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Berkeley ELENG 130 - LECTURE NOTES

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1EE130 Lecture 4, Slide 1Spring 2003Lecture #4ANNOUNCEMENTS• Prof. King will not hold office hours this week, but will hold an extra office hour next Mo (2/3) from 11AM-12:30PM• Quiz #1 will be given at the beginning of class on Th 2/6– covers material in Chapters 1 & 2 (HW#1 & HW#2) – closed book; one page of notes allowedOUTLINE– Drift (Chapter 3.1)» carrier motion» mobility» resistivityEE130 Lecture 4, Slide 2Spring 2003Nondegenerately Doped Semiconductor• Recall that the expressions for n and p were derived using the Boltzmann approximation, i.e. we assumed The semiconductor is said to be nondegenerately doped in this case.kTEEkTEcFv33 −≤≤+2EE130 Lecture 4, Slide 3Spring 2003Degenerately Doped Semiconductor• If a semiconductor is very heavily doped, the Boltzmannapproximation is not valid.In Si at T=300K: Ec-EF< 3kT if ND > 1.6x1018cm-3EF-Ev< 3kT if NA> 9.1x1017cm-3The semiconductor is said to be degenerately doped in this case.kTEEkTEcFv33 −≤≤+EE130 Lecture 4, Slide 4Spring 2003Band Gap Narrowing• If the dopant concentration is a significant fraction of the silicon atomic density, the energy-band structure is perturbed Æ the band gap is reduced by ∆EGN = 1018cm-3:N = 1019cm-3:3EE130 Lecture 4, Slide 5Spring 2003Free Carriers in Semiconductors• Three primary types of carrier action occur inside a semiconductor:–drift– diffusion– recombination-generationEE130 Lecture 4, Slide 6Spring 2003Electrons as Moving ParticlesF = (-q) = moaF = (-q)= mn*awhere mn* is the electron effective mass4EE130 Lecture 4, Slide 7Spring 2003Carrier Effective MassIn an electric field, , an electron or a hole accelerates:Electron and hole conductivity effective masses:electronsholesSi Ge GaAsmn/m00.26 0.12 0.068mp/m00.39 0.30 0.50EE130 Lecture 4, Slide 8Spring 2003Average electron or hole kinetic energy2*2123thvmkT ==cm/s103.2m/s103.2 kg101.926.0J/eV)106.1(eV026.03*3753119×=×=×××××==−−mkTvthThermal Velocity5EE130 Lecture 4, Slide 9Spring 2003Carrier Scattering• Mobile electrons and atoms in the Si lattice are always in random thermal motion.– Electrons make frequent collisions with the vibrating atoms• “lattice scattering” or “phonon scattering”– increases with increasing temperature– Average velocity of thermal motion for electrons: ~107cm/s @ 300K• Other scattering mechanisms:– deflection by ionized impurity atoms– deflection due to Coulombic force between carriers• “carrier-carrier scattering”• only significant at high carrier concentrations• The net current in any direction is zero, if no electric field is applied.12345electronEE130 Lecture 4, Slide 10Spring 2003Carrier Drift• When an electric field (e.g. due to an externally applied voltage) is applied to a semiconductor, mobile charge-carriers will be accelerated by the electrostatic force. This force superimposes on the random motion of electrons:12345electron• Electrons drift in the direction opposite to the electric fieldÆ current flows Because of scattering, electrons in a semiconductor do not achieve constant acceleration. However, they can be viewed as quasi-classical particles moving at a constant average drift velocity vd6EE130 Lecture 4, Slide 11Spring 2003Electron Momentum• With every collision, the electron loses momentummn*vd• Between collisions, the electron gains momentum(-q)τmnwhere τmn= average time between scattering eventsEE130 Lecture 4, Slide 12Spring 2003•µp≡ [qτmp/ mp*] is the hole mobilityCarrier Mobilitymn*vd= (-q)τmn|vd| = qτmn/ mn* =µn•µn≡ [qτmn/ mn*] is the electron mobilitySimilarly, for holes:|vd| = qτmp/ mp* ≡µp7EE130 Lecture 4, Slide 13Spring 2003Electron and hole mobilities of selected intrinsic semiconductors (T=300K)Si Ge GaAs InAsµn (cm2/V·s) 1400 3900 8500 30000µp (cm2/V·s) 470 1900 400 500 sVcmV/cmcm/s2⋅=µhas the dimensions of v/ :Electron and Hole MobilitiesEE130 Lecture 4, Slide 14Spring 2003Find the hole drift velocity in an intrinsic Si sample for = 103V/cm.What isτmp, and what is the distance traveled between collisions?Solution:Example: Drift Velocity Calculation8EE130 Lecture 4, Slide 15Spring 20031E14 1E15 1E16 1E17 1E18 1E19 1E2002004006008001000120014001600HolesElectrons Mobility (cm2 V-1 s-1)Total Impurity Concenration (atoms cm-3)Total Doping Concentration NA+ ND(cm-3)impurityphononimpurityphononµµµτττ111111+=+=Mobility Dependence on DopingEE130 Lecture 4, Slide 16Spring 2003vdtA= volume from which all holes cross plane in time tpvdt A = # of holes crossing plane in time tq p vdt A = charge crossing plane in time tqpvdA = charge crossing plane per unit time = hole currentÎ Hole current per unit area J = qpvdDrift Current9EE130 Lecture 4, Slide 17Spring 2003Jp,drift = qpv = qpµpJn,drift = –qnv = qnµnJdrift = Jn,drift + Jp,drift = σ=(qnµn+qpµp)Conductivity of a semiconductor isσ≡ qnµn+ qpµpResistivityρ≡ 1 /σConductivity and Resistivity(Unit: ohm-cm)EE130 Lecture 4, Slide 18Spring 2003n-typep-typeResistivity Dependence on DopingFor n-type mat’l:nqnµρ1≅For p-type mat’l:pqpµρ1≅Note: This plot does not apply for compensated material!10EE130 Lecture 4, Slide 19Spring 2003Electrical Resistancewhere ρis the resistivityResistanceWtLIVRρ=≡(Unit: ohms)V+_LtWIhomogeneously doped sampleEE130 Lecture 4, Slide 20Spring 2003Consider a Si sample doped with 1016/cm3Boron.What is its resistivity?Answer:NA= 1016/cm3, ND= 0 (NA>> NDÆ p-type)Æ p ≈ 1016/cm3and n ≈ 104/cm3Example[]cm 4.1)450)(10)(106.1(1111619−Ω=×=≅+=−−ppnqpqpqnµµµρ11EE130 Lecture 4, Slide 21Spring 2003Example: Dopant CompensationConsider the same Si sample, doped additionallywith 1017/cm3Arsenic. What is its resistivity?Answer:NA= 1016/cm3, ND= 1017/cm3 (ND>>NA Æ n-type)Æ n ≈ 9x1016/cm3and p ≈ 1.1x103/cm3[]cm 12.0)600)(109)(106.1(1111619−Ω=××=≅+=−−npnqnqpqnµµµρEE130 Lecture 4, Slide 22Spring 2003Summary• Electrons and holes moving under the influence of an electric field can be modelled as quasi-classical particles with average drift velocity• The conductivity of a semiconductor is dependent on the carrier concentrations and mobilities• Resistivity |vd| = µ σ=


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Berkeley ELENG 130 - LECTURE NOTES

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