Short Channel and Nonideal Effects in MOSFETs

For long channel devices, the drain current becomes constant in saturation, whereas, for short channel devices, the drain current increases continuously with the drain-to-source voltage.

Fig.5.15 I-V characteristics of two n-channel MOSFETs: (i) L = 0.5 (dashed lines), and (ii) L = 0.75 (solid lines).

Fig.5.16 The variation of the threshold voltage with the effective channel length.
Another interesting feature seen in short channel devices is that the saturation current increases as the device length is reduced.
Now, based on the existing model for the threshold voltage, which states that it is independent of the device length this behavior cannot be explained.
In reality, it has been shown that the threshold voltage is a strong function of the channel length (for short channel devices), and it actually decreases with a decrease in the channel length, which explains the reason behind the larger saturation current.

The Charge Sharing Model

The reduction of the threshold voltage with a reduction in the channel length can be explained by the charge sharing model.

Fig.5.17 The depletion charge profiles for (a) a long channel device, and (b) a short channel device.
For a long channel device, the depletion layer thickness at the source end of the channel and at the drain end of the channel are much less than the channel length L, and, thus, the depletion charge enclosed by these sections are much smaller than the total depletion charge under the gate.
However, for a short channel device, the widths of these depletion regions are a non-negligible fraction of the total depletion charge under the gate.
Note: essentially, the depletion regions near the source and the drain are contributed by the source-substrate and the drain-substrate bias, and gate has no role to play.
Under an applied drain-source bias, the depletion region thickness near the drain will obviously be larger than that at the source side.
The net effect is that the gate now has to compensate for a lower depletion charge density than that for a long channel device, which qualitatively explains the reduction of the threshold voltage with a reduction in the channel length.
The exact analysis of the charge sharing effects requires a two-dimensional analysis, however, to the first order, it is assumed that the effect of the depletion width at the drain side of the channel is to reduce the effective channel length in the saturation region from L to where
Here, is the effective channel length, and the voltage dropped along this section is assumed to be equal to the drain saturation voltage , and is length of the pinched-off portion of the channel (related to the drain depletion width), where the excess drain voltage beyond , i.e., is dropped, where is the applied drain voltage.
With an increase in the length of the pinch-off region also increases, leading to a reduction in the effective channel length .
This effect is called the channel length modulation effect, and this effect leads to a higher drain saturation current, and finite output conductance in the saturation region.
A very crude estimate of the pinch-off length (also referred to as the drain region length) can be obtained from the solution of the one-dimensional Poisson's equation:
A more accurate and realistic expression for may be obtained by assuming that the electrons are injected from the inversion layer into the drain depletion region, and they spread uniformly, leading to the current density
Here, is the diffusion depth of the drain region, and is the thickness of the inversion layer
It is also assumed that the velocity of electrons in this region is saturated, thus their volume density can be given by
Now, the one-dimensional Poisson's equation can be rewritten as:
The solution of this equation leads to the following complicated expression for :
For gate lengths larger than or about 1 , and drain-to-source voltages smaller than or about 10 V, this expression may be simplified to give
In short channel devices, the depletion charge under the channel [dependent on the channel potential and has been represented by the second term within the brackets in the right-hand side of Eq.(5.7)], which has been neglected in the charge control model [Eq.(5.19)], has to be accounted for.
This effect may be taken into account by introducing an additional parameter a into the equations of the charge control model, with the resulting equations given by
Linear Region
Saturation Region
For Si, the (empirical and fitting) parameter a describes the influence of the bulk substrate depletion layer on the device characteristics, and can be approximated by the following expression
The threshold voltage and the parameter K can be determined from the experimentally measured data for a given device.
In addition, the dependence of electron mobility on the longitudinal and transverse electric field in the channel should be included for a more realistic device modeling, however, this simple empirical model gives adequately good fit with the measured data.

Fig.5.18 The measured and calculated I-V characteristics for a Si n-channel MOSFET.