Quantitative Analysis of the Density of Trap States in Semiconductors by Electrical Transport Measurements on Low-Voltage Field-Effect Transistors

A method for extracting the density and energetic distribution of the trap states in the semiconductor of a field-effect transistor from its measured transfer characteristics is investigated. The method is based on an established extraction scheme [M. Grünewald et al., Phys. Stat. Sol. B 100, K139 (1980)] and extends it to low-voltage thin-film transistors (TFTs). In order to demonstrate the significance of this extension, two types of TFTs are fabricated and analyzed: one with a thick gate dielectric and high operating voltage and one with a thin gate dielectric and low operating voltage. From the measured transfer characteristics of both TFTs, the density of states (DOS) is calculated using both the original and the extended Grünewald method. The results not only confirm the validity of the original Grünewald method for high-voltage transistors, but also indicate the need for the extended Grünewald method for the reliable extraction of the trap DOS in transistors with a thin gate dielectric and low operating voltage.

Figure 1

Schematic cross section of the thin-film transistors with the thin gate dielectric, which consists of a 3.6-nm-thick layer of aluminum oxide (${\mathrm{Al}\mathrm{O}}_X$) and a 1.7-nm-thick self-assembled monolayer (SAM) of n-tetradecylphosphonic acid. The chemical structures of n-tetradecylphosphonic acid and of the organic semiconductor 2,9-diphenyl-dinaphtho[2,3-b:$2^{\prime }$,$3^{\prime }$-f]-thieno[3,2-b]thiophene (DPh-DNTT) are also shown.

Figure 2

Transfer curves measured on DPh-DNTT TFTs with a 110-nm-thick gate dielectric (a) and a 5.3-nm-thick gate dielectric (b). The transfer curves are measured in the linear regime of operation. From the transfer curves, the turn-on voltage $V_{\mathrm{on}}$ is extracted and taken as the flat-band voltage $V_{\mathrm{FB}}$. The effective carrier mobility ${\mu }_{\mathrm{eff}}$ is calculated using Eq. (1) and plotted as a function of gate-source voltage; from this plot, the gate-source voltage at which the mobility saturates is obtained and taken as the gate-source voltage at which $E_F=E_V$, with $E_F$ being the Fermi energy and $E_V$ the valence-band energy. The subthreshold slope S is calculated using Eq. (2).

Figure 3

Schematic cross section of a field-effect transistor showing the relevant energy levels. (a) Initial band bending in the semiconductor in the absence of an applied gate-source voltage. (b) The flat-band voltage $V_{\mathrm{FB}}$ is the gate-source voltage necessary to compensate this initial band bending. (c) Applying a gate-source voltage greater than the flat-band voltage ($V_G=V_{\mathrm{GS}}-V_{\mathrm{FB}}$) induces a band bending in the semiconductor that leads to charge accumulation in the semiconductor in close proximity to the semiconductor/dielectric interface. At this interface, the bands of the semiconductor are shifted by an energy $e{V}_0$, with $V_0$ being the interface potential. $E_C$ and $E_V$ are the conduction- and valence-band energies.

Figure 4

Sketch of the potential drop across the gate dielectric and the semiconductor layer of the transistor. In the original Grünewald method, it is assumed that $|V_0|\ll |V_{\mathrm{GS}}|$ and, hence, $V_0$ is ignored. In the extended Grünewald method proposed here, this simplification is removed, and the contribution of $V_0$ is correctly taken into account.

Figure 5

Results of the first step of the Grünewald method in which the relation between the interface potential and the gate-source voltage is calculated from the measured transfer curves. This calculation is performed once using Eq. (7) (original method, shown with black lines) and once using Eq. (14) (extended method, shown with red lines). (a) For the TFT with the thick gate dielectric, the results show that the simplification in the original Grünewald method is indeed justified. (b) For the TFT with the thin gate dielectric, the original differential equation (7) and the extended differential equation (14) produce notably different results, because the magnitude of the gate-source voltage is, in this case, comparable to the magnitude of the interface potential $V_0$ (a few hundred millivolts), so that the latter can no longer be ignored without introducing a significant error.

Figure 6

Results of the second step of the Grünewald method in which the relation between the carrier density and the interface potential is calculated. This calculation is performed once using Eq. (9) (original method, shown with black lines) and once using Eq. (15) (extended method, shown with red lines).

Figure 7

Results of the final steps of the Grünewald method. Using Eq. (10), the trap DOS is calculated, yielding the DOS as a function of $E_F+e{V}_0$, which is then converted into the DOS as a function of $E-E_V$ by taking the gate-source voltage at which the carrier mobility saturates (see Fig. 2) as the gate-source voltage at which the Fermi level crosses the transport level $E_V$. The DOS is calculated once using the results from Eq. (9) (original method, shown with black lines) and once using the results from Eq. (15) (extended method, shown with red lines). (a) For the TFT with the thick gate dielectric, the results show that the simplification in the original Grünewald method does not affect the calculated trap DOS and is thus justified. (b) For the TFT with the thin gate dielectric, the trap DOS functions obtained with and without the simplification deviate substantially, as the original Grünewald method significantly overestimates the trap DOS in this case.

Figure 8

Ratio between the channel-width-normalized contact resistance ($R_C\cdot W$) and the channel-width-normalized total device resistance ($R\cdot W$) for TFTs with a channel length of 100 $\mu \mathrm{m}$, measured using the transmission line method (TLM) and plotted as a function of the difference between the gate-source voltage and the threshold voltage. For both types of TFT (thick and thin gate dielectrics), the contact resistance is small compared to the total resistance.