 0.068 12 0.300 0.247 0.205 0.160 0.140 0.130 0.123 0.117 0.111 0.106 0.101 0.094 0.088 0.083 0.078 0.076 14 0.327 0.282 0.244 0.194 0.167 0.152 0.141 0.133 0.126 0.119 0.113 0.104 0.097 0.091 0.087 0.084 16 0.346 0.307 0.274 0.226 0.195 0.175 0.161 0.151 0.141 0.132 0.126 0.115 0.106 0.100 0.094 0.091 18 0.361 0.327 0.297 0.253 0.221 0.198 0.182 0.168 0.157 0.146 0.138 0.125 0.116 0.108 0.102 0.099 20 0.373 0.342 0.315 0.274 0.243 0.220 0.202 0.186 0.173 0.160 0.151 0.136 0.125 0.117 0.100 0.106 22 0.383 0.354 0.330 0.292 0.263 0.240 0.220 0.204 0.188 0.175 0.164 0.147 0.134 0.125 0.117 0.113 24 0.391 0.365 0.342 0.307 0.279 0.257 0.238 0.220 0.204 0.189 0.177 0.158 0.144 0.133 0.125 0.120 26 0.398 0.374 0.352 0.320 0.294 0.272 0.253 0.236 0.219 0.203 0.190 0.169 0.153 0.142 0.132 0.127 28 0.404 0.381 0.361 0.331 0.306 0.285 0.267 0.250 0.233 0.217 0.203 0.180 0.163 0.150 0.140 0.134 30 0.409 0.387 0.369 0.340 0.316 0.297 0.279 0.262 0.245 0.229 0.215 0.191 0.173 0.159 0.148 0.141 32 0.414 0.393 0.376 0.348 0.326 0.307 0.290 0.273 0.257 0.241 0.227 0.202 0.182 0.167 0.155 0.148 34 0.418 0.398 0.381 0.355 0.334 0.316 0.299 0.284 0.268 0.252 0.238 0.213 0.192 0.176 0.163 0.155 36 0.421 0.403 0.387 0.362 0.341 0.324 0.308 0.293 0.277 0.262 0.248 0.223 0.201 0.185 0.171 0.162 38 0.425 0.407 0.391 0.368 0.348 0.331 0.316 0.301 0.286 0.271 0.258 0.232 0.211 0.193 0.178 0.169 40 0.428 0.410 0.396 0.373 0.354 0.338 0.323 0.309 0.294 0.280 0.266 0.241 0.219 0.201 0.186 0.176 3
T n 5 @P n 2 1/2 1 ~f 2n /2p!# l n /2~n 1 2 2 sin 2 u! 1/2 (2) T n = epitaxial layer thickness, n 1 = index of refraction of the epitaxial layer (n 1 = 3.42 for silicon), u = angle of incidence of the beam upon the epitaxial layer, the other symbols have the same meaning they had in Eq 1. Use the same units for the thickness as for the wavelength. Calculate T n for all of the observed maxima minima calculate the average value of T. NOTE 3 When several extrema are available, somewhat better precision than that reported in Section 11 will result if the longer wavelength points are excluded from the calculation. 9.3 Sample Calculation Typical data a calculation of epitaxial layer thickness for an n-type specimen, using the reflection spectrum shown in Fig. 1, are as follows: 9.3.1 The measured value of substrate resistivity was 0.014 V/cm. 9.3.2 Determine wavelength of first last extrema; l 1 = 31.70 µm l 2 = 15.28 µm. 9.3.3 Read appropriate phase shifts from Table 1: f 21 / 2p = 0.142 f 22 /2p = 0.079. 9.3.4 Find from Fig. 1 the difference in the orders of the extrema considered: m = 3.5. 9.3.5 Substitute in Eq 1 solve for P 2 : P 2 5 3.5 ~31.70!/~31.70 2 15.28! 1 1/2 2 @31.70 ~0.142! 2 15.28 ~0.079!#/~31.70 2 15.28! 5 6.80 1 0.50 2 0.20 5 7.10 ' 7 9.3.6 Substitute in Eq 2 solve for T 2 : T 2 5 ~7 2 1/2 1 0.079!~15.28!~0.1477! 5 14.85 µm NOTE 4 1 2(n 2 1 sin 2 u ) 1/2 = 0.1477 for u = 30. 9.4 Tabulate n n, l n, f 2n /2p, P n, T n for all the maxima minima in Fig. 1 as shown in Table 3. 10. Report 10.1 Report the following information: 10.1.1 Identification of slices. 10.1.2 Substrate conductivity type, 10.1.3 Substrate resistivity, 10.1.4 Epitaxial layer conductivity type, 10.1.5 Estimated epitaxial layer resistivity, TABLE 3 Example of Thickness Computations (See Fig. 1) n l n f2 n /2p P n T n 1 31.70 0.142 3.5 14.71 2 27.48 0.124 4 14.71 3 24.52 0.113 4.5 14.89 4 21.75 0.103 5 14.79 5 19.68 0.095 5.5 14.81 6 17.88 0.088 6 14.76 7 16.42 0.082 6.5 14.75 8 15.28 0.079 7 14.85 Average......... 14.78 10.1.6 Wave number range of infrared apparatus used, 10.1.7 Aperature size, 10.1.8 Wave number scan speed, 10.1.9 Location of measurement with sketch of specimen, 10.1.10 Wave numbers used, l n, 10.1.11 Orders of maxima minima used P n, 10.1.12 Thicknesses calculated, T n, 10.1.13 Average thickness value, T. 11. Precision Bias 11.1 For p-type layers of thickness greater than approximately 2 µm, the measurement can be made with an interlaboratory precision, as defined in Practice E 177, of 6(0.25µ m + 0.025 T) (3S) where T is the layer thickness in micrometres. This precision was established in a round-robin experiment in which eight laboratories made one measurement on each of six layers with thickness in the range of 2.5 to 18 µm. 11.2 For n-type layers of thickness greater than approximately 2 µm, the measurement can be made with an interlaboratory precision of 6(0.25 µm + 0.005 T) (3S). This precision was established in a round-robin experiment in which eight laboratories made one measurement on each of six layers with thickness in the range from 2.5 to 15 µm. 11.3 For n- orp-type layers of thickness 0.5 to approximately 2 µm, the measurement can be made with an interlaboratory precision of 6(0.51 µm + 0.035 T) (3S). This precision was established in a round-robin experiment in which seven laboratories made one measurement on each of five layers with thickness in the range from 1 to 7 µm. NOTE 5 Use of the procedure described in Note 2 for locating positions of extrema in Note 2 resulted in greater variability of the measurement. 11.4 The bias of this technique has not been established, the relation to layer thickness as determined by other methods is not known. NOTE 6 A sampling of six similar FT-IR systems has demonstrated single-system-operator-day precisions of 60.1 µm (2S), as defined in Practice E 177. No full round robin has been run; however, the mean value of thickness determined by each of these six systems has been shown to agree with the overall mean value to within 65 %. The difference between the thickness as determined by this method that determined by the automatic test systems exhibits a small linear dependence on thickness. As an example, for one system over the thickness range 3 to 30 µm on n/n + p/p + wafers with resistivities between 0.002 0.014 V cm, this difference is given by the relation: T s 5 1.0026 T 2 0.283 T s = thickness value from automatic test system, µm, T = thickness value from this method, µm. The factor 1.0026 the term 0.283 µm result from a least-squares fit to the data. An extensive multilaboratory test was conducted in 1986/1987 to determine the precision of epitaxial layer thickness measurements made by FT-IR instruments. For details see Appendix X2. 12. Keywords 12.1 epi; epi thickness; epitaxial layer; FTIR; index of refraction; IR; layer thickness; spectrophotometer 4
APPENDIXES (Nonmatory Information) X1. THEORY OF METHOD X1.1 Detailed discussions of this technique have been published elsewhere. 7,8,9 For this method to be applicable, an observable difference must exist between the optical constants of the epitaxial layer the substrate. The limits on the resistivity of the layer the substrate stated in 1.1 have been found to assure a sufficiently large difference in the optical constants to produce useful maxima minima in the reflection spectrum of a specimen which meets the other stated requirements. The index of refraction of the layer, n 1, is assumed to be independent of wavelength. X1.2 Maxima minima will be observed in the reflection spectrum when the optical path lengths of the ray reflected from the layer surface the ray reflected from the interface differ by an integral number of half wavelengths. Referring to Fig. X1.1, the relative phase, d, of the outgoing rays at C D is: d5@2p~ab 1 BC!/l# n1 2 ~2p AD/l! 1f 1 2f 2 (X1.1) 7 Spitzer, W. G., Tanenbaum, M., Interference Method for Measuring the Thickness of Epitaxially Grown Films, Journal of Applied Physics, Vol 32, 1961, p. 744. 8 Albert, M. P., Combs, J. F., Thickness Measurement of Epitaxial Films by the Infrared Interference Method, Journal Electrochemical Society, Vol 109, 1962, p. 790. 9 Schumann, P. A., Phillips, R. P., Olshefski, P. J., Phase Shift Corrections for Infrared Interference Measurement of Epitaxial Layer Thickness, Journal Electrochemical Society, Vol 113, 1966, p. 368. l = wavelength in vacuum, n 1 = refractive index of the layer which converts the optical path length in the layer to an equivalent path length in vacuum, f 1 = phase shift at point A, f 2 = phase shift at point B AB, BC, AD are distances defined in Fig. X1.1; they must have the same units as l. X1.3 From Fig. X1.1 it is evident that: AB 1 BC 5 2T/cos u8 X1.4 From Snell s law: X1.5 Thus AD 5 2T tan u8 sin u sin u5n 1 sin u8 AB 1 BC 5 2Tn 1 /~n 1 2 2 sin 2 u! 1/2 AD 5 2T sin 2 u/ ~n 1 2 2 sin 2 u! 1/2 X1.6 Substituting these expressions into Eq X1.1: d5@4pt~n 1 2 2 sin 2 u! 1/2 /l# 1f 1 2f 2 X1.7 The order, P, is defined by: d52 Pp (X1.2) (X1.3) (X1.4) (X1.5) (X1.6) (X1.7) (X1.8) X1.8 If two extrema in interference amplitude are observed, the corresponding orders P 1 P 2 are found by solving Eq X1.8 for P eliminating d using Eq X1.7: P 1 5 @2T~n 1 2 2 sin 2 u! 1/2 /l 1 # 1 ~f 11 /2p! 2 ~f 21 /2p! P 2 5 @2T~n 1 2 2 sin 2 u! 1/2 /l 2 # 1 ~f 12 /2p! 2 ~f 22 /2p! where by convention l 1.l 2 P 2 5 P 1 1 m (X1.9) (X1.10) (X1.11) (X1.12) m = 1 2, 1, 3 2, 2, since the difference in orders is a whole or half integer. FIG. X1.1 Geometry of Method X1.9 Solving Eq X1.9, Eq X1.10, Eq X1.12 for P 2 : P 2 5 @ml 1 /~l 1 2l 2!# 1 @~f 11 l 1 2f 12 l 2!/2p~l 1 2l 2!# 2@~f 21 l 1 2f 22 l 2!/2p~l 1 2l 2!# (X1.13) X1.10 For the case of light reflected at an air-insulator interface as in Fig. X1.1, f 1n = p, with the appropriate substitution in Eq X1.13, the result is Eq 1 in 7.1. 5
X1.11 The expression for thickness, Eq 2, can be derived by solving Eq X1.7 Eq X1.8 for T with the suitable substitution of p for f 1n. X2. REPEATABILITY AND REPRODUCIBILITY OF MULTILABORATORY TESTING USING FT-IR INSTRUMENTS Instrument Number TABLE X2.1 Repeatability of Single Instrument Responses for Nine Component Measurements Sample A-2.5 B-5 C-10 D-15 E-20 F-25 G-50 H-120 1 1.52 % 0.82 % 0.00 % 0.66 % 0.00 % 0.57 % 0.21 % 0.58 % 2 0.76 % 0.41 % 0.22 % 0.13 % 0.10 % 0.16 % 0.17 % 1.02 % 3 0.00 % 0.00 % 0.00 % 0.13 % 0.10 % 0.33 % 0.46 % 0.81 % 4 0.76 % 0.00 % 0.00 % 0.13 % 0.10 % 0.16 % 0.63 % 1.02 % 5 0.76 % 0.00 % 0.00 % 0.00 % 0.31 % 0.41 % 0.00 % 0.09 % 6 0.85 % 0.00 % 0.00 % 0.00 % 0.00 % 0.00 % 0.00 % 0.59 % 7 0.00 % 0.00 % 0.00 % 0.13 % 0.10 % 0.08 % 0.04 % 0.08 % 8 1.53 % 0.41 % 1.31 % 0.93 % 0.62 % 0.57 % 0.42 % 0.42 % 9 0.77 % 0.41 % 1.09 % 0.00 % 0.41 % 0.24 % 0.17 % 0.10 % 10 0.15 % 0.41 % 0.22 % 0.53 % 0.41 % 0.65 % 0.66 % 0.36 % 11 0.00 % 0.41 % 0.22 % 0.53 % 0.41 % 0.65 % 0.66 % 0.14 % 12 0.38 % 0.41 % 0.11 % 0.13 % 0.10 % 0.16 % 0.12 % 0.15 % 13 1.53 % 0.20 % 0.11 % 0.13 % 0.10 % 0.16 % 0.08 % 0.17 % 14 0.77 % 0.41 % 0.11 % 0.07 % 0.10 % 0.24 % 0.25 % 0.12 % 15 0.77 % 0.82 % 0.65 % 0.66 % 0.82 % 0.33 % 0.04 % 0.20 % 16 3.77 % 0.83 % 0.66 % 0.54 % 0.73 % 0.33 % 0.37 % 0.26 % 17 0.77 % 0.41 % 0.11 % 0.13 % 0.21 % 0.24 % 0.12 % 0.98 % 18 1.70 % 2.55 % 0.22 % 0.13 % 21.68 % 0.56 % 11.09 %... 19 3.04 % 0.21 % 0.11 % 0.07 % 0.10 % 0.08 % 0.08 % 0.07 % 20 0.18 % 0.21 % 0.00 % 0.00 % 0.05 % 0.16 % 0.33 %... 21 0.00 % 0.84 % 0.11 % 0.26 % 0.40 % 0.32 % 0.94 %... X2.1 Epitaxial wafer samples were produced having nominal epi thickness of 2.5, 5, 10, 15, 20, 25, 50, 120 µm. N type; epi layers were deposited over blanket, uniform, n+ regions that had been implanted into p type polished substrates. The n+, arsenic implant layers were the basis for well defined transition zones, that is, the epi to substrate interfaces were well controlled the in-depth carrier density profiles were very uniform, as verified by spreading resistance profile. X2.1.1 To minimize the influence of radial thickness variations, subsets of eight to ten wafers in each of the thickness categories were examined. All the wafers were put through a screen for radial thickness uniformity. The one wafer in each thickness subset with the most uniform thickness, that is, the minimum percent difference between the center the radial thickness measurements, was selected to be included in the round-robin sample set. X2.1.2 The round-robin required that each of the eight samples be measured three times per day on each of 3 days. The complete round-robin data base contained a total of 1485 measurements from 21 instruments. Generally, each instrument contributed 72 data points. Not all instruments were able to measure thick layers. There were three instruments that could not measure the sample with the thickest epitaxial layer, nominally 120 µm. These instruments each contributed 63 data points. X2.2 Repeatability (Single Instrument): Repeatability values, for nine repetitions, are tabulated in Table X2.1, in terms of two relative stard deviations (2s %); the values are seen to depend both on epitaxial layer thickness on instrument. The single instrument repeatability was found to be better than 1 % (2s %) for 92 % of the test results, better than 4 % for nearly 99 % of the test results. With the exception of two anomalously large values reported for Instrument 18, the repeatabilities for the thinnest epitaxial layer (nominal 2.5 µm) were poorer than those for thicker samples. Based on these results, instruments functioning in good order should demonstrate repeatabilities of less than 4 % (2s %) for epitaxial layers with uniform thickness of at least 2.5 µm. X2.3 Reproducibility (Multiinstrument): Based on analysis including 21 instruments 8 specimens measured using each instrument on each of 3 days; the multiinstrument reproducibility of the measurement is estimated to range from 1.83 % to 9.99 % (2s %). The reproducibility data is tabulated in Table X2.2. This tabulation shows that the poorest reproducibility, 9.99 % (2s %), was obtained in the case of the thinnest (2.6 µm) epi layer, the best, 1.83 % (2s %), was obtained with the thickest, 117 µm epi layer, Sample H-120. TABLE X2.2 Reproducibility of Laboratory Averages Sample Mean 2S 2RS % A-2.5 2.61 0.26 9.99 B-5 4.83 0.16 3.41 C-10 9.20 0.33 3.54 D-15 15.11 0.37 2.42 E-20 19.56 1.11 5.66 F-25 24.58 0.49 1.99 G-50 48.29 1.37 2.84 H-120 117.44 2.14 1.83 6
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