16. MOS fundamentals

Chapter 16. MOS fundamentals

• Metal-oxide-semiconductor field effect

transistor (MOSFET) is the most important device in modern microelectronics.

• In this chapter, we will study:

– Ideal MOS structure electrostatics

– MOS band diagram under applied bias – Gate voltage relationship

– Capacitance-voltage relationship under low frequency and under high frequency.

MOSFET

N-channel MOSFET (n-MMOSFET) uses p-type substrate.

p-Si

When a positive V_G is applied to the gate

relative to the substrate, mobile negative charges (electrons) gets attracted to Si-oxide interface.

These induced electrons form the channel.

MOSFET operation

pinch-off

For a given value of V_G, the current I_D increases with V_D, and finally saturates.

Ideal MOS capacitor

2. The oxide is a perfect insulator with zero current flowing through the oxide layer under all biasing conditions.

The assumptions are:

3. There is no charge centers in the oxide or at the interface between the oxide and semiconductor.

4. The semiconductor is uniformly doped.

6. An ohmic contact has been established between M and S.

7. The MOS capacitor is a one-dimensional structure.

1. Metallic gate is an equipotential region under a.c. and d.c. biasing conditions.

5. The semiconductor is thick so that the bulk is field-free.

8. _M = _S =  + (E_C – E_F)_FB  flat band

Ideal MOS capacitor: band diagram

metal oxide semiconductor

under equilibrium (zero-bias)

The ideal MOS has a flat band in equilibrium!

Effect of an applied bias

Let’s ground the semiconductor and apply d.c. bias (V_G) to the gate.

When V_G ≠ 0, the semiconductor Fermi level is unaffected by V_G and remains

invariant as a function of position, because of zero current flow through the MOS.

When V_G ≠ 0 , the metal Fermi level is also invariant as a function of position.

However, the applied bias separates the Fermi energies of M and S by qV_G,

E_{F, metal} – EF, semiconductor = – q V_G

The EF,semiconductor is fixed (i.e., grounded), the E_F,metal moves, downward if V_G > 0 upward if V_G < 0

Effect of an applied bias

Since oxide has no charge,

according to the Poisson’s equation,

 0

 ε ρ dx

dE

Therefore E-field inside the oxide is constant.

x E q

x E q

x E q

oxide V

oxide C

oxide i

oxide



 



 



 

 1 ^, 1 ^, 1 ^,

constant E

Therefore E_C and E_V are linear function of position with a constant slope.

n-MOS under V

> 0

V_G > 0

E

When V_G > 0, the E_F of metal is lowered relative to the E_F of

semiconductor.

Accumulation of electrons (majority carrier) near the interface of O and S.

The application of V_G > 0 places positive charges on the M gate.





n

n  _i exp ( _F  _i )/ M O S

E_i(surface) moves

downward

n-MOS under small V

< 0

V_G (small) < 0

When V_G < 0, the E_F of metal is raised relative to the E_F of

semiconductor.

Deletion of electrons (majority carrier) near the interface of O and S.  positively-charged donor ions are exposed.

The application of V_G < 0 places negative charges on the M gate.

M O S E

E_i(surface) moves

upward

n-MOS under more negative V

As V_G increases more negatively, the energy band will bend up more and more.

V_G (small) < 0

E

E

V_G < 0

(more negative) E_i(surface) further

moves upward





n

n  _i exp ( _F  _i )/

When E_i(surface) = E_F,

Surface carrier concentrations





n

p  _i exp ( _i  _F )/

i s

s n n

p  

Therefore the surface concentrations of electrons (n_s) and holes (p_s) are ⁿ_s ^{ n}_i ^exp

 





 





n

p_s  _i exp _i ( ) _F / When E_i(surface) < E_F, ps  ni and ns  ni

V_G < 0

When E_i(surface) > E_F, p_s  n_i and n_s  n_i

Especially when E_i(surface) – E_F = E_F – E_i(bulk)

 





i

s n E E bulk kT n N

p  exp  ( ) /   or E_i(surface) – E_i(bulk) = 2[E_F – E_i(bulk)]

For n-MOS capacitor, the applied negative voltage for p_s = N_D is called threshold voltage (V_T).  onset of inversion

 





i

s n E E bulk kT n N

p  exp  ( ) /  

At this voltage, the surface is no longer depleted, because the hole concentration in the surface is equal to the concentration of ionized donors.

n-MOS under V

= V

E_i(surface) – E_F = E_F – E_i(bulk)

n-MOS under V

< V

For further increase in negative bias (V_G < V_T), p_s exceeds n_bulk = N_D.

 The surface minority carrier concentration exceeds the bulk majority carrier concentration.

 It is called inversion.

Ideal p-MOS

Ideal p-MOS v.s. n-MOS

Announcements

• Next lecture: p. 571 ~ 584