## 3 Results and Discussion
### Material Properties Probing  
Previous studies involving microwave probing of semiconducting polymers by means of so-called voltage modulated microwave spectroscopy and flash-photolysis time-resolved microwave conductivity also observed conductivity increase in the upon voltage or light excitation of the polymer [10; 11]. They determined local carrier mobility, attributing their measurements to properties taking place at the mesoscopic scale, and more precisely to polymer intrachain charge transport. The formation of polarons upon light absorption or carrier injection with different excited states associated with the carrier could be discriminated by the energy formation and relaxation dynamics. Strong electric field was also shown to extend the diffusion of carriers along the chain by enhancing hopping rates at potential barriers induced by defects in the chain, and therefore improving carrier transport. Polarons are charge-phonon coupling and are shown to drive intramolecular transport mechanisms in organic semiconductors [29; 30]. In polymers, polaron assisted transport therefore corresponds to intrachain carrier motion. Many different polarons can be considered with materials and structures. Descriptive formalism is acknowledged [31] and polaron lifetime usually ranges from fs to ns [32; 33], allowing spectroscopic characterization from THz down to GHz. Existing measurements report higher carrier mobility compared to conventional low frequency bulk probing methods, typically three to four orders of magnitude \(\sim\)10\({}^{0}\) cm\({}^{2}\) V\({}^{-1}\) s\({}^{-1}\). As conjugation drives the carrier motion, intrachain transport is simpler compared to interchain [34; 35]. Here, existing analytical modelling tools, as proposed in SI, allow for local variations of conductivity \(\sim\upmu\)S to be determined. These could be coarsely explained from \(G=e.p.\mu.S/d\), with G the measured conductance, e the elementary charge, p the carrier density in accumulated P3 HT \(\sim\)10\({}^{18}\) cm\({}^{-3}\)[28], \(\upmu\) the intrachain mobility \(\sim\)10\({}^{0}\) cm\({}^{2}\) V\({}^{-1}\) s\({}^{-1}\)[10], S the contact area \(\sim\)50 \(\times\) 50 nm\({}^{2}\) and d the penetration depth d \(\sim\)25 nm, much lower than the film thickness (\(\sim\)150 nm), consistently with the chosen frequency \(\sim\)10.5 GHz sufficiently high to limit the microwave penetration depth to a fraction of the semiconductor thickness (See Figure S4a,b). In their dielectric resonator configuration, [PERSON] et al. attributed the observed frequency shift of microwave power spectrum to variations of dielectric constant induced by the contribution of trapped carriers in the measurements [13]. In SMM, as illustrated in Figure S4, the penetration depth of the microwave, decreases with both the operating frequency and the conductivity of the probed volume. Upon negative bias, carrier accumulation increases the loss and reduces the penetration depth of the microwave in the P3 HT. This indirectly increases the corresponding capacitance between the tip contact and the conductivity plan at the maximum penetration depth of the microwave (See Figure S4a,b). Consequently, negative biasing would have combined impact of both the frequency shift and the sharpness of the interferometric fringes as shown in Figures 2 and 3 and Figure S2. Especially, a decrease (increase) in the penetration depth (capacitance) upon negative bias corresponds to a frequency shift towards lower values. The analytical model proposed in S6 estimated the capacitance variations of a few aF. With the proposed dimensions above, and \(\delta C=-\frac{\epsilon_{0}\epsilon_{T}}{d^{2}}.S.\delta d\) with \(\epsilon_{0}\epsilon_{T}\) the dielectric permittivity of the material, \(\delta C\)\(\sim\)1 aF variations of capacitance correspond to \(\delta\)d\(\sim\)10 nm.