A little bit of history(-74)

1、ECE 663MOSFETsECE 663A little bit of history.SubstrateChannelDrainInsulatorGateOperation of a transistorVSG 0 n type operationPositive gate bias attracts electrons into channelChannel now becomes more conductive More electronsSourceVSDVSGSubstrateChannelDrainInsulatorGateOperation of a transistorTra

2、nsistor turns on at high gate voltageTransistor current saturates at high drain biasSourceVSDVSGSubstrateChannelDrainInsulatorGateSourceVSDVSGStart with a MOS capacitorECE 663MIS Diode (MOS capacitor) Ideal WQuestionsWhat is the MOS capacitance? QS(yS)What are the local conditions during inversion?

3、yS,crHow does the potential vary with position? y(x) How much inversion charge is generated at the surface? Qinv(x,yS)Add in the oxide: how does the voltage divide? yS(VG), yox(VG)How much gate voltage do you need to invert the channel? VTHHow much inversion charge is generated by the gate? Qinv(VG)

4、Whats the overall C-V of the MOSFET? QS(VG)ECE 663ECEFEVEiIdeal MIS Diode n-type, Vappl=0Assume Flat-band at equilibriumqfSECE 663Ideal MIS Diode n-type, Vappl=0ECE 663Ideal MIS Diode p-type, Vappl=0ECE 663Ideal MIS Diode p-type, Vappl=0ECE 663AccumulationPulling in majority carriers at surfaceECE 6

5、63But this increases the barrier for current flow !n+ p n+ECE 663DepletionECE 663Need CB to dip below EF. Once below by yB, minority carrier density trumps the intrinsic density. Once below by 2yB, it trumps the major carrier density (doping) !InversionyBECE 663Sometimes maths can helpECE 663P-type

6、semiconductor Vappl0Convention for p-type: y positive if bands bend downECE 663Ideal MIS diode p-typeCB moves towards EF if y 0 n increases VB moves away from EF if y 0 p decreases ECE 663Ideal MIS diode p-typeAt the semiconductor surface, = ss s 0 depletion of holess =B - intrinsic concentration ns

7、=ps=ni s B Inversion (more electrons than holes) ECE 663Surface carrier concentrationECEFECE 663Want to find , E-field, Capacitance Solve Poissons equation to get E field, potential based on charge density distribution(one dimension)EEEECE 663Away from the surface, = 0andECE 663Solve Poissons equati

8、on:E = -dy/dxd2y/dx2 = -dE/dx = (dE/dy).(-dy/dx) = EdE/dyEdE/dyECE 663Do the integral:LHS:RHS:Get expression for E field (d/dx):Solve Poissons equation:ECE 663Define:Debye LengthThen:+ for 0 and for 0E 0y 0E 2yB Questions What is the MOS capacitance? QS(yS) What are the local conditions during inver

9、sion? yS,crHow does the potential vary with position? y(x) How much inversion charge is generated at the surface? Qinv(x,yS)Add in the oxide: how does the voltage divide? yS(VG), yox(VG)How much gate voltage do you need to invert the channel? VTHHow much inversion charge is generated by the gate? Qi

10、nv(VG)Whats the overall C-V of the MOSFET? QS(VG)ECE 663Charges, fields, and potentialsCharge on metal = induced surface charge in semiconductorNo charge/current in insulator (ideal)metalinsulsemiconductordepletioninversionECE 663Electric FieldElectrostatic PotentialCharges, fields, and potentialsEC

11、E 663Electric FieldElectrostatic PotentialDepletion RegionECE 663Electric FieldElectrostatic Potentialy = ys(1-x/W)2Wmax = 2es(2yB)/qNAyB = (kT/q)ln(NA/ni)Depletion RegionQuestions What is the MOS capacitance? QS(yS) What are the local conditions during inversion? yS,cr How does the potential vary w

12、ith position? y(x) How much inversion charge is generated at the surface? Qinv(x,yS)Add in the oxide: how does the voltage divide? yS(VG), yox(VG)How much gate voltage do you need to invert the channel? VTHHow much inversion charge is generated by the gate? Qinv(VG)Whats the overall C-V of the MOSFE

13、T? QS(VG)Couldnt we just solvethis exactly? U = byUS = bySUB = byBExact Solutiondy/dx = -(2kT/qLD)F(yB,np0/pp0)dU/F(U) = x/LDUUSF(U) = eUB(e-U-1+U)-e-UB (eU-1-U)1/2Exact SolutiondU/F(U,UB) = x/LDUUSF(U,UB) = eUB(e-U-1+U) + e-UB (eU-1-U)1/2r = qnieUB(e-U-1) e-UB(eU-1)Exact SolutionNA = 1.67 x 1015Qin

14、v 1/(x+x0)ax0 LD . factorQuestions What is the MOS capacitance? QS(yS) What are the local conditions during inversion? yS,cr How does the potential vary with position? y(x) How much inversion charge is generated at the surface? Qinv(x,yS)Add in the oxide: how does the voltage divide? yS(VG), yox(VG)

15、How much gate voltage do you need to invert the channel? VTHHow much inversion charge is generated by the gate? Qinv(VG)Whats the overall C-V of the MOSFET? QS(VG)ECE 663Threshold Voltage for Strong InversionTotal voltage across MOS structure= voltage across dielectric plus seoxVi/tox = esys/(W/2) B

16、efore InversionAfter inversion there is a discontinuity in D due to surface Qinv Vox (at threshold) = es(2yB)/(Wmax/2)Ci = ECE 663Notice Boundary Condition !Local Potential vs Gate voltage VG = Vfb + ys + (kstox/kox)(2kTNA/e0ks)bys + eb(ys-2yB)1/2Initially, all voltage drops across channel (blue cur

17、ve). Above threshold, channel potential stays pinned to 2yB, varying only logarithmically, so that most of the gate voltage drops across the oxide (red curve).yoxysLook at Effective charge widthInitially, a fast increasing channel potential drops across increasing depletion widthEventually, a consta

18、nt potential drops across a decreasing inversion layer width, so field keeps increasing and thus matches increasing field in oxide Wdm/2tinvQuestions What is the MOS capacitance? QS(yS) What are the local conditions during inversion? yS,cr How does the potential vary with position? y(x) How much inv

19、ersion charge is generated at the surface? Qinv(x,yS) Add in the oxide: how does the voltage divide? yS(VG), yox(VG) How much gate voltage do you need to invert the channel? VTHHow much inversion charge is generated by the gate? Qinv(VG)Whats the overall C-V of the MOSFET? QS(VG)Charge vs Local Pote

20、ntial Qs (2e0kskTNA)bys + eb(ys-2yB)1/2Beyond threshold, all charge goes to inversion layerHow do we get the curvatures?EXACTAdd other terms and keepLeading termNEWInversion Charge vs Gate voltage Q eb(ys-2yB), ys- 2yB log(VG-VT)Exponent of a logarithm gives a linear variation of Qinv with VG Qinv =

21、 -Cox(VG-VT)Why Cox? Questions What is the MOS capacitance? QS(yS) What are the local conditions during inversion? yS,cr How does the potential vary with position? y(x) How much inversion charge is generated at the surface? Qinv(x,yS) Add in the oxide: how does the voltage divide? yS(VG), yox(VG) Ho

22、w much gate voltage do you need to invert the channel? VTH How much inversion charge is generated by the gate? Qinv(VG)Whats the overall C-V of the MOSFET? QS(VG)ECE 663CapacitanceFor s=0 (Flat Band):Expand exponentials.ECE 663Capacitance of whole structureTwo capacitors in series:Ci - insulatorCD -

23、 DepletionORECE 663Capacitance vs VoltageECE 663Flat Band CapacitanceNegative voltage = accumulation CCiZero voltage Flat BandECE 663CVAs voltage is increased, C goes through minimum (weak inversion) where d/dQ is fairly flatC will increase with onset of strong inversionCapacitance is an AC measurem

24、entOnly increases when AC period long wrt minority carrier lifetimeAt “high” frequency, carriers cant keep up dont see increased capacitance with voltageFor Si MOS, “high” frequency = 10-100 Hz ECE 663CV Curves Ideal MOS CapacitorECE 663But how can we operate gate attodays clock frequency ( 2 GHz!)i

25、f we cant generate minoritycarriers fast enough ( 100 Hz) ?ECE 663MOScap vs MOSFETECE 663SubstrateDrainInsulatorGateSourceChannelSubstrateInsulatorGateChannelMinority carriers generated byRG, over minority carrier lifetime 100msSo Cinv can be Cox if fast gateswitching ( GHz) Majority carriers pulled

26、 infrom contacts (fast !)Cinv = CoxMOScap vs MOSFETECE 663Example Metal-SiO2-SiNA = 1017/cm3ni 9/cm3s -14 F/cmECE 663Example Metal-SiO2-Sid=50 nm thick oxide=10-5 cmi-14 F/cmECE 663Real MIS Diode: Metal(poly)-Si-SiO2 MOS Work functions of gate and semiconductor are NOT the sameOxides are not perfect

27、Trapped, interface, mobile chargesTunnelingAll of these will effect the CV characteristic and threshold voltageECE 663Band bending due to work function differenceECE 663Work Function Differenceqs=semiconductor work function = difference between vacuum and Fermi levelqm=metal work functionqms=(qm- qs

28、)For Al, qm=4.1 eVn+ polysilicon qs=4.05 eVp+ polysilicon qs=5.05 eVqms varies over a wide range depending on dopingECE 663ECE 663SiO2-Si Interface ChargesECE 663Standard nomenclature for Oxide charges:QM=Mobile charges (Na+/K+) can causeunstable threshold shifts cleanlinesshas eliminated this issue

29、QOT=Oxide trapped charge Can be anywherein the oxide layer. Caused by brokenSi-O bonds caused by radiation damagee.g. alpha particles, plasma processes,hot carriers, EPROMECE 663QF= Fixed oxide charge positive charge layernear (2mm) Caused by incompleteoxidation of Si atoms(dangling bonds)Does not c

30、hange with applied voltageQIT=Interface trapped charge. Similar in originto QF but at interface. Can be pos, neg,or neutral. Traps e- and h during deviceoperation. Density of QIT and QF usuallycorrelated-similar mechanisms. Cureis H anneal at the end of the process.Oxide charges measured with C-V me

31、thodsECE 663Effect of Fixed Oxide ChargesECE 663ECE 663Surface RecombinationLattice periodicity broken at surface/interface mid-gap E levelsCarriers generated-recombined per unit areaECE 663Interface Trapped Charge - QITSurface states R-G centers caused by disruption of lattice periodicity at surfac

32、eTrap levels distributed in band gap, with Fermi-type distributed:Ionization and polarity will depend on applied voltage (above or below Fermi levelFrequency dependent capacitance due to surface recombination lifetime compared with measurement frequencyEffect is to distort CV curve depending on frequencyCan be passivate