Recent Trends in Physics

(c) P-type semiconductor

A P-type semiconductor is made by doping a pure crystal with trivalent atoms (e.g. boron or indium). Each dopant atom leaves a vacancy (hole) in a covalent bond, so holes are the majority carriers and electrons the minority carriers.

Critical density is the density at which the universe is just able to stop expanding (it is flat).

Consider a galaxy of mass $m$ at distance $r$ from us, receding with speed $v=Hr$ (Hubble's law). Only the mass $M$ of the sphere of radius $r$ attracts it:

$M=\tfrac43\pi r^3\rho$

For the galaxy to just escape, its kinetic energy equals the magnitude of its potential energy:

$\tfrac12 mv^2=\frac{GMm}{r}$

$\tfrac12 H^2r^2=\frac{G}{r}\cdot\tfrac43\pi r^3\rho_c$

$\boxed{\rho_c=\frac{3H^2}{8\pi G}}$

If the actual density is greater than $\rho_c$, the universe will eventually collapse; if smaller, it expands forever.

Doping is the process of adding a small, controlled amount of impurity atoms to a pure (intrinsic) semiconductor to increase its conductivity.

N-type semiconductor. A pentavalent impurity (arsenic, phosphorus or antimony, with 5 valence electrons) is added to pure silicon or germanium (4 valence electrons). Each impurity atom replaces a lattice atom and forms four covalent bonds with its neighbours. Its fifth electron is left free, loosely bound, and needs very little energy to become a conduction electron. The impurity is called a donor.

The semiconductor now has many free electrons (the majority carriers) and only a few thermally generated holes (the minority carriers). It is still electrically neutral overall, and since conduction is mainly by negative charge, it is called n-type.

No, a stable hole cannot exist in a metal. In a metal the valence band and conduction band overlap (or the conduction band is partly filled), so there are plentiful free electrons close by in energy. A vacancy left by an electron is filled almost instantly by another electron, so it does not behave as a separate, mobile positive charge carrier. Holes are significant only in semiconductors, where a gap separates the filled valence band from the conduction band.

They do not cancel because they move in opposite directions and carry opposite charges. Under the battery's field, electrons drift towards the positive end, while holes drift towards the negative end. A negative charge moving one way and a positive charge moving the opposite way both give conventional current in the same direction, so the two contributions add: $I=I_e+I_h$. A current flows.

(a) conductivity decreases

Silicon is a semiconductor. Its conductivity depends on the number of thermally generated charge carriers, which falls as the temperature falls, so cooling from $100^\circ$C to $0^\circ$C reduces the conductivity (unlike a metal, whose conductivity rises on cooling).

(b) Its forbidden energy gap is about (1,\text{eV})

A semiconductor has a small forbidden energy gap (about (0.7,\text{eV}) for Ge and (1.1,\text{eV}) for Si), so electrons can easily jump to the conduction band when heated. Its resistance decreases with rise in temperature, and a zero gap corresponds to a conductor.

Nanotechnology is the branch of science and engineering that deals with the design, production, characterisation and application of materials, devices and systems at the nanometre scale (1–100 nm). At this scale, materials are built from a few hundred to a few thousand atoms, and their behaviour is governed by quantum and surface effects rather than by bulk properties. The word "nano" comes from the Greek nanos, meaning dwarf; $1\ \text{nm} = 10^{-9}\ \text{m}$, which is about $10^{-5}$ times the diameter of a human hair.

Three applications in daily life

1. Medicine and drug delivery. Nanoparticles (e.g. liposomes, gold nanoparticles) can carry a drug and release it only at the diseased tissue. This is used in targeted cancer therapy and in nano-silver dressings that kill bacteria in wounds. It reduces the dose needed and the side effects on healthy cells.

2. Electronics and computing. Nanomaterials such as carbon nanotubes and graphene are used to make transistors, sensors and memory chips that are far smaller and faster than conventional silicon devices. They also make lighter, longer-lasting batteries and more efficient solar cells.

3. Cosmetics and textiles. Sunscreen contains zinc oxide and titanium dioxide nanoparticles, which absorb ultraviolet light but are transparent on the skin. Nano-coated fabrics are made stain-resistant, water-repellent and wrinkle-free.

Why nanomaterials show different properties from bulk materials

1. Extremely large surface-area-to-volume ratio. As particle size falls to the nanoscale, the fraction of atoms lying on the surface becomes very large. Surface atoms have fewer neighbours and unsatisfied bonds, so they are more reactive. This is why nano-iron is a far better catalyst and why nanoparticles burn or react much faster than the same material in bulk.

2. Quantum confinement effect. In a nanoparticle the electrons are confined to a region comparable to their de Broglie wavelength. This shifts the allowed energy levels and widens the band gap. As a result, the colour, electrical conductivity and magnetic behaviour change with particle size — for example, gold is yellow in bulk but appears red or purple as nanoparticles, and semiconductor nanocrystals emit light of different colours depending on their size.

3. Dominance of surface and interface forces. Because the number of surface atoms is comparable to the number of interior atoms, surface energy and inter-particle forces become significant. This changes melting point (nanoparticles melt at much lower temperature than the bulk), mechanical strength and chemical stability.

Thus, nanotechnology exploits the fact that at the nanoscale the same element can behave quite differently from its bulk form, and this is the basis of its wide use in medicine, electronics and everyday products.

Superconductivity is the phenomenon in which certain materials, when cooled below a characteristic temperature, offer zero electrical resistance and therefore conduct electric current without any energy loss. Such materials are called superconductors. The temperature at which a material makes the transition from normal conducting state to superconducting state is called its critical temperature ($T_c$). For example, mercury becomes superconducting at $T_c = 4.2\ \text{K}$, and the ceramic $\text{YBa}_2\text{Cu}_3\text{O}_7$ at about $90\ \text{K}$.

Meissner effect: When a superconductor is cooled below its critical temperature in the presence of an external magnetic field, it expels the magnetic field completely from its interior, so that the magnetic flux density inside it becomes zero ($B = 0$). This expulsion of magnetic flux is called the Meissner effect. Because of this, a superconductor behaves as a perfect diamagnet with magnetic susceptibility $\chi = -1$. A direct consequence is that a small magnet placed above a superconducting disc is repelled and levitates above it. The effect shows that superconductivity cannot be explained merely by zero resistance; it is a distinct thermodynamic state of matter.

Important applications:

1. Superconducting magnets (MRI machines and maglev trains): Superconducting coils carry large currents without heating, producing very strong magnetic fields. These are used in MRI scanners in hospitals and in the electromagnets that levitate and propel maglev trains.
2. Transmission of electric power and fast electronic devices: Superconducting cables transmit electrical power over long distances with no $I^2R$ loss, and superconducting Josephson junctions are used to make extremely fast switching devices (SQUIDs) for sensitive magnetic-field measurements.

Light Emitting Diode (LED)

Construction: An LED is a heavily doped p-n junction diode made from direct band-gap semiconductors such as gallium arsenide phosphide (GaAsP), gallium phosphide (GaP) or gallium arsenide (GaAs). The p-region is made very thin so that light generated inside can escape easily, and the whole junction is enclosed in a transparent plastic or glass dome that acts as a lens and protects the junction. The p-side is connected to the positive terminal and the n-side to the negative terminal of the battery, so the diode is forward biased.

Working principle: When the diode is forward biased, electrons from the n-region and holes from the p-region move towards the junction and recombine there. In a direct band-gap semiconductor, each recombination releases energy equal to the band-gap energy $E_g$ as a photon of light, whose frequency is

$\nu = \frac{E_g}{h}$

where $h$ is Planck's constant. Since the colour of the emitted light depends on $E_g$, LEDs of different colours are made by choosing different semiconductor materials. The LED conducts only when the forward voltage exceeds the threshold (about 1.8 V for red and 3 V for blue LEDs), and it emits light continuously while forward biased. It is operated in series with a resistor to limit the current and prevent damage.

p-n Junction Diode as a Solar Cell

A solar cell is a large-area p-n junction diode made of a semiconductor such as silicon, with a very thin p-layer on top so that light can reach the junction. It is used without any external bias.

When sunlight falls on the junction, photons with energy greater than the band gap are absorbed and create electron-hole pairs. The strong built-in electric field at the depletion region separates these charge carriers: electrons are swept to the n-side and holes to the p-side. This separation of charge makes the p-side positive and the n-side negative, so a photovoltage (about 0.5–0.6 V for silicon) is developed across the junction. When an external load is connected, electrons flow through the external circuit from the n-side to the p-side, i.e. a current flows in the external circuit from p to n. Thus light energy is converted directly into electrical energy. The I-V characteristic of a solar cell lies in the fourth quadrant, and its efficiency is typically 15–20%.

Differences between LED and Solar Cell

(Any two of the above differences are sufficient.)