Carrier velocity saturation

Cryoelectronics. Operation of CMOS devices at lower temperatures offers several advantages and some disadvantages (53). Operation at Hquid nitrogen temperatures (77 K) has been shown to double the performance of CMOS logic circuits (54). In part, this is the result of the increase in electron and hole mobilities with lower temperatures. The mobiHty decreases at high fields as carrier speeds approach saturation. Velocity saturation is more important for cryoelectronics because saturation velocities increase by only 25% at 77 K but saturation occurs at much lower fields. Although speedup can... 

The Johnsonfigure of merit, based on saturated carrier velocity and dielectric strength (product of power x frequency squared x impedance), predicts the suitability of a material for high power applications. It is normalized with the value of one given to silicon. As shown in Table 13.2 below, diamond is clearly the preferred material on this basis. 

The high-field saturation of the carrier velocity can have various origins, e.g. a finite bandwidth of a non-parabolic transporting (here valence) bands, or the emission of optical phonons. It is believed that the high-field saturation of the drift carrier velocity in the crystal directions where the band model concept can be applied is due to the first one. Then [420],... 

Soon after, photoconductivity experiments were interpreted totally differently. It was proposed that electrons have in fact very high low-field mobilities, on the order of 104 cm2/V s or more, their velocity saturating at the sound velocity as field is increased above a value of a few V/cm. The moving carriers were supposed to be polarons dressed with acoustic phonons [218,219]. This has not generally been accepted nor conclusively disproved. However, space-charge injection current experiments yielded electron mobilities on the order of 6 x 103 cm2V s [220]. 

Fig. 6.1. A schematic showing the structure and regions of operation of a NMOS c-Si FET. The voltages shown are for illustration only. When Vas exceeds the threshold voltage and Vds is small the channel is inverted at both sides with approximately the same Q and the device behaves as a resistor. When a substantial Vns is applied, the field induced by the gate is partially canceled on the drain end. When the potential at the drain end drops below Vr, Q 0 and the carrier velocity increases to compensate, which leads to pinch-off and a saturation of the transistor characteristic. The carriers are all physically located very close to the gate dielectric interface, the triangle is illustrating that the carrier density is not constant. Since the current flow is constant across the length of the channel, the velocity and lateral field in saturation are not uniform.

Saturated velocities Maximum carrier velocity induced by electric field (due to onset of inelastic scattering). 

Diamond has an excellent electron-carrier mobility exceeded only by germanium in the p-type and by gallium arsenide in the n-type. The saturated carrier velocity, that is, the velocity at which electrons move in high electric fields, is higher than silicon, gallium arsenide, or silicon carbide and, unlike other semiconductors, this velocity maintains its high rate in high-intensity fields as shown in Fig. 11.15. 

In summary it appears fair to conclude that there is no need to invoke a mobility greater than about 100 cm (Vs) "l for carrier transport along a defect-free PDA chain, compatible with optic po-laron transport, yet experiments available to date cannot rule out existence of an ultra-high mobility either. The experiment that clarifies whether or not the drift velocity of a free carrier is saturated with field as predicted by the acoustic polaron model (54,59) needs still to be done. If performed in the time domain it requires ps-photoconduction work under conditions where the transit time of a carrier along an individual chain exceeds the response time of the circuit. Experiments done on a ns-time scale will always reveal barrier- or trap-controlled transport with pronounced ID-features. High frequency ac-photoconduction studies would be extremely useful to answer the fundamental question about the nature of the transport process of an excess carrier on a conjugated perfect ID chain. 

The low field nobility of a charge carrier on a polydiacetylene chain is ultra high, and yet the drift velocity saturates at a low vaiue comparable to the sound velocity Conventional ideas applicable to conventional semiconductors cannot eiqplain these phenomena The motion is that of a Solitary Wave Acoustic Polaron (SWAP) The SWAP is characteristic of a one dimensional system The properties of the SWAP are described ... 

Figure 41-11. A comparison of the kinetics of carrier-mediated (facilitated) diffusion with passive diffusion. The rate of movement in the latter is directly proportionate to solute concentration, whereas the process is saturable when carriers are involved. The concentration at half-maximal velocity is equal to the binding constant (KJ of the carrier for the solute. maximal rate.)...

When a saturable transporter is involved in the permeation process, the permeability is no longer a constant value but is dependent on the concentration of the substrate. In that case it is necessary to characterize the parameters of the carrier-mediated process, Km, the Michaelis-Menten constant related with the affinity by the substrate and Vmax, the maximal velocity of transport. If a passive diffusion process occurs simultaneously to the active transport pathway then it is necessary to evaluate the contribution of each transport mechanism. An example of how to characterize the parameters in two experimental systems and how to correlate them are described in the next section. 

FIGURE 9.5 Graph showing initial velocity of transport processes across lipid membranes. Passive diffusion (compound dissolves directly into lipid membrane) is driven by a concentration gradient and is not saturable. In contrast, carrier-mediated transport is saturable, reaching a maximal rate when the carrier molecules are saturated with substrate. Transport proteins mediate these processes. 

Sze, S. M., Physics of semiconductor devices, 2nd ed., John Wiley, New York, 1981. Karl, N. et al.. High-field saturation of charge carrier drift velocities in ultrapurified organic photoconductors, Synth. Metal, 42, 2473, 1991. 

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