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

Summary form only given. Ballistic transport is collision-free carriers drift in a conducting channel whose ballistic length L B is smaller than the scattering-limited mean free path ℓ B . 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 L B is exp(-L B / ℓ B ). The probability that it will go ballistic (collision-free) is (1-exp (-L B I ℓ B ). This modifies the traditional long-channel mobility μ ∞ to a size-limited mobility μ L given by μ L = μ ∞ [1-exp(-L B /ℓ B )] (1). The ballistic mean free path I B 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 v F for which the probability of tunnelling through the metal-semiconductor contact is the highest. This Fermi velocity is 2.0 × 10 6 m/s for the Fermi energy of 11.6 eV for an Al contact. With this injection velocity v inj the ballistic mean free path is given by ℓ B = ℓ ∞ (ν inj / v m ) (2) where v m is the mobility velocity appropriate to 2-D electron gas. ℓ B >; ℓ ∞ was identified in the experiments of Luskawoski et. al. A pocket mean free path ℓ p was added to ℓ ∞ to get a ballistic mean free path ℓ B = ℓ ∞ + ℓ P 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 ℓ B -1 = ℓ ∞ -1 + ℓ p -1 . The ballistic length L B through which the an injected carrier travels is sum of the channel region and contact region (L B = L + L con ) . The metal contact can be separated by more than 10 nm from the channel region (L con ≈ 10nm). Since the information about the contacts is not available in the published papers, L con is neglected making L B ≈ L . Fig. 1 shows the comparison of Eq. (1) to the experimental data discussed in. In The ballistic mean free path to fit the ballistic mobility data was found to be much larger than extracted from long-channel mobility, consistent with Eq. (2). When corrected for the intrinsic velocity v inj for arbitrary degeneracy in the channel and injection velocity v from the contacts, the application of Matthiessen-like rule modifies the expression for μ L given by Shur that is given by μ L /μ ∞ =1(1 + (ℓ B /L)) (3) The mobility degradation towards falling channe