Announcements• HW1 is posted, due Tuesday 9/4• Discussion Section 102 (We 9-10) moved to 289 Cory• Lab sections:– If a section is over-subscribed, then priority will be given to students officially registered for this section.EE105 Fall 2007 Lecture 2, Slide 1 Prof. Liu, UC Berkeleystudents officially registered for this section.• Paid position for videotaping EE105 lectures is availableLecture 1, Slide 1Lecture 2OUTLINE• Basic Semiconductor Physics (cont’d)– Carrier drift and diffusion•PN Junction DiodesEE105 Fall 2007 Lecture 2, Slide 2 Prof. Liu, UC Berkeley•PN Junction Diodes– Electrostatics– CapacitanceReading: Chapter 2.1-2.2Lecture 1, Slide 2Dopant Compensation• An N-type semiconductor can be converted into P-type material by counter-doping it with acceptors such that NA> ND.• A compensated semiconductor material has both acceptors and donors.EE105 Fall 2007 Lecture 2, Slide 3 Prof. Liu, UC Berkeleyacceptors and donors.P-type material(NA> ND)DAiDANNnnNNp−≈−≈2ADiADNNnpNNn−≈−≈2N-type material(ND> NA)Types of Charge in a Semiconductor• Negative charges:– Conduction electrons (density = n)– Ionized donor atoms (density = ND)• Positive charges:–Holes (density = p)EE105 Fall 2007 Lecture 2, Slide 4 Prof. Liu, UC Berkeley–Holes (density = p)– Ionized acceptor atoms (density = NA)• The net charge density (C/cm3) in a semiconductor is() ADNNnpq−+−=ρCarrier Drift• The process in which charged particles move because of an electric field is called drift. • Charged particles within a semiconductor move with an average velocity proportional to the electric field.–The proportionality constant is the carrier mobility.EE105 Fall 2007 Lecture 2, Slide 5 Prof. Liu, UC Berkeley–The proportionality constant is the carrier mobility.→→→→−==EvEvnephµµNotation:µµµµp≡ hole mobility (cm2/V·s)µµµµn≡ electron mobility (cm2/V·s)Hole velocityElectron velocityVelocity Saturation• In reality, carrier velocities saturate at an upper limit, called the saturation velocity (vsat).bE01µµµ+=EE105 Fall 2007 Lecture 2, Slide 6 Prof. Liu, UC BerkeleyEvEvbvsatsat0001µµµ+==Drift Current• Drift current is proportional to the carrier velocity and carrier concentration:EE105 Fall 2007 Lecture 2, Slide 7 Prof. Liu, UC Berkeleyvht A = volume from which all holes cross plane in time tp vht A = # of holes crossing plane in time tq p vht A = charge crossing plane in time tq p vh A = charge crossing plane per unit time = hole current Hole current per unit area (i.e. current density) Jp,drift= q p vhConductivity and Resistivity• In a semiconductor, both electrons and holes conduct current:EqnEqpJJJEqnJEqpJnpdriftndriftpdrifttotndriftnpdriftpµµµµ+=+=−−== )( ,,,,,EE105 Fall 2007 Lecture 2, Slide 8 Prof. Liu, UC Berkeley• The conductivity of a semiconductor is– Unit: mho/cm• The resistivity of a semiconductor is– Unit: ohm-cmEEnpqJEqnEqpJJJnpdrifttotnpdriftndriftpdrifttotσµµµµ≡+=+=+=)( ,,,,npqnqpµµσ+≡σρ1≡Resistivity Example• Estimate the resistivity of a Si sample doped with phosphorus to a concentration of 1015cm-3and boron to a concentration of 1017cm-3. The electron mobility and hole mobility are 700 cm2/Vs and 300 cm2/Vs, respectively.EE105 Fall 2007 Lecture 2, Slide 9 Prof. Liu, UC BerkeleyElectrical ResistanceV+_tWIhomogeneously doped sampleEE105 Fall 2007 Lecture 2, Slide 10 Prof. Liu, UC Berkeleywhere ρis the resistivityResistanceWtLIVRρ=≡(Unit: ohms)LCarrier Diffusion• Due to thermally induced random motion, mobile particles tend to move from a region of high concentration to a region of low concentration. – Analogy: ink droplet in water • Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient.EE105 Fall 2007 Lecture 2, Slide 11 Prof. Liu, UC Berkeleyproportional to the carrier concentration gradient.– The proportionality constant is the diffusion constant.dxdpqDJpp−=Notation:Dp≡ hole diffusion constant (cm2/s)Dn≡ electron diffusion constant (cm2/s)Diffusion Examples• Non-linear concentration profile varying diffusion current• Linear concentration profile constant diffusion currentdLxNp−= exp−=LxNp 1EE105 Fall 2007 Lecture 2, Slide 12 Prof. Liu, UC BerkeleyLNqDdxdpqDJppdiffp=−= ,ddppdiffpLxLNqDdxdpqDJ−=−=exp ,Diffusion Current• Diffusion current within a semiconductor consists of hole and electron components: ,,dxdnqDJdxdpqDJndiffnpdiffp=−=EE105 Fall 2007 Lecture 2, Slide 13 Prof. Liu, UC Berkeley• The total current flowing in a semiconductor is the sum of drift current and diffusion current:)(,dxdpDdxdnDqJdxdxpndifftot−=diffndiffpdriftndriftptotJJJJJ,,,,+++=The Einstein Relation• The characteristic constants for drift and diffusion are related: qkTD=µEE105 Fall 2007 Lecture 2, Slide 14 Prof. Liu, UC Berkeley• Note that at room temperature (300K)– This is often referred to as the “thermal voltage”.mV26≅qkTThe PN Junction Diode• When a P-type semiconductor region and an N-type semiconductor region are in contact, a PN junction diode is formed. VDI+–EE105 Fall 2007 Lecture 2, Slide 15 Prof. Liu, UC BerkeleyIDDiode Operating Regions • In order to understand the operation of a diode, it is necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias.VD= 0VD> 0VD< 0EE105 Fall 2007 Lecture 2, Slide 16 Prof. Liu, UC BerkeleyVD= 0VD> 0VD< 0Carrier Diffusion across the Junction• Because of the difference in hole and electron concentrations on each side of the junction, carriers diffuse across the junction:EE105 Fall 2007 Lecture 2, Slide 17 Prof. Liu, UC BerkeleyNotation:nn≡ electron concentration on N-type side (cm-3)pn≡ hole concentration on N-type side (cm-3)pp≡ hole concentration on P-type side (cm-3)np≡ electron concentration on P-type side (cm-3)Depletion Region• As conduction electrons and holes diffuse across the junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed.– The charge density in the depletion region is not zero.– The carriers which diffuse across the junction recombine with majority carriers, i.e. they are annihilated.EE105 Fall 2007 Lecture 2, Slide 18 Prof. Liu, UC Berkeleywith majority carriers, i.e. they are annihilated.width=Wdepquasi-neutral regionquasi-neutral regionCarrier Drift across the
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