Calibration of Low‐Temperature Photoluminescence of Boron‐Doped Silicon with Increased Temperature Precision

Low‐temperature photoluminescence spectroscopy enables the determination of the dopant concentration of shallow impurities in silicon. This measurement method is therefore well suited for identifying and analyzing dopants (intentional impurities in silicon). A method is presented which allows the determination of the boron concentration in silicon in a range from 2.2⋅1012$2.2 \cdot \left(10\right)^{12}$ to 2.2⋅1016 cm−3$2.2 \cdot \left(10\right)^{16} \left(\text{cm}\right)^{- 3}$ at temperatures from 4.2 to 20 K with increased temperature accuracy. This method requires only one calibration function for the photoluminescence intensity ratio of the boron‐bound exciton IBTO(BE)$I_{\left(\text{B}\right)_{\text{TO}} \left(\right. \text{BE} \left.\right)}$ and the free exciton IITO(FE)$I_{I_{\text{TO}} \left(\right. \text{FE} \left.\right)}$ . The measurement temperature is obtained from the intrinsic silicon photoluminescence line of free excitons ( ITO(FE)$I_{\text{TO}} \left(\right. \text{FE} \left.\right) \left.\right)$ ) using a fitting method, which distinguishes the TO $\text{TO }$ and LO$\text{LO}$ components of the free exciton peak. The determined calibration function is IBTO(BE)/IITO(FE)=(5.8±0.1)⋅10−18 cm3⋅cboron⋅e(56.7±0.7)KT$\left(I_{B_{\text{TO}} \left(\right. \text{BE} \left.\right)}\right)/\left(I_{I_{\text{TO}} \left(\right. \text{FE} \left.\right)}\right) = \left(\right. 5.8 \pm 0.1 \left.\right) \cdot \left(10\right)^{- 18} \left(\text{cm}\right)^{3} \cdot c_{\text{boron}} \cdot \left(\text{e}\right)^{\frac{\left(\right. 56.7 \pm 0.7 \left.\right) \text{K}}{T}}$ . The obtained exciton binding energy to boron, Eb=4.9±0.1 meV$E_{\text{b}} = 4.9 \pm 0.1 \text{meV}$ , agrees well with literature data.