Physics 111 – BSC Lecture 4 Page 1 of 11 Jim Siegrist Phone: 486-4397 Email: [email protected] Room (at LBL): 50-4055 Advice: Get papers back from TAs. ‘Best’ labs posted across hall from 111 labs in glass case each week. No labs accepted after solution posted. Anyone objecting to having their labs posted – let me know via email. Today: lec 4 Diodes lec 5 TH Feb 1 lec 6 TH Feb 8 lec 7 TH Feb 15 Utility of following discussion: Complaints about not enough solid state detail ⇒ small signal models not well motivated. I will give some detail, but you promise to remember: good design ⇒ circuit NOT sensitive to details of device parameters Instruments & Devices: Semiconductor Diode Pure semiconductor: covalent bonds, (all 4 valence electrons used), 1.1 eV band gap (silicon) ⇒ thermal excitations important T 0 K‘free’ holes & electrons≠° ≈ 1010 carriers/cm3 for Si @ 300°K (~1023 for metal) ⇒ semiconductor Doping Add impurities to control the e-hole balance. 5 valence electrons ⇒ extra electron gets loose (donor) 3 valence electrons ⇒ extra hole gets loose (acceptor) • Donor – phosphorus, arsenic, antimony electrons majority carrier, holes minority carrier ≡ n-typePhysics 111 – BSC Lecture 4 Page 2 of 11 • Acceptor – boron, gallium, aluminum, indium holes majority carrier, electrons minority carrier ≡ p-type N-TYPE immobile + ionsmobile emobile holenet charge = 0 P-TYPE immobile ions-mobile e-mobile hole 1015 carriers ⇒ ≈ 1015 donor atoms/cm3 Si has ~ 5 x 1022 atoms/cm3 ⇒ 1 impurity/50 x 106 Si 20 μg of phosphorus/kg SI ⇒ extreme care in manufacture Application of a voltage causes a drift of charge, carried by both holes & electrons. Total current is the sum of the 2 currents. * As in a metal, but 2 carriers Diffusion Current Suppose concentration of holes varies with position: P(0)P(x)xJP ⇒ ∃ concentration gradient dxdPPhysics 111 – BSC Lecture 4 Page 3 of 11 Density of holes on one side of surface > on the other. Because of random thermal motion, they want to drift toward lower concentration region. This current is proportional to the concentration gradient: dxdPqDJPP−= DP = diffusion constant for holes ()directionxinJdxdPP+>< 0,0 An electric field will be set up within the Si block to hold the equilibrium current to zero. * Very different from metal NB: Drift current density under influence of E given by ()EnpqJnpdriftμμ+= p/n = hole/electron density μp/μn = hole/electron mobility P-N Junction PN Electrons & holes diffuse both ways ⇒ depletion region (0.5 μm thick) is generated (or space charge layer) PNxρ Ecounteracts diffusionx xcontact potentialVVoPhysics 111 – BSC Lecture 4 Page 4 of 11 Reverse Bias VPNV‘anode’ ‘cathode’N - electrons carry currentP - holes carry currentdirection of current - easy to remember This polarity causes holes & electrons to move away from the junction. ≈ 0 current (some current because thermal e-hole generation. Holes anywhere on n side drift to gap & are then pulled by the field). = reverse saturation current ≡ IS (≈ independent of V, depends on T) (N.B. Addition of minority carriers (T, …) inferences this isat – important for transistor operation) Forward Bias VPNVINow current flows - sum of electron & hole current. Contacts metal – semiconductors are ohmic, voltage drop across crystal (ideally) 0, then applied V appears to add to junction potential. • Time varying signals: charge goes into/out of space charge layer ⇒ looks like a capacitance ≡ transition capacitance CT, function of reverse voltage. (10 → 200 pF). Important for transistor operation • Field is reduced in the space-charge layer, allows majority carriers to diffuse across the junction to the side where they are in the minority (injection of minority carriers). • Time varying signals: diffusion, or storage capacitance CD (more later). CD » CT ~ 10 μF ( however, rCD = τ ~ nsec, so time constant is small)Physics 111 – BSC Lecture 4 Page 5 of 11 Diode behavior in both regions described by (‘exponential diode’) ()1300@26/1038.1tan'arg123neglectqkTVKmVqkTKTKJtconssboltzmannkechelectronqeIIkTqVS⇒>>=°=°×==⎟⎠⎞⎜⎝⎛−=− Forward bias ⇒ SkTqVSIeII >>= Reverse bias ⇒ SIiqkTV −=⇒<< Silicon: IS ~ 10 pA ()()TSSSkTqVSVVpAmAmVmAIVpAIIIqkTVkTqVIIeII≡⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎠⎞⎜⎝⎛=≈⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛−=⎟⎠⎞⎜⎝⎛56.~1020ln26~2010~lnln1lnln on ⇒ ~ 0.6V drop off ⇒open Real Diode Characteristics: VrVV .6 V for siliconT≈Power Limitations - IV < maxgood operating regionIPhysics 111 – BSC Lecture 4 Page 6 of 11 High forward currents: ohmic contacts take over & diode behaves as a resistor. High reverse voltages: minority carriers gain sufficient speed to knock loose additional electrons (in deplection region where field is high) ⇒ larger reverse current – avalanche multiplication Maximum reverse voltage VR ≡ maximum reverse blocking voltage. Zeners have a well controlled VR (independent of i), can be used as a voltage references 6.8 V Instruments & Devices + Circuit Analyses Diodes as Network Elements IVnon-linear (theorems don’t work) I. Graphical Method V1linearnetI1Thevenin Eqv.RTHILIDVLVDVOCPhysics 111 – BSC Lecture 4 Page 7 of 11 If we can find I1, V1, we are done. We know VD vs. ID from characteristic curve (manufacturer’s or measured) We know VL = VOC – ILRTH Plot this on the i-v characteristic line. 2 points = open circuit voltage & short-circuit current THocscocRviv =, IVV-Icharacteristic(load line)LLvoc TH/RI1V1diode characteristicDC operating pointslope = 1/R-THVOCsee example page 157 S&S Source is time varying: (see page 164 S&S) RTH remains constant, VOC varies ⇒ Load line has constant slope ⎟⎠⎞⎜⎝⎛−THR1, but the intercept (VOC) moves as a function of time, so the operating point moves:Physics 111 – BSC Lecture 4 Page 8 of 11 AC AmplitudeV(t)OC 3V(t)OC 2V(t)OC 1slope = 1/R-THsmall-signal approx. output...VItimeV1timeI1Small Signal Approx:Taylor expand aboutsome operating point use tangents to curve atthat point to describethe behavior.rescue linear circuit lawsby .linearizing⇒⇒ II. Linearize (the behavior for small deviations about the operating point.) ⇒ taylor expand, keep 1st term. N.B. doesn’t work over whole range!