The model used to fit the saturation in charge transfer with increasing laser fluence (Fig. 4) was based on two assumptions: (i) The local peak THz field immediately above the sample surface Epk_sample(r) (r is the radial distance from the center of the beam) scales linearly with local excitation fluence F(r) up to Fs, i.e., Epk_sample(r) = {AF(r), F(r) < Fs; AFs, F(r) ≥ Fs}, in which A is the low-fluence proportionality constant and Fs corresponds to the fluence that drives the type II to type I crossover. (ii) The peak field measured by EO sampling Epk_EO can be approximated by averaging Epk_sample(r) over the illuminated region on the sample. In addition, our excitation beam has a Gaussian intensity profile, and the fluence F0 we report is the total pulse energy divided by the area within the Gaussian beam diameter (1/e2) projected onto the sample. The peak local fluence at the center of the beam is therefore 2F0.

It is then straightforward to show that Epk_EO has the following dependence on F0: Epk_EO (F0) = {AF0, F0 < Fs/2; AFs [ln(2F0/Fs) + 1]/2, F0Fs/2}, in which A′ is the overall low-fluence proportionality constant. We note that this model is valid if (i) the charge transfer rate and efficiency only weakly depend on the band offset energies as long as the alignment remains type II, (ii) the illuminated area is considerably smaller than the diffraction-limited spot after refocusing, and (iii) F0 is within few times of Fs. Condition (i) is a simplification motivated by the robustness of ultrafast charge transfer in different types of samples. Conditions (ii) and (iii) depend on experimental setup and are reasonably well satisfied for the measurement conditions relevant for Fig. 4.

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