“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
5.449
https://scientific-jl.com/ped
Volume-83, Issue-1, June -2025
14
INFLUENCE OF QUANTUM DOT SIZE ON THE
CHARACTERISTICS OF FIELD EFFECT TRANSISTORS
Kanatbay Ismailov, Khayratdin Kamalov,
Khudaybergenov Abdumukhamed
Karakalpak State University, Nukus,
Uzbekistan 2025-06-01
Abstract
A quantum dot (QD) with discrete energy levels connected to source and drain
connections that display continuous energy distributions can be used to represent the
channel in nanoscale field effect transistors (FETs). Contact states also permeate the
channel region, and the initially sharp discrete states in the channel expand and "spill
over" into the contacts as a result of this coupling.The result is a broadened density of
states (DOS) in the channel that obeys a sum rule preserving electron count. This
broadened DOS is commonly described by a Lorentzian function . This paper
investigates how varying the size of cubic quantum dots affects the DOS and
subsequent FET characteristics.
Introduction
This article provides a thorough analysis of the basic properties of Field Effect
Transistors (FETs), with a particular emphasis on the impact of the size of the quantum
dots (QDs) placed in the channel. We study the effects of QD dimension modifications
on important parameters including the density of states (DOS) as an energy function.
Since the source-to-drain current flow in FETs is directly impacted by these energy
levels, it is essential to comprehend the DOS peaks and their location with different
QD sizes. By analyzing QDs with side lengths
𝑎 = 7 nm, 14 nm, 28 nm,
and
56 nm
,
we aim to identify trends and correlations to inform future current-voltage
characteristic simulations and device optimization. This research contributes valuable
insights towards tailoring QD dimensions for enhanced transistor performance .
Theoretical Background
In this section, we summarize the main theoretical formulas employed in the
modeling of QD-based FETs.
𝐸
𝑛
=
ℏ
2
𝜋
2
2𝑚
∗
𝑎
2
(𝑛
𝑥
2
+ 𝑛
𝑦
2
+ 𝑛
𝑧
2
)
𝐷(𝐸) = ∑
Γ/2𝜋
(𝐸 − 𝐸
𝑛
)
2
+ (Γ/2)
2
𝑛
𝐼 =
2𝑒
ℎ
∫ 𝑇(𝐸)[𝑓
𝐿
(𝐸) − 𝑓
𝑅
(𝐸)]𝑑𝐸
“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
5.449
https://scientific-jl.com/ped
Volume-83, Issue-1, June -2025
15
where
𝐸
𝑛
are discrete energy levels in the QD,
Γ
is the broadening parameter,
𝐷(𝐸)
is the density of states,
𝑇(𝐸)
the transmission function, and
𝑓
𝐿,𝑅
(𝐸)
are the Fermi
functions of left and right contacts .
Results and Discussion
Density of States for Small QDs:
𝒂 = 𝟕 𝐧𝐦
and
𝒂 = 𝟏𝟒 𝐧𝐦
Figures 1 and 2 show the density of states (DOS) as a function of energy for quantum
dots
with
side
lengths
7
nm
and
14
nm,
respectively.
Figure 1:Density of States vs Energy for QD size
𝑎 = 7 𝑛𝑚
at
𝑇 = 300 𝐾
.
Figure 2:Density of States vs Energy for QD size
𝑎 = 14 𝑛𝑚
at
𝑇 = 300 𝐾
.
Comparing these two figures reveals that as the quantum dot size increases from
7 nm to 14 nm, the discrete energy levels become more closely spaced, and the overall
DOS broadens. This behavior is expected from quantum confinement effects, where
smaller QDs have more widely spaced energy levels due to stronger confinement .
“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
5.449
https://scientific-jl.com/ped
Volume-83, Issue-1, June -2025
16
Density of States for Large QDs:
𝒂 = 𝟐𝟖 𝐧𝐦
and
𝒂 = 𝟓𝟔 𝐧𝐦
Figures 3 and 4 display the DOS for larger quantum dots with side lengths of 28
nm and 56 nm.
Figure 3:Density of States vs Energy for QD size
𝑎 = 28 𝑛𝑚
at
𝑇 = 300 𝐾
.
As the QD size further increases, the energy levels become very closely spaced and
the DOS approaches a quasi-continuous distribution, similar to bulk materials.
Figure 4: Density of States vs Energy for QD size
𝑎 = 56 𝑛𝑚
at
𝑇 = 300 𝐾
.
This indicates the diminishing effect of quantum confinement and the transition
towards classical behavior .
Conclusion
Our study confirms that quantum dot size strongly influences the electronic
structure and density of states in FET channels. Smaller QDs exhibit discrete, well-
“PEDAGOGS”
international research journal ISSN:
2181-3027
_SJIF:
5.449
https://scientific-jl.com/ped
Volume-83, Issue-1, June -2025
17
separated energy levels leading to sharper DOS peaks, while larger QDs show
broadened levels approaching bulk-like continuous distributions.These differences
have a direct impact on the device’s performance and electron transport characteristics.
In order to completely mimic current-voltage characteristics for QD-based FETs and
enable improved nanoelectronic device design, future work will concentrate on
integrating tunneling rates, Coulomb interactions, and temperature dependency.
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