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					Design and Implementation of VLSI Systems
                (EN1600)
                lecture07

                  Sherief Reda
    Division of Engineering, Brown University
                   Spring 2008



    [sources: Weste/Addison Wesley – Rabaey Pearson - Baker Wiley]
MOS transistor theory


• Schedule for 4 lectures
  –   Ideal (Shockley) Model
  –   Non-ideal model
  –   Inverter DC characteristics
  –   SPICE
gate-oxide-body sandwich = capacitor
                                           polysilicon gate
                              Vg < 0
 Operating modes                       +
                                           silicon dioxide insulator
                                           p-type body
  • Accumulation                       -


  • Depletion
                        (a)
  • Inversion
                        0 < V g < Vt
                                           depletion region
                                       +
                                       -



                        (b)

• The charge accumulated
  is proportional to the V >V g    t
                                           inversion region
                                       +
  excess gate-channel                  -   depletion region

  voltage (Vgc-Vt)
                        (c)
The MOS transistor has three regions of
operation
• Cut off
   Vgs < Vt




• Linear (resistor):
   Vgs > Vt & Vds < VSAT=Vgs-Vt
   Current prop to Vds
                                    NMOS transistor, 0.25um, Ld = 10um, W/L = 1.5, VDD
                                    = 2.5V, VT = 0.4V


• Saturation:
   Vgs > Vt and Vds ≥ VSAT=Vgs-Vt
    Current is independent of Vds
How to calculate the current value?
• MOS structure looks like parallel plate
  capacitor while operating in inversion
  – Gate – oxide – channel
• Qchannel = CV
• C = εoxWL/tox = CoxWL (where Cox=εox/tox)
• V = Vgc – Vt = (Vgs – Vds/2) – Vt

                                           gate
                                            Vg
                                         +         +
                                source Vgs    Cg Vgd drain
                               Vs      -            -     Vd
                                           channel
                                  n+  -              + n+
                                             Vds
                                        p-type body
Carrier velocity is a factor in determining the
current

 • Charge is carried by electrons
 • Carrier velocity v proportional to lateral E-field
   between source and drain
 • v = μE           μ called mobility
 • E = Vds/L
 • Time for carrier to cross channel:
    t=L/v
I=Q/t
• Now we know
  – How much charge Qchannel is in the channel
  – How much time t each carrier takes to cross
         Qchannel
  I ds 
            t
        Cox
               WV  V  Vds     V
                 gs              ds
                            2   
                       t
                L
       Vgs  Vt  ds Vds
                     V
                      2
                        
In linear mode (Vgs > Vt & Vds < Vgs-Vt)
        Qchannel
 I ds 
           t
       Cox
              WV  V  Vds     V
                gs              ds
                           2   
                      t
               L                            Can be ignored for small Vds

      Vgs  Vt  ds Vds
                    V
                     2
                       




For a given Vgs, Ids is proportional (linear) to Vds
In saturation mode (Vgs > Vt and Vds ≥ Vgs-Vt)
       Qchannel
I ds 
          t
      Cox
             WV  V  Vds      V
               gs               ds
                          2    
                     t
              L
     Vgs  Vt  ds Vds
                   V
                    2
                      
         V  V  Vdsat
I ds    gs                  V       pinched off
                                dsat
                       2      
               t


        
          V       Vt 
                           2
            gs
        2
Now drain voltage no longer increases current
Operation modes summary




            
                        0                Vgs  Vt      cutoff
            
            
     I ds    Vgs  Vt  ds       V V  V
                           V
                                     ds                linear
                                   
                                2         ds dsat


                 
                     Vgs  Vt 
                                 2
                                        Vds  Vdsat   saturation
                  2
Transistor capacitance




 Gate capacitance: to body + to drain + to source
 Diffusion capacitance: source-body and drain-body capacitances
Gate capacitance as a function of Vgs




                    QuickTime™ and a
                       decompressor
              are need ed to see this picture.
Source/Drain diffusion capacitance

• Csb, Cdb
• Undesirable, called parasitic
                                         Channel-stop implant
  capacitance                               AN
                                             1
• Capacitance depends on area and            Side wall
  perimeter                     W          Source
                                           ND
   – Use small diffusion nodes
                                         Bottom
   – Comparable to Cg
   – Varies with process       xj   Side wall
                                                        Channel
                                    LS                  NA
                                                  Substrate
Summary
• Covered ideal (long channel) operation (Shockley model) of
  transistor
• Next time: short-channel transistors
• TA

				
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posted:10/31/2011
language:English
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