1858 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 53, NO. 8, AUGUST 2006
Charge Trapping in High-k Gate Stacks Due to the
Bilayer Structure Itself
John R. Jameson, Peter B. Griffin, James D. Plummer, Fellow,IEEE, and Y. Nishi, Fellow,IEEE
Abstract—Charge trapping at the interface between the two
dielectric layers of a high-k gate stack is shown to be caused
by Maxwell–Wagner instability, which is the following. The fact
that the high-k and interfacial layers have different compositions
means that they will also have different conductivities. Then, a
gate bias will produce a discontinuity in current at their interface,
causing charge to accumulate there until, in steady state, the same
current flows through both layers. Maxwell–Wagner instability is
shown to be coupled to a second instability, dielectric relaxation
of the high-k layer; continuity of current in steady state requires
that the electric fields in the two dielectric layers remain fixed, so
the change in polarization of the high-k layer due to dielectric
relaxation must be compensated for by the conduction of addi-
tional charge to the interface. Evidence for this behavior in high-k
gate stacks is found in the thickness dependence of their dielectric
relaxation current, with the correct dependence being obtained
only from a model in which the two instabilities act simultaneously.
Uniform dielectrics do not exhibit Maxwell–Wagner instability,
and perfect crystals do not exhibit dielectric relaxation, making
the ideal high-k gate dielectric a uniform single-layer perfect
crystal bonded epitaxially to the Si substrate.
Index Terms—Amorphous materials, bilayer dielectrics, charge
trapping, dielectric relaxation, high-k dielectrics, Maxwell–
Wagner polarization, threshold voltage instability, transition-
metal oxides.
I. INTRODUCTION
T
RANSITION-METAL oxides have been leading candi-
dates in the quest to replace the traditional SiO
2
gate
dielectric of MOS transistors with a material having a higher
dielectric constant. Unfortunately, all of the transition-metal
oxides considered to date seem to share two deficiencies. First,
they all cause an SiO
2
-like interfacial layer to grow when
they are deposited directly on Si [1]. Second, they all produce
electrical instabilities in MOS devices. Electrical instabilities
have been the subject of numerous experimental studies [2]–[8],
and it seems possible to interpret many of them as arising from
the trapping of charge somewhere within the gate stack. In
particular, the high-speed experiments of Kerber et al. [2], [3]
seem to paint a vivid picture of electrons filling up a gate
stack when a gate bias is applied, then rushing out after the
bias is removed, producing dramatic instabilities in the drain
current of transistors at short timescales. By cycling the gate
Manuscript received June 22, 2005; revised January 30, 2006. This work was
supported by the Initiative for Nanoscale Materials and Processes. The work
performed at the Stanford Nanofabrication Facility of NNIN was supported by
the National Science Foundation under Grant ECS-9731293. The review of this
paper was arranged by Editor M.-C. Chang.
The authors are with the Center For Integrated Systems, Stanford University,
Stanford, CA 94305-4075 USA (e-mail: jameson@stanford.edu).
Digital Object Identifier 10.1109/TED.2006.877700
voltage on and off [2]–[5], one also observes gradual shifts in
the properties of devices, implying that the electrons that flow
into the gate stack while the bias is on do not have time to flow
out completely when the bias is off.
For high-k gate stacks to be suitable for commercial devices,
these electrical instabilities must be eliminated, so it is im-
perative to understand why charge trapping takes place. It has
been widely accepted that the trapped charge resides in local-
ized electronic states associated with structural defects [2]–[8].
However, “What is the electronic structure of the trapped
charge?” is not the same question as “Why does the charge
accumulate there in the first place?” The purpose of this paper is
to suggest that the bilayer structure itself causes charge to accu-
mulate in high-k gate stacks, for the following reason. The fact
that the two layers of a high-k gate stack have different compo-
sitions means that they will also have different conductivities
1
.
Then, the application of a gate bias will immediately produce a
discontinuity in current density at the interface between the two
layers, causing charge to accumulate there until, in steady state,
the same current density flows through both layers. If the gate
bias is removed, a discontinuity in current density will again be
produced, this time causing the charge to rush out of the gate
stack, as the experiments described above seem to suggest.
To the authors’ knowledge, this behavior has not previously
been discussed in the literature on high-k gate stacks. How-
ever, it is a well-known and ancient phenomenon, having first
been described in the 19th century by Maxwell himself [11],
then somewhat later and more extensively by Wagner [12].
Nowadays, it is called “Maxwell–Wagner polarization,” though
in the present paper, we will refer to it as “Maxwell–Wagner
instability” to emphasize its time-dependent nature. The reader
is referred to the text by von Hippel [13] for a discussion
of aspects of the phenomenon not considered here, such as
its effect on the frequency response of a bilayer capacitor.
Maxwell–Wagner instability occurs in every composite dielec-
tric system, and semiconductor devices have provided several
well-known examples besides high-k gate stacks. The most
famous of these is the traditional MOS structure, whose ac-
cumulation (or inversion) layer develops precisely because the
conductivity of the SiO
2
layer is much too low to conduct
away the charge carried to the interface by the Si. Indeed,
“accumulation layer” would also seem an appropriate term for
the charge that builds up at the interface between the two layers
1
We use the term “conductivity” to refer to the general field-current char-
acteristic of a layer, which could have contributions from a variety of sources
(e.g., tunneling, emission over a Schottky barrier, etc.), but which is generally
not a simple linear relation between the field and current (as in a metal).
0018-9383/$20.00 © 2006 IEEE