The document discusses MOSFET theory and operation, including: - MOSFET device structure and types (depletion and enhancement mode). - Regions of operation depending on gate-source and drain-source voltages. - Effects that occur at small device geometries including short channel effects like drain-induced barrier lowering, velocity saturation, and hot carriers. - Operation and efficiency of solar cells made from semiconductor materials, and how efficiency depends on the material bandgap. Design improvements like PERL cells are also discussed.

1. ECS-504
DIGITAL CIRCUITS AND SYSTEMS
Shivank Rastogi
18BEC022
BTECH-ECE 5TH SEMESTER
Faculty of Engineering&Technology
Jamia Millia Islamia, New Delhi

2. MOSFET THEORY Small Geometry Effect Solar Cell
• MOSFET stands for Metal Oxide Silicon Field Effect Transistor or
Metal Oxide Semiconductor Field Effect Transistor.
• MOSFET is a 4 terminal device with Terminal source, Drain, Gate
and Body
• Source and Body are generally connected together
• The Gate potential controls the formation of channel
• MOSFETs are available in two basic forms:
Depletion Type – the transistor requires the Gate-Source
voltage, ( VGS ) to switch the device “OFF”. The depletion mode
MOSFET is equivalent to a “Normally Closed” switch.
Enhancement Type– the transistor requires a Gate-Source voltage,
( VGS ) to switch the device “ON”. The enhancement mode MOSFET is
equivalent to a “Normally Open” switch.

3. MOSFET THEORY Small Geometry Effect Solar Cell
Depletion-Mode MOSFET:
The depletion type MOSFET transistor is equivalent to
a “normally closed” switch. The depletion type of
transistors requires gate – source voltage (VGS) to
switch OFF the device.
Enhancement-Mode MOSFET:
The Enhancement ode MOSFET is equivalent to
“Normally Open” switch and these types of
transistors require gate-source voltage to switch
ON the device.

4. MOSFET THEORY Small Geometry Effect Solar Cell
• Four basic types of MOSFETs-cross sections at V G = 0 V, output and transfer characteristics

5. In MOSFET we have various regions of
operation
By varying V-
GS
By varying V-DS
Under linear distribution
of charge
Accumulation region, VG < 0
Depletion/Weak Inversion region,
VG > 0
Strong Inversion region, VG >>0
Linear/Triode region, VDS < (VGS-
VTH)
Saturation region, VDS > (VGS-
VTH)
Under Linear region:
ID 
CO X W (VGS VTH)VD
L
Resistance
R : (VGS VTH)
R  1/
Transconductance:
OX
L
C W
Under Saturation region: (can act as current
source)
2L
CO X W (VGS VTH )2
ID, sat 
Transconductan
ce
dVG L

dID

COXW (VGS VTH )
g m ,sat
dI
dVG L
C WV
gm,lin D
O X D
Triode
Mode
MOSFET THEORY Small Geometry Effect Solar Cell
CCharacteristics and Region of
Operation

6. MOSFET THEORY Short Geometry Effect Solar Cell
Channel Length
• The channel length is a very critical parameter in CMOS
technology for performance projection, device design, modeling
and circuit simulation of MOSFETs
• The so-called channel length is a broad description ofthree
different channel lengths in the MOSFET. One is the mask
channel length Lm, which denotes the physical length ofthe gate
mask. Another is the electrical effective channel length LetT'
which defines the length ofa region near the Sj-Sj02 interface in
which the inversion free-carrier density is controlled by the gate
voltage. The channel length is given by:
Del Leff is the effective channel length reduction
etT is the effective channel length reduction
• The third channel length used frequently is the
metallurgical channel length Lmet, which is the
distance between the source and drain
metallurgical junctions at the SjS;02 interface

7. MOSFET THEORY Short Geometry Effect Solar Cell
Channel Length Modulation and Pinch off :

8. MOSFET THEORY Short Geometry Effect Solar Cell
Short Channel Effect :
• A MOSFET device is considered to be short when the channel length is the
same order of magnitude as the depletion-layer widths (xdD, xdS) of the
source and drain junction. As the channel length L is reduced to increase
both the operation speed and the number of components per chip, the so-
called short-channel effects arise.

9. MOSFET THEORY Short Geometry Effect Solar Cell
Short Channel Effect:
• A MOSFET is considered to be short when the channel length ‘L’ is the same order of magnitude as the
depletion-layer widths (xdD, xdS). The potential distribution in the channel now depends upon both,
transverse field Ex, due to gate bias and also on the longitudinal field Ey, due to drain bias When the Gate
channel length <<1 m, short channel effect becomes important . This leads to many undesirable effects in
MOSFET.
The short-channel effects are attributed to two physical phenomena:
1. the limitation imposed on electron drift characteristics in the channel,
2. the modification of the threshold voltage due to the shortening channel length.
In particular five different short-channel effects can be distinguished:
1. surface scattering
2. drain-induced barrier lowering and punchthrough
3.velocity saturation
4.impact ionization
5.hot electrons

10. MOSFET THEORY Short Geometry Effect Solar Cell
Drain-induced barrier lowering and punchthrough:
When the depletion regions surrounding the drain extends to
the source, so that the two depletion layer merge (i.e., when
xdS + xdD = L), punchtrough occurs. Punchthrough can be
minimized with thinner oxides, larger substrate doping,
shallower junctions, and obviously with longer channels. The
current flow in the channel depends on creating and sustaining
an inversion layer on the surface. If the gate bias voltage is not
sufficient to invert the surface (VGSthe carriers (electrons) in
the channel face a potential barrier that blocks the flow.
Increasing the gate voltage reduces this potential barrier and,
eventually, allows the flow of carriers under the influence of
the channel electric field. In small-geometry MOSFETs, the
potential barrier is controlled by both the gate-to-source
voltage VGS and the drain-to-source voltage VDS. If the drain
voltage is increased, the potential barrier in the channel
decreases, leading to drain-induced barrier lowering (DIBL).
The reduction of the potential barrier eventually allows
electron flow between the source and the drain, even if the
gate-to-source voltage is lower than the threshold voltage. The
channel current that flows under this conditions (VGS<Vto) is
called sum threshold current

11. MOSFET THEORY Short Geometry Effect Solar Cell
SURFACE SCATTERING: • For small-geometry MOSFETs, the electrons
mobility in the channel depends on a two-
dimensional electric field (Ex, Ey). The surface
scattering occurs when electrons are accelerated
toward the surface by the vertical component of
the electric field Ex
• As the channel length becomes smaller due to the
lateral extension of the depletion layer into the
channel region, the longitudinal electric field
component Ey increases, and the surface mobility
becomes field-dependent. Since the carrier
transport in a MOSFET is confined within the
narrowinversion layer, and the surface scattering
(that is the collisions suffered by the electrons
that are accelerated toward the interface by ex)
causes reduction of the mobility, the electrons
move with great difficulty parallel to the
interface, so that the average surface mobility,
even for small values of Ey, is about half as much
as that of the bulk mobility.

12. MOSFET THEORY Short Geometry Effect Solar Cell
Velocity Saturation:
• The electron velocity is related to the electric
field through the mobility: V= μE
• For higher fields the velocity does not increase with electric field, we have degradation of mobility because of
scattering by vertical field. This leads to earlier saturation of current. i.e.,before VGS-VTH. Net result is
reduction in drain current .
• The velocity saturation reduces the transconductance of short-channel devices in the saturation condiction.

13. MOSFET THEORY Short Geometry Effect Solar Cell
IMPACT IONIZATION: The presence of high longitudinal fields can accelerate
electrons that may be able of ionizing Si atoms by impacting
against them
Normally most of the e- are attracted by the drain, so it is
plausible a higher concentration of holes near the source
If the holes concentration on the source is able to creates
a voltage drop on the source-substrate n-p junction of
about 0.6V then
e- may be injected from source to substrate
e- travel toward the drain, increasing their energy and
create new e-h pairs
e- may escape the drain fields and afect other device
They can gain enough energy as they travel toward the
drain to create new eh pairs. The situation can worsen if
some electrons generated due to high fields escape the
drain field to travel into the substrate, thereby affecting
other devices on a chip.

14. MOSFET THEORY Short Geometry Effect Solar Cell
Hot Electrons:
The channel Hot Electrons effect is caused by electrons flowing in the channel for large VDS
e- arriving at the Si-SiO2 interface with enough kinetic energy >3.1ev to surmount the surface potential barrier
are injected into the oxide
This may degrade permanently the C-V characteristics of a MOSFETs

15. MOSFET THEORY Short Geometry Effect Solar Cell
CONCLUSION:
FOR IMPACT IONIZATION
FOR PUNCH THROUGH
Short Channel Effects are governed by
complex physical phenomena and mainly
Influenced because of both vertical and
horizontal electric field components.
To meet the current requirements of
Electronic devices, the miniaturization of
devices is important. And so is Second Order
effects which otherwise degrade the
performance of devices.

16. MOSFET THEORY Short Geometry Effect SOLAR CELLS
INTRODUCTION: • Solar cells and photodetectors are devices that convert
an optical input into current. A solar cell is an example
of a photovoltaic device, i.e, a device that generates
voltage when exposed to light.
• The photovoltaic effect was discovered by Alexander-
Edmond Becquerel in 1839, in a junction formed
between an electrode (platinum) and an electrolyte
(silver chloride).
• The first photovoltaic device was built, using a Si pn
junction, by Russell Ohl in 1939. The functioning of a
solar cell is similar to the photodiode (photodetector). It
is a photodiode that is unbiased and connected to a load
(impedence).

17. MOSFET THEORY Short Geometry Effect SOLAR CELLS
SOLAR SPECTRUM: • The solar spectrum typically extends from the IR to the
UV region, wavelength range from 3 µm to 0.2 µm. But
the intensity is not uniform.
• A typical solar spectrum, as a plot of spectral irradiance
vs. wavelength, is shown in figure .
• The area under the curve gives the total areal intensity
and this is approximately 1.35 kW m−2 .
• The solar spectrum can be approximated by a black
body radiation curve at temperature of approximately
5250 ◦C.
• There is also a difference in the spectra measured at the
top of the atmosphere and at the surface, due to
atmospheric scattering and absorption.

18. MOSFET THEORY Short Geometry Effect SOLAR CELLS
Solar Cell working principle: • A simple solar cell is a pn junction diode.The n
region is heavily doped and thin so that the light can
penetrate through it easily. The p region is lightly
doped so that most of the depletion region lies in the
p side.
• The penetration depends on the wavelength and the
absorption coefficient increases as the wavelength
decreases.
• Electron hole pairs (EHPs) are mainly created in the
depletion region and due to the built-in potential and
electric field, electrons move to the n region and the
holes to the p region. When an external load is
applied, the excess electrons travel through the load
to recombine with the excess holes.
• The shorter wavelengths (higher absorption
coefficient) are absorbed in the n region and the
longer wavelengths are absorbed in the bulk of the p
region
• The total width of the region that contributes to the
solar cell current is wd + Le + Lh, where wd is the
depletion width
Principle of operation of a pn
junction solar cell. Radiation is
absorbed in the depletion region
and produces electrons and holes.
These are separated by the built-in
potential. Depending on the
wavelength and the thickness
different parts of the device can
absorb different regions of the
solar spectrum

19. MOSFET THEORY Short Geometry Effect SOLAR CELLS
Solar Cell Materials and Efficiency:
Solar cell
efficiency as a
function of band
gap of the
semiconductor
material. There is
an particular
band gap range
where the
efficiency is
maximum.
: Si solar cell with an
inverted pyramid
structure to enhance
absorption of the incoming
radiation. These are called
PERL cells. The inverted
pyramid structure causes
multiple reflections at the
surface, which help in
absorption of the incoming
radiation
• The efficiency of the solar cell depends on the band gap
of the material
• Polycrystalline solar cells are cheaper to manufacture
but have a lower efficiency since the microstructure
introduces defects in the material that can trap carriers
• Amorphous solar cells have an even lower efficiency
but can be grown directly on glass substrates by
techniques like sputtering so that the overall cost of
manufacturing is lowered
• There are also design improvements in the solar cell
that can enhance the efficiency. PERL (passivated
emitter rear locally diffused) cells, shown in figure
have an efficiency of 24% due to the inverted pyramid
structure etched on the surface that enhances
absorption.

20. REFERENCES
• http://www0.cs.ucl.ac.uk/staff/ucacdxq/projects/vlsi/report.pdf
• https://dokumente.unibw.de/pub/bscw.cgi/d9299614/04_Short-Channel%20MOSFET.pdf
• https://nptel.ac.in/content/storage2/courses/117101058/downloads/Lec-8.pdf
• https://nptel.ac.in/content/storage2/courses/113106062/Lec19.pdf
THANK YOU!
Submitted By:
Shivank Rastogi
18BEC022