## 513.121 Physics of Semiconductor Devices30.11.2017

Problem 1
A photodiode consists of semiconducting layers $n$+ / $n$ / $p$ / $p$+. No bias voltage is applied.

(a) Draw the band diagram (conduction band, valence band, Fermi energy).

(b) Draw the electric field and the charge density. Which way is does current flow when light falls on the photodiode?

(c) The sensitivity of the photodiode increases when it is reverse biased. Explain why this happens.

Problem 2
There are four mechanisms that typically cause currents to flow: thermionic emission, diffusion, drift, and tunneling.

Explain briefly which kind of current mechanisms are important in the following devices. For instance, in a MOSFET, there is tunneling at source, drain, and body tunnel contacts; drift is the dominant current mechanism for the drain current when the MOSFET is turned on while diffusion is the dominant mechanism for the drain current (sub-threshold current) when the transistor is turned off .

(a) pn diode
(b) Schottky diode
(c) JFET
(d) bipolar transistor
(e) thyristor

Problem 3
(a) Draw an $n$-channel MOSFET showing the source, drain, gate, and body contacts.

(b) How should this MOSFET be biased so that it is in the saturation regime?

(c) If a very high source-drain voltage is applied, electrons near the drain accelerate to high velocities and scatter other electrons from the valence band to the conduction band. This is called impact ionization. What happens to the electron-hole pairs that are generated? (Where does the electron go and where does the hole go?)

(d) The subthreshold current is a diffusion current that flows in the body due to a gradient in the concentration of electrons. The source-body junction is unbiased. The drain-body junction is reverse biased. How can you use this information to determine the gradient in the concentration of electrons?

Problem 4
A semiconductor is doped pnpnp where the p-regions are heavily doped and the n-regions are lightly doped.

(a) How could you measure the doping of the n-regions?

(b) What would happen as you apply a larger and larger voltage across this structure?

 Quantity Symbol Value Units electron charge e 1.60217733 × 10-19 C speed of light c 2.99792458 × 108 m/s Planck's constant h 6.6260755 × 10-34 J s reduced Planck's constant $\hbar$ 1.05457266 × 10-34 J s Boltzmann's constant kB 1.380658 × 10-23 J/K electron mass me 9.1093897 × 10-31 kg Stefan-Boltzmann constant σ 5.67051 × 10-8 W m-2 K-4 Bohr radius a0 0.529177249 × 10-10 m atomic mass constant mu 1.6605402 × 10-27 kg permeability of vacuum μ0 4π × 10-7 N A-2 permittivity of vacuum ε0 8.854187817 × 10-12 F m-1 Avogado's constant NA 6.0221367 × 1023 mol-1