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MOS Fundamentals. Introduction. Ideal Structure. Ideal Structure – Assumptions. = Φsc. Ideal Structure – Energy Band Diagram. E 0 is the energy of an electron at rest in vacuum is called the electron affinity: it is equal to E 0 – E c F s is the workfunction of the semiconductor
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Ideal Structure – Energy Band Diagram • E0 is the energy of an electron at rest in vacuum • is called the electron affinity: it is equal to E0 – Ec • Fs is the workfunction of the semiconductor • FM is the workfunction of the metal
Ideal Structure – Energy Band Diagram Are there any charges anywhere inside the ideal MOS structure under equilibrium conditions? What would the charge density plot look like for the above band diagram?
Ideal Structure – Charge Density What is the electric field inside the metal? How about inside the semiconductor far from the oxide interface?
Ideal Structure – Applied Bias So, just as in a PN junction, the applied bias separates the Fermi energies at the two ends of the structure by an amount equal to qVG
Ideal Structure – Applied Bias Barrier heights are fixed! Applied bias causes potential drops and, Ec (Ev) band bending NO band bending in the metal Constant slope in the oxide
Ideal Structure – Applied Bias Hole concentration at the surface, ps, increases systematically from less than ni when Ei (surface) <EF, to ni when Ei (surface) = EF, to greater than ni when Ei (surface) exceeds EF.
Ideal Structure – Applied Bias Surface no longer depleted!
Ideal Structure – Applied Bias Surface appears to change in character Ps exceeds nbulk = ND and surface appears to be p-type. Minority carrier concentration at the surface exceeds the bulk majority carrier concentration
Electrostatics • Analytical relationship for charge density (ρ), electric field (E), and electrostatic potential (ϕ) • Note: ϕ is used for potential inside the MOS-C and VG for applied potential. • Metal -> equipotential region -> charge appearing near the metal-oxide interface resides only a few Angstroms into the metal • -> δ-function of charge at the M-O interface. • No charge in the oxide (ideal case), therefore, the magnitude of the charge in the metal is simply equal to the sum of the charges inside the semiconductor.
Electrostatics Since there are no charges in the oxide, it follows that the electric field is constant in the oxide and the potential is a linear function of position. Therefore, solving for the electrostatic variables inside an ideal MOS-C essentially reduces to solving for the electrostatic variables inside the semiconductor component of the MOS-C…easy, you’ve done this before for PN junctions (revisit chapter 5) Apply Poisson’s equation and use depletion approximation
Electrostatics What is ϕs under flat band conditions?
Electrostatics Look over Exercise 16.2
Electrostatics Beyond inversion, further increase in applied bias causes charge to be added to the inversion layer and not into the space charge layer.
Electrostatics – Gate Voltage Relationship ϕ=0 in Semiconductor bulk Ideal insulator -> no carriers or charges x0 is oxide thickness
Electrostatics – Gate Voltage Relationship Electrostatic Boundary Condition D=εΕ QO-S is the charge/unit area located at the interface Ks: Semiconductor dielectric constant (11.8 for Si) KO: Oxide dielectric constant (3.9 for SiO2)
Capacitance-Voltage Characteristics N-type MOS-C
Capacitance-Voltage Characteristics Low Frequency: Electrons in the inversion layer can follow the a.c. signal and the small-signal capacitance reverts to Cox, as in accumulation. High Frequency: Inversion layer carriers cannot change their number fast enough, and the depletion region width oscillates. The MOS capacitance is frozen at its minimum value.
