Polarization self-screening in [0001] oriented InGaN/GaN light-emitting
diodes for improving the electron injection efficiency
Zi-Hui Zhang1, Wei Liu1, Zhengang Ju1, Swee Tiam Tan1, Yun Ji1, Xueliang Zhang1,
Liancheng Wang1, Zabu Kyaw1, Xiao Wei Sun1,* and Hilmi Volkan Demir1,2,*
1
LUMINOUS! Centre of Excellence for Semiconductor Lighting and Displays, School
of Electrical and
Electronic Engineering, School of Physical and Mathematical
Sciences Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore
2
Department of Electrical and Electronics, Department of Physics, and UNAM-
Institute of Material Science and Nanotechnology, Bilkent University, TR-06800,
Ankara, Turkey
The [0001] oriented GaN/AlxGa1-xN heterojunction possesses very strong
polarization effect. For a two-dimensional (2D) charge profile at the GaN/AlxGa1-xN
interface, the interface charge density can be computed by  Spol  n  P , where P
represents the polarization density and n denotes the unit vector normal to the
GaN/AlxGa1-xN interface. The interface charge density (P) in terms of the AlN
composition (x) is depicted in Fig. S1, in which we show the polarization levels of 40%
and 100%, respectively. The polarization level represents how many percentiles of the
theoretical predicted polarization charges are included due to the crystal relaxation
through generating dislocations.1 The calculation models are developed by Fiorentini
et al.1 Fig. S1 illustrates that the polarization density of the 100% polarization level is
*)
Electronic mails: exwsun@ntu.edu.sg and volkan@stanfordalumni.org
1
larger than that of the 40% polarization level. However, both curves have shown a
linear relationship as the x varies.
Nevertheless, when the AlN is compositionally decreasing along the [0001] growth
orientation in the AlxGa1-xN region, then the negative polarization induced bulk
charges are produced in the AlxGa1-xN region. The bulk charge density is represented
by  BPol ( z )    P ( z ) , where the P ( z ) denotes the polarization density as a function of
the
grading
position
(z).
 BPol ( z )    P( z ) can
be
further
modified
to
 BPol ( z )    P( z )  (P / x)  (x / z ) if the polarization density is alloy-composition
(i.e., x) dependent in the AlxGa1-xN region. Fig. S1 shows a linear relationship
between P and x. Therefore, P / x is 1.85 × 1017 m-2 and 4.63 × 1017 m-2 for the 40%
and 100% polarization levels, respectively. In addition, the  BPol ( z ) is also affected by
x / z that is a constant if the AlN composition (x) is linearly graded along the growth
orientation. Therefore,  BPol ( z ) is regarded as the bulk charge density and hence
  BPol ( z )   m 3 .
2
Fig. S1 Polarization charge density in terms of the AlN composition in the
GaN/AlxGa1-xN heterojunciton
1
V. Fiorentini, F. Bernardini, and O. Ambacher, Appl. Phys. Lett. 80, 1204-1206
(2002).
3