1. MOSFETs - An Introduction
Chapter 17.
MOSFETs - An Introduction
Sung June Kim

2. CONTENTS Qualitative Theory of Operation
Quantitative ID - VD Relationships
Subthreshold Swing
ac Response

3. Qualitative Theory of Operation
Assumption
Ideal Structure
Long Channel Enhancement-Mode
MOSFET=MOS-Capacitor + 2 pn junctions
n - channel (p-type substrate)

4. Visualization of various phases of VG > VT MOSFET operation

5. VD = 0 Case
When VG  VT, very few electrons in the channel, an open circuit between the n+ region
When VG > VT,
Inversion layer is formed
The conducting channel (induced “n-type” region, inversion layer) connects the D & S
VG → the pile up of electrons & conductance 
 VG determines the maximum conductance
Thermal equilibrium prevails, and ID=0

6. The VD is increased in small steps starting from VD = 0
The channel acts like a simple resistor
ID  VD
The reverse bias junction current is negligible
voltage drop from the drain to the source starts to negate the inverting effect of the gate
VD → Depletion of the channel & # of carriers & conductance & slope-over in the IV

7. Pinch - off (VD = VDsat)
Disappearance of the channel adjacent to the drain
The slope of the ID-VD becomes approximately zero(Point B)

8. Post-pinch-off (VD > VDsat)
The pinched-off portion widens from just a point into a depleted channel section L
The pinched-off section absorbs most of the voltage drop in excess of VDsat
For L << L, the shape of the conducting region and the potential across the region do not change & Constant ID
For L ~ L, ID will increase with VD > VDsat

9. ID - VD Characteristics
General form of the ID - VD (L << L )
For VG  VT , ID  0
For VG >VT , transistor action: ID is modulated by VG
VD > VDsat : saturation region
VD < VDsat : linear(triode) region
The slope
increases with VG
VDsat increases with VG

10. Quantitative ID - VD Relationships
Effective Mobility
: Impurity Scattering
+ Lattice Scattering
+ Surface Scattering

11. Effective Mobility

13. Square - Law Theory VD < VDsat Drift current is dominant
At an arbitrary point y
Inversion layer charge density(q/cm^2)

14. Integrating

15. VD  VDsat
ID is approximately constant

16. Bulk-Charge Theory
As VD increases, the depletion width widens from S to D.
With changes in the depletion width, W(y), taken into account,
where, making use of the delta-depletion results,
Combinig (1) to (2), and introducing
One obtains the bulk-charge theory analogue of QN(y)
…(1)
…(2)

17. Bulk-Charge Theory ID -VD relationship
An expression for VDsat can be obtained by noting when ,
Inversion layer charge density(q/cm^2)

18. Inversion layer charge density(q/cm^2)

19. Subthreshold transfer characteristics
At weak inversion, diffusion current dominates
In long channel MOSFETS the subthreshold current varies exponentially with VG and is independent of VD provided VD > a few kT/q

20. Subthreshold swing

21. 17.3 a.c. Response
Cgs(Cgd): The interaction between G and the channel charge near S(D)
Cgsp,Cgdp: parasitic or overlap capacitances

22. Small-signal equivalent circuitD in
MOSFET
out S S G S D vd + - vg
gmvgs gd

23. A capacitor behaves like an open circuit at low frequencies.G S D vd + - vg
gmvgs gd
Cgd
Cgs
A capacitor behaves like an open circuit
at low frequencies.

24. ID(VD,VG) + id = ID(VD + vd , VG +vg)
id = ID(VD + vd , VG +vg) - ID(VD,VG)

25. id G S D vd + - vg
gmvgs gd

26. Table 17.1
Below pinch-off (VD≤VDsat)
Above pinch-off (VD>VDsat)

27. At the higher operational frequencies encountered in practical applications, the circuit must be modified to take into account capacitive coupling between the device terminals.
The overlap capacitance is minimized by forming a thicker oxide in the overlap region or preferably through the use of self aligned gate procedures.  Cgd is typically negligible. G S D vd + - vg
gmvgs gd
Cgd
Cgs

28. Cutoff Frequency
The fT be defined as the frequency where the MOSFET is no longer amplifying the input signal under optimum conditions.
 Value of the output current to input current ratio is unity

29. Small Signal Characteristics
gd vs. VG(VD=0)
Extrapolating the linear portion of the gd-VG characteristics into the VG axis and equating the voltage intercept to VT
Deduce the effective
mobility from the slope

30. Gate Capacitance vs. VG (VD=0)
Diagnostic purposes in much the same manner as the MOS-C C-VG characteristics
Unlike the MOS-C , a low-frequency characteristics is observed even for frequencies exceeding 1MHz
Because the source and drain islands supply the minority carries