Nanotechnology Notes FE Sem 2 Semiconductor Physics | MU

When a piece of material is cut down to a few nanometres, it starts behaving like a different substance: gold turns red, insulators may conduct, melting points drop, and a single extra electron can switch a transistor. Nanotechnology uses these size effects to build better electronics, materials and medicines. This last module of the Semiconductor Physics elective introduces nanotechnology, the optical, electrical, structural and mechanical properties of nanomaterials, the importance of the surface-to-volume ratio, bonding in solids with emphasis on van der Waals interactions, and three applications: lithography, the single-electron transistor (SET) and spin valves. It maps to course outcome CO6 (apply the knowledge of nanotechnology to emerging areas of technology).

Summary

Introduction to nanotechnology: One nanometre (nm) is \(10^{-9}\) m, about the length of ten hydrogen atoms in a row; a human hair is about 50 000 to 100 000 nm thick. Nanoscience is the study of phenomena and properties of materials at the scale of roughly 1 to 100 nm, where they differ significantly from those of the bulk. Nanotechnology is the design, fabrication and application of structures, devices and systems by controlling shape and size at this scale. The idea was introduced by Richard Feynman in his 1959 talk "There's Plenty of Room at the Bottom"; the word nanotechnology was coined by Norio Taniguchi in 1974; the scanning tunnelling microscope (Binnig and Rohrer, 1981) made it possible to see and move individual atoms; fullerenes (C60) were discovered in 1985 and carbon nanotubes became widely known through Iijima's 1991 work. Nanomaterials are classified by how many dimensions are in the nanoscale: zero-dimensional (all three, for example quantum dots, nanoparticles, fullerenes), one-dimensional (nanowires, nanotubes, nanorods), two-dimensional (thin films, graphene, nanosheets) and three-dimensional nanostructured bulk materials (nanocrystalline solids, nanocomposites). They are made by top-down methods (cutting bulk material down, such as lithography, etching and ball milling) or bottom-up methods (building from atoms and molecules, such as chemical vapour deposition, sol-gel, self-assembly and molecular beam epitaxy). Two reasons explain why properties change at the nanoscale: the huge fraction of atoms at the surface (surface effects), and quantum confinement, when the size becomes comparable to the electron's de Broglie wavelength, so energy levels become discrete and size dependent.

Optical properties: The colour and light absorption of nanoparticles depend on their size and shape. Gold nanoparticles of about 10 to 20 nm look ruby red, and silver nanoparticles look yellow, because the free electrons oscillate collectively when light falls on them (surface plasmon resonance) and absorb strongly at a particular wavelength that depends on size and shape; this is how stained glass windows got their colours centuries ago. In semiconductor nanocrystals (quantum dots), quantum confinement increases the effective band gap as the size decreases, so the absorption edge and emission shift to shorter wavelengths (blue shift): CdSe quantum dots emit red when large and blue when small. This tunable colour is used in QLED displays, bio-imaging and solar cells. Nanoparticles smaller than the wavelength of light scatter very little, so nano-ZnO and TiO2 sunscreens look transparent while still absorbing UV.

Electrical properties: In bulk materials conductivity depends on the material alone; at the nanoscale it also depends on size. Energy bands split into discrete levels as particles shrink, so a metal nanoparticle can behave like a semiconductor or insulator. In very thin wires conduction can be ballistic (no scattering over the wire length) and the conductance becomes quantised in steps of \(2e^2/h\). Carbon nanotubes can be metallic or semiconducting depending on how they are rolled. Electrons can tunnel through very thin barriers, which is useful in tunnelling devices but causes leakage in tiny transistors. Adding or removing a single electron to a tiny island changes its potential noticeably, giving Coulomb blockade, the basis of the single-electron transistor. Increased scattering at surfaces and grain boundaries can raise the resistivity of nanoscale metal wires.

Structural properties: Since a large fraction of atoms lie at the surface with fewer neighbours, nanoparticles can show changes in lattice parameter (often a small contraction), crystal structure (some materials adopt different phases at small sizes), and stability. The melting point falls as particle size decreases because surface atoms are less tightly bound; gold particles a few nanometres across melt hundreds of degrees below the bulk value of 1064 °C. Nanocrystalline materials contain a high volume fraction of grain boundaries. Shape (spheres, rods, cubes, tubes, sheets) and the arrangement of surface atoms strongly influence reactivity, which is why nanoparticles make excellent catalysts.

Mechanical properties: Nanomaterials are often much stronger and harder than bulk materials. Smaller grains block the motion of dislocations, so strength increases as grain size decreases (Hall-Petch relation, down to about 10 to 20 nm, below which grain-boundary sliding can make materials softer). Nanostructures are also nearly defect-free, so their strength approaches the theoretical limit: carbon nanotubes and graphene have Young's modulus around 1 TPa and tensile strengths of tens of GPa, about a hundred times stronger than steel for the same cross-section, while being far lighter. Nanocomposites (nanotubes, nanoclay or nanoparticles in polymers or metals) give light, strong, tough materials for sports equipment, aircraft and cars. Some nanoceramics become more ductile or even superplastic.

Importance of surface to volume ratio: For a sphere of radius r, surface area \(4\pi r^2\) and volume \(\tfrac{4}{3}\pi r^3\) give \(S/V = 3/r\); for a cube of side a, \(S/V = 6/a\). As size decreases the ratio increases inversely: making particles 10 times smaller makes S/V 10 times larger. Dividing a 1 cm cube into 10 nm cubes increases the total surface area a million times, from 6 cm² to 600 m² (larger than a basketball court) with the same amount of material. Also, the fraction of atoms at the surface becomes large: in a cube with 10 atoms on each edge almost half the atoms are on the surface, while in a 1 cm crystal the fraction is negligible. Consequences: much higher chemical reactivity and catalytic activity (platinum and gold nanoparticles as catalysts in fuel cells and converters), faster dissolution and better drug delivery, higher adsorption for sensors and filters (gas sensors respond strongly because the whole particle is affected by surface reactions), lower melting points, and changes in electrical, magnetic and optical properties; it is the reason nanomaterials can be both more useful and more toxic than bulk materials.

Bonding in solids and van der Waals interactions: Atoms in solids are held together by bonds of different kinds. Primary (strong) bonds: ionic (transfer of electrons and electrostatic attraction between ions, for example NaCl; hard, brittle, high melting, insulating), covalent (sharing of electron pairs, directional, for example diamond, Si, Ge; very hard and high melting), and metallic (positive ions in a sea of free electrons, for example Cu, Na; good conductors, ductile). Secondary (weak) bonds: hydrogen bonds (between a hydrogen atom bonded to an electronegative atom and another electronegative atom, for example in ice and DNA) and van der Waals bonds. Van der Waals interactions are weak attractive forces between neutral atoms or molecules that arise from electric dipoles. There are three contributions: (i) Keesom (orientation) forces between permanent dipoles; (ii) Debye (induction) forces between a permanent dipole and the dipole it induces in a neighbouring molecule; (iii) London dispersion forces, present between all atoms and molecules, even non-polar ones like argon, because fluctuations of the electron cloud create an instantaneous dipole that induces a dipole in a neighbour, and the two attract. The van der Waals attraction energy varies as \(-1/r^6\); it is short-ranged and weak (bond energies about 0.01 to 0.1 eV per atom, compared with 1 to 10 eV for primary bonds). At very short distances the electron clouds overlap and a strong repulsion arises (Pauli exclusion). The total interaction is described by the Lennard-Jones potential \(U(r) = 4\varepsilon\left[\left(\dfrac{\sigma}{r}\right)^{12} - \left(\dfrac{\sigma}{r}\right)^6\right]\), where ε is the depth of the potential well and σ the distance at which U = 0; the equilibrium separation is \(r_0 = 2^{1/6}\sigma \approx 1.12\sigma\) with energy −ε. Van der Waals bonds hold together solid noble gases, molecular crystals (solid CO2, iodine), the layers of graphite and of 2D materials such as MoS2 (which is why they slide and can be peeled into single layers), and polymer chains. At the nanoscale they are especially important: they make nanoparticles and nanotubes clump together (agglomeration), they let geckos climb walls using millions of nanoscale hairs on their feet, they cause stiction in MEMS, they hold the tip-sample interaction in atomic force microscopy, and they drive self-assembly of molecules and van der Waals heterostructures (stacks of different 2D layers).

Application: lithography: Lithography is the process of transferring a pattern onto a substrate; it is the main top-down technique for making integrated circuits and nanostructures. Photolithography steps: (1) clean the wafer and grow or deposit the layer to be patterned (for example SiO2); (2) spin-coat a thin film of light-sensitive polymer (photoresist) and soft-bake it; (3) align a mask (a glass plate with an opaque chromium pattern) and expose the resist to ultraviolet light through it; (4) develop the resist: in a positive resist the exposed regions dissolve, in a negative resist the exposed regions harden and the unexposed regions dissolve; (5) hard-bake and etch the uncovered underlying layer (wet chemical or dry plasma etching), or deposit material through the openings (lift-off); (6) strip the remaining resist. The process is repeated dozens of times to build a chip layer by layer. The smallest feature (resolution) is set by diffraction: \(R = k_1\lambda/NA\), where λ is the wavelength, NA the numerical aperture of the projection lens and k₁ a process factor (practical minimum about 0.25 to 0.3). To print smaller features the industry moved from mercury lamp UV (436 nm, 365 nm) to deep UV excimer lasers (248 nm KrF, 193 nm ArF), immersion lithography (water between lens and wafer, NA up to about 1.35), multiple patterning, and extreme ultraviolet (EUV) lithography at 13.5 nm using mirrors in vacuum. Other nanolithography methods: electron-beam lithography (writes patterns directly with a focused electron beam; very high resolution, below 10 nm, but slow, used to make masks and research devices), ion-beam lithography, X-ray lithography, nanoimprint lithography (pressing a mould into a resist, cheap and high resolution) and dip-pen or scanning-probe lithography (an AFM tip writes molecules directly).

Application: Single Electron Transistor (SET): (The syllabus writes it as Single Electron Transfer; the device is the single-electron transistor.) A SET consists of a tiny conducting island (a metal or semiconductor nanoparticle or quantum dot, a few nanometres to tens of nanometres across) connected to the source and drain through two tunnel junctions (very thin insulating barriers through which electrons can tunnel) and coupled capacitively to a gate electrode. Because the island is so small, its total capacitance C is tiny (attofarads), and adding a single electron raises its electrostatic energy by the charging energy \(E_C = e^2/2C\). If \(E_C\) is much larger than the thermal energy kT, an electron cannot tunnel onto the island unless the applied voltages supply this energy, so current is blocked even with a small source-drain voltage: this is Coulomb blockade. Changing the gate voltage shifts the island's energy levels; at particular gate voltages the energies for N and N + 1 electrons on the island become equal, the blockade is lifted, and electrons tunnel through one at a time (source to island to drain). As the gate voltage is swept, the current shows a series of sharp peaks, called Coulomb oscillations, with period \(\Delta V_G = e/C_G\), each peak corresponding to the addition of one more electron. Thus a SET switches on and off with the transfer of single electrons. Conditions: \(E_C \gg kT\) (in practice about ten times or more), and the tunnel resistance must exceed the resistance quantum \(h/e^2 \approx 25.8\) kΩ so that the electron number on the island is well defined. For room-temperature operation the island must be only a few nanometres in size. Advantages: extremely low power (one electron per switching event), extreme sensitivity to charge, very small size. Disadvantages: needs very low temperature unless islands are a few nanometres, sensitive to random background charges, low current and output voltage, difficult fabrication. Applications: ultra-sensitive electrometers (detecting a fraction of an electron charge), single-electron memory, current standards in metrology (single-electron pumps), infrared and charge detectors, readout of quantum bits, and possible future low-power logic.

Application: spin valves: Spintronics uses the spin of the electron, as well as its charge. A spin valve is a multilayer device consisting of two ferromagnetic layers (for example NiFe or CoFe, a few nanometres thick) separated by a thin non-magnetic metal spacer (usually copper, a few nanometres). The magnetisation of one layer (the pinned or reference layer) is fixed by coupling it to an adjacent antiferromagnetic layer (exchange bias, for example IrMn), while the magnetisation of the other layer (the free layer) can rotate easily in a weak external field. Working: conduction electrons scatter differently depending on whether their spin is parallel or antiparallel to the magnetisation of the layer they pass through. When both layers are magnetised parallel, electrons of one spin type pass through both layers with little scattering, giving a low resistance. When the layers are antiparallel, electrons of both spin types are strongly scattered in one or the other layer, giving a high resistance. This large change of resistance with the relative magnetisation is giant magnetoresistance (GMR), discovered independently in 1988 by Albert Fert and Peter Grünberg (Nobel Prize in Physics 2007). The GMR ratio is \((R_{AP} - R_P)/R_P\), typically about 5 to 20 percent at room temperature in spin valves. If the spacer is replaced by a thin insulator such as MgO, electrons tunnel between the layers and the effect, tunnelling magnetoresistance (TMR), is much larger (over 100 percent); this is a magnetic tunnel junction. Applications: read heads of hard disk drives (GMR spin-valve heads from the late 1990s, later TMR heads), which enabled huge increases in storage density; magnetoresistive random access memory (MRAM), which is non-volatile, fast and durable; magnetic field and current sensors (automotive position and speed sensors, compasses); and biosensors that detect magnetic nanoparticle labels.

Mind map

Photolithography step by step

Important definitions

Formulas

Key points to remember

• Nanoscale = 1 to 100 nm; properties change because of surface effects and quantum confinement.
• Smaller quantum dots have larger band gaps and emit bluer light.
• Gold nanoparticles look red due to surface plasmon resonance.
• Melting point falls and strength rises as particle or grain size decreases (within limits).
• S/V = 3/r: ten times smaller particle, ten times larger S/V.
• Van der Waals energy ∝ −1/r⁶; weak but universal; important for adhesion, graphite layers and self-assembly.
• Lennard-Jones minimum at r0 = 1.12σ with depth ε.
• Lithography resolution improves with shorter λ, higher NA and lower k1; EUV uses 13.5 nm.
• Positive resist: exposed part dissolves. Negative resist: exposed part stays.
• SET works by Coulomb blockade; needs EC ≫ kT and tunnel resistance ≫ 25.8 kΩ.
• Spin valve: parallel = low resistance, antiparallel = high resistance; GMR by Fert and Grünberg (1988).

Solved examples

Example 1. Compare the surface-to-volume ratio of a sphere of radius 1 cm with that of a nanoparticle of radius 10 nm.

1 cm: \(S/V = 3/10^{-2} = 300\) m⁻¹. 10 nm: \(S/V = 3/10^{-8} = 3\times10^{8}\) m⁻¹. The nanoparticle's ratio is \(10^{6}\) times larger.

Example 2. A cube of 1 cm side is divided into cubes of 10 nm side. Find the number of small cubes and the total surface area.

Number \(= (10^{-2}/10^{-8})^3 = (10^{6})^3 = 10^{18}\). Area of each \(= 6\times(10^{-8})^2 = 6\times10^{-16}\) m². Total \(= 10^{18}\times6\times10^{-16} = 600\) m², compared with \(6\times10^{-4}\) m² (6 cm²) for the original cube: a million-fold increase.

Example 3. Find the fraction of surface atoms in cubic clusters having 10 and 100 atoms along each edge.

n = 10: \((1000 - 8^3)/1000 = (1000 - 512)/1000 = 0.488\), about 49 percent. n = 100: \((10^{6} - 98^3)/10^{6} = (10^{6} - 941192)/10^{6} = 0.0588\), about 5.9 percent. Small clusters are dominated by surface atoms.

Example 4. For argon, σ = 0.34 nm in the Lennard-Jones potential. Find the equilibrium separation.

\(r_0 = 2^{1/6}\sigma = 1.1225\times0.34 = 0.382\) nm. At this distance the attractive and repulsive forces balance and the energy is −ε.

Example 5. A SET island has a total capacitance of 1 aF. Find the charging energy in eV and compare it with kT at 300 K. What capacitance is needed for E_C = 10 kT at 300 K?

\(E_C = e^2/2C = (1.6\times10^{-19})^2/(2\times10^{-18}) = 1.28\times10^{-20}\) J \(= 0.080\) eV. \(kT = 0.0259\) eV, so \(E_C \approx 3kT\): not enough for clean room-temperature operation. For \(E_C = 10kT = 0.259\) eV: \(C = e/(2\times0.259) = 1.6\times10^{-19}/0.518 = 3.1\times10^{-19}\) F \(\approx 0.31\) aF.

Example 6. Estimate the self-capacitance and charging energy of a spherical metal island of radius 5 nm in vacuum.

\(C = 4\pi\varepsilon_0r = 4\pi\times8.85\times10^{-12}\times5\times10^{-9} = 5.56\times10^{-19}\) F \(= 0.556\) aF. \(E_C = e/2C\) (in eV) \(= 1.6\times10^{-19}/(2\times5.56\times10^{-19}) = 0.144\) eV, about 5.6 kT at 300 K.

Example 7. A spin valve has resistance 10 Ω in the parallel state and 12 Ω in the antiparallel state. Find the GMR ratio.

\(\text{GMR} = (12 - 10)/10 = 0.20 = 20\%\).

Example 8. Find the resolution of (a) ArF immersion lithography with λ = 193 nm, NA = 1.35, k1 = 0.3 and (b) EUV with λ = 13.5 nm, NA = 0.33, k1 = 0.4.

(a) \(R = 0.3\times193/1.35 = 42.9\) nm. (b) \(R = 0.4\times13.5/0.33 = 16.4\) nm. Shorter wavelength allows much finer features even with a lower NA.

Important questions and answers

Q1. What is nanotechnology? Why do materials show different properties at the nanoscale? (5 marks)

Nanotechnology is the understanding and control of matter at dimensions of about 1 to 100 nm to create materials, devices and systems with new properties. Reasons for different behaviour: (i) Surface effects: S/V ∝ 1/size, so a large fraction of atoms are at the surface with unsatisfied bonds, increasing reactivity, lowering melting point and changing structure. (ii) Quantum confinement: when size is comparable to the electron wavelength, continuous bands become discrete levels and the band gap increases as size decreases, changing optical and electrical properties. (iii) Fewer defects lead to near-theoretical strength. Mention the classification (0D to 3D) and fabrication approaches (top-down, bottom-up) with examples.

Q2. Explain the optical, electrical, structural and mechanical properties of nanomaterials. (6 marks)

Optical: surface plasmon resonance in metal nanoparticles (red gold, yellow silver); size-tunable emission of quantum dots (blue shift as size falls); transparency of nano-oxides. Electrical: discrete energy levels; metal-to-insulator changes in small particles; ballistic transport and quantised conductance in nanowires and CNTs; tunnelling; Coulomb blockade; higher resistivity due to surface scattering in thin metal wires. Structural: lattice contraction; new crystal phases; lower melting point; many grain boundaries; shape-dependent surface facets. Mechanical: higher hardness and strength from small grains (Hall-Petch) and few defects; CNT and graphene Young's modulus about 1 TPa; reinforcement in nanocomposites; possible superplasticity of nanoceramics. Give one example each.

Q3. Explain the importance of surface to volume ratio in nanomaterials. (4 marks)

For a sphere S/V = 3/r; for a cube S/V = 6/a; the ratio grows as size shrinks. Example: dividing 1 cm³ into 10 nm cubes raises area from 6 cm² to 600 m². A large fraction of atoms is at the surface (about half for a 10-atom-edge cube). Consequences: high catalytic activity (Pt, Au nanoparticles), high sensitivity of gas and bio sensors, efficient drug delivery, fast reactions in batteries and fuel cells, lower melting and sintering temperatures, changes in magnetism and conductivity, but also higher toxicity and tendency to agglomerate.

Q4. Explain van der Waals interactions in solids. (5 marks)

Van der Waals forces are weak attractive forces between neutral atoms or molecules due to electric dipoles. Types: Keesom (permanent dipole-permanent dipole), Debye (permanent dipole-induced dipole), London dispersion (instantaneous dipole-induced dipole, acting even between non-polar atoms). The attractive energy varies as −1/r⁶; at short distances electron cloud overlap gives strong repulsion (∝ 1/r¹²), giving the Lennard-Jones potential \(U = 4\varepsilon[(\sigma/r)^{12} - (\sigma/r)^6]\) with equilibrium at \(r_0 = 2^{1/6}\sigma\). Bond energy is about 0.01 to 0.1 eV, much less than ionic, covalent and metallic bonds. Solids bonded this way (solid argon, molecular crystals, graphite layers) have low melting points and are soft. Importance at the nanoscale: agglomeration of nanoparticles, stacking of 2D layers and exfoliation of graphene, gecko adhesion, stiction in MEMS, AFM imaging and molecular self-assembly. Draw U versus r showing the minimum.

Q5. Explain photolithography with a neat diagram. State how resolution can be improved. (6 marks)

Steps with sketches: oxidised wafer; resist spin-coating; exposure through a mask; development (positive and negative resist results side by side); etching of oxide; resist stripping. Resolution \(R = k_1\lambda/NA\) and depth of focus \(\propto \lambda/NA^2\). Improvements: shorter wavelength (g-line 436 nm, i-line 365 nm, KrF 248 nm, ArF 193 nm, EUV 13.5 nm), higher NA (immersion lithography with water, NA ≈ 1.35), lower k₁ (phase-shift masks, optical proximity correction, off-axis illumination, multiple patterning). Alternatives for nanoscale patterns: electron-beam, ion-beam, X-ray and nanoimprint lithography.

Q6. Explain the construction and working of a single-electron transistor. (6 marks)

Construction: a nanoscale conducting island between source and drain, separated from each by a tunnel junction (thin insulating barrier) and coupled to a gate through a gate capacitor C_G. Total island capacitance \(C = C_S + C_D + C_G\) is in the attofarad range. Working: adding one electron raises the island energy by \(E_C = e^2/2C\). With \(E_C \gg kT\) and a small bias, tunnelling is forbidden (Coulomb blockade) and no current flows. Adjusting the gate voltage aligns the energies of N and N + 1 electron states; then one electron tunnels from source to island and then from island to drain, and the cycle repeats, giving current. Sweeping V_G gives periodic current peaks (Coulomb oscillations) spaced by e/C_G; the I-V_DS curve shows a flat zero-current gap (Coulomb staircase in asymmetric devices). Conditions: E_C ≫ kT, R_T ≫ h/e². Applications: electrometers, single-electron memory and pumps (current standard), charge sensors for qubits, future ultra-low-power logic. Limitations: low temperature or very small islands needed, background charge noise, low drive current.

Q7. What is a spin valve? Explain GMR and its applications. (5 marks)

Structure (from bottom): antiferromagnetic pinning layer (IrMn), pinned ferromagnetic layer (CoFe), non-magnetic spacer (Cu, a few nm), free ferromagnetic layer (NiFe). Working: resistance depends on spin-dependent scattering. Parallel magnetisations: one spin channel passes with low scattering, giving low resistance. Antiparallel: both spin channels scatter strongly in one of the layers, giving high resistance. An external field rotates the free layer and switches the resistance, so the device senses magnetic fields. GMR = (R_AP − R_P)/R_P; discovered by Fert and Grünberg in 1988. With an insulating MgO barrier, TMR is much larger. Use the two-current resistor model (two parallel channels with small and large resistances) to explain. Applications: HDD read heads, MRAM, magnetic sensors in cars and phones, biosensors.

Exam tips

• For properties questions, use four headings (optical, electrical, structural, mechanical) with one example each.
• Show S/V numerically; a one-line calculation makes the answer stronger.
• Draw the Lennard-Jones curve and mark r0 and −ε.
• For lithography draw the step sequence and contrast positive and negative resists.
• For SET, write the two conditions and draw the island with two tunnel junctions and a gate.
• For spin valves, draw the layer stack and the parallel/antiparallel states with low/high resistance.

FAQs

Is a nanoparticle just a very small piece of bulk material?

Not quite. Because so many of its atoms are at the surface and its electrons are confined, its colour, melting point, reactivity and conductivity can be very different from the bulk.

Why do SETs usually need very low temperatures?

Thermal energy kT can give electrons enough energy to overcome the charging energy. Unless the island is only a few nanometres across, E_C is not much larger than kT at room temperature, so devices are cooled.

Why are van der Waals forces important if they are so weak?

They act between all atoms, and at the nanoscale surfaces are very close and very large in total area, so these forces dominate adhesion and assembly of small objects.

What is the difference between GMR and TMR?

GMR uses a metallic spacer and spin-dependent scattering; TMR uses a thin insulating barrier and spin-dependent tunnelling, giving a much larger resistance change.

These notes follow the University of Mumbai first-year engineering syllabus (NEP 2020, Semiconductor Physics, Semester II) and were prepared with AI help and checked.