Quantifying Phosphorous Levels in Ultrathin Si Films using Second Harmonic Generation

Non-destructive assessment of dopant concentration plays a pivotal role in contemporary semiconductor manufacturing. In this investigation, we introduce an inventive method for appraising the dopant concentration in doped Si thin films (DSTF) utilizing second harmonic generation (SHG). This technique involves analyzing the charge trapping triggered by internal photoemission (three photon absorption) and the concomitant electric field-induced SHG. Our proposed method includes the development of a strategy for estimating DSTF's dopant concentration by considering tunneling probability and the Fermi-Dirac distribution, irrespective of its crystalline structure. Our method facilitates the precise measurement of dopant concentrations spanning from 10¹⁷ to 10²⁰ atoms/cm³, allowing for real-time monitoring.

The non-monotonic variation of the second-order susceptibility χ⁽²⁾ with dopant concentration may be attributed to the presence of interstitial defects and dopant agglomeration in highly doped silicon. The trapping rate at t = 0, denoted as R(0), exhibits a nonlinear dependency on dopant concentration due to the combined effects of ionization energy reduction, bandgap narrowing, and tunneling effect. As the quantity of electron density generated and trapped at the interface or surface directly impacts R(0), a substantial correlation between R(0) and surface electron density (n_sur) is evident.