1. Sung June Kim kimsj@snu.ac.kr http://nanobio.snu.ac.kr
Chapter 16.
MOS FUNDAMENTALS
Sung June Kim

2. Contents MOS Structure Ideal Structure Assumption
Effect of an Applied Bias
Capacitance - Voltage Characteristics

3. Metal - Oxide (SiO2) - Semiconductor (Si)
MOS Structure
Metal - Oxide (SiO2) - Semiconductor (Si)
The most common field plate (gate) materials are heavily doped polycrystalline silicon.
The silicon-side terminal is called the back or substrate contact.
The more general designation: metal-insulator-semiconductor (MIS)

4. Ideal Structure Assumption
(1) The metallic gate is sufficiently thick so that it can be considered an equipotential region.
(2) The oxide is a perfect insulator.
(3) No charge centers located in the oxide or at the interface.
(4) Uniformly doped.
Semiconductor with
band bending
Semiconductor Ec EF Ei Ev
( Ec - EF )  M
Metal
Insulator
 i
Fig. Individual energy band diagrams for the metal, insulator, and semiconductor components.

5. (7) One-dimensional structure.
(5) The semiconductor is sufficiently thick so that a field-free region(“bulk”) is encountered before reaching the back contact.
(6) An ohmic contact between the semiconductor and the metal on the back side.
(7) One-dimensional structure.
(8) No work function difference between metal and semiconductor.(M = S)
Semiconductor with
band bending
Semiconductor Ec EF Ei Ev
( Ec - EF )  M
Metal
Insulator
 i
Fig. Individual energy band diagrams for the metal, insulator, and semiconductor components.

6. Energy band diagram of an ideal MOS structure with no bias. 
E F
E v
E c
Energy band diagram of an ideal MOS structure with no bias.

7. Effect Of An Applied Bias - Qualitative description
General observations
Even with VG  0, semiconductor Fermi energy is unaffected by the bias and remains invariant as a function of position because of the assumed zero current flow.

8. In the metal, no band-bending. In the oxide and semiconductor,
Since the barrier heights are fixed quantities, the movement of the metal Fermi level leads to a band bending.
In the metal, no band-bending.
In the oxide and semiconductor,
an upward slope when VG>0
a downward slope when VG < 0.
With no oxide charges, the Poisson's equation yields a constant slope in the oxide.
Band bending in the semiconductor is somewhat more complex.

9. Specific biasing regions
Accumulation ( VG < 0 )
VG < 0 raises EF(metal) and the hole concentration inside the semiconductor,
increases as one approaches the
oxide-semiconductor interface.
VG < 0 places negative charges on the gate. To maintain a balance of charge, positively charged holes must be drawn toward the Si-SiO2 interface.

10. Depletion ( 0 < VG < VT )
VG > 0 slightly lowers EF(metal) and the hole concentration is decreased (depleted) in the vicinity of the Si-SiO2 interface.
VG > 0 places positive charges on the gate, which in turn repels holes from the interface and exposes the negatively charged acceptor sites.

11. Onset of Inversion (VG = VT )
As VG is increased positively, the bands at the Si surface will bend down more and the electron concentration at the surface (ns) will increase from less than ni when E i (surface) > EF, to ni when Ei (surface) = EF, to greater than ni when Ei (surface) < EF.
At VG=VT,
Exposed
Acceptors
VG = VT +Q -Q
Electrons

12. Inversion ( VG > VT ) For VG > VT , ns > NA.
The surface region :p-type -> n-type
In inversion, the depletion width changes little since

13. No Bias (VG = 0) EC EF EV
Metal
Insulator Si

14. Accumulation (VG < 0)EC EF EV
Metal
Insulator Si

15. Depletion ( 0 < VG < VT )EC EF EV
Metal
Insulator Si

16. Inversion ( VG > VT ) EC EF EV
Metal
Insulator Si

17. Effect Of An Applied Bias - Quantitative formulation
Preparatory considerations

18. Accumulation : Flat band : Depletion : Onset of inversion :
For an p-type semiconductor,
Accumulation :
Flat band :
Depletion :
Onset of inversion :
Inversion :

19. Energy band diagrams and corresponding block charge diagram in an ideal n-type MOS-capacitor

20. Energy band diagrams and corresponding block charge diagram in an ideal n-type MOS-capacitor

21. Accumulation : Flat band : Depletion : Onset of inversion :
For an n-type semiconductor,
Accumulation :
Flat band :
Depletion :
Onset of inversion :
Inversion :

25. Delta-depletion solution Delta-depletion assumption :
The functional form of the accumulation charge & the inversion charge : d - function.
Because the depletion width increases only slightly once the semiconductor inverts, it is assumed the d - function of charge added in inversion precisely balances the charge added to the gate.
The actual depletion charge is replaced with a squared-off distribution

26. Accumulation :
Because of the assumed d - function, the electric field and potential are zero for all x > 0.
Depletion :
The maximum depletion width,

28. Inversion :
The solution is established by merely adding a  - function of surface charge to the solution existing at the end of depletion.
The depletion charge, the x > 0 electric field, and the x > 0 potential remain
fixed at their values.

29. Exact solution for the charge density and potential assuming
(a) Accumulation (Φ s = -6kT/q)

30. (b) Middle of depletion (Φs = Φ F = 12kT/q)
(c) Onset of inversion (Φ s = 2Φ F = 24kT/q)

31. (d) Deep into inversion

32. Gate voltage relationship (delta-depletion solution)
Because OX is constant in an ideal oxide with no charges,
Since there is no charges at the interface, (in the depletion region)

33. At threshold,

34. fs is a rather rapidly varying
function of VG when the device
is in depletion. However,
when it is accumulated or inverted, it takes a large change in VG to
produce a small change in fs.
; delta-depletion solution, exact solution.

35. Capacitance - Voltage Characteristics
High- and low- frequency C-V characteristics.

36. CV characteristic is of considerable practical importance.
+ VG –
+  VG –
VG : Slowly changed
 VG : AC signal ( high frequency/low frequency)

37. Qualitative theory Accumulation
The state of the system can be changed very rapidly. The majority carrier can equilibrate with a time constant on the order of to sec.
The small ac signal merely adds or subtracts a charge close to the edges of an insulator. parallel-plate capacitor, CO. M O S
- Q
- Q Q Q Co

38. Withdrawal of majority carriers
Depletion
Withdrawal of majority carriers
The charge state can be changed very rapidly.
The depletion width quasi-statically fluctuates about its dc value  two parallel plate capacitors (Co and Cs ; oxide and semiconductor capacitance) in series.
DC bias   W   C(depl) M O S
+Q +Q W
- Q
- Q Co CS

39. The charge fluctuation depends on the frequency of the AC signal
Inversion
W = WT
The charge fluctuation depends on the frequency of the AC signal
Low frequency :
Minority carriers can be generated or annihilated in response to the ac signal. Just as in accumulation, charge is added or subtracted close to the edges of insulator. M O S
-Q
+Q WT

40. Since WT=constant, CHF(inv) = C(depl)minimum = constant
High frequency :
The relatively sluggish generation-recombination process can’t supply or eliminate minority carriers in response to the ac signal. The number of minority carriers in the inversion layer remains fixed and the depletion width fluctuates about the WT dc value. Two parallel-plate capacitors in series.
Since WT=constant, CHF(inv) = C(depl)minimum = constant M O S WT
-Q
+Q

41. A portion of the inversion layer can be created/annihilated.
For medium frequency
A portion of the inversion layer can be created/annihilated.
CHF(inv) < CMF(inv) < CLF(inv) M O S
+Q WT
-Q
-Q’

42. Delta-Depletion Analysis (skip)
Depletion bias

43. the delta-depletion theory
(xo=0.01mm, NA=1017/cm3,T=300K )
0.5
1.0
1.5
2.0
-0.5
-1.0
0.2
0.4
0.6
0.8
Low frequency
High frequency
C/Co

44. Exact Calculation
Doping dependence
With increased doping, the high-frequency inversion capacitance increases significantly and the depletion bias region widens substantially.

45. Low frequency characteristics
Given modern-day MOS-Cs with long carrier lifetimes and low carrier generation rates, even freq. as low as several Hz will yield high-freq. C-V.
If a low-freq. characteristic is required, the quasi-static technique must be employed.
The quasi-static displacement current flowing through the device is proportional to the low-freq. capacitance.
(I : displacement current, R : voltage ramp rate)

46. High frequency characteristics
Normal measurement frequency ~ 1MHz.
In the ramped-measurement, a deep-depletion phenomenon may appear.

47. Deep depletion
Note that at even the slowest ramp rates one does not properly plot out the inversion portion of the high-freq. characteristic.

48. In accumulation or depletion, only majority carriers are involved Charge configuration rapidly reacts to the changing gate bias.
In inversion region, minority carriers should be generated
The generation process is sluggish and has difficulty supplying the minority carriers needed for the structure to equilibrate.

49. Deep depletion : the nonequilibrium condition where there is a deficit of minority carriers and a depletion width in excess of WT  C < CHF(inv)
Ramp rate   C 
The limiting case occurs when the semiconductor is totally devoid of minority carriers - totally deep depleted.
Same form as simple depletion case

50. Non-equilibrium charge configuration inside an p-type MOS-CWT W
W>WT WT
-Q
Missing electrons
(a) under deep depletion
(b) under total deep depletion