Building a more complex molecule C 2 Isolated impurities From E. A. Moore: “Molecular Modelling and bonding”, Royal Soc. Chem.

Building a solid Graphite/Diamond Isolated impurities From W. A. Harrison: “Electron Structure” Royal Soc. Chem.

Building a metal (Copper) Isolated impurities From J. A. Burdick Phys. Rev (1963)

Isolated atoms Condensed Phase Conduction Band Valence Band Available States No States available 1/R E Building a Semiconductor Valence band Conduction band Isolated impurities Fill up the states with electrons just like you fill up atomic or molecular states, fill from the lower energy up being careful to abide by Pauli. The material properties are dominated at by the highest energy states that are occupied. Localized states near impurities; These control the properties of the semiconductor

Impurities in Semiconductors “Electrons” in solids can behave as if they have a different mass and charge than free electrons. Why, the dynamics of the material are really determined by the “excitations” of the system (how it’s behaviour differs from the equilibrium state). E.G. for Donors in Si you might expect E=(  o /  ) 2 (m*/m o )E H For Si this works out to be about 25meV, and this is in reasonable agreement with the experimental results for shallow donors (even though we have left out a lot of details that account for differences between elements like P and As etc.

Band structure and Impurties in Si and Ge From S. SM.Sze “Physics of Semiconductor devices”, Wiley (1969))

Nano Technology/Materials Why interesting? Technological Applications (7 responses) How do we make things that small? (8 responses) Confinement energy becomes important (DVB) What would you like to hear more about? Quantum computing (7 responses) Applications in general (5 responses) life sciences (4) Buckyballs/Carbon Nanotubes (5 responses) How to make them? (4 responses)

Key Properties of Materials Electrical Conductivity Hall Effect (balance of Lorentz and Electric forces within a wire carrying a current in a magnetic field). –Useful for measuring carrier concentration and type (electrons vs. holes) –Ubiquitous for measuring magnetic fields Thermo-electric Effects –Electrons carry both charge and energy, hence the two can be coupled. –Used widely for measuring temperature Piezoelectric effects (strain voltages) –Used in SPM’s, small sensors etc.

Lecture 32 Semiconductor Laser

The Field-Effect Transistor

From T. N. Thies IBMJRD (2000) From Mayer and Lau (1990) Inside an Integrated Circuit Materials Science: Interdiffusion, anisotropic etching, electromigration, diff. therm. exp. Condensed-matter Physics: Quantum Hall effects, quantum interference, non-local transport

Integer Quantum Hall Effect 1985 Nobel Prize Von Klitzing

Fractional QHE 1998 Nobel Prize Laughlin, Tsui, Stormer A very rich area of CMP for 2 decades, Anyons, Skyrmions, Coulomb drag …

Fractional QHE 1998 Nobel Prize Laughlin, Tsui, Stormer A very rich area of CMP for 2 decades, Anyons, Skyrmions, Coulomb drag … Take-home lesson: It’s the excitations (stupid!); the low-lying Excitations of a many- Particle system determine Its properties!

The Field-Effect Transistor

Photo-lithography (the birth of nano-tech)

From T. N. Thies IBMJRD (2000) From Mayer and Lau (1990) Inside an Integrated Circuit Materials Science: Interdiffusion, anisotropic etching, electromigration, diff. therm. exp. Condensed-matter Physics: Quantum Hall effects, quantum interference, non-local transport

Fractional QHE 1998 Nobel Prize Laughlin, Tsui, Stormer A very rich area of CMP for 2 decades, Anyons, Skyrmions, Coulomb drag … Take-home lesson: It’s the excitations (stupid!); the low-lying Excitations of a many- Particle system determine Its properties!

Vorlesung Quantum Computing SS ‘08 20 ENIAC Electronic Numerical Integrator And Computer vacuum tubes weight 20 t, power consumption 150 kW 1946

Vorlesung Quantum Computing SS ‘08 21 Moore’s law

Vorlesung Quantum Computing SS ‘08 minimum size of chip components (nm) source: quantum effects in silicon technology barrier silicon year proteins, macro-molecules size of viruses and DNA semiconductor industry exponential extrapolation ?? e : breaking the barrier? We may be starting to see this flatten out, latest Intel processors are using a “32 nm” process, and they are planning for 22nm. Previous generations had used a “45nm” process.

Gold Nano-particles Color varies with particle size (red stained glass From the middle ages uses gold nano-particles)

Gold Nano-particles Color varies with particle size (red stained glass From the middle ages uses gold nano-particles) For even more exciting applications see the Dragnea group site in IU Chem.:

Self-Assembly routes to nanomaterials

Nanostructures from Self-Assembly This self-assembly can be used to make materials with molecular size control (e.g. MCM-41 and related silicates)

Discovery of the Neutron T&R Figure 12.1 Chadwick (1932, building on earlier work by Both and Becker, and later I. Curie, and Joliot) demonstrated that the unknown radiation must have a mass of the same order as the proton by measuring the energy of recoil nuclei of various mass.

Size of Nuclei T&R Figure 12.2 R = r o A 1/3

Trends in Nuclear Stability See also: T&R Fig Please note two things from this figure: 1.The binding energy per nucleon peaks at 56 Fe (CALM) 2.Note the peaks at 4 He 16 O, and (to some extent) at 12 C.

Closing a shell-> Stable atom, high ionization energy

Magic numbers in Nuclei (protons) From E. Segre “Nuclei and Particles Note the sharp drop in separation energy at atomic numbers of 9, 21, 29,51, and 83

Magic numbers in Nuclei (neutrons) From E. Segre “Nuclei and Particles

Shell model for Nuclei From E. Segre “Nuclei and Particles” 3-D Harmonic Oscillator Spherical Square well

Trends in Nuclear Stability T&R Figure 12.5 See also Nudat2 at:

Types of Radiation

Types of Radiation Alpha (  ): 4He nucleus; very easy to stop (paper,etc.) Beta (  ) Electrons or positions, relatively easy to stop NOTE: you can also get high-energy electrons through “internal conversion” and the Auger process, but strictly speaking, these do not come from beta decay, and are therefore not, technically, “beta” particles (even though they behave exactly the same way). Gamma (  ) High-energy photons (of nuclear origin) X-rays High-energy photons (of atomic origin) Neutron (n) Protons, ions

Types of Nuclear Decay Alpha (  ): 4He nucleus; Beta (  ) Electrons or positions, of nuclear origin Electron Capture Gamma (  ) (gamma, internal conversion do not change nucleons). Spontaneous fission proton Neutron (n)

Examples What is the binding energy per nucleon of 56Fe? The mass of I is u and that of Te is u. What decay mode is possible between these two nuclei?