Introduction to Inorganic Chemistry/Electronic Properties of Materials: Superconductors and Semiconductors

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  Chapter 10: Electronic Properties of Materials: Superconductors and Semiconductors[edit]

  10.1 Metal-insulator transitions[edit]

  10.2 Superconductors[edit]

  10.3 Periodic trends: metals, semiconductors, and insulators[edit]

  10.4 Semiconductors: band gaps, colors, conductivity and doping[edit]

  10.5 Semiconductor p-n junctions[edit]

When p-type and n-type semiconductors are joined, electrons and holes are annihilated at the interface, leaving a depletion region that contains positively and negatively charged donor and acceptor atoms, respectively. By the difference in Fermi levels, the electric field is generated from n-type to p-type to reach an equilibrium.

Semiconductor p-n junctions are important in many kinds of electronic devices, including diodes, transistors, light-emitting diodes, and photovoltaic cells. To understand the operation of these devices, we first need to look at what happens to electrons and holes when we bring a p-type and n-type semiconductor together.
When we look at the p-n junction, the number of holes in p-type and the number of electrons in n-type are increased after the electrons and holes recombinations.
The electric field, which is created in depletion region by electrons and holes recombination, moves from the electrons to the holes. At high doping levels, the narrow depletion layer occurs. The other way, the wide depletion level exists at low doping levels. In the depletion region, the field causes the bands to become "bend". In elsewhere, the field is zero.
In the middle of p-n junction, the Fermi level energy, EF, is between the valence band, vb, and the conduction band, cb, and the semiconductor is intrinsic (n = p = ni)

  10.6 Diodes, LED's and solar cells[edit]

n-side is bias with "-"

Diodes are made of Ge or Si and control the current flow in one certain direction. If n-side is bias with "+" and p-side is with "-", the current does not flow at all because built in electric field repels the electrons from p-side and increases the depletion region layer width. In the other way, if n-side is bias with "-" and p-side with "+", it forward the bias. The electric field is decreased by pumping the electrons and the holes into the junction. The current flows easily since it flows in the direction of built in electronic field.

Diode i-v.jpg

The figure on the left is the diode "forward bias" direction, the current flows easily. The figure on the right is the diode i-v diagram. x-axis stands for v, and y-axis stands for i. The linear line is the resistor.


LED is the light-emitting diode. Since LED is the type of diode, it also contains p-n junction. When the current flows in the direction of the electric field in p-n junction, LED gives off the light. This light comes from the energy in the electrons in p-n junction. The light can be given off with "hv = Eg" by combining the injected carriers.

Direct-gap materials such as GaAs and GaP have efficient luminescence and are also good light absorbents. It has the minimum of conduction band and the maximum of valence band. It makes to have the high probability of emission. Indirect-gap semiconductors such as Si and Ge absorb the light less efficiently and have a lower probability and slower rate of the electrons and holes recombination. The momentum selection rule prevents the light absorption/emission. So that, there are no pure Si LEDs or Si- lasers.

photovoltaic effect on p-n junctions.

Solar cell, or photovoltaic cell, converts the light directly to electricity by photovoltaic effect. Photovoltaics is the field of technology and research related to the application of solar cells as solar energy. Sometimes the term solar cell is reserved for devices intended specifically to capture energy from sunlight, while the term photovoltaic cell is used when the source is unspecified.

Photocurrent flows in toward reverse bias direction. Built-in separates e- h+ pair (e- flows downhill, h+ flows uphill).If hν≥Eg, light of energy absorbed in depletion layer makes e- h+ pair. Light with hν>Eg still just gives Eg worth of energy in e- h+ pair. Light absorbed outside of depletion region is wasted (no field).

short circuit diagram

In the left diagram, Vphoto is often about half the Eg. Photocurrent is limited by photo flux and recombination rate. The area of the orange rectangle indicates the power generated by the solar cell, which can be calculated as power = i x v. Assemblies of cells are used to make solar modules, which may in turn be linked in photovoltaic arrays. Good solar cell absorbs 1 e- per photon (Φ quantum yield = 1). In other words, in order to make the good solar cell, the area of the orange box should be maximized.

Solar cells have many applications. Individual cells are used for powering small devices such as electronic calculators. Photovoltaic arrays generate a form of renewable electricity, particularly useful in situations where electrical power from the grid is unavailable such as in remote area power systems, Earth-orbiting satellites and space probes, remote radiotelephones and water pumping applications. Photovoltaic electricity is also increasingly deployed in grid-tied electrical systems.

Field effect transistor (FET) is a transistor that uses an electric field to control the shape and conductivity of a charge carrier in a semiconductor material. It is classified as unipolar transistor, contrasting to bipolar transistor.

FinFET schematic DE

The field effect transistor can be understood as the current amplifier. It controls the current of source and drain: with current flowing into gate electrode, gate (transconductor) for flow of electron or electron hole is created by electric field of a channel. Typical structure made in Si is the metal-oxide-semiconductor FET (MOSFET). The "MOS" refers to the "gate" structure.When vlotage is applied between source and drain (figure at right), current cannot flow because either n-p or p-n junction is bad-biased. When (-) potential is applied to gate, e- are driven away from the surface, and locally, semiconductor is "inverted" to p-type. Then the current flows easily between source and drain. The field-effect transistor is off-state for most of the time. This process is purposely make the semiconductor to be biased to "open" the channel. Once it is opened, it comes to thermal equilibrium easily.

Vg vs. source-drain conductance.jpg

Transistor is most useful in this range (red circle), having a big current charge between source and drain when a small signal is applied to gate. Therefore good amplifier is the one right on the edge of turning on so when only small field is applied, the conduction happens. The challenge is now on insulator. The insulator should have thin effects while its layer is still thick. Also the entry component must be compatible and not having redox reaction for oxygen on the surface. Amplification occurs when gate has high input impedance. This can be used in appropricate circuit for voltage amplification or logical O/I (on/off).

  10.7 Amorphous semiconductors[edit]

Amorphous semiconductors is not a newly found material. Iron reach siliceous glassy materials were recovered from the Moon which were billion years old, and people have been preparing glassy materials for thousand of years.

energy diagram depending on degree of state

Two common types of amorphous semiconductors are silion and selenium. Si and Se can both be made in glassy form (messed up structure), usually by sputtering or evaporation at relatively low temperature. Locally, each atom has "normal" valence, but there are many defects and irregularities in the structure. Some Si are 3-coordinate, having dangling bonds, and its energy of orbital is in meddle of gap. Anderson localizaton happens for the localization of electrons inside the semiconductor. Amorphous Si is insulating and not very good as a semiconductor because it is passive and has the dangling bond with low coordination number. By hydrogenation, it makes bonding and antibonding combination, making the carriers inside the mobility gap localized, and removes mid-gap states. These compounds are insulating in dark, but are good photoconductors.

Xerographic photocopy process en.svg

Amorphous Se is used in xerography. The pattern for copied material is made in the dark. Carbon is put on to the pattern by exposing it to light and causing conduction discharges static surface charge toner does not stick.

"What should we do with those localized, dangling electrons of amorphous Si?"
This question led Amorphous Si to be used in solar cell. the mobility gap is about 1.7 eV, which is bigger than crystalline Si gap.It is able to be vapor-deposited in large-area sheets. p+Si-aSiH-n+Si cell have around 10% power conversion efficiency. The device with amorphous Si generally degrades because of hydrogen loss by continual exposure to UV light.

  10.8 Discussion questions[edit]

  10.9 Problems[edit]

Cuprate superconductor structure.jpg

1. The structure of a high temperature superconductor containing barium, europium, copper, and oxygen is shown at the right. What is the stoichiometry of the compound? This structure is actually closely related to perovskite, ABO3. Mark the positions of the missing atoms that would be found in a perovskite.

2. VO2 can exist in insulating or metallic form, depending on temperature and pressure. Which form would be stabilized by increasing the pressure? Explain your answer.

3. Offer a brief explanation of why bandgaps for octet p-block semiconductors (1) decrease with increasing average principal quantum number, and (2) increase with increasing electronegativity difference.

4. Indicate the type of conduction (n or p) in the following: (a) Zn-doped GaAs, (b) In1+xAs1-x, where x << 1, (c) Li0.05Cu0.95O, (d) WO2.999

5. Using 1 eV = 1240 nm, predict the colors of ZnO (Eg = 3.2 eV), AlP (2.5 eV), ZnSnP2 (2.1 eV), CdGeP2 (1.8 eV), and InP (1.27 eV).

6. Pure Ge is much more conductive than pure Si. Given their bandgaps (0.74 and 1.15 eV, respectively), estimate the ratio of their conductivities at room temperature.

7. Sketch a silicon p-n junction, showing the depletion region, band bending, and the Fermi level in the absence of light or applied potential. In the dark, the p-n junction acts as a rectifier. Which way does current flow with an applied bias? In the light, the junction acts as a photodiode. Which way does current flow in this case?

  10.10 References[edit]