Section 12 Intro to Devices Extensive reading materials on reserve including Robert F Pierret Semiconductor Device Fundamentals EE143 Ali Javey Bond Model of Electrons and Holes Si Si Si Si Si Si Si Si Si Sili Silicon crystall in i a two dimensional representation Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si When an electron breaks loose and becomes a conduction electron a hole is also created EE143 Ali Javey Semiconductors Insulators and Conductors Ec E g 1 1 eV Ec E g 9 eV empty Ev Ev Si Semiconductor Top of conduction band SiO insulator 2 Totally filled bands and totally empty bands do not allow current flow Just as there is no motion of liquid in a totally filled or y empty p y bottle totally Metal conduction band is half filled Semiconductors have lower EG s than insulators and can be doped EE143 Ali Javey filled Conductor Ec Intrinsic Carriers electron Bottom of conduction band Energy gap 1 12 eV hole Top of valence band n electron conc p hole conc ni EE143 Ali Javey Dopants in Silicon Si Si Si Si Si Si Si As Si Si B Si Si Si Si Si Si Si As a Group V element introduces conduction electrons and creates N type silicon and is called a donor B a Group III element introduces holes and creates P type silicon and is called an acceptor EE143 Ali Javey Types of charges in semiconductors Hole Electron I i d Ionized Donor Ionized Acceptor Mobile Charge Carriers they contribute to current flow with electric field is applied Immobile Charges they DO NOT contribute to current flow with ith electric l t i field fi ld is i applied li d However they affect the local electric field EE143 Ali Javey Fermi Function The Probability of an Energy State Being Occupied by an Electron f E Ef is called the Fermi energy or the Fermi level 1 1 e E E f kT Boltzmann approximation f E e E Ef 3kT f E e E E f f E 1 e Ef Ef kT Ef Ef kT Ef 2kT f E 1 e E f E kT f E 0 5 kT E E f kT k kT Ef 2kT Ef 3kT E E f 1 EE143 Ali Javey E f E kT E E f kT Electron and Hole Concentrations n N c e E F EC kT p N v e EV E F kT Nc is called the effective d i off states density Nv is called the effective densityy off states off the valence band Remember the closer Ef moves up p to E c the larger g n is the closer Ef moves down to Ev the larger p is For Si Nc 2 8 1019 cm 3 and Nv 1 04 1019 cm 3 EE143 Ali Javey Shifting the Fermi Level EE143 Ali Javey Quantitative Relationships n electron concentration cm 3 p hole concentration cm 3 ND donor concentration cm 3 NA acceptor concentration cm 3 Assume completely ionized to form ND and NA 1 Charge neutrality condition ND p NA n 2 Law of Mass Action n p ni2 What happens pp when one doping species dominates EE143 Ali Javey General Effects of Doping on n and p I N d N a ni i e N type n Nd Na p ni n 2 If N d N a n Nd II N a N d ni i e P type If N a N d p Na p ni and 2 Nd p Na Nd n ni and EE143 Ali Javey 2 p n ni N a 2 Carrier Drift When an electric field is applied to a semiconductor mobile carriers will be accelerated by the electrostatic force This force superimposes on the random thermal motion of carriers 2 3 1 electron 4 3 2 1 electron 4 5 5 E 0 E E g Electrons drift in the direction opposite to the E field Current flows Average drift velocity v E C i mobility Carrier bili EE143 Ali Javey Carrier Mobility Mobile carriers are always in random thermal motion If no electric field is applied the average current in any direction is zero Si Mobility is reduced by 1 collisions with the vibrating atoms phonon phonon scattering scattering 2 deflection by ionized impurity atoms Coulombic scattering BAs EE143 Ali Javey Total Mobility 1600 1 1400 E le ctro n s 1 1000 2 1 1 Mobiility cm V s 1200 1 phonon 1 phonon 1 impurity 1 impurity 800 600 400 H o le s 200 0 1E 14 1E 15 1E 16 1E 17 1E 18 1E 19 3 3 n a tom s cm T o ta l Im p urity uN rity odn cm ce n ratio a CN EE143 Ali Javey 1E 20 Conductivity and Resistivity Jp drift qpv qp pE Jn drift q qqn nE n drift qnv Jdrift Jn drift Jp drift E qn n qp p E conductivity of a semiconductor is qn n qp p Resistivity 1 EE143 Ali Javey DOPANT DENSITY cm 3 D Relationshipp between Resistivityy and Dopant p Densityy P type P type N type RESISTIVITY cm 1 EE143 Ali Javey I V W Sheet Resistance L L Rs R W Wt t Material with resistivity L Rs is the resistance when W L in ohms square Rs t if is independent of depth x Rs value for a given conductive layer e g doped Si metals in IC or MEMS technology gy is used for design and layout of resistors for estimating values of parasitic resistance in a device or circuit EE143 Ali Javey Diffusion Current Particles diffuse from higher concentration to lower concentration locations EE143 Ali Javey Diffusion Current J n diffusion dn qDn dx J p diffusion dp qD p dx D is called the diffusion constant Signs explained p n x EE143 Ali Javey x Generation Recombination Processes Recombination continues until excess carriers 0 Time constant of decay is called recombination lifetime EE143 Ali Javey Continuity Equations Combining all the carrier actions n t nt diff nt thermalR G nt others Now by the definition of current we know n t drift n t drift n t diff 1 q J Nx N x J Ny y J Nz N z 1q J N Since a change in carrier concentration must occur from a net current Therefore we can compactly write the continuity equation as n t 1q J N nt thermalR G nt other p t JP 1 q p t thermalR th lR G EE143 Ali Javey p t other th PN Junctions Donor s N type P type V I I V Reverse bias Forward bias N P diode symbol A PN jjunction is present p in almost everyy semiconductor device EE143 Ali Javey Energy Band Diagram and Depletion Layer N region P region Ef a Ec b Ec Ef Ev Ev Ec Ef Ev c Neutral N region Depletion layer n 0 and p 0 in the depletion layer Neutral P region Ec Ef Ev …
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