Transistors and Semiconductor Physics

Question 1

Schottky Long-Channel Ideal Transistor Model

Answer 1

Question 2

Linear Region for an Ideal Transistor

Question 3

Cutoff Region for an Ideal Transistor

Question 4

Saturation Region for an Ideal Transistor

Question 5

Four non-ideal MOSFET effects

Answer 5

1) Velocity saturation & mobility degradation: In saturation, drain-to-source current (I_ds) increases less than quadratically with increasing gate-to-source voltage (V_gs)
2) Channel length modulation: In saturation, drain-to-source current (I_ds) increases slightly with the drain-to-source voltage (V_ds)
3) Body Effect: Threshold voltage (V_T) is influenced by the source-to-bulk voltage (V_sb)
4) Subthreshold conduction (junction leakage): There is current flow in nominally OFF transistors

Question 6

Velocity saturation & mobility degradation

Answer 6

In saturation, drain-to-source current (I_ds) increases less than quadratically with increasing gate-to-source voltage (V_gs)

Question 7

Channel length modulation

Answer 7

Main Idea: The drain current in a MOSFET does not actually plateau once the semiconductor is saturated. Instead, it continues to rise as the drain-to-source voltage (V_ds) increases.

In saturation, drain-to-source current (I_ds, sometimes called just the drain current, increases slightly with the drain-to-source voltage (V_ds). This is because the effective channel length (L_eff) becomes slightly shorter as V_ds increases.

The MOSFET is not truly saturated until Vds reaches Vgs

Question 8

Body Effect

Answer 8

Threshold voltage (V_T) is influenced by the source-to-bulk voltage (V_sb). when V_sb increases, it widens the depletion region under the gate, requireing a larget gate-to-source voltage (V_gs) to invert the channel and turn the MOSFET on.

Question 9

Subthreshold conduction (junction leakage)

Answer 9

There is current flow in nominally OFF transistors. This happens because even when the transistor is below threshold, there is a weak inversion layer that allows a small current to flow due to diffusion of carriers

Question 10

Vertical electric field in a MOSFET

Answer 10

Responsible for attracting charge-carriers into the channel.

The charge of the channel is proportional to the electric field strength… The electric field strength is just the gate-to-source voltage over the oxide layer thickness:

E_vert = Vgs/t_ox

Question 11

Lateral electric field in a MOSFET

Answer 11

Responsible for accelerating charge-carriers from drain to source. [need more information]

The electric field strength is just the drain-to-source voltage over the drain-to-source length

E_lat = Vgs/L_ds

Question 12

“The Channel” in MOSFETs

Question 13

Summary of non-ideal effects of a MOSFET based on the I-V plot

Answer 13

1) Before saturation, the slope (dI/dv) is greater than expected (due to velocity Saturation and Mobility Degradation)
2) At saturation, the slope is greater than expected (due to channel length modulation)

Question 14

Importance of λ in VLSI Design Rules

Answer 14

1) Scalability: λ is independent of the absolute feature size. This allows designs to be scalable across different processes and technologies by scaling λ.
- This minimizes the need to redesign when moving from one technology node to another.
2) Simplification and Generalization: Instead of specifying exact distances for every rule, designers can use multiples of λ so that their rules can be more generalized.
3) Portability: Lambda-based rules make designs portable across different foundries or technology nodes, provided the λ scaling factor is adjusted accordingly for each node.

Question 15

MOS- Prefix

Answer 15

“Metal-Oxide-Semiconductor”

[more]

Question 16

-FET Suffix

Answer 16

“Field Effect Transistor”

[more]

Question 17

Relationship between channel length and switching speed

Answer 17

Simply due to the fact that resistance is a geometric property… the further the charge carriers need to go, the more resistance (Rds) they will have to overcome. or a consistent voltage, this means lower current I_ds

Question 18

“Channel” in MOSFETs

Answer 18

The space between the drain and the source

Question 19

Energy bands

Answer 19

Refer to the ranges of energy that electrons can occupy in a solid material. These bands are:

1) Valence Band: The highest energy band that is completely filled with electrons at absolute zero temperature.
2) Conduction Band: The energy band above the valence band, where electrons can move freely, allowing electrical conduction.

The energy difference between these two bands is called the bandgap

Question 20

Bandgap

Answer 20

The energy difference between the conduction and valence bands. Electrons must gain energy (e.g., from thermal excitation) to move from the valence band to the conduction band.
The size of the bandgap determines if the material behaves as a conductor, insulator, or semiconductor.

Question 21

Valance Band

Answer 21

The valence band is the energy range where the outermost electrons (valence electrons) reside. These electrons are bound to atoms but can be involved in bond formation.

Question 22

Conduction Band

Answer 22

The conduction band is the energy range where electrons can move freely and conduct electricity. For electrons to jump from the valence band to the conduction band, they must gain energy equal to or greater than the bandgap energy

Question 23

Hole concentration in the valance band

Answer 23

[needs verification]

Question 24

Importance of charge carriers in the valance band

Question 25

Electron concentration in the valance band

Answer 25

Question 26

Temperature-Dependence of electron energy levels

Answer 26

[more]

Quantified using Fermi-Dirac Statisitics

Question 27

Band Theory

Answer 27

The band theory explains the electrical behavior of semiconductors by describing the distribution of electrons in energy bands:

Valence Band: Electrons here are bound to atoms and do not contribute to conduction.
Conduction Band: Electrons in this band are free to move, allowing electrical conduction.
Bandgap: The energy difference between the valence and conduction bands. In semiconductors, this gap is moderate, allowing some electrons to jump from the valence band to the conduction band under thermal excitation or applied energy.
The number of electrons in the conduction band determines the material’s electrical conductivity. Semiconductors have a small bandgap compared to insulators, allowing controlled conductivity when energy (e.g., heat or light) is applied. Doping can also introduce free carriers to enhance conduction

Question 28

CMOS Transistors