MOSFET. Id-Vd curve. I DS Transfer curve V G. Lec. 8. Vd=1V. Saturation region. V Th

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1 MOSFET Id-Vd curve Saturation region I DS Transfer curve Vd=1V V Th V G 1

2 0 < V GS < V T V GS > V T V Gs >V T & Small V D > 0 I DS WQ inv WC v WC i V V VDS V V G i T G n T L n I D g V D (g conductance of the channel) 2 g 1 R W L I V C ( V i D D G V T ) n

3 V G >V T & V D =V g -V th Pinch-off V s =0 V g =5 V d =3 Vg-Vth=3 V th =2 Vd=3 A Vd=3 When the voltage at A becomes equal to (V G -V Th ), this region will go back to the point of onset of inversion. 3 So when V D = (V G -V Th ), we says pinch-off occurs at the drain and this voltage is called as saturation drain voltage (V Dsat )

4 V Gs >V T & Higher V D > 0 : Saturation region V s =0 V g =5 V d =4 The region of PN + V th =2 region. Most of voltage beyond V Dsat will drop across this region, similarly to P-N junction under reverse bias. However, the difference is that a lot of electrons at N inversion are pulled by a high electric field to N +. is a depletion (In contrast, reverse current of PN junction has nearly zero due to limited number of minority electrons.) N + N P N+ Thus electrons accumulated at the inversion region roll across the depletion region to the drain with saturation current I ds (sat). 4

5 5

6 0 < V x < V DS. so inversion layer charge at any point is Q inv (x) = C i (V G V T V x ) (Z=Width) Small V D V D (sat) = Vg - Vt 6

7 Transfer curve g m ( transconducta nce) I V W L D G C V i n D n Lg m C V W i d You can calculate mobility!!! 7

8 Vg=0, Vd=0 Vg>Vth, Vd=0 Vg>Vth, Vd>Vg-Vth 8

9 MOSFET Operation Mechanism Current flow vs voltage potential is same as water flow vs potential energy. Water flows from high potential energy to low potential energy. When V SB = 0, V DB = 0 and V GB = 0 volt Source Gate Drain Gate Source (n + ) Drain (n + ) p bi Channel bi Reference level (bulk) ; assume that V B = ground n + p Water or Electrons 9

10 MOSFET Operation Mechanism Inversion When V SB = 0 V, V DB = 0 V and V GB > V T Source Gate Drain =0 bi 2 F S S bi Reference level (bulk) ; assume that V B = ground Channel Water or Electrons No current flows. Inversion layer is formed, but no potential difference no current flow 10

11 MOSFET Operation Mechanism When V SB = 0 V, V DB = V DB1 V and V GB > V T (V DB1 <<V GB ) Source bi Gate Drain bi Reference level (bulk) ; assume that V B = ground V DB1 o Non-saturation (Linear region) Current flows. Inversion layer is formed & potential difference is existed. Current flows 11

12 MOSFET Operation Mechanism When V SB = 0 V, V DB = V DB2 V and V GB > V T (where V DB2 >V DB1 ) Source bi Gate Drain bi Reference level (bulk) ; assume that V B = ground V DB2 Current is influenced by drain voltage. Inversion layer is formed & potential difference is existed. Water channel is narrowed near drain region. 12

13 MOSFET Operation Mechanism When V SB = 0 V, V DB = V DBsat and V GB > V T Source bi Gate Drain bi Reference level (bulk) ; assume that V B = ground V DBsat Pinch off. Pinch off. o On-set of Saturation 13

14 MOSFET Operation Mechanism When V SB = 0 V, V DB > V sat and V GB > V T bi Source Gate Drain bi Reference level (bulk) ; assume that V B = ground V DBsat V DB Pinch off. 14

15 Flat Band condition, V DS =0 15

16 Flat Band condition, V DS >0 V DS =0 V DS >0 When Vds is applied, one of the junction will be reverse-biased. 16

17 Inversion condition, V DS =0 17 Under an inversion condition, Si near the surface becomes n-type. So, current path from drain to source will be n + nn +.

18 Inversion condition, Small V DS 18

19 Inversion condition, pinch-off with depletion 19

20 V Gs >V T & Higher V D > 0 : Saturation region, Long channel device ' Vsat L - L V V d L sat ' ' I WC V V max DS i G T ε (high electric field) WC i V G V T ' n n V Dsat L 20 N + N P N+

21 V Gs >V T & Higher V D > 0 : Saturation region, Short channel device ' Vsat L - L In short channel device, no longer V '' d V L sat Therefore, ε > ε pinch-off. This increase I d after pinch-off. In very-short MOSFET, carrier velocity reaches saturation velocity (v sat ) before pinch-off (Vd=Vg-Vth). I Dsat WC i i V V G WC V V G T n T v sat 21 (linear scale) v ( y )x x Mobility depends on vertical electric fields. Saturation velocity depends on gate voltage.

22 Long channel device: Quadratic dependence of Id on Vg Short channel device: Linear dependence of Id on Vg I Dsat WC i V G V T v sat 22

23 - Nanoscale MOSFET: Ballistic regime Within nano-channel, there is no scattering.. ( is no more valid because vs is not reached in pinch-off region (no scattering ) - Instead, drain current is dependent of carrier injection in source region, called source-injection limited transport.. 1 /1 ( Equilibrium state energy band diagram Electron wave model e ikx 해석가능 (r is reflection coefficient, 1+r is total available carriers in source) - If carrier concentration in channel region is high, v inj is also high due to less barrier btw channel and source. Energy band diagram When V D is applied. - If mobility is high, mean free path becomes longer, reflection coefficient is lower, and finally sourceinjection-limited drain current becomes larger. 23