Bohr quantized the atom… An atom has a set of energy levels Some (but not all) occupied by electrons Not really dealing with isolated atoms, but 3D solids As atoms approach each other, each affects the other Energy levels are altered, splitting into bands Each atom in the system produces another energy level in the band structure

Broadening of energy levels as atoms approach Degenerate: All electrons in an orbital have the same (lowest) energy Electronic structure of Solids Electron energy gas Outer levels begin to interact Overlapping levels

Energy bands for solid sodium at internuclear distance of 3.67Å

Immediate implication for X-Ray microanalysis… Electron transitions from split levels (bands) will result in photon emission energies that do not reflect the discrete degenerate level…

Conduction band: First empty band above the highest filled band Valence band: Outermost band containing electrons nucleus Conduction band Valence band Outermost band containing elelectrons Electron energy Bandgap Partially full Full Empty band

Transitions from the valence band involved in characteristic X-ray emission will be energy shifted depending on bond lengths, etc. Resulting X-Rays will not be monochromatic These will be Kα X-rays for ultra-light elements nucleus Conduction band Valence band Electron energy Bandgap Partially full Empty band N=1 (K) N=2 (L)

Classification of solids: Conductors Insulators Semiconductors Conductors: Outermost band not completely filled Essentially no band gap overlap lots of available energy states if field is applied Metals and Alkali metals

Insulators: Valence band full or nearly full Wide band gap with empty conduction band Essentially no available energy states to which electron energies can be increased Dielectric breakdown at high potential Conduction band Empty Valence band Full EgEg Wide bandgap

Semiconductors: Similar to insulators but narrow band gap At electrical temperatures some electrons can be promoted to the conduction band Most are cubicDiamond FCC (single element) Some common band gaps: Elementgap (ev) Ge0.6 Si1.1 GaAs1.4 SiO29.0 Conduction band Almost Empty Valence band Almost Full Conduction band Empty Valence band Full T > 0K T = 0K EgEg bandgap S Zn Mark McClure, UNC- Pembroke Zinc blende (FCC ZnS)

Semiconductors are either intrinsic or extrinsic Intrinsic Semiconductors: Pure state Example: Covalently bonded, tetravalent Si lattice Promotion of an electron to the conduction band leaves “hole” in the valence band = electron-hole pair Apply an electric field and the electron will migrate to + The hole will migrate to – (that is, the electron next to the hole will be attracted to the +, leaving a hole toward -) Net propagation of hole EcEc EvEv EgEg - +

Extrinsic Semiconductors: Doped with impurity atoms p-type n-type Dope Si with something like pentavalent antimony (5 valence electrons) Narrows the band gap relative to Si easy to promote Sb electron Majority carriers are electrons in conduction band Minority carriers are holes in valence band Lattice doped with donor atoms localized energy levels just below conduction band

Si Sb EcEc EvEv EdEd Si lattice with n-type dopant

p-type Dope Si with something like trivalent indium (3 valence electrons) Incomplete bonding with Si Nearby electron from Si can fill hole Majority carriers are holes in the valence band Minority carriers are electrons in the conduction band Lattice doped with acceptor atoms localized energy levels just above valence band

Si In EcEc EvEv EaEa Si lattice with p-type dopant

Fermi Level: That energy level for which there is a 50% probability of being occupied by an electron Conduction band EcEc EvEv EgEg Valence band EcEc EvEv EgEg Conduction band EfEf EfEf Intrinsic n-type Recombination Electron-hole pairs not long lasting Electron encountering hole can “fall” into it Free time = microsecond or less

The p-n junction Single crystal of semiconductor Make one end p-type (dope with acceptors) Make the other end n-type (dope with doners) The junction of the two leads to rectification Current only passed in one direction (diode) In the region of the junction Recombination = depletion of region with few charge carriers Results in “built-in” electric field Depletion width W Space-charge layers Direction of built-in field pn

Energy band diagram for p-n junction at equilibrium Depletion width W Space-charge layers Direction of built-in field pn E cp E vp E cn E vn E fn E fp eV 0 Apply eV 0 to get diffusion

Energy band diagram for p-n junction – applied forward bias Depletion width W Space-charge layers Direction of built-in field pn E cp E vp E cn E vn E fn E fp eV Apply small V to get diffusion Depletion width reduced Built-in field reduced Barrier height reduced Diffusion current increased If V forward = V 0 No barrier Pass large current in one direction +-

Energy band diagram for p-n junction – applied reverse bias Depletion width W Space-charge layers Direction of built-in field pn E cp E vp E cn E vn eV Depletion width increased Built-in field increased Barrier height increased - Diffusion current decreased Becomes Capacitor No current passed +-

So: Can use reversed bias p-n junction as voltage regulator Zener diode Voltage too high? Overcome gap energy and pass current Can use forward bias p-n junction for rectification AC → DCtransformer Analog-to-digital conversion LED Recombination – “tune” bandgap to achieve photon emission at the required wavelength GaAs (IR) GaInN (blue) GaAsP (red) YAG:Ce (white) Ternary and quaternary compounds allow precise bandgap engineering PIN diode (p and n sections separated by high resistance material) light detection X-ray detection electron detection -Each of these serve to excite electron-hole pairs -Bias properly and get amplification rather than simple propagation

Bipolar transistor = pair of merged diodes - NPN or PNP NPNPNP collector emitter collectoremitter base Three voltages (NPN) Collector = + relative to base (collects electrons) Emitter = - relative to base (emits electrons) Small adjustments of the current on the base results in large changes in collector current. = current amplifier Amplify weak signals Use small currents to switch large ones

Simple optical encoding: Generate sine wave by LED passing ruled slide Phototransistor sees varying light intensity current output varies with base current Diode rectifies AC→DC Square waves Digital output to counter