EECS 105 Fall 2003 Lecture 13 Lecture 13 Part I MOS Small Signal Models Prof Niknejad Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Lecture Outline Department of EECS MOS Small Signal Model 4 6 Diode Currents in forward and reverse bias 6 1 6 3 University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Total Small Signal Current iDS t I DS ids iDS iDS ids vgs vds vgs vds 1 ids g m vgs vds ro Transconductance Department of EECS Conductance University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Role of the Substrate Potential Need not be the source potential but VB VS Effect changes threshold voltage which changes the drain current substrate acts like a backgate g mb i D v BS Q iD v BS Q Q VGS VDS VBS Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Backgate Transconductance VT VT 0 Result Department of EECS g mb iD vBS Q iD VTn Q VSB 2 p 2 p VTn vBS Q gm 2 VBS 2 p University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Four Terminal Small Signal Model 1 ids g m vgs g mb vbs vds ro Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad MOSFET Capacitances in Saturation Gate source capacitance channel charge is not controlled by drain in saturation Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Gate Source Capacitance Cgs Wedge shaped charge in saturation effective area is 2 3 WL see H S 4 5 4 for details C gs 2 3 WLCox Cov Overlap capacitance along source edge of gate Cov LDWCox Underestimate due to fringing fields Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Gate Drain Capacitance Cgd Not due to change in inversion charge in channel Overlap capacitance Cov between drain and source is Cgd Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Junction Capacitances Prof A Niknejad Drain and source diffusions have different junction capacitances since VSB and VDB VSB VDS aren t the same Complete model without interconnects Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad P Channel MOSFET Measurement of IDp versus VSD with VSG as a parameter Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Square Law PMOS Characteristics Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Small Signal PMOS Model Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad MOSFET SPICE Model Many levels we will use the square law Level 1 model See H S 4 6 Spice refs on reserve for details Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Part II Currents in PN Junctions Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Diode under Thermal Equilibrium Minority Carrier Close to Junction Thermal Generation p type J p drift J n drift ND n type J n diff J p diff NA E0 Recombination q bi Carrier with energy below barrier height Diffusion small since few carriers have enough energy to penetrate barrier Drift current is small since minority carriers are few and far between Only minority carriers generated within a diffusion length can contribute current Important Point Minority drift current independent of barrier Diffusion current strong exponential function of barrier Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Reverse Bias Reverse Bias causes an increases barrier to diffusion Diffusion current is reduced exponentially p type ND n type NA q bi VR Drift current does not change Net result Small reverse current Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Forward Bias Forward bias causes an exponential increase in the number of carriers with sufficient energy to penetrate barrier Diffusion current increases exponentially p type ND n type NA q bi VR Drift current does not change Net result Large forward current Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Diode I V Curve Id Is I d Vd I S Id IS 1 qVd kT e 1 qVd kT Diode IV relation is an exponential function This exponential is due to the Boltzmann distribution of carriers versus energy For reverse bias the current saturations to the drift current due to minority carriers Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Minority Carriers at Junction Edges Minority carrier concentration at boundaries of depletion region increase as barrier lowers the function is minority hole conc on n side of barrier p n x xn p p x x p majority hole conc on p side of barrier e Barrier Energy kT pn x xn q B VD kT e NA Department of EECS Boltzmann s Law University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Law of the Junction Minority carrier concentrations at the edges of the depletion region are given by pn x xn N Ae q B VD kT n p x x p N De q B VD kT Note 1 NA and ND are the majority carrier concentrations on the other side of the junction Note 2 we can reduce these equations further by substituting VD 0 V thermal equilibrium Note 3 assumption that pn ND and np NA Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Minority Carrier Concentration pn 0 e p side qVA kT n side n p0e qV A kT pn x pn 0 pn 0 e qVA kT x Lp 1 e pn 0 np 0 Wp xp xn Minority Carrier Diffusion Length Wn The minority carrier concentration in the bulk region for forward bias is a decaying exponential due to recombination Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Steady State Concentrations Assume that none of the diffusing holes and electrons recombine get straight lines pn 0 e p side qVA kT n side n p0e qV A kT pn 0 np 0 Wp xp xn Wn This also happens if the minority carrier Ln p Wn p diffusion lengths are much larger than Wn p Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 13 Prof A Niknejad Diode Current Densities pn 0 e p side n p0e qVA kT dn p n side qV A kT dx x n p 0e qVA kT np0 x p Wp pn 0 np0 np0 Wp xp J xn diff n J pdiff Wn
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