Schematic drawing of the geometry used to measure the temperature, polarization, and crystal orientation dependence of TPA Si and GaP crystals. Pump and probe beams are focused within the sample using a 10× or 15× microscope objective lens (L1); after passing through the sample, the probe beam is refocused on a PD using a lens (L2). The polarization of the probe relative to the pump is controlled by a WP and polarizers (P1 and P2). Pump scattering is removed by another polarizer (P3) when pump and probe polarizations are perpendicular. The orientation angle of the sample is specified by the angle between the polarization of the pump beam and the direction of the crystal. The two inset figures describe the different ways that the relative delays between the pump and the probe beams are generated in the two experiments. In the Si experiment, the relative delay is adjusted by an optical delay line. In the GaP experiment, two lasers with slightly different repetition rates generate the relative delay.
Transient changes in probe power normalized by the average probe power, , at zero delay time as a function of pump power, , for Si [panel (a)] and GaP [panel (b)] crystals using and 790 nm light sources, respectively. Pump and probe polarizations are orthogonal and pump polarizations are parallel to the direction of the crystals. The symbols are measurements and the lines are fits to linear equations with . In Si, all data points are used to fit it, but in GaP, only five data points at low power are used.
Transient absorption of the probe beam as a function of the time delay between pump and probe for four types of Si crystals using the light source. The data are labeled by the orientation, carrier type, resistivity, and thickness of each wafer. Laser polarizations and sample orientations are the same as Fig. 2. The signal measured by the rf lock-in is normalized by the average voltage output of a PD detector and the incident power in the pump beam; in other words, we plot , where is the power in of the probe beam and is the power of the pump beam. Near zero delay time, the fluctuations in the data for the thinnest Si wafer (0.3 mm thickness) are due to optical interference between reflections from the front and back surfaces of the wafer.
Transient absorption of the probe beam as a function of the time delay between pump and probe for Si [panel (a)] and GaP [panel (b)] crystals; and 790 nm light sources generate transient TPA in Si and GaP, respectively. The pump and probe powers are 88 and 2 mW in Si; and 3 mW and 0.4 mW in GaP, respectively. The pump and probe polarizations are denoted and , respectively. In both configurations of the relative polarizations, we select the crystal orientation that produces the maximum signal.
Normalized transient absorption at zero delay time as a function of the orientation of the pump and probe polarizations and the orientation of the Si(001) [panel (a)] and GaP(001) [panel (b)]. The symbols are measurements and the solid lines are fits to Eqs. (1) and (2) used to determine the ratio in Si and in GaP. Maximum TPA is produced when the polarizations of the pump and probe beams are parallel and aligned along a direction of the Si crystal. Minimum is when these polarizations, aligned along a direction of the Si crystal, are orthogonal to one another.
Temperature dependence of the TPA for perpendicular polarizations of the pump and probe aligned along the and directions of Si [panel (a)] and GaP [panel (b)] crystals. The laser source is an Er:fiber laser operating at a center wavelength of [panel (a)] and a Ti:sapphire laser operating at a center wavelength of 790 nm [panel (b)]. The symbols denote measurements. For Si, solid lines, which appear linear on these axes to the eye, are fits to Eq. (3) using one fitting parameter, the constant of proportionality, . For GaP, the dashed lines are fits to Eq. (4); the differences between the dashed lines and the data are attributed to contributions to the absorption from indirect transitions. The solid lines in panel (b) are fits to Eq. (5).
Temperature, measured at two spots relative to a resistive heater as indicated in the schematic in the figure inset, is measured as a function of time after heating, 10 ms–50 s, at two points separated by 5 mm along a Si strip. A Cr layer with 120 nm thickness is used as the electrical contact; the gap between the contacts is 2 mm.
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