Carrier-density-wave transport property depth profilometry using spectroscopic photothermal radiometry of silicon wafers I: Theoretical aspects

Abstract

Articles you may be interested inThree-layer photocarrier radiometry model of ion-implanted silicon wafers J. Appl. Phys. 95, 7832 (2004); 10.1063/1.1748862Carrier-density-wave transport property depth profilometry using spectroscopic photothermal radiometry of silicon wafers II: Experimental and computational aspects A theoretical model for the photothermal radiometric ͑PTR͒ signal from an indirect band-gap semiconductor excited by a laser of arbitrary wavelength is presented. The model has been used to investigate the spectral dependence of the sensitivity of the PTR signal to variations in the electronic transport parameters of the sample. Simulations show slight variations of the sensitivity to carrier lifetime and carrier diffusivity with excitation wavelength due to changes in the strength of the thermal contribution to the signal that are a result of changes in the difference between the photon energy and the band gap. The sensitivity of the PTR signal to changes in the front surface recombination velocity is shown to have a strong dependence on the excitation wavelength with the sensitivity decreasing as the absorption depth of the excitation source increases, allowing spectroscopic carrier-density-wave depth profilometric measurements.

Carrier-density-wave transport property depth profilometry using spectroscopic photothermal radiometry of silicon wafers II: Experimental and computational aspects

“…The decreasing photon energy results in an increase in the photon flux and thus, assuming no strong variation of quantum efficiency with wavelength, an increase in the PTR amplitude due to the greater number of electrons contributing to the depth integral. 2 This expected feature is not present for the amplitude curves presented in Fig. 2͑a͒.…”

“…The theoretical PTR response contains improper integrals with infinite upper limits and must be evaluated numerically. 2 Based on the physical quantity represented by the integrand, it is necessary that the integral approach a finite upper limit. This was verified through rigorous investigation of the dependence of the integrand on physically reasonable values of the electronic and thermal parameters.…”

Influence of probe beam size on signal analysis of modulated free carrier absorption technique

“…Due to the absorption of the excess free carriers to the probe beam, the intensity of the transmitted probe beam is modulated, resulting in the MFCA signal. The MFCA signal is the ratio of the modulated ( I) and unmodulated (I) portions of the intensity of the transmitted probe beam [5], which can be expressed as follows: (6) Here r d and I 0 are radius and centre intensity of the probe beam, and d is the separation between the pump and probe beams. I is proportional to the number of excess free carriers in the volume where the probe beam covers.…”

“…In MFCA, the excess carriers are created by an intensity-modulated pump laser beam with photon energy greater than the energy gap of semiconductor wafer and diffuse on the surface and in the bulk of the wafer until recombine. The excess free carrier concentration can be calculated by solving the continuity equation along with the boundary conditions at the surfaces [6]. Here the expression is integrated over the sample depth (with thickness L): …”

Accuracy of photocarrier radiometric measurement of electronic transport properties of ion-implanted silicon wafers

“…1 It was derived from the well-known infrared photothermal radiometry ͑PTR͒, a technique extensively used in semiconductor characterization. [2][3][4][5][6][7][8][9] Both techniques rely on the detection of infrared emission from the semiconductor sample optically excited by an intensity-modulated laser beam with photon energy greater than the fundamental energy gap of the material. To simultaneously determine the transport properties, both the amplitude and phase of the PTR or PCR signal are recorded as a function of the modulation frequency over a wide range and then fitted with an appropriate theoretical model via a multiparameter fitting procedure.…”