Hopping Conduction Observed in Thermal Admittance Spectroscopy

We observe variable-range hopping conduction in thermal admittance spectroscopy and develop a method to evaluate the signal under this condition. As a relevant example of demonstration we employ $\mathrm{Cu}(\mathrm{In},\mathrm{Ga})(\mathrm{Se},\mathrm{S}{)}_2$ thin-film solar cells and show that the fundamental $N1$ signal, which has been discussed for more than a decade in terms of minority carrier traps, does not display trap parameters, but is generated by the freezing-out of carrier mobility with decreasing temperature when hopping conduction prevails. This effect offers a new approach to carrier hopping and to semiconductors suffering from small mobility.

Figure 1

Conductance (a) and capacitance spectra (b) of a CIGS thin-film solar cell as a function of temperature and frequency. For clarity, only 8 out of 32 measured curves are displayed.

Figure 2

(a) Standard evaluation of the trap response obtained from Fig. 1a gives the known curved line. A linear fit over the complete temperature range gives an activation energy of 42 meV. (b) The evaluation in terms of mobility freeze-out under VRH conduction shows a clear linear behavior. Only $G(\omega )$-maxima below 150 K were used for the linear fit, to avoid the influence of a transition region in the conduction mechanism. The evaluation of total freeze-out ($\omega \mathrm{CR}=1$) for $G(\omega )$ peaks at $T<55\mathrm{K}$ [see inset if Fig. 1a] according to VRH conduction gives a parallel line.

Figure 3

Measured serial conductance as a function of frequency at $T=34\mathrm{K}$. The fit confirms a power law $G(\omega )=A{\omega }^s$ as expected in the case of hopping conduction and yields $G^{-1}(f=1\mathrm{MHz})=5\Omega {\mathrm{cm}}^2$ which is small compared to the dc resistance $R_A>11\mathrm{k}\Omega {\mathrm{cm}}^2$ as deduced from $IV$ measurements.