PHT.301 Physics of Semiconductor Devices
28.06.2024

Problem 1

A simplified bandstructure of GaP is shown below.

(a) What is the bandgap of this semiconductor? Is it a direct semiconductor or an indirect semiconductor?

(b) Label the light hole band and the heavy hole band.

(c) Sketch the density of states for this semiconductor. Use the bandstructure to decide if the density of states rises faster in the valence band or in the conduction band. Label the valence band edge, the conduction band edge, and the Fermi energy in your drawing.

(d) A pn-diode is made from GaP where the p-side is heavily doped and the n-side is lightly doped. Draw the band diagram (conduction band, valence band, and Fermi energy) for a reverse bias.

Problem 2

(a) Make a drawing of a light-emitting diode including the metal contacts.

(b) Explain what you have to do to efficiently couple the light out of the diode.

(d) What determines the center wavelength of the light that an LED emits? There is some spread of wavelengths around this center wavelength. What causes this spread?

Problem 3
A drawing of a transistor from Wikipedia is shown below.

(a) What kind of transistor is this? Label the three contacts.

(b) What is the purpose of the two n+ regions? What is the purpose of the light blue regions? What is the purpose of the yellow regions?

(d) If you shine light on this transistor and measure the voltage between the two upper contacts, what voltage will you measure? What polarity will this voltage have, positive on the p contact or negative on the p contact? Explain your reasoning.

Solution

<hr />

(a) This kind of transistor is a NPN bipolar-junction transistor (BJT).

The (E) emitter- , (B) base- and (C) collector-contacts are labeled below:
	
	<img src="bipolar_edit.png" width="200">

(b) Purpose of the regions:
	<ul>
	 <li>Upper (small) n+ region: This small - heavily doped - region is used as emitter. The small size leads to a little base-emitter capacitance $C_\text{BE}$ and allows for high-speed operation. The heavy doping leads to a good emitter-efficiency $\gamma_\text{E}$ close to 1</li>
	 <li>Red region: This lighter doped - region inbetween (E) and (C) is the base. The light doping leads to smaller recombination inside the base.</li>
	 <li>Lower (wide) n+ region: To achieve an ohmic contact between the collector and the yellow metal contact a highly doped subcollector is used. This prevents a Schottky-contact.</li>
	 <li>Light blue region: This region is very lightly doped and used as collector. By using light doping the depletion region mostly grows inside the collector and reduces the Early-effect and punchthrough inside the base.</li>
	 <li>Yellow regions: These three regions are the metal contacts.</li>
	 
	</ul>

(c) One would expect a Schottky-contact (metal to p-semiconductor)
between the red base and the yellow metal contact due to low doping.
High doping is necessary for an ohmic contact which is often done by a doping profile with
high concentration near the metal contact.

(d) Photons which have enough energy (at least the bandgap energy) generate an electron-hole pair in the semiconductor.
	<ul>
		<li>When considering the two upper contacts (B) and (E) the electric field of the unbiased depletion-zone points from the emitter (n+ region) to the base (p region). Hence, generated electrons will move from p to n+ region and holes from n+ to p region (Drift current).</li>
		<li>Generated electron-hole pair outside the depletion-zone: Locally the charge carrier concentrations are increased which leads to diffusion. Mainly relevant for the minority carriers, as the majority carriers are multiple orders higher due to doping. The carriers diffuse to the depletion zone, where - again - the electric-field $\vec{E}$ moves the carriers.</li>
		<li>The above stated processes lead to more electrons at the n+ contact and more holes on the p contact, hence the voltage is positive on the p contact and negative on the n+ contact.</li>
		<li>If enough light shines on the (B)-(E) junction it will be forward-biased by the generated voltage, like in a solar-cell which is not sufficiently loaded by a low-impedance load. If one measures the voltage (voltmeter has high-impedance inputs) approximately $0.6~\text{ V}$ will show at sufficient light levels.</li>
	</ul>

Problem 4
(a) Draw an $p$-channel MOSFET showing the source, drain, gate, and body contacts.

(b) The MOSFET is biased in saturation. Draw the depletion region in your drawing from part (a). Put + and - signs in the drawing to show how the charge is distributed.

(c) A voltage is applied between the source and the body. Explain how this shifts the threshold voltage. Which direction is the threshold voltage shifted and how far can it be shifted?

(d) Explain what latch-up is in CMOS circuits.

PHT.301 Physics of Semiconductor Devices28.06.2024

PHT.301 Physics of Semiconductor Devices
28.06.2024