Protocols overview

Both protocols are based on the measurement of the absorption peak height of a characteristic absorption band. But both absorption bands overlap with a (different) band of the silicon lattice. Therefore, the use of an oxygen and carbon free reference specimen is necessary to eliminate the silicon lattice bands. The protocols also include proceedings to calibrate the spectrometer. An overview over the most important requirements can be found in Table 5.1.

The next two subsections give an overview and cite the requirements of these protocols.

5.1.1 SEMI MF1188-1107: Test method for interstitial oxygen content

This method makes use of a linear relationship between the absorption coefficient at 1107 cm⁻¹ and the interstitial oxygen concentration. A short baseline from 1040 cm⁻¹ to 1160 cm⁻¹ is used to obtain the absorption coefficient. The lower oxygen concentration detection limit is 1·10¹⁶atoms cm⁻³. The reproducibility for different laboratories was found to be 3 % and the bias should not exceed 6 %.

Sample and reference requirements The samples must be polished on both sides and their thickness must be between 400µm and 4000µm. The thickness of the reference sample is required to match the thickness of the test sample within ±0.5%. If the sample resistivitity is below 1 Ωcm forn-type silicon and 3 Ω cm forp-type silicon, the reference material has also to match the resistivity, because of significant free carrier absorption. As the lattice bands change with temperature, it is required to maintain the temperature at 27±5^◦C.

Instrumental checks First, the noise level has to be measured. For this, two spectra obtained with empty sample beam are divided by each other. The resulting transmittance spectrum should be 100±0.5 % over the range from 900 to 1300 cm⁻¹. If this criterion is not met, measurement time must be increased, until it does. Mid-scale linearity is determined by

Figure 5.1: Schematic spectrum for the defini-tions of baseline, peak wavenumberWp, minimum transmittanceTp and baseline transmittanceTb

registration of a silicon spectrum in the range from 1600 to 2000 cm⁻¹. The transmittance value should be 53.8±2 %. Elsewise, the instrument must be realigned.

Sample preparation and measurement Before measuring, the specimens must be etched in 4.9 % or 10:1 diluted hydrofluoric acid in order to remove surface oxides. Also their thickness x must be determined within ±0.2 %. Then the spectra are measured with a resolution of 4 cm⁻¹ or better and a minimum of 64 scans over the range from 900 to 1300 cm⁻¹.

Calculation The oxygen only transmittance spectrum is obtained by rationing the emission spectrum of the test sample to the emission spectrum of the reference sample. In the oxygen only transmittance spectrum, plotted from 900 to 1300 cm⁻³, a straight line must be drawn connecting the transmittances at 1040 cm⁻¹ and 1160 cm⁻¹. This line is called baseline. Then the wavenumber of the minimum transmittance has to be located in the region from 1102 cm⁻¹ to 1112 cm⁻¹ and is calledWp. The minimum transmittance value is called Tp and the value of the baseline at the wavenumberW_p is calledT_b. These numbers are visualized in Figure5.1.

The net absorption coefficient αO of the interstitial oxygen is then calculated by α_O=−1

xln





(0.09−e^1.70x) + q

(0.09−e^1.70x)²+ 0.36T_p²e^1.70x (0.09−e^1.70x) +

q

(0.09−e^1.70x)²+ 0.36T_b²e^1.70x T_b T_p



, (5.1)

where x is the thickness of the specimen. This can be converted to a concentration, either by using a linear regression curve of a set of calibration specimens or by multiplication of the absorption coefficient with the IOC-88 calibration factor, which was found by an international Grand Round Robin experiment and is given by

CO,ppm= 6.28 ppm cm (5.2)

C_O,dens= 3.14·10¹⁷atoms cm⁻². (5.3)

Finally, they state that the full width at half maximum (FWHM) of the oxygen band is 32 cm⁻¹ and that measurements which result in a greater FWHM may be erroneous.

In all following experiments, the etching with hydrofluoric acid was skipped, because of the dangerous handling. Therefore we may overestimate the oxygen concentration in our samples.

And of course this effect becomes more important for thinner samples. In order to determine the influence of this neglect, we do a rough estimation for the oxygen content on the surface.

With an molar weight of 28.1 g/mol and a density of 2.3 g cm⁻³ (both values from [Sch64,

5.1 Protocols overview

p. 94]), we get an atomic density of about 5.0·10²²cm⁻³. Under the assumption, that all atoms within a distance of the lattice constant of 5.4·10⁻¹⁰m [Sch64, p. 94] are part of the surface, we have a surface atomic density of 2.7·10¹³cm⁻². Morita et al. [MOH⁺90] showed, that oxygen layers grow layer by layer at room temperature. In their case up to four layers grew in around 70 days. For our calculations we assume five layers with the same number of oxygen atoms as on the silicon surface. Hence we have a surface concentration of oxygen σ_O= 1.3·10¹⁴cm⁻². Let c_O be the bulk concentration of oxygen. Then the effective oxygen concentration c_eff measured by the FTIR is given as

c_eff = c_Od+ 2σ_O

d =c_O+2σ_O d ,

with the wafer thickness d. The right hand term is referred to as surface concentration. As-suming a thickness of 100µm we obtain a surface concentration of 2.7·10¹⁶cm⁻³. Hence, if the bulk oxygen concentration is above 3.0·10¹⁷cm⁻³, the contribution of the surface concen-tration to the effective concenconcen-tration is below 10 % and as these calculations are based on a worst case scenario, the influence will be even less. For samples with a thickness of 2000µm, this limit is at 1.5·10¹⁶cm⁻³.

5.1.2 SEMI MF1391-0704: Test method for substitutional carbon content

This method uses a linear relationship between the absorption coefficient at 605 cm⁻¹ and the substitutional carbon concentration. A baseline from 560 to 640 cm⁻¹ is used to calculate the absorption coefficient. The lower detection limit is 5·10¹⁵cm⁻³, and the standard deviation was found in a round robin to increase with the concentration and is around 10 % for a carbon concentration of around 4 ppma and 20 % for 0.5 ppma.

Sample and reference requirements Sample as well as reference specimens must have a thickness of about 2 mm with a thickness variation over the measurement area of 0.005 mm or less. The reference specimen has to match the thickness of the sample within 0.5 mm. Both specimens are required to have resistivity above 3 Ω cm forp-type and 1 Ω cm forn-type silicon.

Their surface preparation shall be identical, but polished.

Instrumental checks Like in the case of the oxygen protocol, the 100% transmittance line in the region from 500 to 700 cm⁻¹ must be met within ±0.5 %. For the 0% line, the recorded energy below 300 cm⁻¹ should be less than one percent of the maximum signal in the region from 200 to 1000 cm⁻¹. For mid-scale linearity, the transmittance of a silicon sample must be 56.8±2 % in the range from 1600 to 2000 cm⁻¹. If this criterion is not met, the sample must be aligned at a small angle to the axis.

Sample preparation and measurement The thicknesses of sample and reference specimen have to be measured within ±0.005 mm at their centers. Also the temperature of the sample chamber must be determined within±2 K. The spectra have to be taken with a resolution of 2 cm⁻¹or better in a range of 500 to 700 cm⁻¹in a vacuum, dry nitrogen or dry air atmosphere.

Oi Ci

thickness ≥400µm ≥2000µm

resistivity ≥0.1 Ωcm ≥3 Ωcm (p-type)

≥0.5 Ωcm ≥1 Ωcm (n-type) resolution ≤4 cm⁻¹ ≤2 cm⁻¹

spectral range 900-1300 cm⁻¹ 500-700 cm⁻¹

FWHM 32 cm⁻¹ 6 cm⁻¹

Table 5.1: Protocols requirements overview

Calculation The carbon-only absorbance spectrum is obtained by subtraction of the reference absorbance spectrum multiplied by the quotient of test sample thickness and reference sample thickness. Alternatively, the quotient may be adjusted in the manner, that the region around the peak is as flat as possible. The baseline is then defined as straight line from 560 cm⁻¹ to 640 cm⁻¹, where the endpoints are defined as average of the absorbance from 550 to 570 cm⁻¹ and from 630 to 650 cm⁻¹, respectively. The wavenumber of maximum absorbance in the region from 603 to 607 cm⁻¹ is calledWp. The maximum absorbance is calledAp and the absorbance of the baseline at Wp is called A_b. The carbon absorption coefficient is then calculated by

α_C= 23.03

x (A_p−A_b), (5.4)

where x is the specimen thickness. The conversion to carbon concentration is done by multi-plication of the absorption coefficient with

C_C,ppma= 1.64 ppma mm (5.5)

or C_C,dens= 8.2·10¹⁷atoms cm⁻². (5.6)

Finally, if the FWHM of the carbon peak exceeds 6 cm⁻¹, the spectrum was not properly obtained.