EE105 Spring 2007 Microelectronic Devices and Circuits Lecture 2 Semiconductor Basics Periodic Table of Elements 2 Electronic Properties of Silicon Silicon is in Group IV atomic number 14 Atom electronic structure 1s22s22p63s23p2 Crystal electronic structure 1s22s22p63 sp 4 Diamond lattice with 0 235 nm bond length Very poor conductor at room temperature why 1s 2 2s 2 2p 6 3sp 4 Hybridized State 3 The Diamond Structure 3sp Tetrahedral Bond 2 35 A 5 43 A 4 Energy States of an Atom E3 E2 Allowed Energy Levels Forbidden Band Gap E1 Atomic Spacing Lattice Constant Quantum Mechanics The allowed energy levels for an atom are discrete 2 electrons with opposite spin can occupy a state When atoms are brought into close contact these energy levels split If there are a large number of atoms the discrete energy levels form a continuous band 5 Silicon Si has four valence electrons Therefore it can form covalent bonds with four of its neighbors When temperature goes up electrons in the covalent bond can become free 6 Electron Hole Pair Interaction With free electrons breaking off covalent bonds holes are generated Holes can be filled by absorbing other free electrons so effectively there is a flow of charge carriers 7 Free Electron Density as a Function of Temperature Eg ni 5 2 1015 T 3 2 e 2 kT electrons cm3 ni T 3000 K 1 08 1010 electrons cm3 ni T 6000 K 1 54 1015 electrons cm3 Eg or bandgap energy determines how much effort is needed to break off an electron from its covalent bond There exists an exponential relationship between the free electron density and bandgap energy 8 N Type Doping If Si is doped with group V elements such as phosphorous P or arsenic As then it has more electrons and becomes N type electron Group V impurities are called Donors 9 P Type Doping If Si is doped with group III elements such as boron B then it has more holes and becomes P type Group III impurities are called Acceptors 10 Summary of Charge Carriers 11 Thermal Equilibrium Pure Si Balance between generation and recombination determines no po Strong function of temperature T 300 K G Gth T Gopt R k n p G R k n p Gth T n p Gth T k ni 2 T 10 3 ni T 10 cm at 300K 12 Mass Action Law The product of electron and hole densities is ALWAYS equal to the square of intrinsic electron density regardless of doping levels po no ni 2 T 300 K ni 1010 cm 3 Majority Carrier Conc Doping Conc N Type P Type Minority Carrier Conc Mass Action Law n0 N d N d ni2 p0 Nd p0 N a N a ni2 n0 Na 13 Compensated Doping Si is doped with both donor and acceptor atoms More donors than acceptors Nd Na N type no N d N a po ni2 Nd Na More acceptors than donors Na Nd P type po N a N d no ni2 Na Nd 14 First Charge Transportation Mechanism Drift Mobility v h p E ve n E The process in which charge particles move because of an electric field is called drift Charge particles will move at a velocity that is proportional to the electric field 15 Mobility vs Doping in Silicon at 300K Typical values mn 1350 V sec cm2 mp 450 V sec cm2 16 Current Flow General Case I v W h n q I J v n q Wh Electric current is calculated as the amount of charge in v meters that passes thru a cross section if the charge travel with a velocity of v m s 17 Current Flow Drift J n mn E n q J p mp E p q J tot mn E n q mp E p q q mn n mp p E Since velocity is equal to E drift characteristic is obtained by substituting v with E in the general current equation The total current density consists of both electrons and holes 18 Velocity Saturation m0 m 1 bE m0 vsat b m0 v E m0 E 1 vsat A topic treated in more advanced courses is velocity saturation In reality velocity does not increase linearly with electric field It will eventually saturate to a critical value 19 Second Charge Transportation Mechanism Diffusion Charge particles move from a region of high concentration to a region of low concentration 20 Current Flow Diffusion Diffusion Coefficient dn dx dp J p qD p dx dn dp J tot q Dn Dp dx dx J n qDn Diffusion current is proportional to the gradient of charge dn dx along the direction of current flow Total diffusion current density consists of both electrons and holes 21 Example Linear vs Nonlinear Charge Density Profile J n qDn dn N qDn dx L J n qD dn qDn N x exp dx Ld Ld Linear charge density profile means constant diffusion current whereas nonlinear charge density profile means varying diffusion current 22 Einstein s Relation p D kT q While the underlying physics behind drift and diffusion currents are totally different Einstein s relation provides a link between the two 23 Resistivity of Uniformly Doped Si J n mn E n q s E s nqmn 1 1 r s nq mn V R I Ohm s Law V E L I J tW I V EL L J A RtW RtW RtW 1 L L R r s tW tW E s E 24 Sheet Resistance Rs IC resistors have a specified thickness not under the control of the circuit designer Eliminate thickness t by absorbing it into a new parameter the sheet resistance Rs L r L R r Wt t W L RS W Number of Squares 25 Using Sheet Resistance Rs Ion implanted or diffused IC resistor 26 Idealizations Why does current density Jn turn What is the thickness of the resistor What is the effect of the contact regions 27
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