bohr quantized the atom…
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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
Ele
ctro
n en
erg
y
gas
Outer levels begin to interactOverlapping 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
Bandgap
Bandgap
Partially full
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 gapoverlaplots 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 bandEssentially no available energy states to which electron energies can be increased
Dielectric breakdown at high potential
Conduction band Empty
Valence band Full
Eg Wide bandgap
Semiconductors:Similar to insulators but narrow band gap
At electrical temperatures some electrons can be promoted to the conduction band
Most are cubic Diamond FCC (single element)
Some common band gaps:
Element gap (ev)
Ge 0.6
Si 1.1
GaAs 1.4
SiO2 9.0
Conduction band Almost Empty
Valence band Almost Full
Conduction band Empty
Valence band Full
T > 0K T = 0K
Eg bandgap
SZn
Mark McClure, UNC-Pembroke
Zinc blende (FCC ZnS)
Semiconductors are either intrinsic or extrinsicIntrinsic 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
Ec
Ev
Eg
- +
Extrinsic Semiconductors:
Doped with impurity atomsp-typen-type
n-typeDope 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
Ec
Ev
Ed
Si lattice with n-type dopant
p-typeDope Si with something like trivalent indium (3 valence electrons)
Incomplete bonding with SiNearby 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 atomslocalized energy levels just above valence band
Si
In
Ec
Ev
Ea
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
Ec
Ev
Eg
Valence band
Ec
Ev
Eg
Valence band
Conduction band
Ef
Ef
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
-------
p n
Energy band diagram for p-n junction at equilibrium
++++++
Depletion width W
Space-charge layers
Direction of built-in field
-------
p n
Ecp
Evp
Ecn
Evn
Efn
Efp
eV0
Apply eV0 to get diffusion
Energy band diagram for p-n junction – applied forward bias
++++++
Depletion width W
Space-charge layers
Direction of built-in field
-------
p n
Ecp
Evp
Ecn
Evn
Efn
Efp
eV
Apply small V to get diffusion
Depletion width reduced
Built-in field reduced
Barrier height reduced
Diffusion current increased
If Vforward = V0
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
-------
p n
Ecp
Evp
Ecn
Evn
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
N P N P N P
collector emitter collector emitter
base 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 slidePhototransistor sees varying light intensitycurrent output varies with base current
Diode rectifies
AC→DC
Square waves
Digital output to counter