chap1 - $ ECE432 Physics of Semiconductor Devices...

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Unformatted text preview: ' $ ECE432 Physics of Semiconductor Devices Instructor: Patrick Roblin Department of Electrical & Computer Engineering The Ohio State University Columbus, OH 43210 & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 0 The Ohio State University % ' $ Class Webpage Address: http://www.ece.osu.edu/~roblin/ee432CL/ Easy path: http://www.ece.osu.edu/~roblin ! ece432 ! Class Webpage Username: ece432 Password: 2006 Content: Homework problems and solution Lecture notes Previous exams & Instant Feedback Form (Word document) Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 1 The Ohio State University % ' $ Review: Chapter 1 & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 2 The Ohio State University % ' $ Semiconductor Materials II Zn Cd III IV BC Al Si Ga Ge In V VI N PS As Se Sb Te Elemental: Si, Ge IV compounds: SiC, SiGe III-V compounds: AlP, AlAs, GaN, GaP, GaAs, GaSb, InP, InAs, InSb & II-VI compounds: ZnS, ZnSe, ZnTe, CdS, CdSe, CdTe Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 3 The Ohio State University % ' $ Material Types Crystalline Amorphous Polycrystalline Examples: Crystal: Quartz (SiO2 ) found in? Amorphous: glass (SiO2 ) quasi-frozen liquid ! cathedral stain glass windows are thicker at the bottom polycrystaline: recrystalized glass ! cathedral stain glass windows become brittle due polycrystalline strainOHIO after recrystalization S ATE T & Patrick Roblin T.H.E UNIVERSITY 4 The Ohio State University % ' & Patrick Roblin $ Stain Glass Window by Ann Torrini T.H.E OHIO S ATE T UNIVERSITY 5 The Ohio State University % ' $ Cubic Crystals Simple Cubic Body−centered Cubic Face−centered Cubic Not Cubic Left invariant under 48 symmetries: identity, inversion, rotation 22 , 2 , and 24 . 3 & Why is the 4th structure not cubic? Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 6 The Ohio State University % ' $ Lattice Vector: Periodicy in 3D kz z a1 y a2 a3 ky 4 π/a a x kx a) Face-centered cubic in direct space b) Body-centered cubic in indirect space The 3D lattice consists of all the points generated by the lattice vectors R = n1a1 + n2a2 + n3a3 (1) OHIO T with n1 , n2 and n3 integers and a1 , a2 and a3 the lattice translation vectors.S ATE & Patrick Roblin T.H.E UNIVERSITY 7 The Ohio State University % ' $ Diamond and Zinc-blende crystal Tetrahedral bonds Ga As 2 6 a6 6 26 4 32 76 76 76 76 54 3 7 7 7 7 5 011 n1 R = 1 0 1 n2 110 n3 Only invariant under 24 symmetries (no inversion symmetry). & Patrick Roblin Basis (2) T.H.E OHIO S ATE T UNIVERSITY 8 The Ohio State University % ' $ Reciprocal (Indirect) Space Owing to the lattice periodicty any physical quantity f (r) veri es: f (r) = f (r + R) As f (r) is periodic we can expand it using a Fourier series. X f (r) = AK eiK:r (3) K where K is the so-called reciprocal lattice vector and AK the Fourier coe cient. Now using the translation property we have X f (r + R) = AK eiK:(r+R) = f (r): K It results that we must have exp(iK:R) = 1 such that the reciprocal lattice vectors verify K:R = n 2 with n an integer. OHIO & Patrick Roblin T.H.E S ATE T UNIVERSITY 9 The Ohio State University % ' $ Reciprocal Space for Faced-Centered Crystal For the face-centered-cubic lattice the reciprocal lattice vectors K verifying this relation are given in the orthonormal coordinates of the Bravais cell by 2 32 3 6 ;1 1 1 7 6 m1 7 6 76 7 K = 2a 6 1 ;1 1 7 6 m2 7 (4) 6 76 7 4 54 5 1 1 ;1 m3 kz z a1 y a2 a3 & Patrick Roblin ky 4 π/a a x kx a) Face-centered cubic in direct space b) Body-centered cubic in indirect space T.H.E OHIO S ATE T UNIVERSITY 10 The Ohio State University % ' $ Brillouin Zone X L L Γ X K X L L & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 11 The Ohio State University % ' $ Body-Centered Crystal and the Brillouin Zone Top view of 5 Brillouin zones & Patrick Roblin Side view of 5 Brillouin zones T.H.E OHIO S ATE T UNIVERSITY 12 The Ohio State University % ' & Patrick Roblin $ Built Your Own T.H.E OHIO S ATE T UNIVERSITY 13 The Ohio State University % ' Quantum Mechanic: Particle-Wave Duality Particle ! Example: electron in free space Energy E Momentum p = mv ! ! ! ! ! & $ Patrick Roblin Wave (j j2 probability of presence of particle) = A sin(!t ; k:r) Frequency h! Wavevector hk T.H.E OHIO S ATE T UNIVERSITY 14 The Ohio State University % ' $ Classical & Quantum Atom Model continuum E3 E2 E1 E3 E1 Classical E2 Quantum The electron cannot go below the ground state of energy E1 . & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 15 The Ohio State University % ' $ Other Quantum E ect: Tunneling Potential Energy 1111111 0000000 1111111 0000000 1000000 0111111 0000000 1111111 0000000 1111111 Space Similar to sound crossing a wall. The wave penetration decreases exponentially with the barrier area. & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 16 The Ohio State University % ' $ Atomic Structure of C, Si and Ge Energy r 4f 4d Atomic potential py px x x 4p E4 pz Ge 32 1s 2 2s 2 2p6 3s2 3p6 3d10 4s 2 4p 2 4s 3d 3p E3 14 Si 1s 2 2s 2 2p6 3s2 3p2 C6 3s 1s 2 2s 2 2p2 2p E2 2s s & E1 1s nucleus T.H.E Pauli exclusion principle: 1 electron per state Patrick Roblin 17 OHIO S ATE T UNIVERSITY The Ohio State University % ' $ s1 p3 Hybrid s px py pz Tetrahedral bonds Ga & Patrick Roblin s1 p3 As hybrid Basis T.H.E OHIO S ATE T UNIVERSITY 18 The Ohio State University % ' $ Crystal Potential Energy E pot & Patrick Roblin E 0 T.H.E OHIO S ATE T UNIVERSITY 19 The Ohio State University % ' $ Band Formation from the Surface for N Atoms Energy E pot E χ 0 antibonding Conduction band 4 N states Ec e− Eg Forbidden band h+ Ev 4 N states bonding Valence band Position & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 20 The Ohio State University % ' $ Empty Crystal Perturbed E(k x) π a & Patrick Roblin 0 π a π 2a 1D Brillouin zone kx T.H.E OHIO S ATE T UNIVERSITY 21 The Ohio State University % ' $ Direct and Indirect Bandgap Energy Energy Eg k − space & Patrick Roblin Valence Forbidden Conduction bands: Direct Bandgap Eg k−space Indirect Bandgap T.H.E OHIO S ATE T UNIVERSITY 22 The Ohio State University % ' $ BandStructure Energy k - space Parabolic Free particle 1 k m v2 = 2p2 = 2hm2 2 m & Patrick Roblin Energy Energy k-space k-space Linear Photon/Phonon hjkjc Periodic Crystal A ; A cos(ka) T.H.E OHIO S ATE T UNIVERSITY 23 The Ohio State University % ' $ Si, Ge and AlSb Bandstructure Band structure of Si Band structure of Ge 10 Band structure of AlSb 10 e−CB hh−VB lh−VB 8 10 e−CB hh−VB lh−VB 8 8 4 4 2 2 2 0 Energy in eV 6 Energy in eV 6 4 Energy in eV 6 0 0 −2 −2 −4 −4 −6 Patrick Roblin −2 −4 & e−CB hh−VB lh−VB −6 −6 −8 −8 −8 −10 0 0.5 1 Normalized wave number −10 0 0.5 1 Normalized wave number −10 0 0.5 1 Normalized wave number T.H.E OHIO S ATE T UNIVERSITY 24 The Ohio State University % ' $ AlAs, GaAs and InAs Bandstructure Band structure of AlAs Band structure of GaAs 10 Band structure of InAs 10 e−CB hh−VB lh−VB 8 10 e−CB hh−VB lh−VB 8 8 4 4 2 2 2 0 Energy in eV 6 Energy in eV 6 4 Energy in eV 6 0 0 −2 −2 −4 −4 −6 Patrick Roblin −2 −4 & e−CB hh−VB lh−VB −6 −6 −8 −8 −8 −10 0 0.5 1 Normalized wave number −10 0 0.5 1 Normalized wave number −10 0 0.5 1 Normalized wave number T.H.E OHIO S ATE T UNIVERSITY 25 The Ohio State University % ' $ Lecture # 2 & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 26 The Ohio State University % ' $ Band Diagram Energy Energy E pot E χ E 0 χ Conduction band Conduction band Ec Ec Forbidden band E Forbidden band g g Valence band Valence band Position Patrick Roblin E Ev Ev & 0 Position T.H.E OHIO S ATE T UNIVERSITY 27 The Ohio State University % ' $ MBE Technology GaAs Substrate Molecular beams Shutters Sources Si & Patrick Roblin In Al As Ga T.H.E MBE chamber OHIO S ATE T UNIVERSITY 28 The Ohio State University % ' $ Lattice Matched Ssytems Substrate Substrate GaAs InP 3.5 AlAs (Γ) 3 2.5 Γ and X bandgaps AlAs (X) In.52Al.48As (X) 2 GaAs (X) InP (Γ) 1.5 In.52Al.48As (Γ) In Ga As (X) GaAs (Γ) .53 .47 InAs (X) 1 In & Patrick Roblin Ga .53 0.5 As (Γ) .47 InAs (Γ) 0 5.6 5.65 5.7 5.75 5.8 5.85 5.9 Lattice parameter (Angstrom) 5.95 6 6.05 6.1 T.H.E OHIO S ATE T UNIVERSITY 29 The Ohio State University % ' $ Pseudomorphic Materials Bulk Si 1-x Gex Bulk Si 1-x Gex strained Bulk Si 1-x Gex relaxed Misfit dislocation Bulk Si Patrick Roblin Bulk Si a) & Bulk Si b) c) T.H.E OHIO S ATE T UNIVERSITY 30 The Ohio State University % ' $ Critical Thickness 3 10 Si1−xGx relaxed with dislocations c Critical thickness h (nm) 2 10 Si1−xGx metastable 1 10 Si G stable 1−x x & Patrick Roblin 0 10 0 0.1 0.2 0.3 0.4 0.5 0.6 Ge mole fraction x 0.7 0.8 0.9 1 T.H.E OHIO S ATE T UNIVERSITY 31 The Ohio State University % ' Quantum Well 0.2 10 20 30 40 Position (monolayer) 0.4 0.2 0 20 40 Position (monolayer) 0.2 0.2 1 0.5 1 1.5 Wave vector index 2 5 10 15 Wave vector index 20 0.2 0.4 0.2 0 0 100 200 300 Position (monolayer) 0.5 Wave vector index 0.4 0 0 60 0.4 0 0.4 0 0 50 Energy (eV) Energy (eV) Energy (eV) 0.4 0 Energy (eV) Energy mini−bands Energy (eV) Energy (eV) Energy levels and potential & $ Energy levels split as the electrons cannot be in the same state. Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 32 The Ohio State University % ' $ Band Formation Energy bands in a superlattice 0.5 0.4 Energy (eV) 0.3 0.2 0.1 & Patrick Roblin 0 0 2 4 6 8 10 12 14 Well or barrier width (monolayers) 16 18 20 Bands formation as the spacing between the wells decreases. T.H.E OHIO S ATE T UNIVERSITY 33 The Ohio State University % ' Energy Spectrum & Waves in a Superlattice Energy levels Energies and wave functions 0.4 Energy (eV) 0.5 0.4 Energy (eV) 0.5 0.3 0.3 0.2 Patrick Roblin 0.2 0.1 & $ 0.1 0 5 10 15 Eigenstate number 20 0 50 100 150 200 Position (monolayers) T.H.E OHIO S ATE T UNIVERSITY 34 The Ohio State University % ' Energy Spectrum & Waves in a Random lattice Energy levels Energies and wave functions 0.4 Energy (eV) 0.5 0.4 Energy (eV) 0.5 0.3 0.3 0.2 0.2 0.1 & $ 0.1 0 5 0 10 15 20 Eigenstate number 50 100 150 200 Position (monolayers) T.H.E OHIO The waves no longer propagate inside the superlattice: Anderson's localization. S ATE T Patrick Roblin UNIVERSITY 35 The Ohio State University % ' $ Metals, Semiconductors & Insulators Energy EMPTY STATES EMPTY STATES EMPTY STATES Ec FORBIDDEN BAND Eg Eg FORBIDDEN BAND FORBIDDEN BAND Ev EMPTY STATES FILLED STATES FILLED STATES Insulator FILLED STATES Semiconductor Metal Conductor: electrons available for conduction & empty states available (not separated by a bandgap) for conduction Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 36 The Ohio State University % ' $ Charge Carriers in Semiconductors ENERGY ENERGY Vibrations (phonons) & Patrick Roblin 0 k−space 0 k−space T > 0o K 0o K T.H.E OHIO S ATE T UNIVERSITY 37 The Ohio State University % ' $ Electrons & Holes = = = = = = + e− = Si − Si = Si = = = = = = = = Si = Si = Si = = Si = Si = Si = = = = = = = Patrick Roblin = = Si = Si = Si = = Si = Si = Si = & = = = = = = Si = Si = Si = T.H.E OHIO S ATE T UNIVERSITY 38 The Ohio State University % ' $ E ective Mass Energy Energy Eg k − space & Valence Forbidden Conduction bands: Direct Bandgap h2k2 Ec(k) = Ec + 2mn Patrick Roblin Eg k−space Indirect Bandgap h2 k 2 Ev (k) = Ev ; 2mp T.H.E OHIO S ATE T UNIVERSITY 39 The Ohio State University % ' $ E ective Masses Energy Energy Eg k − space Valence Forbidden Conduction bands: Direct Bandgap & Patrick Roblin mn mp Eg k−space Indirect Bandgap Si GaAs 1.1 m0 0.07 m0 small mass ) electron fast 0.56 m0 0.8 m0 large mass ) hole slow T.H.E OHIO S ATE T UNIVERSITY 40 The Ohio State University % ' $ Intrinsic Material Intrinsic material ) material is pure: no impurities present EC Vibrations Vibrations EV vibrations break Si bonds (absorption of phonons) electrons recombine with holes (emission of phonons) & In equilibrium: n0 = p0 = ni the intrinsic concentration. Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 41 The Ohio State University % ' $ Extrinsic Material III s2p B Al Ga In & Patrick Roblin IV s2p2 C Si Ge V s2p3 N P As Sb e; missing extra e; Acceptors Donors Impureties (Acceptors or Donors) introduce carriers T.H.E OHIO S ATE T UNIVERSITY 42 The Ohio State University % ' $ Donors = = = = Si = Si = Si = Energy E pot E = = = Si P + 0 Conduction band Ec Forbidden band = = Si = − e Ed Eg Ev = Si = Si = Si = Valence band = = = Position A donor is an atom with s2 p3 con guration providing an excess electron It is ionized at room temperature: n = Nd if Nd >> ni & mnq4 Ed = 8 2 2h2 0r Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 43 The Ohio State University % ' $ Acceptors Energy = = = E pot E = Si = Si = Si = = = = Si Al + Si − 0 Conduction band Ec Forbidden band Ea Eg = = Ev = Si = Si = Si = Valence band = = = Position An acceptor is an atom with s2 p con guration lacking a bond electron It is ionized at room temperature: p = Na if Na >> ni & mpq4 Ea = 8 2 2h2 0r Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 44 The Ohio State University % ' $ Fermi Dirac Distribution At thermal equilibrium the probability for a quantum particle to have an energy E is: 1h i f (E ) = E ;EF 1 + exp kT with k = 1:38 10;23 J/o K the Boltzman constant. kT = 0:026 eV at room temperature (27o C= 300o K). Enforces the Pauli principle: 1 electron per state. & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 45 The Ohio State University % ' $ Fermi Dirac Distribution Fermi Dirac distribution Fermi Dirac distribution Fermi Dirac distribution 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 Energy in eV 1 0.2 0.2 300oK o 0K 0 0 −0.2 −0.2 −0.4 −0.4 −0.4 −0.6 Patrick Roblin 0 −0.2 & 3000oK −0.6 −0.6 −0.8 −0.8 −0.8 −1 0 0.5 Occupation Number 1 −1 0 0.5 Occupation Number 1 −1 0 0.5 Occupation Number 1 T.H.E OHIO S ATE T UNIVERSITY 46 The Ohio State University % ' $ Fermi Level E EC intrinsic EF Ei = EF EF = Ei EV 0 1 f(E) E EC EF n−type EF Ei EF > Ei EV 0 & Patrick Roblin f(E) E EC p−type 1 Ei EF EV EF < Ei EF T.H.E 0 47 1 f(E) OHIO S ATE T UNIVERSITY The Ohio State University % ' $ Electron & Hole Concentrations at Equilibrium Using the density of state 1 2m 3=2 pE N (E ) = 2 2 2 h the electron and hole concentrations in equilibrium n0 and p0 are given by: ; Nc exp EFkT Ec Ec Z Ev p0 = 1 ; f (E )]N (E )dE ' Nv exp Ev ; EF kT n0 = with Z 1 f (E )N (E )dE ' ;1 2 2 mn kT Nc = 2 2 !3=2 2 2mp kT and Nv = 2 h h2 mn and mp are density of state e ective masses (see textbook). & Patrick Roblin !3=2 T.H.E OHIO S ATE T UNIVERSITY 48 The Ohio State University % ' $ Intrinsic and Extrinsic Concentration For both extrinsic and intrinsic materials the product: ; Eg n0 p0 = Nc Nv exp EvkT Ec = Nc Nv exp ; kT = CONSTANT For an intrinsic device we have n0 = p0 = ni for EF = Ei ) CONSTANT = n2 i q ni = NcNv exp ; 2Eg kT n0 p0 = n2 For both extrinsic and intrinsic materials we have i The electron and hole extrinsic concentrations can also be written as: n0 = ni exp EF ; Ei & kT ; p0 = ni exp Ei kTEF Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 49 The Ohio State University % ' $ Temperature Dependence of ni 16 500 K 250 K 10 Silicon Germanium GaAs 15 10 14 10 2.5 × 1013 cm−3 13 10 12 −3 ni(cm ) 10 11 10 1.5 × 1010 cm−3 10 10 9 10 8 10 & Patrick Roblin 7 10 6 10 −3 2 × 10 cm 6 2 2.2 2.4 2.6 2.8 3 −1 1000/T(K) 50 3.2 3.4 3.6 T.H.E 3.8 4 OHIO S ATE T UNIVERSITY The Ohio State University % ' $ Lecture #3: Chapter 3 review & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 51 The Ohio State University % ' $ Compensation EC intrinsic Ed E F= E i Ea EV Donor and acceptors present in the same concentration compensate each other leaving the semiconductor intrinsic. & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 52 The Ohio State University % ' $ E ective Donor Concentration EC n−type Ed EF Ei Ea EV When donors are present in larger concentration than acceptors (Nd > Na ) the e ective donor concentration is Nd ; Na . & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 53 The Ohio State University % ' $ E ective Acceptor Concentration EC p−type Ed EF Ei Ea EV When acceptors are present in larger concentration than donors (Na > Nd ) the e ective acceptor concentration is Na ; Nd . & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 54 The Ohio State University % ' $ Space Charge Neutrality In a uniform material we have p0 + Nd+ = n0 + Na; (local space charge neutrality) p0 n0 = n2 (mass action law i The general solution is obtained by solving: n2 + (Na; ; Nd+)n0 + n2 = 0 0 i For (Nd ; Na ) >> ni n0 ' Nd ; Na For (Na ; Nd ) >> ni & p0 ' Na ; Nd Patrick Roblin and n2 = n2 << n i p0 = ni N ; N i 0 d a and n2 = n2 << n i n0 = p i N ; N i 0 a d T.H.E OHIO S ATE T UNIVERSITY 55 The Ohio State University % ' $ Charge Density and Field Charge Density: (x) = ;qn(x) ; qNa (x) + qp(x) + qNd (x) Electric Field Electrostatic potential dE (x) = (x) E (x) = ; dVdx(x) dx Force on an electron Potential Energy p F (x) = ;qE (x) F (x) = ; dEdx(x) Potential energy for an electron submitted to an electrostatic potential V (x): F (x) = ;qE (x) ! ; dEp(x) = ;q ;dV (x) dx dx It results that Ep(x) = ;qV (x) + Constant. Note: the Constant is arbitrary & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 56 The Ohio State University % ' $ Uniform Field Example p V0 Ep (x) V(x) V(L) ε Ep (0) <0 −qV0 V0 Ep (L) V(0) x L 0 (x) = 0 ) L dE (x) = = 0 ) E (x) = E < 0 0 dx Z V (x) Zx , dV = ; E0dx ) V (x) = V (0) ; E0x 0 ( E = ; dVdxx) V V V = V (L) ; V (0) = ;E L ) E = ; V ) V (x) = V (0) + L x L 0 0 (0) 0 0 0 Electron potential energy: & x x L 0 Ep(x) = ;qV (x) = Ep(0) ; q V0 x L Patrick Roblin with 0 0 Ep(0) = ;qV (0) T.H.E OHIO S ATE T UNIVERSITY 57 The Ohio State University % ' ENERGY 0 $ Equilibrium k−space n q X hk = 0 De nition of electron current: Jn = ;q vn(ki) = ; m i ni i with vn the electron velocity vn (ki) = 1 dE = hki OHIO h dki mn S ATE T & Patrick Roblin n X real−space T.H.E UNIVERSITY 58 The Ohio State University % ' $ Ohm's law: Jn = nE0 ENERGY DRIFT DRIFT 0 k−space real−space dp = dhk = ;qE ) p = hk = m v (t) = hk (0) ; qE t 0 i i 0 ni dt dt n q X hk = q2nt E = E ) pi = hki = hki(0) ; qE0t ) Jn = ; m i OHIO m 0 n0 Newton's law: & Patrick Roblin T.H.E ni 59 n S ATE T UNIVERSITY The Ohio State University % ' $ Trajectory Electron & Holes in the Band Diagram and the Bandstructure ENERGY ENERGY ENERGY Ec B A Con duct ion B Forb idde Ev Vibrations (heat) and n Ba Vale nce Vibrations (heat) E − qV(x) nd c Band E − qV(x) v 0 k−space x & Patrick Roblin x A B position x 0 k−space T.H.E OHIO S ATE T UNIVERSITY 60 The Ohio State University % ' $ Amber, Bats and other Oddities Conduction Band Forbidden Band Valence & Patrick Roblin Band T.H.E OHIO S ATE T UNIVERSITY 61 The Ohio State University % ' $ Hole and Electron Current Density Electron Current Density: Jn = qn n E (A/m2 ) with p E (A/m2 ) Average hole drift velocity: mn vn = Average electron drift velocity: Hole Current Density: Jp = qp = qt n with vp = p p n E = qt E mp Total Current: J = Jn + Jp & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 62 The Ohio State University % ' $ Electron & Hole Mobility Mobility at 300o K Si Ge GaAs n (cm2 /V/sec) 1350 3900 8500 480 1900 400 p (cm2 /V/sec) qt The mobility n = mn is large if the average scattering time tn is large. This n occurs if we have: less impureties less vibration (temperature is small) Smaller e ective masses also increase the mobility. & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 63 The Ohio State University % ' $ Velocity Saturation μF vd vs = μF c Fc F Velocity saturation arise due to the heating of the carriers by Joule e ect which in turns decreases their mobility. FC is on the order of kV/cm and vS about 107 cm/sec. OHIO S ATE T Short channel transistors usually operate in the regime of velocity saturation. & Patrick Roblin T.H.E UNIVERSITY 64 The Ohio State University % ...
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