Channel modeling and detector design for dynamic mode high density probe storage.

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Channel Modeling and Detector Design for
Dynamic Mode High Density Probe Storage
Naveen Kumar, Pranav Agarwal, Aditya Ramamoorthy and Murti V. Salapaka
Abstract—Probe based data storage is a promising
solution for satisfying the demand for ultra-high capacity
storage devices. One of the main problems with probe
storage devices is the wear of tip and media over the
lifetime of the device. In this paper we present the dynamic
mode operation of the cantilever probe that partially ad-
dresses the problems of media/tip wear. A communication
system model which incorporates modeling of the cantilever
interaction with media is proposed for the system. We
demonstrate that by using a controllable canonical state
space representation, the entire system can be visualized
as a channel with a single input which is the tip-media
interaction force. A hypothesis testing formulation for bit-
by-bit detection is developed. We present three different
classes of detectors for this hypothesis test. In particular,
we consider two different cases where statistics on the
tip-medium interaction are available and not available.
Simulation results are presented for all these detectors and
their relative merits are explored.
I. INTRODUCTION
In recent times, the explosive growth of the per-
sonal computer industry and the Internet has created
the demand for ultra-high capacity storage devices. The
ubiquitous use and increased demands of consumer
electronics (e.g. pen drives and MP3 players, digital
cameras) and the Internet is driving the need for high
density data storage devices. Demands of a few Tb per
in.2are predicted in the near future. Commercially used
data storage techniques are primarily based on magnetic,
optical and solid state technologies. However all these
technologies are reaching fundamental limits on their
achievable areal densities. Magnetic storage suffers from
the super-paramagnetic effect that limits the minimum
size of a magnetic domain. Optical devices are limited
by the wavelength of the utilized laser and solid state
devices are limited by the minimum size of a transistor
that can be created.
Naveen Kumar and Aditya Ramamoorthy are with Dept. of Elec-
trical and Computer Engg. at Iowa State University, Ames IA 50010.
Pranav Agarwal and Murti V. Salapaka are with the Dept. of Electrical
and Computer Engg. at University of Minnesota, Minneapolis, MN
55455. This work is supported by a New Faculty Development Grant
Award and a startup grant to Prof. Ramamoorthy and NSF grant ECS-
0601571 to Prof. Salapaka.
A promising high density storage methodology, that
is the focus of this paper utilizes a sharp tip at the
end of a micro cantilever probe to create (or remove)
and read indentations (see [13]). The presence/absence
of an indentation represents a bit of information. The
main advantage of this method is the significantly higher
areal densities that are possible. Recently, experimentally
achieved tip radii near 5 nm on a micro-cantilever were
used to create areal densities close to 4 Tb/in2. The areal
density in this method is primarily limited by the tip
geometry. The effective area of the tip that interacts with
the media can be made considerably smaller with tech-
nologies such as carbon nanotube attachments (see [1],
[3]) that have the promise to yield sub-nanometer small
features. Thus, unlike the previous storage technologies,
the fundamental limit of areal densities possible is far
from being reached.
A particular realization of a probe based storage
device that uses an array of cantilevers is provided
in [4]. However, there are fundamental drawbacks of
current probe based devices (including [4]) that are
related to the static mode operation. In static mode,
the cantilever is analogous to a gramophone needle
(cantilever tip) of the gramophone player that moves
due to the topography of the record (media) i.e. the
cantilever is in continuous contact with the medium. The
information content is present in low frequency in this
case. However, it can be shown experimentally that the
system gain at low frequency is very small. Therefore,
in order to overcome measurement noise at output, the
interaction force between tip and medium should be large
which degrades the medium and probe over time and
significantly reduces reliability.
The problem of tip and media wear can be partly
addressed by using dynamic mode operation but the
conventional dynamic methods, though gentle on the
medium, are too slow to be useful in data storage
applications. In the dynamic mode operation given in
this paper, the cantilever is forced sinusoidally using a
dither piezo. The oscillating cantilever interacts with the
medium intermittently as it gently taps the cantilever and
thus the lateral forces are reduced which decreases media

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wear drastically. Other advantages of this scheme such
as high resolution are discussed later in more detail.
The primary objective of a probe based data storage
system is ultra-fast detection of topographic features
on the media as against determining the height of the
feature (which is useful in nano-imaging applications).
In the ultra-fast detection task, the exact topographic
profile of a particular feature is not as much of a
concern as distinguishing the presence or absence of
the feature. However, as density increases, the readback
signal suffers from increase in noise and linear/nonlinear
distortions. This makes data detection more difficult,
and requires increasingly powerful detection techniques.
Data detection can be improved by increasing the tip-
medium interaction force but it increases tip and medium
wear and reduces the reliability of system. Thus, what we
really want are low-complexity detectors that have a low
probability of error at a given tip-medium interaction.
In this paper the dynamic mode operation that utilizes
high quality factor probes (for enhanced resolution and
smaller forces) that yields two orders higher read speeds
(compared to existing dynamic mode techniques) is
presented. The problem of modeling the data storage unit
as a communication system and the design of efficient
detectors for the channel model are discussed in detail.
We pose the problem of detecting the presence/absence
of the tip-medium interaction as a hypothesis testing
problem. The problem is first posed as a composite
hypothesis test where prior statistics on the tip-medium
interaction force are not available. Next, we obtain statis-
tics of interaction forces from a realistic Simulink model
of the system that models the inherent nonlinearities in
the system. We then develop detectors that utilize this
prior information. Simulation results are presented for
all the detectors and their relative merits are explored.
The paper is organized as follows. In Section II
the physical model of the probe based data storage
system is presented. Section III deals with the problem
of designing and analyzing the data storage unit as a
communication system and finding efficient detectors
for the channel model. Section IV reports results from
simulation and Section V summarizes the main findings
of this paper and provides the conclusions and future
work.
II. PHYSICAL MODELING
The main components of a probe based high density
data storage device are analogous to that of an atomic
force microscope (AFM) (see Figure 1(a)) reported in
[2]. The components are (1) a microcantilever probe
that has a sharp tip at one end. The supported end can
be forced using piezoelectric material (termed the dither
(a)(b)
(c)(d)
Fig. 1.
device. (b) Shows a block diagram representation of the cantilever
system G being forced by white noise (η), tip-media force h and
the dither forcing g. The output of the block G, the deflection p is
corrupted by measurement noise υ that results in the measurement
y. Tip media force h = φ(p). (c) shows an experimentally obtained
thermal spectra (setting g = h = 0 in the block diagram shown
in (b)) that demonstrates that the thermal response of the cantilever
is discernable only near the resonant frequency of the cantilever. (d)
shows the typical tip-media interaction forces of weak long range
attractive forces and strong repulsive short range forces.
piezo). (2) The detection system that consists of a laser
that is incident on the tip end of the cantilever. The
incident laser is reflected into a split photodiode that
provides a voltage signal proportional to the difference
in the laser power incident on its different halves. (3) The
control system that takes the measured signal as input
and provides the control signal to the nanopositioning
device and possibly the cantilever support. (4) The
nanopositioning device which provides the capability
of positioning the media with respect to the cantilever
probe in the lateral x and y directions and the vertical z
direction.
A. Models of cantilever probe, the measurement process
and the tip-media interaction
The cantilever is a flexure member and the first
mode approximation is given by the spring mass damper
dynamics described by
¨ p +ω0
Q˙ p + ω2
where p, f, y and υ denote the deflection of the tip,
the force on the cantilever, the measured deflection
and the measurement noise respectively whereas the
parameters ω0and Q are the first modal frequency (res-
onant frequency) and the quality factor of the cantilever
respectively. The quality factor characterizes the energy
losses to the surrounding environment.
The input-output transfer function with input f and
output p is given as G =
(a) Shows the main components of a probe based storage
0p = f(t), y = p + υ,
(1)
1
s2+ω0
Qs+ω2
0. The cantilever
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model described above can be identified precisely (see
[9]). Viewing the cantilever as a filter proves crucial for
channel modeling purposes.
The interaction force between the tip and the media
(h) depends on the deflection p of the cantilever tip. Such
a dependence is well characterized by the Lennard-Jones
like force that is typically characterized by weak long-
range attractive forces and strong short range repulsive
forces (see Figure 1(d)). Thus the probe based data
storage system can be viewed as an interconnection of a
linear cantilever system G with the nonlinear tip-media
interaction forces in feedback (see Figure 1(b) and note
that p = G(h + η + g) with h = φ(p)); see [11]).
B. Currently employed probe based data storage method
and the dynamic mode operation
All of the current probe based data storage efforts
(primarily by IBM, Zurich Research Labs) employ the
static mode operation (see [13]). In the static mode,
the signal content (the information in h) is primarily
present in a frequency range much below the resonant
frequency of G. Note that the deflection measurement is
given by y = G(h + η) + υ as in static mode there
is no dither forcing g. As the magnitude of |G(jω)|
away from resonance is very small, the force h has to
be large so that Gh overcomes the measurement noise
υ particularly the
domain |Gη| << |υ| and therefore measurement noise,
and not the thermal noise η, is the main limiting factor).
The large force h required by the static mode leads to
more wear. Another reason for enhanced wear is that the
cantilever drags along in the lateral directions (analogous
to the gramophone needle scratching the record). An
abundance of experimental data under various operating
conditions on media and tip wear is available (see [12]).
The problem of wear can be partly addressed by using
the dynamic mode operation. In the dynamic mode the
cantilever is forced sinusoidally using the dither piezo
(g = γ sinω0t). In the absence of any other force, the
deflection p = Gg of the cantilever will be sinusoidal
with amplitude |G(jω0)|γ. The tip-media force alters
this motion and the media characteristics can be gleaned
from the observed changes in the cantilever motion. This
operation effectively shifts the information about the
media to a frequency range centered near the resonance
of the cantilever filter G (see [5]). As presented earlier,
in this frequency range the
the gain |G(jω0)| is large. The output is G(h+η)+υ and
η has to be overcome by the signal with |Gη| >> |υ|
in the relevant frequency range (see Figure 1(b)). As
the thermal forcing is white with variance
(kB, T and c are the Boltzmann constant, temperature
1
fpart in υ (in the low frequency
1
fnoise is not effective and
√2kBTc
and damping factor
the cantilever) that is small, the force signal resolution
is limited by η. It is evident that the magnitude of the
smallest force that can be resolved in dynamic mode
varies as
resolution. As smaller forces can be resolved, the tip-
media interaction forces can be small thus reducing the
force on the media and tip. This can lead to smaller
wear. Another important reason for lesser wear is that in
dynamic mode the oscillating cantilever interacts with
the media intermittently as it gently taps the cantilever
and thus the lateral forces are reduced. It is therefore the
preferred mode of imaging soft medias like biological
material and polymers [14].
ω0m
Q
with m the effective mass of
?
1
Qand higher the quality factor, better the
C. Information source model
The simplest model of the tip-media interaction is ob-
tained when the media’s influence on the cantilever tip is
approximated by an impact condition where the position
and velocity of the cantilever tip instantaneously assume
a new value (equivalent to resetting to a different initial
condition). This is satisfied in most typical operations
because in the dynamic mode, the time spent by the tip
under the media’s influence is negligible compared to the
time it spends outside the media’s influence [10]. Indeed
typically the oscillation amplitudes range from 10-80 nm
whereas the tip-media interaction is effective from 2-5
nm separations and lower separations.
III. CHANNEL MODEL AND DETECTORS
In this section, we present our modeling of the can-
tilever as a communication system and the design of
efficient detectors for the channel model.
The cantilever system has a long impulse response.
For achieving channel equalization with low complexity
we need to shorten the impulse response. The shortening
of an impulse response can be achieved by using the
technique presented in [8] where observers are employed
for the purpose of imaging. The observer framework also
provides a means of canceling the effect of the dither
forcing at the output.
Under the spring-mass-damper model of the can-
tilever, a state space representation of the filter G can
be obtained as ˙x = Ax + Bf, y = Cx + υ where
f = η + g (assuming no media forces h) and A,B and
C are given by,
?
Based on the model of the cantilever an observer to
monitor the state of the cantilever can be implemented
A =
01
−ω2
0
−ω0/Q
?
, B =
?
0
1
?
, C =?
01
(2)
?
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[6]. The observer dynamics and the associated state
estimation error dynamics is given by,
Observer
????
˙ˆx
ˆ y
=
=
Aˆx + Bg + L(y − ˆ y);ˆx(0) =ˆx0,
Cˆx,
State Estimation Error Dynamics
??
=(A − LC)˜x + Bη − Lυ,
=
x(0) −ˆx(0),e = y − ˆ y = C˜x + υ.
where L is the gain of the observer,ˆx is the estimate
of the state x and g is the external known dither forcing
applied to the cantilever. The error in the estimate is
given by˜x = x−ˆx, whereas the error in the estimate of
the output y is given by e. It can be shown that under the
presence of the noise sources η and υ, the error process e
approaches a zero mean wide sense stationary stochastic
process in steady state. The error process is white if the
Kalman gain is used [8].
The discretized model of the cantilever dynamics is
given by
??
˙˜x
=
Ax + B(g + η) − Aˆx − Bg − L(y − ˆ y),
˜x(0)
xk+1= Fxk+ G(gk+ ηk) + δθ,k+1ν ,
yk= Hxk+ vk,k ≥ 0 ,
where the matrices F, G, and H are obtained from
matrices A, B and C and δi,j denotes the dirac delta
function. θ denotes the time instant when the impact
occurs and ν signifies the value of the impact. The
impact is modeled as an instantaneous change or jump in
the state by ν at time instant θ. When a Kalman observer
is used, the profile in the error signal due to the media
can be pre-calculated as (see [8]),
(3)
ek= yk− ˆ yk = Γk;θν + γk,
where {Γk;θ ν} is a known dynamic state profile with
an unknown arrival time θ defined by Γk;θ = H(F −
LKH)k−θ, for k ≥ θ. LKis the Kalman observer gain
and {γk} is a zero mean white noise sequence which is
the measurement residual had the impact not occurred.
The statistics of γ are given by, E{γjγT
V = HP˜xHT+ R and P˜xis the steady state error
covariance obtained from the Kalman filter that depends
on P and R which are the variances of the thermal noise
and measurement noise respectively. Thus determining
when the cantilever is “hitting” the media and when it
is not, can be formulated as a binary hypothesis testing
problem with the following hypotheses,
(4)
k} = V δijwhere
H0
H1
:
:
ek= γk,k = 1,2,...,M
ek= Γk,θν + γk,k = 1,2,...,M
If the system is treated like a communication channel
where there exists a front-end timing recovery unit, the
time of the hit i.e. θ is known quite accurately. Therefore
for the purposes of this hypothesis test, it can be assumed
that θ is known. For simplicity we set θ = 1. Thus, under
H1, the innovation signal becomes
¯ e = Γν + ¯ γ
(5)
where ¯ e = [e1e2...eM]T,¯ γ = [γ1γ2...γM]Tand Γ =
[H H(F − LKH)...H(F − LKH)M−1]Tand V × I
denotes error covariance matrix of ¯ γ where I stands for
M × M identity matrix. In (5) ν has two components
i.e. ν = [νpos,νvel] and it signifies magnitude of impact.
Essentially the impact is modeled as an instantaneous
change in the state by ν at time instant θ.
A. Reformulation of state space representation
It is to be noted that although we have modeled
the cantilever system as a spring-mass-damper model
(second order system with no zeros and two stable
poles)(see (1)), the experimentally identified channel
transfer function that is more accurate in practice has
right half plane zeros that are attributed to delays present
in the electronics. Given this scenario, the state space
representation used in [8] leads to a discrete channel
with two inputs as seen above because the structure
of B is no longer in the form of [0 1]T. However,
source information enters the channel as a single input
as the tip-medium interaction force. Thus the problem
can be reformulated as one of a channel being driven
by a single input by choosing an appropriate state
space representation. For the state space model used to
derive the hypothesis given above, it is known that the
pair (A,B) is controllable which implies there exists a
transformation which will convert the state space into a
controllable canonical form such that B = [0 1]T. Note
that this kind of structure of B will force the discretized
model (3) to be such that one component of ν is equal
to 0 i.e. ν = [0,νvel]Twhere νvel is some value of
ν. With B chosen as above, the entire system can be
visualized as a channel that has a single source and
following hypothesis is obtained,
H0
H1
:
:
¯ e = ¯ γ
¯ e = Γ0νvel+ ¯ γ
(6)
where Γ0 is given by Γ = [Γ1 Γ0]. In this paper, the
above hypothesis with one parameter is used. This sim-
plifies the detector structure and analysis substantially.
B. Detector Design and Analysis
We now present the different detectors that we have
developed for the hypothesis testing problem in (6). For
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this purpose we used a high fidelity Simulink model
that mimics the experimental station that provides a
qualitative as well as a quantitative match to the ex-
perimental data. This model incorporates a Lennard-
Jones like nonlinearity (shown in Figure 1(b)) together
with the cantilever transfer function that is identified
experimentally. There is a means to introduce bit profiles
and to simulate the media interaction with the cantilever.
The output of the nonlinear block gives statistics on the
tip-media force which in turn provides statistics on ν.
Note that ν is a measure of the tip-medium interac-
tion force and as such it is difficult to experimentally
verify this nanoscale force accurately. Therefore we
first present detectors that do not assume any prior
distribution on ν i.e. we treat the problem as a com-
posite hypothesis test and develop Neyman-Pearson like
detectors for it.
1) Locally Most Powerful (LMP) Test: The tip-media
interaction force contains attractive and repulsive forces.
From model simulations, we have observed there is a
hit on media, the repulsive force dominates in tip-media
interaction force and the sign of ν is always same for all
hits. This information can be used to develop a locally
most powerful (LMP) test for hit detection. In case of
LMP, the likelihood ratio can be easily derived in closed
form and is given by [7],
llmp(M) = ¯ eTV−1Γ0.
The decision rule in this case is defined as, llmp(M) ≶H0
τ1where τ1is LMP threshold. Probability of false alarm
is given by,
H1
PF
=
Q
?τ1
2)dx, σ =
σ
?
,
where Q(x) =?∞
2) Generalized Likelihood Ratio Test (GLRT): In
[8], the GLRT is developed for a model which has ν
containing two parameters. Unlike the two parameters
model, the likelihood ratio can be computed easily for
one parameter model and is given by,
x
1
√2πexp(−x2
?ΓT
0V−1Γ0
and τ1is LMP threshold.
l(M)=
l2
lmp,
where llmpis likelihood ratio for LMP case. The decision
rule in this case is given by, l(M) ≶H0
denotes GLRT threshold value. From likelihood ratio,
we have
H1τ2 where τ2
PF
=2Q
?√τ2
σ
?
,
where σ =
?ΓT
0V−1Γ0and τ2is GLRT threshold.
3) Bayes Detector: Simulations from the model can
be run for a large number of hits in order to gather
statistics on the discretized output of nonlinearity block
which models the tip-media force. The discretized output
is multiplied by discretized B of state space to obtain
the statistics for ν.
We modeled the histogram in Figure 2(d) by a Gaus-
sian pdf with the appropriate mean and variance. The
hypothesis test in (6) now contains νvel∼ N(α,λ2). By
simple calculation, it can be shown that likelihood ratio
is,
l(M) = ¯ eTV−1µ?+1
2¯ eTV?¯ e − ¯ eTV?µ?
where µ?= Γ0α and V?=
has rank 1 which means l(M) has sum of M + 1
Gaussian terms and one Gaussian square term. It is hard
to compute probability of detection and false alarm in
closed form in this case.
Γ0ΓT
0
(V2
λ2+V ΓT
0Γ0). Matrix V?
IV. SIMULATION RESULTS
In order to see the performance of all detectors,
simulations are performed with cantilever parameters
obtained from experimental data. The parameters of
simulation are, first resonant frequency of the cantilever
f0 = 63.15 KHz, quality factor Q =206, the value of
forcing amplitude |G(jw0)|γ = 24nm, tip-media sep-
aration is 28 nm, discretized thermal and measurement
noise variance are 0.1 and .001 respectively. We used a
topographic profile where the medium height alternated
between high and low. The high and low regions denote
the bit ’1’ and ’0’ respectively. The simulation was
performed with the above parameters using the Simulink
model described previously. Tip-media interaction were
varied by changing the height of media corresponding to
bit ’1’. The innovations were obtained at the output of
the observer for different tip-media interaction. The in-
novation signal was passed through all the three detectors
for hit detection. For these results we assumed that the
correct sampling instants were known to all the detectors.
In practice, this can be justified if there is a front end
timing recovery unit that allows this synchronization.
Developing timing recovery units is part of future work.
In Figure 2 we have plotted the probability of mis-
detection (denoted PMD) vs. probability of false alarm
(denoted PF) for all the detectors. It is clearly observed
that LMP and Bayes gives less probability of mis-
detection than GLRT. For example, in case of 1.5 nm
tip-media interaction and PF = 1.9 × 10−3, PMD for
Bayes, LMP and GLRT are 2.3 × 10−3, 2.72 × 10−3
and 1.27×10−2respectively (see Figure 2(b)). Figure 2
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