Thin-film transistor operation: parameter calculation

It is common practice to develop 'figures of merit' which allow comparison between different materials, devices, and technologies. Electrical characterization of a TFT device includes the measurement of its transfer and output characteristics which are used to calculate some key device parameters. Transfer characteristics are graphical representation of drain current against gate voltage while output characteristics represent drain current as a function of drain voltage. Figure 3.6 shows an ideal form of these characteristics calculated using Equation 3.19.

Important parameters that can be obtained are (i) threshold voltage VT, (ii) switch on voltage Von, (iii) ratio of on current to off current (Ion/Ioff), (iv) subthreshold slope/swing SS, and the most important (v) the charge carrier mobility, μ. Following is a brief overview of these key parameters.

Figure 3.6: (a) The transfer characteristics of an ideal TFT calculated using gradual channel approximation (Equation 3.19). It shows how the VT and Von can be found out using ID and square root of ID. (b) The output characteristics of an ideal device showing linear and saturation regimes for several gate voltages. The output is approximately linear for low VD but beyond the pinch-off point (indicated by the thin line) the device saturates.

THE THRESHOLD VOLTAGE (VT)

For a conventional MOSFET, there is a physical meaning for VT. It is the gate voltage marking the transition between weak inversion and strong inversion. Since there is no such identified mechanism in a TFT, Von is sometimes preferred over VT. Von is the gate voltage at which conduction in the channel begins to increase

(a)

V

L og(I

)

V

(I

) ⅟² I

V

V

V

> V

Off

On

V

saturation Linear

(b)

and can easily be determined from the transfer curve where ID starts to rise exponentially, above the noise floor/leakage current as shown in the Figure 3.6(a).

ON-OFF RATIO (Ion/Ioff)

Another performance metric is the Ion/Ioff ratio discussed earlier. The higher the ratio the better is the switching capability of the TFT. The latter can be assessed from the transfer curve with VG swept through an appropriate voltage range. The off current translates into how much power is lost when the device is off so an extremely low value is desirable. The off current is determined from one or more current leakage mechanisms such as gate dielectric leakage and source-drain leakage. These currents depend upon the size of the device and therefore can be effectively minimised by the channel dimensions and also with efficient patterning of the semiconductor. The on current indicates the maximum current that the device can drive and is determined by the charge carrier mobility and device dimensions.

SUBTHRESHOLD SWING (SS)

In the subthreshold region of operation i.e. below VT, a TFT is in a switching transition from off to on and ID changes exponentially from a low off current (10^-12–10^-8A) to a high on current. For VG < VT, most of the induced charge goes into deep states in the semiconductor bandgap and semiconductor insulator interface so only a small number of electrons participate in conduction. As VG

increases, a higher density of electrons leads to an exponential increase of current until switch on is achieved. This operating regime is characterised by a subthreshold slope, S, defined as the gate voltage required to increase the drain current by an order of magnitude. Inverse of this slope is termed as the subthreshold swing (SS). The latter can be extracted from the TFT transfer characteristics in subthreshold regime using the following equation:





G

I S V



  3. 22

A small value of S indicates the speediness of the device in changing between off and on states and how efficiently the conduction channel is formed. It is therefore a very important figure of merit for comparing different TFTs.

MOBILITY (μ)

Channel mobility, μ, is a critical parameter for all TFTs. It determines TFT performance in terms of current drive and frequency response and it is discussed in detail by Hoffman (47). Details relevant to the present work are presented here briefly.

Mobilities in linear and saturation regimes can easily be calculated by differentiating Equation 3.19, for the linear and the saturation regimes. In the linear regime, mobility is given as:



while in saturation regime, the mobility is:

2

It is common practice, and also evident from Equation 3.24, that plotting I_DSAT against VG results in a straight line. The slope when squared yields the saturation mobility while the x- intercept with the VG axis gives VT.

These methods for calculating mobility are commonly employed but are subjected to errors when mobility is gate voltage dependent. This dependence is due to interface roughness scattering, velocity saturation, electron trapping etc. It has led to the definition of several different kinds of mobilities, which are distinguished by the procedure employed for their estimation from measured data.

One of them is the average mobility, μAVE, extracted from the channel conductance measured in the linear regime of operation and physically corresponds to the average mobility of all carriers in the channel whether above or below VT. The defining relation for average mobility is given by Equation 3.25:

.

It is nearly identical to the commonly used expression of effective mobility μEFF, in MOSFET. The primary difference is the use of Von in the place of VT. In the case of multiple trapping and release models (3.3.3) this gives a physically

meaningful gate voltage dependent mobility since it is the average over both trapped and free carriers.

3.4.4 The role of dielectric-semiconductor interface in thin-film