Threshold voltage does not depend on the size of the transistor. It is related to physical parameters. Lets say, gate metal workfunction and substrate implantation. You can find the theory in many books: Pierret, Sze, etc. 

Santiago Sir  i know its dependency on physical parameters but somewhere iread that with length increement it increases and with width increement it decreases,but i dont know from where it comes. And in question also they ask about dependancy on size only.

Hi, hope this french file will help you, It contains the direct relations between physical components sizes of CMOS and the threshold voltage :)

Hi,

in fact the threshold voltage in advanced CMOS is a quite complicated function of both W and L.

In traditional CMOS (say, 0.5um CMOS and earlier), there were manlyi two effects: a roll-off of VT with decreasing L (referred to as short-channel effect), and a roll-up of VT with decreasing W (referred to as narrow-channel effect).

With CMOS technologies using pocket/halo implants near source and drain to mitigate short-channel effects, channel doping is non-uniform along the channel (high close to source and drain, and low at channel center). When using shorter channel lengths, the center part (low doped) is smaller, and hence the average channel doping higher -- hence an increase in VT when reducing channel lengths, called reverse short-channel effect (RSCE).  At very short-channel devices, again the traditional roll-off of VT occurs since the short-channel effect is still there. Typically a peak occurs, at a channel length typically about 1.5*Lmin, which can be about 50-100mV above the VT of shortest channel, then drops off towards longer channel length. This is all very much technology-dependent, and no general rule or equation applies to all cases.

Comparable effects occur at narrow-channel (narrow-channel effect and inverse narrow width effect (INWE). The picture is more complicated for combined short- and narrow-channel devices (small devices), where these effects compete one against the other. Devices from CMOS technologies below 100nm typically also show an important VT dependence on device layout details (due e.g. to stress effects), which further complicates the picture.

Usually, engineers will use a compact MOSFET model (say EKV3, BSIM6, PSP, HiSim,...) to describe this. Equations are available from the compact modeling groups, while semiconductor vendors have libraries with model parameters of their devices in PDKs (process design kits).

Hi Ritika Khurana

I have verified a greater influence of L on VTH than compared to the effects of W.

The impact of L on the value of VTH can be explained by the reverse short channel effects (Y. Tsividis book). For the new technologies, the curve VTH versus L seems to be like the figure 3 of the attached paper. It seems a exponential decay curve. This simulation was done using 130 nm CMOS process, although I also simulated it with other short channel technologies.

W/L ratio is the most important parameter of the inverter .inverter channel & flow of current and all parameters of CMOS /NMOS are effected . It is well known that VTH variability is inversely proportional to the transistor area. Therefore, when designing the transistor channel length, the straightforward choice is to use large values of L . However, for advanced technologies with very short-channels, VTH is a function of L and thus, the output voltage of VTH-based references also becomes a function of L. if increase in VTH with decreasing L is called reverse short channel effect.

Approximately, dependency of the threshold voltage to the ratio of w/l is neglected. Because it is too complicated.

Threshold voltage of a transistor is influenced by its size due to INWE. Consequently, a narrow width device tends to have lower threshold voltage as compared to wide devices. Threshold voltage also depends on the length of the device due to pocket implants and drain induced barrier lowering. Consequently, threshold voltage may demonstrate a hook shaped characteristics with change in channel length. However, this answer covers only limited source of threshold voltage variation with transistor size. Actually, size dependence of threshold voltage depends on process node also. You need to understand the particular process that you intend to use.

The threshold voltage is lowered due length decrease to a submicrometer size.

Also the width shrinkage causes change in the threshold voltage. This is due to charge sharing phenomenon and induced barrier lowering.

The effect of the the shrinking the size of the transistor on the threshold voltage was treated intensively in the .literature both theoretically and experimentally.

Even the effect of Vth lowering with reduced channel length is included in the text books of the MOS devices.

Best wishes

By decreasing the length and width of transistor, threshold voltage increases.

Devices with small geometry have higher drain current at same Vgs hence short channel device has lower threshold voltage.