Allowed and Forbidden Energy Bands - allowed energy bands associated with different atomic orbitals may overlap, as in (a) - the regions between allowed energy bands are called forbidden bands or band gaps Electrical Conductivity and Energy Bands - in sodium (a good metal conductor) there are 2(2l+1) with l = 0 available electron states per atom in the 3s shell only one of which is filled with the single valence electron - as a result the 3s shell of sodium is only half filled (see figure) - thus the electrons are free to change their energies within the 3s band - this allows electrons to pick up a kinetic energy from an applied electric field leading to a electron drift velocity generating current that makes Na a good metallic conductor phys4.18 Page 1 - magnesium (Mg) has an electron configuration 1s 2 2s 2 2p 6 3s 2, i.e. it has a filled 3s shell - therefore the filled 3s shell on its own would not allow for electrons to gain energy, if the 3p band was separated by a gap from the 3s band - in Mg however, the 3s and 3p bands overlap in energy (see figure) - the 3p band can accommodate 2(2l+1) = 6 electrons per atom, i.e. jointly the 3s and the 3p orbitals form a band that can accommodate 8 N electrons - thus the conduction band is only 25 % filled rendering Mg a good conductor Insulators - in insulators the electron states in the valence band are completely filled - the next higher available energy band, the conduction band, is separated from the valence band by a band gap - in an insulator the band gap is large enough in energy so that electrons are not thermally excited across it phys4.18 Page 2
- carbon (C, 1s 2 2s 2 2p 2 ) is an insulator even though it has a only partially filled p band - at some intermediate C-C separation an overlapping sp band accommodating 8N electron states is formed - at the equilibrium separation however the band is split into two bands accommodating 4N electrons (hybridization) each that are separated by an energy gap of 6 ev making Carbon (diamond) an insulator - similar reasoning applies to silicon (Si, 1s 2 2s 2 2p 6 3s 2 3p 2 ) - for Si the energy gap is only 1 ev - at room temperature a noticeable number of electrons are thermally excited across the energy gap, where states are available and electrons can gain energy and conduct current - because of the intermediate conductivity such materials are called semiconductors phys4.18 Page 3 Impurity Semiconductors - small amounts of impurities can drastically change the conduction in semiconductors - consider arsenic atoms (As, 4s 2 4p 3 ) embedded in a Si crystal, 4 of the electrons form covalent bonds with the Si, the fifth electron is only weakly bound (0.05 ev) and can easily move in the crystal and contribute to conduction - the arsenic provides electronic energy levels, called donor levels, close to the conduction band - these donor levels supply electrons (negative charges) to the current transport (n-type semiconductor) - similar reasoning applies for gallium (Ga, 4s 2 4p 1 ) impurities embedded in Si that can act as acceptor levels - in this case an electron misses to form 4 covalent bonds - at little energy cost an electron can fill the vacancy, but leaving another vacancy (a hole) behind phys4.18 Page 4
Electron and Hole Current Transport - in a semiconductor doped with n-type impurities (P, Sb, Bi, As) electrons are the dominant (majority) charge carriers responsible for electrical current - in a p-doped (Ga, In, Tl) semiconductor holes are the dominant charge carries - in an applied field holes move in the opposite direction of electrons but contribute a current in the same direction (see figures) - in semiconductors small amounts of dopants on the order of 1 ppb can drastically change the conductivity by orders of magnitude - this control of conductivity is of enormous importance in all semiconductor technology - other semiconductors are (group IV) Ge and (groups III-V) GaAs, GaP, InSb, InP phys4.18 Page 5 Semiconductor Devices - most microelectronics devices used industrially consist of junctions (interfaces) between n- type and p-type doped semiconductors - with modern photolithography technology millions of such junctions (and additionally capacitors, resistors and inductors) can be fabricated on a single chip of a few square millimeter area fabrication technology: - diffusion of (p,n) dopants in vapor form into a single crystal semiconductor wafer through a mask - the mask is generated optically by exposing a light sensitive material (resist) through a metalized mask containing an image of the structure - the resolution is (diffraction) limited by the wavelength of the light (e.g. 193 nm UV light) used in this process to about 65 ~ 100 nm - future reduction in the feature size may require use of alternative radiation sources (Xrays, electron or ion beams) phys4.18 Page 6
Electronic Circuits basis of modern information and communication based society first transistor at Bell Labs (1947) intel dual core processor (2006) 2.000.000.000 transistors smallest feature size 65 nm clock speed ~ 2 GHz power consumption 10 W phys4.18 Page 7 Junction Diode - in a junction between a p-type and an n-type material current transport occurs preferentially in one direction, see I-V curve - in the p-region current is transported by holes, in the n- region by electrons At no bias voltage (V=0): - in the p-region electrons are thermally excited from the valence band into acceptor states generating free holes (p majority carriers) - also electrons are thermally excited into the conduction band creating free electrons (p-side minority carriers) - equivalently, in the n-region electrons are thermally excited from donor states into the conduction band generating free electrons (nside majority carriers) - also electrons are thermally excited into the conduction band creating holes in the valence band (n-side minority carriers) phys4.18 Page 8
Thermal and Recombination Currents - the minority carriers (electrons on the p-side, holes on the n-side) can diffuse across the junction interface (electrons from p to n and holes from n to p) generating a small thermal current I th - the majority carriers (holes on the p-side and electrons on the n-side) are thermally excited across the barrier recombining with majority carriers in the other part of the junction (electrons with holes on the p-side and holes with electrons on the n-side) generating a recombination current I r - with no bias applied the thermal and recombination currents are small and balance each other and there is no net transport current - the Fermi energy is identical in both regions - the recombination current is very sensitive to bias voltage across the junction (because of the bias dependence of the thermal barrier), whereas the thermal current is independent of bias, this fact is responsible for the asymmetry of the current voltage characteristic phys4.18 Page 9 Reverse Bias (V < 0) - voltage applied to the junction with p-end negative and n-end positive - holes diffuse to the p-end, electrons to the n-end which suppresses recombination current - electron hole pairs are still thermally excited and sustain a small constant reverse current Forward Bias (V>0) - voltage applied to the junction with p-end positive and n-end negative pushing electrons and holes into the junction area - recombination current increases at the junction because of the constant supply of electrons and holes and the increase of the electron energy on the n-side by ev phys4.18 Page 10
p-n Junction - acts as a rectifier for electrical current, i.e. a large forward recombination current flows for positive bias and a small reverse thermal current flows for negative bias - a depletion region is formed at the p-n junction interface where at zero bias electrons from the donor levels on the n-side recombine with holes of the acceptor levels on the p-side reducing the number of charge carriers - the extent of the depletion region is typically a few micron phys4.18 Page 11 Light Emitting Diodes (LEDs) - carrier recombination can generates photons in a forward biased diode efficiency ~ 20 % semiconductor diodes (GaAs) power P ~ 0.01-5 W General Electric (1962) phys4.18 Page 12
Applications phys4.18 Page 13