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VE320 Intro to Semiconductor Devices
Summer 2024 — Problem Set 7
Due: 11:59 pm 28th July
1) Several conceptual questions
a) Explain the difference in the I-V relationship between the Schottky barrier diode and the Ohmic contact diode.
b) Explain the difference in the I-V relationship between the metal-semiconductor and the two-terminal MOS structure.
c) Explain the reason why there’s a maximum depletion layer width.
2) Energy band diagrams
a) Draw the equilibrium energy band diagram of a Schottky barrier diode and an Ohmic contact diode (both with ann-type semiconductor).
b) Draw the equilibrium energy band diagram of the two-terminal MOS structure if the work function of the metal is bigger than that of the semiconductor.
3) A Schottky diode at T =300K is formed with Pt on n-type silicon with a doping concentration of Nd = 5 × 1015 cm −3 . The barrier height is found to be φBn = 0.89v. The effective Richardson constant is A∗ = 120A/k2 -cm2 . Determine (a) φn, (b) vbi, (c) JST, and (d) va such that Jn = 5A/cm2 .
4） A Schottky diode with n-type GaAs at T = 300K yields the plot shown in the
Figure below, where the unit of C ′ is fF/cm2. Determine (a) vbi, (b) Nd, (c) φn , and (d) φB0. You can approximately read the graph below.
5) The high-frequency C–V characteristic curve of a MOS capacitor is shown in the figure below. The area of the device is 2 × 10 −3cm2 . The metal-semiconductor work function difference is φmS = −0.50v, the oxide is SiO2, the semiconductor is silicon, and the semiconductor doping concentration is 2 × 1016 cm −3 . (a) Is the semiconductor n or p-type? (b) What is the oxide thickness? (c) What is the equivalent trapped oxide charge density?
6) The high-frequency C–V characteristic curve of a MOS capacitor is shown in the figure below. The oxide is SiO2 and the semiconductor is silicon. The area of the MOS capacitor is 3 × 10 −3cm2 . (a) Is the semiconductor component of the MOS capacitor doped n-type or p-type? (b) Draw the MOS capacitor energy band diagram corresponding to point (2) on the C – V characteristic. (c) Draw the block charge diagram corresponding to point (1) on the C – V characteristic. (d) What is the oxide thickness? (e) Determine xdT and the associated semiconductor doping concentration for the given MOS capacitor.
7) Consider ann-channel depletion mode MOSFET with ann polysilicon gate. The n-channel doping is Nd = 1015 cm −3 and the oxide thickness is 500 Å . The equivalent fixed oxide charge is Qs(′)s = 1010 cm −2 . The metal-semiconductor work function difference is φms = −0.272v. Then-channel thickness is equal to the maximum induced space charge width. (Disregard the space charge region at then-channel–p-substrate junction.) (a) Determine the channel thickness and (b) calculate the threshold voltage.