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 × 10⁶ 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 canno- - t 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 channel length is steeper as predicted from Eq. (1) than that predicted from Eq. (3) showing the importance of the injection velocity from the contacts in ballistic transport.