Mobility diminution in a nano-MOSFET due to carrier injection from the ohmic contacts

Ballistic transport is collision-free carriers drift in a conducting channel whose ballistic length LB is smaller than the scattering-limited mean free path ℓB. In such channels, the probability of scattering is still finite. The probability that a carrier after being injected from the Ohmic contacts will undergo collision in traversing a ballistic length LB is exp (−LB /ℓB. The probability that it will go ballistic (collision-free) is (1- exp (−LB/ ℓB)). This modifies the traditional long-channel mobility µ∞ to a size-limited mobility µL given by [1] µL = µ∞[1- exp(−LB / ℓB)] The ballistic mean free path ℓ differs from the channel mean free path ℓ∞ as contacts play a predominant role in the ballistic transport. The carriers are injected from the metallic contacts at a Fermi velocity νF for which the probability of tunnelling through the metal-semiconductor contact is the highest. This Fermi velocity is 2.0 × 10⁶ m/s for the Fermi energy of 11.6 eV for an Al contact [2]. With this injection velocity νinj the ballistic mean free path is given by ℓB = ℓ∞ (νinj/ νm) where νm is the mobility velocity appropriate to 2-D electron gas [3]. ℓB > ℓ∞ was identified in the experiments of Luskawoski et. al [4]. A pocket mean free path ℓP was added to ℓ∞ to get a ballistic mean free path ℓB =ℓ℞ +ࡁP that is not consistent with the scattering theory for two reasons. Firstly, mean free paths from two distinct regions cannot be combined. Secondly, the inverse mean free paths are normally combined as ℓB⁻¹ = ℓ∞⁻¹ + ℓP ⁻¹