Channel Length and Series Resistance

Many of the models used to describe the drain current for a MOSFET are some- what simplified. For example, two assumptions that are frequently made are that there is no deviation from the mask-designed gate length and that the parasitic resistances associated with the source and drain contact regions can be neglected. Of course, in

(a)

(b)

Figure 3.4: Example of DIBL extraction for a Si pMOSFET (a) with and (b) without the effects of punchthrough.

practice, neither is true, and it is important that both the change from the mask-designed channel length,∆L, and the series resistance,R_sd are determined, such that the effec- tive carrier mobility can be compared accurately between devices. Such corrections are particularly important for gate lengths below a few microns, when these effects become increasingly significant.

There are several reasons why the effective channel length,L_eff, of a MOSFET can differ from the mask-defined gate length,L. Dopants from the source/drain regions can extend underneath the gate stack, either from the initial ion implantation step to form the source/drain regions, or by diffusion during subsequent annealing steps in the process. In addition, fringing effects of the electric field at the end of the gate electrode result in non-vertical electric fields at the end of the channel. Further differences can arise from lithographic errors and the ambiguity in definingexactly where the channel starts and ends can. Finally, the effective channel length can also depend on the bias conditions of the MOSFET. The effective channel length is related to the gate length by:

Lef f =L−∆L (3.9)

In a real MOSFET, since the resistance of the source and drain contact regions is not negligible, some of the applied voltage,Vds, is dropped across these resistances. This so-calledseries resistance can then lead to a lower than expected value of the drain current.

There are several contributions to the series resistance of a MOSFET [Schroder, 2006]. The most important contribution to the series resistance is the resistance of the heavily doped source and drain regions underneath the metal contacts. This is strongly dependent upon the doping dose and activation anneal temperature, with the resistance usually decreasing as both of these factors are increased. Where an extension implant

is used, this will add significantly to the total resistance. The second most important contribution is the ‘spreading resistance’ where carriers travel from the heavily doped semiconductor regions, which are typically tens of nanometres thick, into an inversion layer, just a few nanometres thick. In addition, there will also be a resistance associated with the source and drain contact pads, although since these are usually made of metal, this component is negligibly small. However, the Schottky barrier between the metal contact pad and the heavily doped semiconductor surface will have a resistance, but this is likely to be small since the depletion layer formed will be very narrow, and carriers will tunnel through easily.

As a result, the potential difference along the channel is usually modified to include the effects of these resistances according to:

V_ds0 =Vds−IdsRsd (3.10)

whereRsd is the combined series resistance of the source and drain regions.

3.3.4.1 Linear Regression of Resistance versus Channel Length

The drain current,I_ds, of a MOSFET operating in the linear regime, taking into account the effects of series resistance and deviations to the channel length, can be expressed as:

I_ds =Q_invµ_{ef f}V_ds0 W Lef f

(3.11) The measured resistance of a device,Rm, is given by [Chern et al., 1980]:

R_m = Vds Ids

=R_channel+R_sd (3.12)

Figure 3.5: Example of series resistance and effective length extraction using the 1st regression method for bulk silicon MOSFETs.

R_channel= Vds0

Ids

(3.13) Combining equations 3.11, 3.12 and 3.13, the measured resistance of the device is given by:

Rm= _{W µ}L−∆L ef fQinv

+R_sd (3.14)

where the effective gate length,L_eff has been written as L−∆L.

Equation 3.14 suggests that plotting Rm versus L for different values of gate overdrive should produce a series of straight lines that should meet at the point where

L=∆Land Rm =Rsd. An example of this is shown in Figure 3.5 for Si pMOSFETs investigated in the present work..

Despite the technique being favoured for its simplicity, it is possible to extract inaccurate values ofRsd and∆L. The main error is due to the difficulty of accurately defining a point where all of the lines meet. In such a case, this usually indicates thatR_sd

and∆L vary with gate overdrive, when the technique assumes they do not. Secondly, since the resistance of all devices must be measured at the same gate overdrive, the

threshold voltage must be extracted using a technique that accurately compares both long and short devices. Finally, there is also some ambiguity in choosing which devices to use in the method. Large devices can have a large leverage on the gradient of the regression line and can introduce large errors in ∆L. However, it has been reported by some authors that the measured resistance is lower than expected for the shortest devices, causing the straight lines to deviate from linearity. Usually, the technique works best for devices withL≤ 1 - 2µm.

3.3.4.2 Double Regression Method

Terada and Muta [1979] proposed an alternative method to extractR_sd and∆L

based on the linearity betweenRm andL. Writing equation 3.14 in the form:

Rm =AL+Rsd−A∆L;A= _{W µ} 1

ef fqNs (3.15)

For a given value of Vgt, a plot of Rm versus L will have a gradient of A and an intercept of R_sd −A∆L. If the slope and the intercept are determined from the linear regression and plotted against each other for different values of Vgt, then this should produce another straight line with a gradient of−∆L and an intercept ofRsd, which can be determined from a second regression. Whilst this technique overcomes the problem of finding a suitable intercept using the first regression method, it suffers from many of the same problems. For example, if R_sd and ∆L are functions of Vgt, then the second regression may not produce a straight line.