The Electromagnetic Properties of Materials

Transcription

1 The Electromagnetic Properties of Materials Electrical conduction Metals Semiconductors Insulators (dielectrics) Superconductors Magnetic materials Ferromagnetic materials Others Photonic Materials (optical) Transmission of light Photoactive materials Photodetectors and photoconductors Light emitters: LED, lasers

2 Current Density <δv> j = ne δv = neµe σ = ne2 τ m = ne2 l mv ρ = mv ne 2 l j = - ne<δv> Electron current is by diffusion n = conduction electrons/unit vol µ = mobility Quality of metallic conductor n = bonding and crystal structure µ = microstructure sensitive σ = neµ

3 Resistivity T ρ = ρ 0 + AT impurity increasing purity phonon Resistivity Impurities and phonons add Phonon linear in T Impurity independent of T Use residual resistivity to measure purity

4 Semiconductors: The Bottom Line Semiconductors are poor conductors of electricity Semiconductors are useful because they are controllable Can adjust conductivity Can choose type of conductor: electrons or positive holes Most microelectronic devices use semiconductor junctions Diodes (n p) Transistors (n p n or p n p) Other devices are based on controlling band gap Especially photonic materials (optical properties) We shall cover these later

5 Semiconductors Semiconductor type and conductivity Conductivity dominated by carrier density Intrinsic semiconductors (excitation across band gap) Extrinsic semiconductors n-type (donors) or p-type (acceptors) Permit precise control over σ and type of carrier Semiconductor junctions n p diode n p n bipolar transistor Field effect transistor (mosfet) Manufacturing semiconductor devices Lithography Doping Packaging

6 Intrinsic Semiconductor e - conduction band Filled bands separated by a gap E F approximately in center of the gap E E F E G valence band Excitation creates two carriers: Free electron in conduction band Hole in valence band Conductivity controlled by carrier density x σ = n e eµ e + n p eµ p

7 Carrier Density in an Intrinsic Semiconductor Electrons (n) n N 0 exp E G 2kT E E F E G conduction band valence band Holes (p) x p N 0 exp E G 2kT (= n) n = p = E c E v P(E)N(E)dE p(e)n(e)de

8 Conductivity of an Intrinsic Semiconductor σ sums electrons and holes: σ = neµ e + peµ p N 0 e(µ e + µ p )exp E G 2kT σ N 0 eµ e exp E G 2kT (µ e >> µ p ) Plot ln(σ) vs. 1/kT: Straight line Slope is (E G /2)

9 Semiconductors Semiconductor type and conductivity Conductivity dominated by carrier density Intrinsic semiconductors (excitation across band gap) Extrinsic semiconductors n-type (donors) or p-type (acceptors) Permit precise control over σ and type of carrier Semiconductor junctions n p diode n p n bipolar transistor Field effect transistor (mosfet) Manufacturing semiconductor devices Lithography Doping Packaging

10 Extrinsic Semiconductors: n-type e Si Si P Si Si E ÎE G Conduction band Valence band } ÎED donor levels x n-type semiconductors are doped with donors Common donor has 1 extra valence electron (e.g., P in Si) Donor electron in excited state weakly bound to extra + on donor Corresponds to localized donor levels just below conduction band Electrons are excited from donor levels to produce carriers Conduction is by electrons

11 Extrinsic Semiconductors: p-type Si Si B Si Si E ÎE G Conduction band Valence band acceptor levels } ÎEA x p-type semiconductors are doped with acceptors Common acceptor has 1 less valence electron (e.g., B in Si) Hole in valence state weakly bound to effective - on acceptor Corresponds to localized acceptor levels just above valence band Electrons are excited to acceptor levels to produce free holes Conduction is by holes

12 Extrinsic Semiconductors: Conductivity of an n-type Semiconductor intrinsic Carrier density determines σ σ = neµ e ln(n) E G /2kT E D /2kT saturation extrinsic higher N n N 0 exp E E c F kt p N 0 exp E F E V 2kT n = N + D + p 1/kT n = N 0 N D 2 exp ΔE D 2kT N D N 0 exp E G 2kT (low T) (saturation) (high T)

13 Extrinsic Semiconductors: Degeneracy Conduction band E donor band acceptor levels Valence band At a critical concentration, donor states overlap Donor band = continuous band of donor states Degenerate semiconductor is a metallic conductor Overpopulation of acceptors also creates degeneracy

14 Extrinsic Semiconductors: Titration Conduction band E donor levels acceptor levels Valence band x Donor electrons fill acceptor levels n-type behavior is not achieved until acceptors filled Acceptors must be titrated before donor states overlap Semiconductors must have high purity prior to doping Converse applies: acceptors titrate donors Can convert n-type to p-type if donor concentration is small

15 Semiconductor Junctions Join n- and p-type regions to create a junction Junctions have asymmetric electrical properties Can be done by doping adjacent regions Write junction devices onto a single crystal (chip) This is the basis of all microelectronics

16 The Band Structure at an n p Junction n p E e e e e e e e E F E e e e e e e E F x x Join n and p regions Just prior to join, E F high on n-side Electrons flow from n to p (holes flow p to n) Charges at interface create potential, Δφ, across interface Potential raises E on p-side (ΔE = -eδφ ) Equilibrium (current stops) when E F (n)=e F (p) The electron and hole occupancies are constant across the interface at every E

17 Current-Voltage Characteristic: n p Junction Electron current density j e = j + e + j e = j 0 e exp ev kt 1 Hole current density j p = j e V Total current I e = - I j = j p j e = 2 j 0 e exp ev kt 1

18 Mechanism of Conduction under Bias - n The image cannot be displayed. Your computer may not have enough memory to open the image, or p the image may have been corrupted. Restart your computer, + + n The image cannot be displayed. Your computer may not have enough memory to open the p image, or the image may have been corrupted. Restart your computer, - E e e e e e e } ev e E F E e e e e e e ev { e E F x x Forward bias: Electrons and holes diffuse across interface from majority side Recombine with majority carriers Reverse bias: Electrons and holes diffuse from minority side Carrier density replenished by excitation

19 The Bipolar Transistor emitter base collector n p n E e e e e e e e e e e e e E F The transistor is an n p n (or p n p) device Two n p junctions joined in opposite orientation Characteristics Voltages controlled independently (V e, V b, V c ) Base is thin compared to emitter and collector x

20 The Bipolar Transistor under Bias - n p n + e E e e e e e e e e e e e e E F x Transistor acts like a closed switch when V b =0 p n junction is in reverse bias Only leakage current transmitted

21 The Bipolar Transistor as a Switch Controlled by V b + - n p n + E e e e e e e e e The image cannot be displayed. Your computer may not have enough memory e e e e e e e E F V b > 0 opens switch So long as V b > V e, electrons flow into the base To achieve equilibrium, electrons recombine with holes in base Given small size of base, holes are exhausted by recombination Holes cannot be replenished Collector in reverse bias Emitter voltage attracts holes Base becomes transparent to electrons Current controlled by V b -V e

22 The Bipolar Transistor as an Amplifier Controlled by V c + - n p n + E e e e e e e e e e e e e e E F x Current is controlled by ΔV eb After saturation, j e = 2 j 0 e exp eδv eb kt 1 Potential drop into collector imparts energy ΔE = -e ΔV bc Transistor functions as a power amplifier with amplification set by ΔV bc

23 The Field Effect Transistor: Metal-Oxide-Semiconductor Junctions (MOS) V + inversion depletion normal metal oxide p metal oxide n p - p E E F metal o x i d e conduction band e e e e valence band E F MOS can invert semiconductor type Positive potential lowers E C, attracts electrons When E C -E F < E G /2, semiconductor inverts (p n) Potential creates field effect - n-region near surface p-region in depth p - (depleted zone) acts as insulator

24 MOSFET: Metal-Oxide-Semiconductor Field Effect Transistor V + gate source drain V V + metal oxide n p - n + n + p channel I V g >V I V g = 0 V Construct n p n junction at MOS as shown In this case n p n called source gate drain (V d > V s ) When V g = 0, gate drain in reverse bias Switch is off When V g > V I, gate is n-type and current flows Switch is on

25 Semiconductors Semiconductor type and conductivity Conductivity dominated by carrier density Intrinsic semiconductors (excitation across band gap) Extrinsic semiconductors n-type (donors) or p-type (acceptors) Permit precise control over σ and type of carrier Semiconductor junctions n p diode n p n bipolar transistor Field effect transistor (mosfet) Manufacturing semiconductor devices Lithography Doping Packaging

26 Semiconductor Device Processing oxide passivation metallic conductors silicon chip active devices (transistors, etc.) Manufacture millions of devices simultaneously on a chip Steps in manufacture (simplified) Crystal growth and dicing to chip Photolithography to locate regions for doping Doping to create n-type regions Overlay to create junctions Metallization to interconnect devices Passivation to insulate and isolate devices Higher level packaging to interconnect chips

27 Photolithography light mask coating oxide silicon coating oxide silicon Minimum feature size depends on wavelength of light Visible light: ~ 1 µm Ultraviolet light: ~ 0.1 µm Electrons, x-rays nm New and exotic methods Must have photoresist suitable to the light Or use light to cut through oxide directly

28 Doping dopant ions dopant distribution Add electrically active species Simple method: Coat surface and diffuse Diffusion field is electrically active More precise:ion implantation: Accelerate ions of the electrically active species toward surface Ions embed to produce doped region

29 Doping: The Chemical Distribution c ion implantation laser anneal diffusion laser light dopant distribution x Initial distribution is inhomogeneous Diffusion produces gradient from surface Ion implantation produces concentration at depth beneath surface Can homogenize by laser annealing Use a laser to melt rapidly, locally Rapid homogenization n melted region Rapid re-solidification since rest of body is heat sink

30 Overlay to Create Junctions n n n p n p Once primary doping is complete Re-coat Re-mask Re-pattern Dope second specie to create desired distribution of junctions

31 Metallization diffusion barrier conductor diffusion barrier conductor diffusion barrier conductor Si oxide devices Si oxide Si oxide After devices are made Coat with oxide for insulation Etch for conductor pattern Coat and etch (Al) Coat surface with Al(Cu) Pattern and etch to create desired pattern of conductors Damascene process (Cu, which is difficult to pattern-etch) Pattern oxide with trenches for Cu lines Coat with Cu, polish off to leave filled trenches

32 Passivation and Packaging = oxide = metal = devices = semiconductor Coat with insulator to isolate device Oxide to isolate metallic conductors Hermetic seal, usually polymer, to insulate form environment Sealing is difficult since electrical contacts must penetrate Interconnect devices Wire and solder chips to boards Boards to one another to make electronic device