Following the standard C-V measurement procedure, a strong negative DC bias is applied to accumulate the majority carriers in the a-Si:H near the top interface. The current response and SHG photons counts are monitored in the time domain. The sinusoidal current wave is observed as a result of the voltage function. For each particular frequency of the AC voltage, one can obtain the magnitude and phase of the complex device impedance, and eventually produce the Bode plot over a large frequency range as shown in Figure 5.5. The impedance Bode plot indicates that, in the low frequency range (< 103Hz), the device display high impedance which is dominated by the a-Si:H bulk resistance. As the driving frequency increases, the impedance of device geometrical capacitance decreases and allows more AC current flowing through the device. When the frequency reach 1MHz, the total impedance of the whole device is limited by the ITO series resistance.
A circuit model is established to quantitatively analyze the complex impedance Bode plot. In this model, different electronic elements correspond to different parts of the sample (Figure 5.4).
Figure 5.3: The panel (a) shows the measured SHG intensity versus the applied bias on the sample. The red circles are the SHG data, the blue line is the fitted curve based on the interference of the idler SHG and the EFISH contribution. This fitting result yields a 84 deg phase difference, allowing the SHG in the reverse bias region can be approximated by SHG = VA∗ FVSHG+ SHGOf f set. In lower panel, we show the -3 V DC biased 0.5Vpp voltage sinusoidal wave in (b), the resulting current sinusoidal wave in (c), the real time SHG data and sinusoidal fitting curve in (d).
86 R0 is the ITO and the electrode/ITO contact resistance. R1 is the resistance of bulk amorphous silicon. C1 is the geometrical capacitance due to the device architecture. Here we assume that, C2 is the capacitance of the depletion region while R2is the resistor hindering the carrier movement in the depletion region, and this RC pair together models the carrier dynamics in the depletion region of ITO/a-Si:H interface. Based on this circuit model, the device impedance can be fully described and fitted by Eq(1), yielding the component values of R0, R1, R2, C1 and C2. The fitting result indicates that the device impedance characteristic is primarily governed by the R0, R1 and C1, while R2 and C2 pair contributes a small amount charge flow of the total current signal. However, successful fitting to the impedance Bode plot does not necessarily prove our assumption for the origination and physical location of R2 and C2. However, time-resolved SHG provided further evidence to validate this hypothesis.
Figure 5.4: Shows the device structure of the sample, bias geometry, and optical experimental configuration. The circuit elements in the dash line rectangle make up the circuit model resembling the actual device.
˜ Z(ω) =
˜ VA(ω)
˜
I(ω) = ZR0+ ZaSi with ZaSi=
1 1/ZR1+ 1/ZC1(ω) + 1/(ZC2(ω) + ZR2) (5.1) ˜ VC2(ω) ˜ VA(ω) = ZaSi ZaSi+ ZR0 ∗ ZC2(ω) ZC2(ω) + ZR2 (5.2)
SHG(t) = VC2(t) ∗ FVSHG+ SHGOf f set ⇒ ˜ SHG(ω) ˜ VA(ω) = ˜ VC2(ω) ˜ VA(ω) ∗ F SHG V (5.3)
The SHG intensity can reveal the voltage drop across the top ITO/a-Si:H junction, hence, the time-resolved SHG data can be converted into the real-time voltage on C2, aka VC2, via the linear relationship described in Equation (5.3). In Figure 5.3(b) panel, 50 kHz 0.5 Vpp sinusoidal voltage function and -3V DC offset are imposed on the sample. We observed a sinusoidal SHG signal in the time domain (Figure 5.3(d) panel) indicating VC2 behaves as sinusoidal wave. The SHG wave is fitted with sinusoidal function, allowing one to obtain the magnitude ratio and relative phase between SHG oscillation and applied voltage function. By comparing the SHG oscillation magnitude and relative phase to the input voltage function over wide frequency range, we plot the SHG Bode plot as showed in Figure 5.5(b) panel. In this figure, starting from 200 kHz, the SHG oscillation magnitude attenuates rapidly, and the relative phase deviates from 0. These SHG behaviors corresponding to the carriers in the depletion region being unable to respond fast enough to the changes in the applied bias.
From the equivalent circuit model, we draw the fitting functions 5.1 and 5.2. ZX represents the impedance of component “X”. The impedance of capacitor, ZC(ω) is frequency dependent. Accent of “∼” represents the complex vector of the sinusoidal oscillation signal. We draw 5.3 from the linear relationship between the SHG and the voltage drop on C2 capacitor. FVSHG is the conversion factor between SHG intensity and the static voltage drop on the depletion region. The additional information of VC2provided by SHG Bode plot, in conjunction with the impedance Bode plot, are adequate to determine each circuit element in the model, especially, the accurate value of C2 capacitor, i.e. capacitance of the depletion region.
The solid lines in Figure 5.5 are the fit results to the Equations (5.1) to (5.3). We assume that measurement error is dominated by shot-noise, as indicated by the error bars. Fit quality is excellent with χ2 < 3, and fitted curves clearly capture current and SHG data in the fitted frequency range. The extracted circuit element values are summarized in Table 5.1. The successful
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Figure 5.5: Panel (a) shows the bode plot of the device impedance. Panel (b) shows the ratio of fitted SHG AC amplitude over driving voltage AC amplitude versus frequency, and the relative phase between fitted SHG signal and voltage AC signal at different frequency. The solid lines in the graphs are the fitting curve from the model described in Equations (5.1) to (5.3).
fit to the SHG data shows that the dynamics of the trapped carrier can be modeled as RC circuit over a large frequency range, where the resistor mimics the carrier trapping effect in the depletion region.