Lecture 3ANNOUNCEMENTS• HW2 is posted, due Tu 9/11• TAs will hold their office hours in 197 Cory• Prof. Liu’s office hours are changed to TuTh 12-1PM in 212/567 Cory• EE105 accounts can access EECS Windows Remote Desktop serversOUTLINEEE105 Fall 2007 Lecture 3, Slide 1 Prof. Liu, UC BerkeleyOUTLINE• PN Junction Diodes (cont’d)– Electrostatics (cont’d)– I-V characteristics– Reverse breakdown– Small-signal modelReading: Chapter 2.2-2.3, 3.4The Depletion ApproximationIn the depletion region on the N side:( )bxqNEqNdxdEsiDsiDsi+===εεερ EE105 Fall 2007 Lecture 3, Slide 2 Prof. Liu, UC Berkeleyρρρρ(x)x-qNAqNDIn the depletion region on the P side:( )xaqNEqNdxdEsiAsiAsi−=−==εεερ DAbNaN=a-bMore on the Built-In Potential (V0)Q: Why can’t we harness V0and use the PN junction as a battery? A: A built-in potential also exists at a junction between a metal and a semiconductor (e.g. at a contact).+–V0?EE105 Fall 2007 Lecture 3, Slide 3 Prof. Liu, UC Berkeleymetal and a semiconductor (e.g. at a contact).• If we connect the P and N regions together, there is no net voltage drop across the device:VbpVbnV0Vbn+V0+Vbp=0V(x)xa-bV0No net current flows across the junction when the externally applied voltage is 0 V!0Effect of Applied Voltage• The quasi-neutral N-type and P-type regions have low resistivity, whereas the depletion region has high resistivity.– Thus, when an external voltage VDis applied across the diode, almost all of this voltage is dropped across the depletion region. (Think of a voltage divider circuit.)• If VD< 0 (reverse bias), the potential barrier to carrier diffusion is increased by the applied voltage.EE105 Fall 2007 Lecture 3, Slide 4 Prof. Liu, UC BerkeleyDdiffusion is increased by the applied voltage.• If VD> 0 (forward bias), the potential barrier to carrier diffusion is reduced by the applied voltage.VD+–ID• A forward bias decreases the potential drop across the junction. As a result, the magnitude of the electric field decreases and the width of the depletion region narrows.PN Junction under Forward Bias ρρρρ(x)qNDaEE105 Fall 2007 Lecture 3, Slide 5 Prof. Liu, UC Berkeleyx-qNAa-bV(x)xa-bV0ID0Minority Carrier Injection under Forward Bias• The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse across the junction.– The carriers which diffuse across the junction become minority carriers in the quasi-neutral regions; they recombine with majority carriers, “dying out” with distance.EE105 Fall 2007 Lecture 3, Slide 6 Prof. Liu, UC Berkeleynp(x)np0AipNnn20=Equilbrium concentration of electrons on the P side:edge of depletion regionx'0x'Minority Carrier Concentrations at the Edges of the Depletion Region• The minority-carrier concentrations at the edges of the depletion region are changed by the factor – There is an excess concentration (∆∆∆∆pn, ∆∆∆∆np) of minority carriers in the quasi-neutral regions, under forward bias.• Within the quasi-neutral regions, the excess minority-carrier concentrations decay exponentially with TDDVVkTqVee//=EE105 Fall 2007 Lecture 3, Slide 7 Prof. Liu, UC Berkeleycarrier concentrations decay exponentially with distance from the depletion region, to zero:( )nTDLxAVVippppeNenxnxnnxn//201)()()(′−−=′∆′∆+=′x'Notation:Ln≡ electron diffusion length (cm)( )nTDLxVVnAinpndiffneeLNnqDxddnqDJ//2,1′−−=′=Diode Current under Forward Bias• The current flowing across the junction is comprised of hole diffusion and electron diffusion components:•Assuming that the diffusion current components are 0,0,0,0,====+++=xdiffnxdiffpxdriftnxdriftptotJJJJJEE105 Fall 2007 Lecture 3, Slide 8 Prof. Liu, UC Berkeley•Assuming that the diffusion current components are constant within the depletion region (i.e. no recombination occurs in the depletion region):( ) where1 2/+=−=pDpnAniSVVStotLNDLNDqnJeJJTD( )1/20,−==TDVVnAinxdiffneLNnqDJ( )1/20,−==TDVVpDipxdiffpeLNnqDJCurrent Components under Forward Bias• For a fixed bias voltage, Jtotis constant throughout the diode, but Jn(x) and Jp(x) vary with position.JtotEE105 Fall 2007 Lecture 3, Slide 9 Prof. Liu, UC Berkeleyx0 a-bI-V Characteristic of a PN Junction• Current increases exponentially with applied forward bias voltage, and “saturates” at a relatively small negative current level for reverse bias voltages.“Ideal diode” equation: EE105 Fall 2007 Lecture 3, Slide 10 Prof. Liu, UC Berkeley()+==−=pDpnAniSSVVSDLNDLNDAqnAJIeIITD2/1“Ideal diode” equation:Parallel PN Junctions• Since the current flowing across a PN junction is proportional to its cross-sectional area, two identical PN junctions connected in parallel act effectively as a single PN junction with twice the cross-sectional area, hence twice the current.EE105 Fall 2007 Lecture 3, Slide 11 Prof. Liu, UC BerkeleyDiode Saturation Current IS• IScan vary by orders of magnitude, depending on the diode area, semiconductor material, and net dopant concentrations.–typical range of values for Si PN diodes: 10-14to 10-17A/µm2+=DppAnniSNLDNLDAqnI2EE105 Fall 2007 Lecture 3, Slide 12 Prof. Liu, UC Berkeley–typical range of values for Si PN diodes: 10to 10A/µm• In an asymmetrically doped PN junction, the term associated with the more heavily doped side is negligible:– If the P side is much more heavily doped,– If the N side is much more heavily doped,≅DppiSNLDAqnI2≅AnniSNLDAqnI2Reverse Breakdown• As the reverse bias voltage increases, the electric field in the depletion region increases. Eventually, it can become large enough to cause the junction to break down so that a large reverse current flows:EE105 Fall 2007 Lecture 3, Slide 13 Prof. Liu, UC Berkeleybreakdown voltageReverse Breakdown Mechanismsa) Zener breakdown occurs when the electric field is sufficiently high to pull an electron out of a covalent bond (to generate an electron-hole pair). b) Avalanche breakdown occurs when electrons and holes gain sufficient kinetic energy (due to acceleration by the E-field) in-between scattering events to cause electron-EE105 Fall 2007 Lecture 3, Slide 14 Prof. Liu, UC BerkeleyE-field) in-between scattering events to cause electron-hole pair generation upon colliding with the lattice.Constant-Voltage Diode Model EE105 Fall 2007 Lecture 3, Slide 15 Prof. Liu, UC
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