Proceedings Editorial board:
Nguyen Duc Hoa Ngo Ngoc Ha Chu Manh Hung
Sponsors:
I
11
a A. COMMITTEE
1) International Advisory and Organizing Committee •
Nguyen Due Chien (chairman), Vietnam
Hanoi University
of Science and Technology,
• •
Tom Gregorkiewicz (co-chairman), University of Amsterdam, The Netherlands Nguyen Van Hieu (co-chairman), Hanoi University of Science and Technology, Vietnam
• • •
Dinh Van Phong, Hanoi University of Science and Technology, Vietnam Do Tien Dung, Ministry of Science and Technology, Vietnam Giorgio Sberveglieri, University of Brescia, Italy
• • • • • •
Wen-Chang Chen, National Taiwan University, Taiwan Mark Golden, University of Amsterdam, The Netherlands Nguyen Phuc Duong, Hanoi University of Science and Technology, Vietnam Than Due Hien, Hanoi University of Science and Technology, Vietnam Vu Ngoc Hung, Hanoi University of Science and Technology, Vietnam Nguyen Due Hoa, Hanoi University of Science and Technology, Vietnam
2) Local Organizing Committee • • • • • • • • • • • • • • •
Nguyen Van Hieu, Hanoi University of Science and Technology, Vietnam Nguyen Phuc Duong, Hanoi University of Science and Technology, Vietnam Nguyen Due Hoa, Hanoi University of Science and Technology, Vietnam Pho Thi Nguyet Hang, Hanoi University of Science and Technology, Vietnam Ph am Thanh Huy, Hanoi University of Science and Technology, Vietnam Ngo Ngoc Ha, Hanoi University of Science and Technology, Vietnam Mai Anh Tuan, Hanoi University of Science and Technology, Vietnam Vu Ngoc Hung, Hanoi University of Science and Technology, Vietnam Bui Thi Hang, Hanoi University of Science and Technology, Vietnam Pham Due Thanh, Hanoi University of Science and Technology, Vietnam Chu Manh Hoang, Hanoi University of Science and Technology, Vietnam Pham Van Tuan, Hanoi University of Science and Technology, Vietnam Tran Ngoc Khiem, Hanoi University of Science and Technology, Vietnam Vu Thu Hien, Hanoi University of Science and Technology, Vietnam Nguyen Ngoc Lan, Hanoi University of Science and Technology, Vietnam Nguyen Phuong Loan, Hanoi University of Science and Technology, Vietnam To Thanh Loan, Hanoi University of Science and Technology, Vietnam
III
• • • • • • • • •
Nguyen Khac Man, Hanoi University of Science and Technology, Vietnam Dao Thuy Nguyet, Hanoi University of Science and Technology, Vietnam Luong Ngoc Anh, Hanoi University of Science and Technology, Vietnam Nguyen Van Duy, Hanoi University of Science and Technology, Vietnam Tran Thi Viet Nga, Hanoi University of Science and Technology, Vietnam Nguyen Anh Tuan, Hanoi University of Science and Technology, Vietnam Luong Ngoc Anh, Hanoi University of Science and Technology, Vietnam Hoang Quoc Khanh, Hanoi University of Science and Technology, Vietnam Dang Thi Thanh Le, Hanoi University of Science and Technology, Vietnam Nguyen Van Quy, Hanoi University of Science and Technology, Vietnam Chu Manh Hung, Hanoi University of Science and Technology, Vietnam Nguyen Van Duy, Hanoi University of Science and Technology, Vietnam Nguyen Minh Hong, Hanoi University of Science and Technology, Vietnam Nguyen Van Toan, Hanoi University of Science and Technology, Vietnam
3) Program and Publication Committee
• • • •
Nguyen Phuc Duong, Hanoi University of Science and Technology, Vietnam Nguyen Duc Hoa, Hanoi University of Science and Technology, Vietnam Ngo Ngoc Ha, Hanoi University of Science and Technology, Vietnam Chu Thi Xuan, Hanoi University of Science and Technology, Vietnam Chu Manh Hung, Hanoi University of Science and Technology, Vietnam Dao Thuy Nguyet, Hanoi University of Science and Technology, Vietnam
4) Publication Editors • • • •
Phan Manh Huong, University of South Florida, USA Nguyen Phuc Duong, Hanoi University of Science and TecImology, Vietnam Le Anh Tuan, Hanoi University of Science and Technology, Vietnam Nguyen Van Hieu, Hanoi University of Science and Technology, Vietnam
5) Secretariat board
• • • • •
Ngo Ngoc Ha, Hanoi University of Science and Technology, Vietnam Chu Manh Hung, Hanoi University of Science and Technology, Vietnam Chu Thi Xuan, Hanoi University of Science and Technology, Vietnam Dao Thuy Nguyet, Hanoi University of Science and Technology, Vietnam Nguyen Ngoc Lan, Hanoi University of Science and Technology, Vietnam Nguyen Thi Phuong Loan, Hanoi University of Science and Technology, Vietnam
IV
CONTENTS No. Titles and authors 1
Page
Controlled Synthesis and Magnetism of Hierarchical by Modified Polyol Methods and Heat Treatment
a-Fe203 Particles
1
Nguyen Viet Long, Yong Yang, Cao Minh Thi, Masayuki
Nogami
Effects of Ultraviolet illumination on N02 gas-sensing characteristics of Sn02 nanowires sensor 2
3
Nguyen Manh Hung, Chu Manh Hung, Hoang Sy Hong, Nguyen Due Khoang, Nguyen Van Toan, Phung Thi Hong Van, Bui Thi Binh, Dinh Van Thien, Nguyen Van Hieu Phase transition pressure
and crystallization
of amorphous
7
silica under high
11
Nguyen Thi Thu Ha, Mai Thi Lan, Nguyen Van Hong 4
Structural simulation of amorphous PbSi03 under compression
16
Nguyen Van Yen, Le The Vinh, Nguyen Van Hong
5
,
Streaming potential measurements in porous media
23
Luong Duy Thanh, Rudolf Sprik 6
7
Structural, optical and electrical properties of stannite CU2ZnSnS4 Zakhvalinskii V.S., Nguyen Thi Tham Hong, Pham Thi Thao, Dang Ngoe Toan, Piliuk E.A., Taran S.V. Bandgap-Dependent Deviations Band-to-Band Tunneling Models Nguyen Hien
8
Dang Chien,
Network structure pressure
Hoang
29
of Local and Nonlocal from Mixed 36 Sy Due, Chun-Hsing
and polyamorphism
Shih, Dinh Sy
of liquid CaSi03
under high 44
Tran Thuy Duong, Nguyen Van Hong 9
An approach of preparing high-pe/jormance
MnBi alloys and magnets
50
Nguyen Van Vuong, Nguyen Xuan Truong 10
New manufacturing process of metal nanowires on a substrate combination of chemical stamping and sputter coating Masahiko
Yoshino, Potejana
Potejanasak,
v
Motoki Terano
by 57
The 3rd International Conference on Advanced Materials and Nanotechnology
Bandgap-Dependent
Hanoi,2016
Deviations of Local and Nonlocal from Mixed Bandto-Band Tunneling Models
Nguyen Dang Chien I·, Hoang Sy DucZ, Chun-Hsing
Shih3, Dinh Sy Hien4
IFaculty of Physics, University ofDalat, Lam Dong 671460, Vietnam 2Department of Postgraduate Studies, University ofDalat, Lam Dong 671460, Vietnam 3Department of Electrical Engineering, National Chi Nan University, Nantou 54561, Taiwan 4Department of Mechanical, Electricai and Electronic Engineering, Ho Chi Minh City University of Technology (HUTECH) 718500, Vietnam *Corresponding author:
[email protected]
Abstract: The nonlocal electric field approach
has been widely accepted for Kane's band-to-band tunneling (BTBT) model to calculate, both analytically and numerically, the tunneling current in tunnel field-effect transistors (TFETs). In this paper, we demonstrate that the tunneling current deviations of the local and non local BTBT models from the mixed model counterpart, which is shown to be a more physically realistic approach by using both local and nonlocal fields, depend significantly on the material bandgap. The deviation of the nonlocal model from the mixed model increases with decreasing the bandgap and applied voltage because the tunneling generation is progressively extended to the small band-bending region. Although the deviation between the local and mixed models is considerably decreased when scaling down the bandgap because of the slow variation of tunneling probability under the change of electric Held, it is still relatively large in low-bandgap semiconductors. With the continuous trend of scaling down bandgap and supply voltage, the mixed BTBT model should be used rather than the nonlocal BTBT app.·oach to properly determine the tunneling current in TFET devices. Keyworlls: Low-bandgap material, band-to-band tunneling, nonlocal BTBT, mixed BTBT model, Kane model
I.
I TRODUCTION
popular model of BTBT generation was developed by Kane [9] based on a two-band model to highlight the physics and predict the BTBT rate in tunnel devices. The Kane model provides a simply unique fonnula of the tunneling rate for both direct and indirect BTBT processes, which makes it favorable to be integrated in numerical simulation tools [13]. However, the Kane formula was derived only for ideal junctions with a uniform electric field. For the general cases of non-uniform fields, both local and nonlocal electric fields have been arbitrarily assumed in the Kane model [14]. A large deviation of tunneling currents calculated by using the local field and obtained from experimental TFETs has been observed [15, 16]. Although the special choice of local field approach using the maximum field yields more appropriate calculations [10], the maximum electric field approximation still exhibits considerable deviations [17]. It has been shown that the Kane model based on the nonlocal field approach was fitted well with experimental data [18-20]. This explains why the nonlocal BTBT model has been being widely used to calculate, both analytically and numerically, the tunneling current of TFET devices. However, the assumption of the nonJocal field has been employed without clear physical origins. Recent researches have realized that the mixed BTBT model that decouples the local and nonlocal fields in the pre-exponential factor of the
The band-to-band tunneling (BTBT) has successfully been exploited as an essential mechanism to produce the on-off transition of three-terminal devices known as tunnel field-effect transistors (TFETs) [1-7]. Not governed by the Boltzmann limit of 60 mY/decade subthreshold swing at room temperature as of conventional metal-oxide-semiconductor field-effect transistors (MOSFETs) [2], TFETs can be operated with the steep on-off switching of a deep sub-60 m V/decade subthreshold swing [3-5]. The possibility of achieving an extremely low subthreshold swing is the key advantage of TFETs that allows of scaling down the supply voltage and thus associated power consumption of integrated circuits [6, 7]. To study the device physics and design of TFETs, the physical mechanism of BTBT has to be fully understood and the modeling of BTBT generation at tulmel junctions has to be properly performed to evaluate the tunneling current in TFETs. Since Zener discovered the tunneling of electrons through the forbidden band of semiconductors [8], many researches have been carried out to elucidate the physics ofBTBT and to calculate the BTBT current of unifornl and nonuniform electric field junctions [9-12]. The most
36
The3,d International Conference
on Advanced
Materials
Hanoi, 2016
and Nanotechnology
Depletion
(b)
(a)
One-Sided p-n Junction in Reversed bias
,;(x)
=- qN, li
X
E
?"(x) = .!..[';(x) + ,;(x + I",,)] 2
X
'"'" =~2liV, qN, o
Depletion
X
re I. (a)Schematicstructure and (b) energy-band diagram of one-sided p-n j unction in reverse-biased condition.
e fonnula is more physically appropriate for ating the tunneling generation [21, 22]. fore,adequately examining the deviations of localand nonlocal from mixed BTBT models a wide range of semiconductor band gaps is nsableto evaluate the appropriateness of the and nonlocal BTBT models and to further tandthe physical nature ofBTBT
that the Kane model only works correctly for a uniform profile of electric field, a reverse-biased ideal p-n junction with a unifonn field is assumed for the model derivation. In general, the BTBT generation rate (G) is equal to the product of the flux of electrons reaching to tunnel junction, tunneling probability and transmission factor:
processes. G = f dN F x P X Fr
In this paper, we numerically calculated and icallyexplained the deviations of tunneling Is calculated by the local and nonlocal models from that by the mixed model rpart.The bandgap-dependent deviations of andnonlocalfrom mixed BTBT models were ed for the first time. The one-sided p-n s in reverse-biased conditions were to qualitatively and quantitatively gate the BTBT processes. This simple junctionwas chosen because the tunneling in this structure is physically identical to e point- and line-tunneling in TFETs [23]. t-bandgap semiconductors of InxGa !_xAs concentration x varying from 0.17 to 1 employedsince it provides a wide range of andthe direct tunneling results in a much probability compared to the indirect g for the same bandgap. The lowest In tion was limited at 0.17 because the oflno.I7Gao.83As (1.18 eV) reaches to that
(1)
where dNF is the incident electron flux, P is the tunneling probability and Fr is the transmission factor defined as the number of available conduction band states into which transmission of a valence electron can be performed. For the direct BTBT, Fr = 1 because both the electron energy and momentum are conserved. By treating the electric field as a constant perturbation field and using the Fermi golden rule in the framework of the time-dependent perturbation theory, Kane obtained the following expression of the tunneling probability:
P=-exp 9 TC2
0
[mn;/2 2nq~ E~/2 )
exp--=-
(2)
(2E E1.1. J
where (3)
first
.; is the electric field, m,. is the reduced mass, n is reduced Plank's constant, Eg is the material
briefly for understanding the ess of the different approaches of the ld presented subsequently. With noting
bandgap, q is the elementary charge, k y and kz are the perpendicular components of wave vector. The electron flux in a ring of perpendicular momentum
ERENT APPROACHES
Kane' direct BTBT
FOR KANE MODEL
model
is
37
The ---
3,.d
10~ 10·' 10" ::: ... :: 10~ a 10·) bIl .5 O::: J 0.0 a§ U N
'"
~
Eo-
18n1i2 E1/2g 2 1/2):2
exp -
,.
g
2nq~ [1OnI/2E3/2)
G
loe(ll
-
q
111.
,.
'::>
18nJi2 E~/2 2 1/2):2
exp ----(10
n,.
g
2nq~ 1/2E3/2)
(5) where Ee is the tunneling-electron energy. In the literature of TFETs, a more compact expression of the tunneling rate by ignoring the exponential term in the square brackets of (5) is usually used. However, the compact form exhibits an observable deviation from the full one as the bandgap decreases below 0.5 eY [22]. To exactly evaluate the local and nonlocal BTBT approaches for lowbandgap semiconductors, therefore, the full fOlmula (5) is used rather than the common compact expression. Now, we consider real tunnel junctions
The local BTBT model implies that the BT transition is dependent solely on the physi particularities of the position at which electro start tUnneling. This sharply conflicts with the that the tunneling of electrons depends on width of tunnel barrier from the starting to ending points of tunnel path. The conflict betwe the local field approach and the basic property tunneling explains appropriately for the la deviation of the model from experiments. In t study, however, the local BTBT model is s provided as a good reference for furt D
whose
38
rdIllternational Conference
on Advanced
Materials
Hanoi,2016
and Nanotechnology 0.8 0.5 0.6 0.9 0.7 0.3 0.4
'';:: Q) U § ~.;;:..~..;>::0; o.l -..::
(a)
.•... o.l
§
V
= 2 Eg/q
Nonlocol and :Vlixed
0.4
0.5
0.6
0.7
0.8
0.9
Bandgap ofInGaAs re 3. Relative deviations
1.0
:'':>
mn,.
g
exp - ---18nfi2E~/2 2nq~ 2 1/2;:.:t [ 1/2E3/2)
(8)
nonlocal BTBT approach, on the contrary, is istentwith the tulmeling property because the T transition in the nonlocal picture depends on physical charactel;stics of locations along el path. The apparent suitability between the ocal approach and the general propelty of eling interprets the good fit between the ocalBTBT model and experimental results.
The above reasonings on the physical meanings and roles of the local and nonlocal electric fields have properly explained the poor and good accuracies of the local and nonlocal BTBT models, respectively. By explicitly analyzing the origins of electric field tenns in the Kane model, the physical picture in the mixed BTBT model becomes reasonable, but not arbitrary as in the local and non local models. Therefore, the mixed BTBT model is expected to provide the more proper calculations of BTBT current than the others even though it probably needs fulther confilmation by experiments in the future.
However,there are several electric field tenns theKanefonnula of BTBT generation as seen in Assigning all those terms by either local or al electric field is probably unreasonable if physicalorigin of some tenns is different from . It is impOltant to note that there is one tric field tem1 in (5) coming from the ssionof electron flux (4). This electric field to the electron velocity in k-space at the Ijunction detelmines the number of electrons ing to the tunnel junction for possible eling transitions. Because this number of ons is completely detennined by the electric
111.
LOCAL
& NON LOCAL
VS. MIXED MODELS
The tunneling current per unit area can be calculated by integrating the BTBT generation rate along the tunnel junction as follows:
39
The
3rd
Hanoi, 2016
International Conference on Advanced Materials and Nanotechnology 18
(b)
V=E,/q
>' •..
e
15 IZ
6
0.0 0.0
o
L2
OA
L6
Normalized
0.0
1.0
L8
0.2
OA
Normalized
Distance
0.6
0.8
1.0
Distance
Figure 4. (a) Relative deviations between local and nonlocal fields as a function of position for different applied voltages, and (b) probability factors as a function of position for Ino.I7GaO.83As and InAs junctions.
1=
(9)
f G(x)dx.
Depending
on using
Ino.17Gao.83As and lnAs junctions, the scale of vertical axes is intentionally fixed with five orders of magnitude in both cases. Generally, the cunent level of the low-bandgap junction is higher, although the applied voltage is lower, than that of the high-bandgap counterpart since the tunneling probability is exponentially inverse-proportional to the bandgap. The deviation between the local and mixed models is greater in the high- than in the low-bandgap junction. Conversely, the deviation between the nonlocal and mixed models is less in the high- than in the low-bandgap junction. In addition, those deviations also depend on the applied voltage, specifically being large at low and small at high voltages. It is inferred from this preliminary observation that the deviations of local and non local from mixed BTBT models are
Glocal'
will have the tunneling
Gllolliocol'
or
current I10m/'
we
Gmixed' 11101l10cal'
or
1mixed calculated by the local, nonlocal or mixed BTBT model, respectively. The deviation between two different models, indexed by subscripts I and 2, is represented by the relative current deviation defined as:
III -lz\ rmx(Ip1z}
(10)
A. Numerical results To ensure precise evaluation of the electric field approaches, the numerical calculation of the tunneling current from (9) is implemented instead of trying reducing (9) to a simple form for analytical comparisons. This is because significant approximations need to be applied to (9) to obtain a compact analytical expression. The variations caused by approximations transfer to the final results and may lead to inaccurate conclusions.
dependent on the bandgap and applied voltage. For investigating the bandgap-dependent deviations of the local and non local from mixed BTBT models in detail, figure 3 plots the relative cunent deviations as a function of bandgap at different applied voltages. Overall, the deviation between the local and mixed models is much greater than that between the nonlocal and mixed models, at least in the investigated range of the bandgap. The deviation between the local and mixed models decreases whereas that between the nonlocal and mixed models increases with decreasing the bandgap, regardless of the applied voltage. It implies that the BTBT is more strongly local and less weakly nonlocal in nature as the bandgap decreases. The role of the local electric field is more important in determining the BTBT rate in lower bandgap materials. Additionally, the
Figure 2 shows the cunent-voltage characteristics of the one-sided p-n junctions using high- and low-bandgap materials in reverse-biased conditions. The nomlalized voltage, which is defined as the applied voltage divided by the bandgap voltage (Eglq), is used for appropriate comparisons because the suitable supply voltage of TFETs has to be scaled down in parallel with the decrease of bandgap [25]. For properly comparing the current deviations of the 40
The3,d /illemational Conference
"
1.0 .. 0.6 ~ .:l c. Q ... "0.0 0.40.8 .~ E ~ .~ :c
