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论文研究-A method for the solution of the electrostatic properties o...
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金属-(n)AlGaN-GaN二维电子气的静电性质的一种求解方法,张金风,郝跃,为了研究AlGaN-GaN二维电子气的静电性质,我们提出了一种简单而有效的方法能够同时确定费米能级高度和求解二维电子气以及导带底的分
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中国科技论文在线
A method for the solution of the electrostatic properties of
metal-(n)AlGaN-GaN two dimensional electron gas
#
ZHANG Jinfeng, HAO Yue
(School of Microelectronics, Xidian University, Xi'an 710071) 5
Foundations: New Teacher Foundation for Doctoral Program of Ministry of Education of China (Grant No.
200807011012)
Brief author introduction:ZHANG Jinfeng, (1977-), female, associate professor, and her main research interests
focus on the GaN-based electronic materials and devices and(Al)GaN short wavelength laser materials and
devices. E-mail: jfzhang@xidian.edu.cn
Abstract: To help explore the electrostatic properties of AlGaN-GaN two dimensional electron gas
(2DEG), we present a simple and efficient method to determine the fermi level EF and solve 2DEG
distribution and conduction band edge simultaneously, whose essence is to fix EF by two 2DEG sheet
density vs. EF relations respectively deduced from Schrödinger and Poisson equations. This method is
applicable to the situation that depletion approximation holds and background doping charge can be
10
omitted, and the polarization effects of nitrides can be combined.
Keywords: AlGaN-GaN heterostructures; two dimensional electron gas; fermi level; sheet density
0 Introduction
Though AlGaN-GaN Modulation doped Field Transistors (MODFET’s) have been 15
intensively investigated, whose basic structure, i.e., AlGaN-GaN heterostructures have many
puzzling properties. The performance of such microwave power devices are determined by sheet
density Ns and mobilityμof the Two Dimensional Gas (2DEG) naturally formed in AlGaN-GaN
heterostructures, and some self-consistent one dimensional Schrödinger-Poisson solvers have been
developed to explore 2DEG charge control theory at quasi-static state [1][2][3]. However, about 20
how to determine an important quantity, i.e., the fermi level E
F
, almost nothing is mentioned. A
quite simple and efficient method to determine E
F
and calculate 2DEG distribution n
2D
(z) and
conduction band edge Ec(z) simultaneously is presented.
1 Basic principles and our method
1.1 Basic charge control theory and the problems 25
2DEG is an effect that electrons accumulated in quantum well of conduction band edge at the
interfaces between AlGaN and GaN, and its charge control theory can be formulated by equations
below [1][2][3]. The quantities appeared are defined in Table 1 for concise description.
Within effective mass approximation, Schrödinger equation has been put as
[]
0)()(
2
)(
2
*
2
2
=−+ zzEcE
m
z
dz
d
iii
ψψ
=
, (1) 30
where Ec(z) satisfies
)()()( zEczqVzEc
Δ
+
−=
. Electron density each subband is then
obtained by
⎥
⎦
⎤
⎢
⎣
⎡
−
+=
+
=
∫
∞
−
)exp(1ln
1
1
2
*
/)(2
*
Tk
EETkm
dE
e
m
n
B
iF
B
E
TkEE
i
i
BF
==
ππ
.
So Ns and 2DEG distribution n
2D
(z) satisfy respectively
∑
=
i
i
nNs
, (2) 35
∑
=
i
iiiD
zznzn )()()(
*
2
ψψ
, (3)
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