MOSFETS

Question 1

The equation for oxide capacitance

Answer 1

the relative permittivity of oxide is epsilon ox

insulator thickness = d_ox

Question 2

The equation for threshold voltage

Answer 2

V_fb= Φ _ms–Q/C’_o

• Where Φ_ms= Φ_m–Φ_s
• Φ_m= workfunction of the gate material
• Φ_s = workfunction of the semiconductor
• Q is the number of charges per unit area
• C’_o= oxide capacitance per unit area

Question 3

The equation for max depletion width under strong inversion

Answer 3

Question 4

What is a unipolar device

Answer 4

A unipolar device is a device that uses one type of carrier for conduction- electrons or holes

Question 5

What is a MOSFET

Answer 5

A Mosfet is a metal oxide semiconductor of the field-effect transistor family.

There is a thin silicon dioxide insulation layer, separating the metal and semiconductor.

Question 6

What is a MOS Capacitor?

Answer 6

A metal-oxide-semiconductor which can have capacitor like behaviour

Question 7

What does n-type mean?

Answer 7

n-type refers to the majority carriers in a semiconductor. In this case, electrons form the majority carrier flow in the material due to being dependent on the doping level. i.e. the device is doped with donor ions

Question 8

What does p-type mean?

Answer 8

The p-type refers to the carriers within a semiconductor. The semiconductor is doped with acceptor ions, this means the majority carriers are the holes in the device.

Question 9

What is a band diagram?

Answer 9

In solid-state physics of semiconductors, a band diagram is a diagram plotting various key electron energy levels as a function of some spatial dimension, which is often denoted x. These diagrams help to explain the operation of many kinds of semiconductor devices and to visualize how bands change with position.

Question 10

What is accumulation in MOSFETs?

Answer 10

A MOS capacitor biased with a small negative voltage is in accumulation.

• -ve charge induces equal opposite +ve charge in the silicon
• +ve accumulation at the silicon due to holes
• Minimum energy for holes level at the oxide
• Applied voltage = sum of the voltage drop across the oxide and band bending in the silicon
• Difference in Fermi level in metal and silicon = applied voltage
• No band bending in silicon E_F due to no current flows

Question 11

Describe Depletion Condition

Answer 11

• +ve charge induces equal opposite –ve charge in the silicon
• -ve charge in the silicon due to depletion of holes in the silicon
• Applied voltage = sum of the voltage drop across the oxide and band bending of silicon
• Voltage drop across oxide and depletion region –determined by the capacitance of oxide and depletion

Question 12

Describe Inversion Condition

Answer 12

• V>>0, increase in voltage drop across oxide and depletion region
• Increased voltage across depletion -> increased depletion width: p-n junction
• EFnear to Ec
• Induced n-type at the surface

Question 13

Describe linear region

Answer 13

The linear region refers to low drain voltage, It has Ohmic characteristics.

• Inversion layer like a resistive material (V=IR)
• Electrons flow from Source to Drain

Question 14

Describe Saturation Region

Answer 14

•Bias: VG> VT
As the voltage increases up to the voltage V_SAT. It reaches the pinch-off point. here the inversion layer is reduced to zero.

Beyond the pinch-off point, the drain current remains essentially the same,
because for V, > V,,,,, at point P the voltage VDSarte mains the same. Thus, the number
of carriers arriving at point P from the source or the current flowing from the drain to
the source remains the same. This is the saturation region, since I, is a constant regardless
of an increase in the drain voltage.

Question 15

What is Pinch Off?

Answer 15

Pinch off refers to what happens when the bias voltage reaches V_sat. Here the Inversion layer reduces to 0.

Question 16

Define drift velocity

Answer 16

The drift velocity is the average velocity of the charge carriers in the drift current.

Question 17

Describe Inversion Layer

Answer 17

(EF- E,) > 0. Therefore, the electron concentration n_P
at the interface is larger than n_i, and the hole concentration given by Eq. 2 is less than
ni, The number of electrons (minority carriers) at the surface is greater than holes (majority
carriers); the surface is thus inverted.

Question 18

Describe NMOS

(substrate and channel)

Answer 18

NMOS has a p-substrate and form an n-channel.

Question 19

Describe PMOS

(substrate and channel)

Answer 19

n-substrate

p-channel

Question 20

Purpose of oxide in semiconductor

Answer 20

Oxide as an isolation layer to prevent current flow from top metal contact to bottom semiconductor contact

Question 21

Describe flat band condition

Answer 21

• Assuming no applied gate voltage
• Therefore no electric field
• Assume qΦ_m= qΦ_s
• Flat energy band in vacuum level for SiO₂

Question 22

Draw Band Diagram of Flat Band Condition

Answer 22

Question 23

What does an applied gate voltage do to the semiconductor part of MOS?

Answer 23

Application of voltage -> band bending in the semiconductor part

Question 24

What is the effect of an applied voltage on the MOS capacitor?

Answer 24

• Accumulation (small -ve voltage)
• Depletion (small +ve voltage)
• Inversion (large +ve voltage)

Question 25

Draw Band diagram for accumulation

Answer 25

Diagram From Top to bottom letters: E_C, E_I, E_F, E_V

Question 26

Draw Band Diagram for Inversion

Answer 26

E_C, E_i, E_F, E_V

Question 27

Draw Band Diagram For Depletion

Answer 27

Question 28

Draw Charge Graph For Accumulation

Answer 28

Question 29

Charge Graph For Depletion

Answer 29

W = depletion width

Question 30

Charge Graph For Depletion

Answer 30

Question 31

Charge Graph for Inversion

Answer 31

Q_M= qN_AW_m+ Q_n

Question 32

The equation for majority carriers in accumulation

Answer 32

**p** = **n_i**exp((**E_I -E_F**)/**kT**)

Question 33

The equation for majority Carriers in Depletion Cond

Answer 33

**n** = **n_i**exp((**E_F** -**E_I**)/**kT**)

Question 34

The equation for majority Carriers in Inversion Cond

Answer 34

n = n_iexp((E_F -E_I)/kT)

Question 35

Features of Inversion Condition

Answer 35

* Produces n-type semiconductor at the oxide-silicon interface by biasing * Without n doping * Advantages: no doping scattering and suppression of carrier ‘freeze-out * Can increase high carrier density by using large bandgap insulator: SiO2, HfO2

Question 36

What is the threshold voltage?

Answer 36

Defined as when strong inversion occurs, varies depending on the device. and is when E_F–E_i\> 0. V_inv = 2 (kT)/q \* ln N_A/n_i