tesi R. Miscioscia.pdf - EleA@UniSA

12 Working Principles
In figure 1, we named tch the channel thickness, tox the
insulator thickness, VGS the gate to source voltage, V(x) the
voltage along the channel starting from the source’s position.
hp. 2) Source and drain are considered as metal-semiconductor
contacts having an ohmic behavior. In this case, their electrical
resistance is hypothesized to be constant with the applied voltage.
For a contact between a metal and a n-type semiconductor this
basic condition is reached when the energetic barrier φB from
metal work-function φM to semiconductor material electron
affinity χS is zero or negative being φB = φM - χS where φM is
evaluated as the difference between the vacuum level (E0) and the
Fermi level (EF) in the metal and χS is the difference between E0
and the conduction band level in the semiconductor EC.
More precisely,
φM ≡ E0 - EF(Metal)
χS ≡ E0 - EF(Semiconductor)
for a metal/(n-type semiconductor) junction the barrier is:
φB = φM - χS
and for a metal/(p-type semiconductor) junction:
φB = (EG + χS) - φM
Being EG = EC - EV the semiconductor’s band-gap. In this case the
barrier is the distance of the metal’s Fermi level from valence
band of the semiconductor.
hp. 3) Carrier diffusion effects are neglected and, for the matter of
simplicity, n-type conduction hypothesized neglecting p-type
carrier concentrations and currents. Once neglected diffusion
currents, just the drift contribution jt to current density will be
considered.