An Ultra-Fast Single Pulse (UFSP) Technique
for Channel Effective Mobility Measurement
––
APPLICATION NOTE
An Ultra-Fast Single Pulse (UFSP) Technique for
Channel Effective Mobility Measurement
APPLICATION NOTE
Introduction
The channel effective mobility (µ
eff
) influences the MOSFET
performance through the carrier velocity and the driving
current. It is one of the key parameters for complementary
metal-oxide-semiconductor (CMOS) technologies. It is widely
used for benchmarking different processes in technology
development and material selection [1, 2]. It is also a
fundamental parameter for device modelling [3]. With device
scaling down to the nano-size regime and the introduction
of new dielectric materials, the conventional measurement
technique for mobility evaluation encountered a number
of problems described in the following section, leading to
significant measurement errors. As a result, a new mobility
extraction technique is needed.
This application note describes a novel Ultra-Fast Single
Pulse technique (UFSP) [4, 5] for accurate mobility evaluation,
including the technique principle, how to connect the device,
and how to use the Clarius software in the 4200A-SCS
Parameter Analyzer.
(a)
(b)
Figure 1. Configuration for (a) conduction current measurement and (b)
gate-to-channel capacitance, C
gc
, measurement.
The principle of conventional mobility measurement is
deceptively simple. However, many challenges and pitfalls are
associated with this testing. Several sources of error are often
ignored in the past.
V
d
-dependence:
The conventional technique applies a
non-zero V
d
(usually 50mV–100mV) for I
ch
measurement but
a zero V
d
for Q
i
measurement. This difference in V
d
used in
two measurements can lead to significant errors in evaluating
mobility for thin oxides, especially in the low electric field
region. One example is given in
Figure 2,
where a higher |V
d
|
results in a substantial reduction of mobility near its peak.
This is because |V
g
–V
d
| reduces for high |V
d
|, so that the
real charge carrier density for the I
ch
is smaller than the Q
i
measured at V
d
= 0.
120
100
Conventional Mobility Measurement
and Challenges
We use a p-channel device of gate length L and width W as
an example. When the channel charge is fairly uniform from
source to drain in the linear region, the channel effective
mobility (µ
eff
) can be written as
L
I
ch
µ
eff
= ___ · ________
W
Q
i
· V
d
where V
d
is a small bias applied on the drain terminal of the
device, Q
i
is the mobile channel charge density (C/cm
2
), and
I
ch
is the conduction current flowing in the channel.
Traditionally, I
ch
is measured at the drain terminal of the
device with the configuration shown in
Figure 1(a).
Q
i
is
extracted from integrating the measured gate-to-channel
capacitance, C
gc
, with respect to V
g
, i.e.,
(1)
Vg
Id ~ Vg config
Vd
A
μ
eff
(cm
2
/V-s)
80
60
40
Vg
~
A
Ccg ~Vg config
Vd = -25 mV
Vd = -50 mV
Vd = -100 mV
8
10
12
20
0
0
2
4
6
N
S
(×10
12
cm
-2
)
Figure 2. Effective channel mobility measured by conventional
technique. I
ch
was measured under various non-zero drain biases,
V
DS
, but Q
i
was measured under V
d
= 0. The extracted mobility clearly
reduces for higher |V
d
|. Insets illustrate the carrier distribution in
the channel.
by using the connection configuration shown in
Figure 1(b).
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An Ultra-Fast Single Pulse (UFSP) Technique for
Channel Effective Mobility Measurement
APPLICATION NOTE
Charge trapping:
The conventional technique used slow
measurement with typical measurement time in seconds. The
fast charge trapping becomes significant for both thin SiON
and high-k dielectric. For slow measurements, trapping can
respond during the measurement and give rise to hysteresis
and stretch-out of the C
gc
–V
g
curve and a reduction of I
ch
.
This results in an underestimation of mobility.
Leaky dielectric:
As gate oxide is downscaled, high gate
leakage current becomes a main challenge for mobility
extraction. It affects both I
ch
and Q
i
measurements and in
turn the mobility. To minimize its impact on C
gc
measurement,
frequencies up to gigahertz have been used, which requires
devices with an RF structure. The RF structure requires more
processing and die space and is not always available.
Cable switching:
The conventional technique involves cable
changing between I
ch
and Q
i
measurements. This slows down
the measurement and can potentially cause breakdown of the
device under test.
Figure 3. Illustration of the working principle of UFSP technique.
0V
V
g
Vd =
-100mV
A
p+
A
p+
n-sub
(a)
The Ultra-Fast Single Pulse Technique
(UFSP Technique)
To overcome the challenges mentioned above, a novel
technique called the Ultra-Fast Single Pulse technique (UFSP)
has been developed and is described as follows.
A p-channel device is used here for illustrating the working
principle of the UFSP technique as shown in
Figure 3.
The
considerations for n-channel devices are similar. To perform
the UFSP measurement, a single pulse with edge time of
several microseconds is applied on the gate terminal of the
device. The gate voltage sweeps toward negative during
the falling edge of the pulse and turns the device on. The
transient currents are recorded at both the source and the
drain terminal of the device. The device is then switched off
during the subsequent rising edge where the gate voltage
sweeps toward positive. The corresponding transient currents
are also to be recorded. Channel effective mobility can be
extracted from these four transient currents measured within
several microseconds.
(b)
Figure 4. Schematic diagram of current flow during the transient
measurement.
To facilitate the analysis, we define currents measured at
drain and source terminal during switching on and off as
I
don
, I
son
, I
doff
, and I
soff
. The current flow in the channel during
the transient measurement is shown in
Figure 4 (a)
and
(b).
Three types of current are present: channel conduction
current, I
ch
, displacement current between gate and source/
drain, I
dis_s
and I
dis_d
, and the leakage current between gate
and source/drain, I
g_s
and I
g_d
. When device is switched off-
to-on, the direction of I
dis_s
and I
dis_d
is toward the channel
center; I
dis_s
has the same direction as I
ch
at the source, but
I
dis_d
is in opposite direction to I
ch
at the drain. When the
device is switched on-to-off, I
dis_s
and I
dis_d
change direction,
but I
ch
does not. I
g_s
and I
g_d
are independent of the V
g
sweep
direction and always flow from the source and drain towards
gate under negative V
g
. Based on the above analysis, channel
WWW.TEK.COM | 3
An Ultra-Fast Single Pulse (UFSP) Technique for
Channel Effective Mobility Measurement
APPLICATION NOTE
current, I
ch
, gate current, I
g
, and displacement current, I
dis
can be separated by using Equations (2)–(4). C
gc
can be
calculated using (5).
I
CH
=
I
DON
+ I
DOFF
+ I
SON
+ I
SOFF
4
(2)
I
G
= I
G_S
+ I
G_D
=
I
SON
+ I
SOFF
– I
DON
– I
DOFF
2
(3)
I
DIS
= I
DIS_S
+ I
DIS_D
=
I
DIS
dV
G
dt
I
DOFF
– I
DON
+ I
SON
– I
SOFF
2
(4)
C
GC
=
(5)
120
100
To calibrate the UFSP technique, a p-channel MOSFET
with thick oxide is used that has negligible I
G
current.
The measurement time (=edge time) is set at 3µs. The
measured four currents are shown in
Figure 5.
The I
ch
, I
g
and C
gc
extracted by using Equations (2) to (5) are shown in
Figure 6(a).
Once C
gc
and I
ch
are evaluated accurately, Q
i
can be obtained by integrating C
gc
against V
g
and channel
effective mobility, µ
eff
, is calculated through Equation (1) as
shown in
Figure 6(b).
μ
eff
(cm
2
/V-s)
80
60
40
20
0
0
2
4
6
8
10
12
N
s
(x10
12
cm
-2
)
Figure 6.
(a). I
ch
, I
g
, and C
gc
extracted simultaneously from the currents in Figure
5 by using Equations (2)–(5).
(b) Channel effective mobility extracted from I
ch
and C
gc
from (a).
Because the UFSP measured I
ch
and C
gc
under the same V
d
,
µ
eff
should be independent of V
d
. The µ
eff
evaluated under
three different V
d
biases is compared in
Figure 7.
Good
agreements are obtained confirming that the errors induced
by V
d
using the conventional techniques have been removed.
Figure 5. Four currents measured from source and drain
corresponding to the off-to-on and on-to-off Vg sweep. Schematic Vg
waveform is shown in inset.
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An Ultra-Fast Single Pulse (UFSP) Technique for
Channel Effective Mobility Measurement
APPLICATION NOTE
100
50.0
45.0
40.0
35.0
μ
eff
(cm
2
/V-s)
80
Current ( μ A)
nMOSFET. EOT = 1.28nm
W/L = 10µm/10µm
Vd = +50mV
60
40
20
0
0
2
4
6
30.0
25.0
I
don
I
son
I
doff
I
soff
I
son
I
soff
Vd = -25 mV
Vd = -50 mV
8
10
20.0
15.0
10.0
Vd = -100 mV
12
5.0
0.0
0
1
I
don
V
g
(V)
2
I
doff
3
N
s
(×10
12
cm
-2
)
Figure 7. The effective channel mobility, µ
eff
, extracted under three
different V
d
by using UFSP technique.
50
40
nMOSFET. EOT = 1.28nm
V
d
= +50mV
3.5
3
2
I
ch
or I
g
(μA)
structure. When it was applied on one ‘leaky’ n-channel
MOSFET with an EOT of 1.28nm, the four currents measured
from the source and drain terminals corresponding to the
off-to-on and on-to-off V
G
sweep are shown in
Figure 8 (a).
By using Equations (2)–(5), I
ch
(‘n’), I
g
(‘o’) and C
gc
(‘x’)
are extracted and plotted in
Figure 8 (b).
I
g
from DC
measurement is also plotted for comparison in
Figure 8 (b).
Good agreement is obtained.
Figure 8 (c)
shows that
electron mobility can be reliably measured for this leaky
device where Ig is as high as 45A/cm
2
. Because the UFSP
the special RF structure for mobility evaluation.
can tolerate high gate leakage, it does not require the use of
30
20
10
0
0
C
gc
I
ch
1
1.5
I
g
2
1
0.5
0
V
g
(V)
300
250
μ
eff
(cm
2
/V-s)
200
150
100
50
0
0
10
nMOSFET
EOT = 1.28nm
Vd = 50mV
N
s
(×10
12
cm
-2
)
20
30
Figure 8.
(a) Four currents measured from the source and drain corresponding
to the off-to-on and on-to-off V
g
sweeps by UFSP technique on an
nMOSFET with EOT of 1.28nm.
(b) I
ch
(‘n’), I
g
(‘o’) and C
gc
(‘x’) are extracted from the currents in (a)
with Equations (2)-(5). The blue line is the leakage current obtained by
DC measurement.
(c) Channel effective mobility, µ
eff
, is calculated by using the extracted
I
ch
and C
gc
with Eqn (1).
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C
gc
(µF/cm
2
)
The UFSP also works well on leaky gate dielectric of standard
2.5
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