Electrons in Solids Energy Bands and Resistance in Conductors and Semiconductors

What Have We Learned About Optical Storage?  Laser light is focused through a (circular) lens onto the surface of a CD  Light striking a (smooth) land undergoes total reflection toward the detector: 1  Light striking a (rough) pit undergoes diffuse reflection so the detector receives less light: 0  The central max of the diffraction pattern must be no larger than one bit if data is to be resolved d sin  = 1.22

What Have We Learned About Electrical Storage  The electric force FE on a charge q0 can be considered due to an electric field which is produced by other charges qi in the area F E = q 0 E  If moving a charge between two points requires work (or does work), the charge gains (or loses) potential energy:  V = –  E  dx  Capacitors store charge Q in proportion to the voltage V between the plates: C = Q/V = C =  0 A/d  Capacitors are used in RAM

What Have We Learned About Magnetic Storage?  Two domains magnetized in same direction is a 0  Two domains magnetized in opposite directions is a 1  Direction of magnetization changes at start of new bit.  Magnetic data is written by running a current through a loop of wire near the disk  As magnetic data passes by coil of wire, changing field induces currents according to Faraday’s Law:

What Have We Learned About Magnetoresistance?  Charges traveling through magnetic field experience magnetic force (provided velocity and field are not aligned): F B = qv x B  In a current-carrying wire, this force results in more frequent collisions and thus an increased resistance: Magnetoresistance  Electrons traveling through magnetized material undergo spin-dependent scattering  When magnetic field is present in magnetic superlattice, scattering of electrons is cut dramatically, greatly decreasing resistance: Giant magnetoresistanced

Stuff to remember about GMR  Electrons (and other elementary “particles”) have intrinsic magnetic fields, identified by spin  The scattering of electrons in a ferromagnetic material depends on the spin of the electrons  Layers of ferromagnetic material with alternating directions of magnetization exhibit maximum resistance  In presence of magnetic field, all layers align and resistance is minimized

What Have We Learned About Spectra?  ENERGY IS QUANTIZED  Different elements have different allowed energies (since different numbers of protons and electrons provide different structure of attraction  Light emitted when electrons move from a high energy level to a lower energy level in an atom will have only certain, QUANTIZED, allowed energies and wavelengths.  Those wavelengths depend solely on the element emitting the light and compose the characteristic emission spectrum for that element

Our Model of the Atom  If the atom is in the “ground state” of lowest energy, electrons fill the states in the lowest available energy levels. The first shell has two possible states, and the second shell has eight possible states. Higher shells have more states, but we’ll represent them with the eight states in the first two sub-shells.  Electrons in the outermost shell are called “valence” electrons. We’ll make them green to distinguish from e - in filled shells E=0 (unbound) n=1 n=2 n=3 n=4 Really eight closely spaced energies, since no two electrons can occupy same state

Atomic Bonding  Electrons in an unfilled valence shell are loosely bound  Atoms will form bonds to fill valence shells, either by sharing valence electrons, borrowing them, or loaning them  When atoms bond in solids, sharing electrons, each atom’s energy levels get slightly shifted E=0 (unbound) n=1 n=2 n=3 n=4

Electron Motion  Electrons can only move to an open energy state  If the atom does not absorb energy, electrons can only move to an open energy state in the same shell (drawing is NOT to scale) E=0 (unbound) n=1 n=2 n=3 n=4

Electrons in Solids  The shifted energies in adjacent atoms combine to create a continuous “band” of allowed energies for each original energy level; each band, however, has a finite number of states equal to the number in original atoms  Electrons can move from the locality of one atom to the next only if an energy state is available within the same band

Conductors & Semiconductors  In conductors, the valence band is only partially-full, so electrons can easily move from being near one atom to being near anotherconductors  In semiconductors and insulators, the valence band is completely full, so electrons must gain extra energy to movesemiconductors  In semiconductors, the band gap between the full valence band and the empty conduction band is small, so electrons move easily with only thermal energy  In insulators, the band gap is larger, so electrons will not easily move into the conduction band

Electrons in an Electric Field  Conduction electrons move randomly in all directions in the absence of a field.  If a field is applied, the electric force results in acceleration in a particular direction: F=ma= –eE  a = –eE/m  As the charges accelerate, the potential energy stored in the electric field is converted to kinetic energy which can be converted into heat and light as the electrons collide with atoms in the wire  This acceleration produces a velocity v = at = –eE t/m

Electrical current  If an electric field points from left to right, positive charge carriers will move toward the right while negative charges will move toward the left  The result of both is a net flow of positive charge to the right.  Current is the net change in positive charge per time

A Basic Circuit

How do we measure all this? No, Ringo, we use the deluxe edition of a multimeter!

Answer the Ohm’s Law - Before You Start Questions in Today’s Activity, Then Continue Through Question 4

 Look at the movement of charges through a wire with a potential difference applied - animationanimation  The net velocity is called drift velocity v d  The charge contained in a cross-sectional volume is  q=Nq(Volume)=NqA  x=NqAv d  t  So the charge per time crossing through A is Electrical current

 The drift velocity is the net velocity of charge carriers after collisions  It is not equal to the velocity caused by acceleration of field on individual charge, but it certainly is proportional to it.  Since current is proportional to v d, current is proportional to electric field How do I figure the drift velocity?

 Electric field is proportional to potential difference or voltage  So,... Where am I going with this?  Ohm gets credit for being the first to notice that many materials displayed this proportionality. He defined resistance as the ratio of V to i.

V = iR  Ohm’s law only applies to materials in which the behavior of charge carriers can be described statistically by the drift velocity  In short, Ohm’s law only applies to ohmic materials.  Were both of your resistors made of ohmic material? Ohm’s Law - worth remembering

A Good Analogy to Remember

On what does resistance depend?

On What Does Resistance Depend?  If I increase the length of a wire, the current flow decreases because of the longer path  If I increase the area of a wire, the current flow increases because of the wider path R =  L/A  If I change to a material with better conductivity, the current flow increases because charge carriers move better  If I change the temperature, the current flow changes

Back to the water analogy

Where does the material factor enter?

Finish The Activity Remember, i = NqAv d, so R  1/ N, 1/ A, 1/ q, 1/ v d

Conductors vs. Semiconductors  Electrons are free to move in the conduction band  As temperatures rise, electrons collide more with vibrating atoms; this effect reduces current  Conductors have a partially-filled valence band which doubles as a conduction band at any temperature  The primary effect of temperature on resistance is due to more collisions at higher temperatures  Semiconductors have a completely-filled valence band, so electrons have to gain energy to enter the conduction band  The primary effect of temperature on resistance is due to this requirement: the higher the temperature, the more conduction electrons

What have we learned today?  When atoms bind, the energy levels in each atom get shifted slightly (the size of the shift is very small compared with the energy difference between different levels)  Atoms in solids form bands of closely-spaced energy levels  Electrons fill the lowest-energy bands first  The highest energy band with electrons in it is called the valence band  If the valence band is not full, electrons can move from atom to atom. This is the case for conductors  Electrons can not move in filled bands. Thus electrons in semiconductors must gain energy (usually from thermal sources) to move from atom to atom.

What else have we learned today?  In many, ohmic, materials, current is proportional to voltage: V = iR  Resistance is proportional to the length of an object and inversely proportional to cross-sectional area: R =  L/A  The constant of proportionality here is called the resistivity. It is a function of material and temperature.  The resistivity of conductors increases with temperature since atomic vibrations increase.  The resistivity of semiconductors decreases with temperature since more conduction electrons exist, and this effect overshadows the vibrations.