VS .NET Code-128 Page 96 Friday, January 18, 2002 9:00 AM in .NET Encoding UPC-13 in .NET Page 96 Friday, January 18, 2002 9:00 AM Page 96 Friday, January 18, 2002 9:00 AM using barcode implementation for none control to generate, create none image in none applications.code 128 generation c# THE DEVICES Code128 3 . always stand for the e none for none ffective dimensions, while a d subscript will be used to indicate the drawn size. The following expressions related the two parameters, with W and L parameters of the manufacturing process: W = W d W L = L d L (3.27).

The Saturation Region As the value of the drain-source voltage is further increased, the assumption that the channel voltage is larger than the threshold all along the channel ceases to hold. This happens when VGS V(x) < VT. At that point, the induced charge is zero, and the conducting channel disappears or is pinched off.

This is illustrated in Figure 3.16, which shows (in an. VGS VDS > VGS VT S n+ VGS - VT NMOS transistor under pinch-off conditions. exaggerated fashion) h none none ow the channel thickness gradually is reduced from source to drain until pinch-off occurs. No channel exists in the vicinity of the drain region. Obviously, for this phenomenon to occur, it is essential that the pinch-off condition be met at the drain region, or VGS VDS VT.

(3.28). Under those circumstan ces, the transistor is in the saturation region, and Eq. (3.25) no longer holds.

The voltage difference over the induced channel (from the pinch-off point to the source) remains fixed at VGS VT, and consequently, the current remains constant (or saturates). Replacing VDS by VGS VT in Eq. (3.

25) yields the drain current for the saturation mode. It is worth observing that, to a first agree, the current is no longer a function of VDS. Notice also the squared dependency of the drain current with respect to the control voltage VGS.

k" n ID = ----- W ( V GS V T ) 2 - ---2 L (3.29). Page 97 Friday, January 18, 2002 9:00 AM Section 3.3 The MOS(FET) Transistor Channel-Length Modulat ion The latter equation seems to suggest that the transistor in the saturation mode acts as a perfect current source or that the current between drain and source terminal is a constant, independent of the applied voltage over the terminals. This not entirely correct. The effective length of the conductive channel is actually modulated by the applied VDS: increasing VDS causes the depletion region at the drain junction to grow, reducing the length of the effective channel.

As can be observed from Eq. (3.29), the current increases when the length factor L is decreased.

A more accurate description of the current of the MOS transistor is therefore given in Eq. (3.30).

I D = I D ( 1 + V DS ) (3.30). with ID the current e none for none xpressions derived earlier, and an empirical parameter, called the channel-length modulation. Analytical expressions for have proven to be complex and inaccurate. varies roughly with the inverse of the channel length.

In shorter transistors, the drain-junction depletion region presents a larger fraction of the channel, and the channel-modulation effect is more pronounced. It is therefore advisable to resort to long-channel transistors if a high-impedance current source is needed. Velocity Saturation The behavior of transistors with very short channel lengths (called short-channel devices) deviates considerably from the resistive and saturated models, presented in the previous paragraphs.

The main culprit for this deficiency is the velocity saturation effect. Eq. (3.

23) states that the velocity of the carriers is proportional to the electrical field, independent of the value of that field. In other words, the carrier mobility is a constant. However, at high field strengths, the carriers fail to follow this linear model.

In fact, when the electrical field along the channel reaches a critical value c, the velocity of the carriers tends to saturate due to scattering effects (collisions suffered by the carriers). This is illustrated in Figure 3.17.

. sat = 105 n (m/s) Co nstant velocity Constant mobility (slope = ) Figure 3.17 c = 1.5 (V/ m) Velocity-saturation effect.

. For p-type silicon, th none none e critical field at which electron saturation occurs is around 1.5 106 V/m (or 1.5 V/ m), and the saturation velocity sat approximately equals 105 m/s.

This means that in an NMOS device with a channel length of 1 m, only a couple of volts between drain and source are needed to reach the saturation point. This condition is easily met in current short-channel devices. Holes in a n-type silicon saturate at the same velocity, although a higher electrical field is needed to achieve saturation.

Velocity-saturation effects are hence less pronounced in PMOS transistors..
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