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Low frequency conductance and capacitance measurements on MOS capacitors in weak inversion
Solid-Start
Ekctnmrcs.
1975. Vol. 18. pp 737-744
Pergamon Prev.
Printed in Great Britain
LOW FREQUENCY CONDUCTANCE AND CAPACITANCE MEASUREMENTS ON MOS CAPACITORS IN WEAK INVERSION
U.S. Naval
N. S. SAKS Laboratory, Washington,
Research
(Received
23 November
D.C. 2037.5, U.S.A.
1974: in retkwdform
26 March
1975)
Abstract-The analysis of capacitance and conductance measurements as a function of frequency on MOS capacitors biased in depletion is well understood. However, little information is available on such measurements for capacitors biased in weak inversion. In this work it is shown that approximations to the theory of surface state response lead to a very simple technique for obtaining the density of fast surface states as a function of energy in the weak inversion region. Low frequency conductance and capacitance measurements have been made on a number of MOS samples and analysis of the data yields N,, as a function of energy in excellent agreement with results obtained by other techniques. As expected, experimental results show that N,, in weak inversion depends strongly on the annealing treatment given the MOS samples. However, annealing is found to have a much greater effect in reducing N,, in weak inversion than at midgap. It is also shown that the depletion layer generation current in the majority of samples measured is due to surface state generation rather than bulk generation.
samples
NOTATION surface potential reduced surface potential, = &/kT position of bulk Fermi level with respect to midgap capture cross section of surface states for capture of electrons capture cross section of surface states for capture of holes time constant for capture of electrons by surface states time constant for capture of holes by surface states thermal velocity of free carriers
concentration concentration
have developed
available (N,,)
for determining
a.c. conductance
in MOS
techniques as described static and
structures.
a.c.
Goetzberger
state parameters
midgap
Declerck,
for
Although depletion, surface
parameters
there
discussed
yields information
However,
as discussed
of
the
quasistatic
states/cm*-eV
surface
inversion.
MOS
samples
Secondly, with
very
and
in detail by
viewpoint
and
parallel
the
data
low
(3) The limiting
the
data
potentials
number
of MOS
samples
density
obtained
by low frequency
about a factor
cross
results
on a
show that the fast surface
conductance
technique
The experimental
results
be a strong
on the conditions
state
a.c. measurements
obtained
of
it is not
capture
Experimental
with results
may
from of this
However,
to obtain
states.
are
by the Nicollian and the quasistaalso show that N,,
function
of energy
of the final low-temperature
APPROXIMATE
The impedance current
A general
or
capacitor
following
by Kuhn[3],
in
Fig. l(a).
One additional
the equivalent
generation-recombination
depletion
sample
in these
were 737
MODEI.
by an MOS
flow has been considered
Slobodskoy[8].
and
presented
near flatband
Consequently,
other (2) N,,
sensitivity
technique.
to analyze
that the
equilibrium.
model,
for
anneal.
1x IO”
midgap,
than
and less data is required.
of the surface
inversion
than the
circuit
simpler
sections
depending
Of
a.c. over
rather
is about 1 x lo9 states/cm*-eV,
in weak
about
regime.
frequency advantages
over a wide range of surface
tic technique.
in
low
equivalent
is much
to inversion.
and Goetzberger
about
is biased
about
near
potentials
a large
is a complex
the series R-C equivalent
R-C
techniques,
in good agreement
only the quasistatic
as discussed
as well as
require
state Ioss[6,7]
possible
rates the ramp rate must be kept small to insure is in thermal
of
that
(1) Using
IO better than the quasistatic
et al. [5], the accuracy
potentials
they
have several
for surface
used
technique
of samples.
is at best
may be much worse for surface strong
Nicollian
little information
by Declerck
about interface
of the data
it is shown
about N,, in weak inversion.
technique
for
model
flatband
or quasi-
information
above,
utilizing
a.c. conductance
cross section
However,
measurements
is obtained
used
technique
in the weak inversion
technique
These
and analysis
work,
conductance
and disadvan-
the surface
is comparatively
state parameters
the three techniques
of
a theoretical
when
this
analysis
[2] and Kuhn [3],
on a number
there is now considerable
state
density.
the other techniques:
states
commonly
capacitance
have been compared
results
of data,
conductance
of techniques
advantages
et al. [5], both from
experimental
surface
most
technique
relative
amount
circuit
of fast surface
by Berglund
conductance [4]. The
state
results
inversion
information
such as capture
surface
In
the low-frequency
suggested
tages of these techniques from
The
by Terman[l],
technique the
are a number
are the high frequency
in weak
measurements.
to
and Schwartz[6]
and some experimental
yield considerable
commonly
the density
the theory
is small and difficult Cooper
state parameters
techniques
INTRODUCTION
there
current
Recently,
procedure.
of holes at the surface intrinsic concentration of carriers difference between midgap and the effective surface state response, defined by eqn (5b)
time
accurately.
on interface
of electrons at the surface
the present
the displacement
measure
circuit
their
equivalent
circuit
nomenclature element,
to account by Lehovec
to a.c. and
for an n-type
is presented
G,, has been added for
layer generation-recombination
not considered
capacitor
in detail by Lehovec
surface
state
currents,
and Slobodskoy.
in to and
which
N. S
738
SAKS
temperature by Goetzberger and Nicollian[9]. Thus CDs and GPDcan be neglected with respect to GP (2) G,D % G,, at all biases of interest for surface state densities less than by Hofstein and 1O’2 states/cm*-eV as shown Warfield [ IO]. Thus, G,, can be eliminated from the equivalent circuit. The resulting simplified circuit is shown in Fig. l(b). For a single level of surface states, the elements C,,, G,,,. and G,,, which describe surface state loss are given
(a)
by[81:
c,, =&TfT(I -fr)
(b)
1 T
(1)
GATE
co,
CI
GP
1
SUBSTRATE
Fig. 1. (a) General equivalent circuit for ax. response of an MOS device after Lehovec and Slobodskoy[S]. (b) Simplified equivalent circuit. Referring to Fig. l(a). the physical mechanisms of a.c. current flow in the MOS structure can be understood in terms of three parallel current paths in series with the oxide capacitance C,,, : (1) a path through CD,the depletion layer space-charge capacitance; (2) a path through GnD, G,,, and C,,, representing the conductance associated with electron flow across the depletion region, the loss mechanism due to trapping of electrons by surface states, and the capacitance due to changes in the net surface state charge as a result of electron trapping, respectively; (3) a path through GPs, Gp~, G,, and C,,, representing the conductance due to the diffusion of holes in the neutral region, the conductance due to the diffusion of holes across the depletion region, the loss mechanism due to trapping of holes by surface states, and the capacitance due to changes in the net surface state charge as a result of hole trapping, respectively. The elements of path (2) form a branch representing majority carrier capture and emission from surface states. The elements of path (3) form a branch representing minority carrier capture and emission from surface states. Holes can also be supplied to the surface by generation-recombination centers as represented by the conductance G, of Fig. l(a). The capacitance C, represents the minority carrier storage in the inversion layer at the silicon-silicon dioxide interface. The equivalent circuit of Fig. I(a) can be simplified somewhat by the following considerations: (1) In silicon diodes at room temperature the generation-recombination current usually dominates the diffusion current. This fact has been verified in the case of MOS diodes at room
where NJ is the number of surface states and fi is the Fermi function which gives the occupancy of the states. These equations must be modified to account for three effects: (I) Surface states occur in a continuum throughout the bandgap; (2) Due to the statistical distribution of fixed charge at the interface, as described by Nicollian and Goetzberger[4], the interface is not an equipotential surface; and (3) When the surface is inverted, the buildup of minority carriers in the inversion layer affects surface state response. This effect is described in detail by Cooper and Schwartz[6], and it means that surface state response is described by two separate models for depletion and weak inversion. These two regions are defined as follows: When the surface is in “depletion”, the majority carrier capture conductance G,,r is larger than the minority carrier capture conductance G,,,. Conversely, in “weak inversion”, G,,, > G,,. From eqns (2) and (3), it is straightforward to show that the ratio of G,, to G,, is given by[4]:
where & is the position of the bulk Fermi level with respect to midgap. Therefore, from (4), G,, equals G,Y when
Depletion is defined by O< 4Y < & +A4, and weak inversion by & t Ac$ < c$$< 2 &. Since AC#Jvaries as the logarithm of the ratio of the capture cross sections, the effective midgap position should not deviate from the real midgap position by more than a few kT. For surface potentials in depletion, low frequency approximations to the theory have been considered by Eaton and Sah[7] who used the series R-C equivalent
Lowfrequencymeasurementson MOScapacitors circuit model. For low frequencies such that 07. 6 1, they have shown that Cm= q Ns,
(7)
where T,, is the time constant for capture of electrons by surface states. For surface potentials in weak inversion and using a series R-C equivalent circuit model, the following expressions have been derived by Cooper and Schwartz [6]:
I
OD
c,, = 4 Nss -x
(I-f*)&)d~s
(9)
739
carrier response dominates minority carrier response and the effective time constant of the surface states is the electron time constant T.. Equations (6), (7) and (8) apply at low frequency. Region (2): In weak inversion, when the surface potential is more than a few kT below the effective midgap position, with negligible generation currents so that G, 6 G., 4 G,,. Due to the small generation current, majority carrier response still dominates surface state response, and the effective time constant of the surface states is the electron time constant T,,.Equations (8)-(11) apply. This is the assumed condition in the literature which treats the weak inversion case[4,6]. Region (3): Weak inversion with large generation currents. If G., a G,, Q G,, then minority carrier response dominates surface state response and the effective time constant is TV. If G., e G, a G,, then minority carrier response still dominates surface state response but the effective time constant of the minority carrier branch of the equivalent circuit is given by (C,, + C,)/G,. EXPERIMENTAL RESULTS
MOS samples were fabricated on (111) orientation n-type IOIl-cm epitaxial silicon wafers. The wafers were chemically cleaned and oxidized in dry 9 at 1000°Cfor a f*= [l+zexp(-2(+~-de)lkT)]-’ (11) 1OOOAoxide (nominal value). After metallization with aluminum, 30 mil diameter contact dots were defined by where P(u,) is the probability distribution function given photolithographic techniques. The wafers were then given by eqn 35in reference[4], u. is the normalized surface a final anneal in dry nitrogen. The temperature of the final potential, and T,, is the electron time constant given by anneal was varied between 200°C and 47s”C to produce eqn (7). In weak inversion f* approaches zero and from samples with different densities of surface states. Samples (9) C,, approaches qN,,. It is not possible to reduce (10) to were mounted in TO-5 headers and placed in an airtight a simpler form using the same level approximation due to shielded apparatus where all measurements were made in a dry nitrogen ambient. the exponential dependence of the electron time constant Capacitance and conductance measurements were and P(u,) on surface potential. a.c. lock-in amplifier In weak inversion if G, @GPs9 G.,, the situation is made with conventional analogous to depletion with T" replaced by TV, where TV is techniques Ill]. The measurement system was carefully the time constant for capture and emission of holes by calibrated to ? 0.1 pf ? 0.2% (reading) over the frequency range 0.2 Hz-100 kHz. Stray capacitance due to the TO-5 surface states and is given by: header and associated wiring was carefully measured and TP’= urhupn, exp I- (4, - &s)/kTl (12) subtracted from the measured capacitance. d.c. leakage in the sample apparatus, an important consideration at very low frequencies, was measured at less than lo-l5 amps. If WTp 6 1, C,, is given by (6) and from (7) we obtain All measurements presented here were made at room temperature. (13) The measured equivalent parallel capacitance (C,,,) and conductance (G,) of a typical sample as a function of applied bias with frequency as the parameter are shown in We have two important results: (1) At low frequencies, C,, is simply equal to qN,, both in depletion and weak Figs. 2 and 3, respectively. The quasistatic capacitance inversion; and (2) Using the series R-C equivalent circuit curve for this sample obtained by the method of Kuhn[3] model, from (6), (7), (IO) and (13), C,,, G,, and G,, are at a voltage ramp rate of 6.28 mV/sec is shown for frequency independent. This is a considerable simplifica- comparison in Fig. 2(d). The accumulation, depletion, tion from the more commonly used parallel R-C weak inversion, and strong inversion regions for this equivalent circuit model because the parallel elements are sample are shown in each figure. The capacitance data shows the usual high-frequency not frequency independent. These results are derived under the assumption that the surface state parameters behavior at 100kHz. At low frequencies the capacitance is strongly frequency dependent in the depletion and weak including N,,, u., and a, are independent of energy. Using equivalent circuit Fig. l(b) and the above inversion regions. It is expected that C, will approach the equations, it is possible to distinguish three different quasistatic capacitance curve at very low frequencies regions of surface state response. Region (1): In depletion, when minority carrier response dominates majority when the surface potential is more than a few kT above carrier response; i.e. when G, a oCD (refer to equivalent the effective midgap position, and G., *G,,. Majority circuit Fig. l(b)). Clearly this condition is not satisfied for
S
740
-3 5
-3.0
-2 5
DEP -,,e-ACC 1 I -20 -I 5 GATE
~ I -0.5
-I 0
0
VOLTAGE
Fig. 2. Capacitance of an MOS sample as a function of gate voltage showing low frequency dispersion effect. (a) 100~00 kHz (b) 2.0 Hz (c) 0.5 Hz (d) quasistatic results, ramp rate equals 6.28 mV/sec. The accumulation, depletion, weak inversion, and strong inversion regions of surface potential are shown at the bottom of the figure.
4 SAMPLE
6AI
SAKS 100 Hz, G, peaks in the weak inversion region and then approaches a constant non-zero value in strong inversion. The peak in the weak inversion region is due to surface state response. As discussed previously, this may be due to either majority or minority carrier response depending on the relative order of magnitude of G, with respect to G,,. In strong inversion, surface state response is negligible with respect to minority carrier response in the inversion layer (C, in series with G,), and G, approaches a bias independent value. The measured data at a given frequency and gate voltage as shown in Figs. 2 and 3 is evaluated according to the equivalent circuit Fig. I(b) as follows: (I) G, and C,, are converted to equivalent series data, the capacitance C,, is subtracted, and then the data is converted back to the equivalent parallel form. This step is performed conveniently by equations 2.15 and 2.16 in[12]. (2) The capacitance CD is subtracted from the equivalent parallel capacitance calculated in step (1). CD at the given gate voltage is obtained from high frequency capacitance measurements (100 kHz or 1.OMHz) assuming no surface state loss. This method does lead to some error in C, near flatband but gives excellent results in the weak inversion region. This step results in equivalent parallel elements G,, and C,,. (3) Finally, G, and C, are converted to equivalent series elements G, and C, which represent the net effect of the elements G.,, G,,, G,, C,,, and C, shown in Fig. l(b). The resulting G,/w, C,, G,, and C, for sample 6A1 at a surface potential in weak inversion (0.103 eV below midgap) as a function of frequency are shown in Fig. 4. Looking first at the series elements G, and C,, G, is independent of frequency as predicted previously. C, is also frequency independent except at the higher frequencies where experimental error is large. The error bars
SAMPLE +r-+B
I. I 3.5
I
I
-30
-25 GATE
I -20
. . . .
.
GA, = -0,103ev
..e*G.
I -15
VOLTAGE
Fig. 3. Measured conductance/w of MOS sample in Fig. 2 as a function of gate voltage with frequency as a parameter. (a) 100.0 kHz (b) 1.0 kHz (c) 90.0 Hz (d) 10.0 Hz (e) 2.0 Hz (f) 0.5 Hz. Tile conductance peak in depletion and weak inversion is due to surface state loss, and the bias independent region in strong inversion is due to the generation current.
this sample at the lowest measurement frequency used, 0.5 Hz. The behavior of the equivalent parallel conductance G, is also significantly different at high and low frequencies. At frequencies greater than approximately I .OkHz the conductance is non-zero only when the surface is in depletion. Surface state response is therefore characterized by majority carrier response and the data can be analyzed to yield G., and C,,. At frequencies below
FREQUENCY
( HZ 1
Fig. 4. Data points show reduced data for sample biased in weak inversion (0.103 eV below midgap) for G,/o, C,,, G,, and C,. Solid lines represent best fit of single time constant eqns (16) and (17) of [41 to G,,/o and C,. Error bars show assumed experimental error. C, and G. are frequency independent except for deviation at high frequency due to experimental error.
Lowfrequency
measurements
show the amount of error assuming f 0.1 pf 20.2% (reading) in the measured quantities C, and G,/u. The error in G, for this particular data is approximately 2 5%, which is too small to display in the figure. The error in C, is larger due to step (2) of the data analysis when CD is subtracted from the capacitance calculated in step (1). Since these two quantities are nearly equal at higher frequencies, a small error in either quantity results in a large error in C,. G,,/w and C,, in Fig. 4 represent the same data in equivalent parallel format. The dots are the experimental data points and the solid lines represent the best fit of the single time constant eqns (16) and (17) in [4] to the experimental data. Again, the fit is good except for C, at high frequency where C,, is small. G, and C, for the same sample at constant frequency (0.5 Hz) are shown in Figs. 5(a) and (b), respectively, as a function of surface potential with respect to midgap. In strong inversion G, approaches a constant value independent of surface potential which is equal to G,. In weak inversion where G, is only weakly dependent on surface potential, G, is equal to either the series combination of G,, and G, or the parallel combination of G., and G, (refer to Fig. l(b)). Because G, 2 G,, G, must be given by the parallel combination of G., and G,, and surface state loss in this sample is dominated by majority carrier response. This is in agreement with the fact that G, decreases with increasingly negative surface potential, which can only occur when surface state response is dominated by the electron time constant.
on MOS capacitors
741
From the equivalent circuit Fig. l(b), the capacitance C, should be equal to C,, in depletion and weak inversion assuming C, is negligible over this range of surface potential. Therefore, from (6) and (9), C, equals qiV,, and the surface state density can be obtained directly from C,. In order to use eqn (6) in depletion, we have assumed that WT.4 1. From (6) and (7) it can be shown that 26X,, 07” =-G”,
and using the data in Fig. 5 it is clear that the condition WT.e 1 is satisfied in depletion. It is not necessary that this condition be satisfied in weak inversion. In strong inversion where C, is large, the capacitance C, should be equal to Cl. The theoretical value for C, calculated for this sample as a function of surface potential is shown in Fig. 5(c). C, is calculated from eqn (7) in [13] with C, = dQ,/d& As shown in Fig. 5, there is good agreement between calculated and experimental C,. For sample 6Al at a measurement frequency of 0.5 Hz, C, equals qN,, both in depletion and weak inversion. N,, obtained in this manner as a function of surface potential with respect to midgap is shown in Fig. 6. Results of the quasistatic technique and of the Nicollian and Goetzberger analysis are also shown. Agreement between the three techniques is excellent. The density of states for this sample increases rapidly with surface potential in weak inversion. This probably introduces some error in the measured density of states since previously it was assumed that N,, is not a strong function of surface potential. Therefore, more accurate results could be obtained in this case by using the integral equations for C,,
SAMPLE &,
EPLETIO+
(14)
= -0.276
681 eV
WEAK ---kSTRONG INVERSION
Fig. 5. (a) Experimental G, and (b) C, at constant frequency (0.5 Hz) as a function of surface potential with respect to midgap. G, decreases from depletion to strong inversion, indicating majority carrier response dominates surface state response in weak inversion. C. equals C., in depletion and weak inversion, and closely approaches theoretically calculated C, (curve(c)) in strong inversion.
Fig. 6. Comparison of density of states as a function of surface potential with respect to midgap obtained by different techniques. A Nicollian and Goetzberger conductance analysis. - Quasistatic analysis. 0 Low frequency analysis at a measurement frequency of 0.5 Hz.
N. S.
742
and G,, [4,6] rather than the approximate equation Css = qNa.
G, and C, for another sample (16Al) as a function of surface potential with respect to midgap with the measurement frequency as a parameter are shown in Figs. 7(a) and (b), respectively. The value of G, for this sample is 9.3 X lo-” f12-‘-cm-*,a factor of more than 300 larger than the previus sample. This large generation current is believed to be a bulk property of this particular wafer because all samples fabricated from the wafer had the same large generation current. The behavior of G, as a function of surface potential is divided into three regions: (I) In depletion, the 1.0 kHz data shows that G, decreases exponentially with increasingly negative surface potential. This is in qualitative agreement with (7) and (8) (although from (14) it can be shown that the condition WT”e 1 is not satisfied at 1.OkHz in depletion), and therefore G, = G.,. (2) In weak inversion, between approximately midgap and 0.17 eV below midgap, G, increases with increasingly negative surface potential. This in in agreement with (12) and (13), and therefore G, = G,, and surface state response is dominated by the minority carrier time constant TV.As noted previously, this can occur only when G, Z+G.,, a condition which is clearly shown to be satisfied by the data in Fig. 7(a). (3) For surface potentials below 0.17 eV below midgap, G,,, > G, and so G, = GW G, is weakly dependent on surface potential as discussed by Goetzberger and Nicollian [9]. In Fig. 7(b), C, obtained at 22.5 Hz and 90. Hz is shown to be in excellent agreement with quasistatic results (solid
SAKS
curve). The data at these two frequencies shows that C, and G, are frequency independent in weak inversion. From (14) at 22.5 Hz (with T. replaced by T,, and G,, replaced by G,,), the experimental data confirms that UT,, Q 1 in weak inversion. However, this condition is not satisfied at 1.0 kHz, and in fact the 1.OkHz data for G, does not agree with the lower frequency data. Curve 7(c) shows the calculated inversion capacitance C,, and again agreement with C, is very good in strong inversion. DlSCUSSION
The behavior of the density of states N,, as a function of energy is qualitatively similar for both samples 6Al and 16A1. N,, has a minimum value of approximately 3 x 10” states/cm*-eV near midgap and increases with energy away from the minimum both in depletion and weak inversion. Similar behavior in N,, has been observed previously [4,14, 151. The increase in N,, in the weak inversion region for these two samples is much greater then the increase in the depletion region. The excellent agreement between quasistatic results and low-frequency results shows conclusively that this behavior in N,, as a function of energy is not an artifact of the measurement technique. However, not all the samples investigated in the course of this work show the same behavior of N,, as a function of energy. G, and C, obtained by low frequency measurements at 0.25 Hz for sample 3A2 are shown in Figs. 8(a) and (b), respectively. It can be deduced from the energy dependence of G, that surface state response for this sample in the weak inversion region is dominated by majority carrier response. N,, at midgap is approximately ,
to-9 -
SAMPLE +.e=-0_27’e”
SAMPLE 342 F=0.25Hz .#.s = -0.266 eV
1681
Fig. 7. (a) Experimental G, for sample 16 Al with high generation current. G, increases from midgap to 0.17 eV below midgap, indicating minority carrier response dominates surface state response in weak inversion. (b) Experimental C. as a function of surface potential with respect to midgap. -, Quasistatic results; 0, 22.5 Hz; x, 90 Hz; 0, I.0 kHz. In strong inversion C, closely approaches theoretica!ly calculated C, (curve(c)).
Fig. 8. (a) G, at a measurement frequency of 0.25 Hz as a function of surface potential with respect to midgap for a sample annealed at 475°C. (b) C, for same sample. In weak inversion Cs equals C,., so this sample shows no increase in density of surface states in weak inversion. Increase in C, in strong inversion is due to inversion capacitance.
Lowfrequency measurements on MOScapacitors 1.7 X 10” states/cm’-eV, and Fig. 8(b) shows that there is no increase in N,, in weak inversion to about 0.2 eV below midgap (at energies farther into inversion, C,, is obscured by the rise in C,). Sample 3A2 was processed in the same way as the other samples except for the temperature of the final nitrogen anneal, which is higher for sample 3A2 (475°C) than for samples 6Al (340°C)or 16A1(3OO”C).It is well known that a final nitrogen or hydrogen anneal decreases the density of surface states in MOS structures[l6]. Comparing samples 3A2 and 6A1, the higher anneal temperature of 3A2 has resulted in approximately a factor of two decrease in N,, at midgap and a factor of 10 decrease near inversion. The preferential annealing of surface states in the weak inversion region may indicate that they arise from a different physical mechanism than the states at midgap. In samples where the majority carrier time constant dominates, the time constant for surface in weak inversion is large and ranges between approximately lo-’ and 10 seconds. It has been suggested that such “slow states” in MOS devices are due to oxide traps near the interface[l4,17]. Annealing temperature is also found to affect the value of G,, the conductance associated with bulk and surface state generation currents. This is shown in Fig. 9, where G, for various samples is plotted against the density of surface states at midgap. Samples 6A1, 6B, and 6C are samples which have been scribed from a single wafer after all processing except for the final nitrogen anneal. The value of G, decreases with increasing anneal temperature. Because it seems unlikely that a low tem10-5
!
,
, ,,
,
,
, /,
,
,
, (
V
o6 -
743
perature anneal will affect the density of bulk traps in the depletion region, the generation current in these samples is apparently dominated by surface state generation. The surface state generation current is given by [18]: I,,, =
4 ni
so
so = l/2 d\/(gnuP) v,,,g kT N,,
(19 (16)
where so is the surface recombination velocity and N,, is taken at the effective midgap position for surface state response defined by (5b). From Fig. 7(a), the minimum in G, near midgap occurs when T”= TV,i.e. when (r. = a,. The experimental data shows that this is on the order of only 25 to 50 mV below midgap, confirming the validity of using N,, at midgap. The four samples with the smallest density of states at midgap in Fig. 9 show an approximately linear dependence of G, on N,,, in agreement with (15) and (16). Using the relationship Zgen= G, d$~G,(24~) and equations (15) and (16), the value of d(a.u,) determined from the straight line region of Fig. 9 is 2.5 X 1OP cm*. Sample 6C, the sample which is annealed at the lowest temperature and has the highest density of states at midgap, has a large generation conductance which does not fit the linear dependence of G, on N,, of the other samples in Fig. 9. (The generation conductance of sample 6C is so large that surface state response in weak inversion is dominated by minority carrier response.) From (15) and (16), the value of q(a. up) for sample 6C is 3.6 x 1O-‘4cm2, a factor of greater than 100larger than the annealed samples. This large capture cross section is further evidence that surface states which can be annealed by this low temperature process arise from a different physical mechanism than the states which do not anneal. Fahrner and Goetzberger[l9] have reported a similar dependence of capture cross section on N,, on samples with a high density of states (-10” - lO”/cm*eV). CONCLUSIONS
10-e0
Fig. 9. G,, conductance due to generation currents in the depletion layer, as a function of N,. at midgap for: I, Sample 3A3; 0, sample 3A2; A, sample 6B; x , sample 6Al; V, sample 6C. Anneal temperatures are 475°C. 475°C. 750°C. 34O”C, and 25OT, respectively.
The density of fast surface states in MOS structures both in the depletion and weak inversion regions can be obtained in a straightforward manner from low frequency conductance and capacitance measurements at room temperature. The technique has been shown to yield results in excellent agreement with other techniques. The low frequency measurements also yield the value of the conductance across the depletion layer due to generationrecombination currents. A self-consistency check of the technique can be made by making measurements as a function of frequency. The measured conductance and capacitance are frequency dependent but the reduced data C, and G, should be frequency independent if the analysis of the data has been performed correctly. The energy range over which N,, can be obtained by low frequency measurements is limited to the region between flatband and inversion. This is due to the fact that the surface state capacitance C,, is small compared to CD near flatband or to C, near inversion.
N. S. SAKS
744 In the majority
this
work
dominant
majority
time
agreement results
of samples
the
constant
show
constant
with
Slobodskoy The
behavior
temperature
the
below
475°C
show
with N,,? in weak inversion The position
samples states
is nearly
Annealing near
constant
the minimum, These
in weak
inversion
2.
and
on the Samples
in
at midgap
N,,
near
as shown in
the density
midgap
to
of
inversion.
on the density effect which
physical
conductance
to generation
layer also depends of the samples of surface
generation
current
generation
generation
states
there
rather
6. 7. 8. 9. IO.
of states
on N,,
near of
are annealed
mechanism
Il. 12. 13.
than
and N,,
currents
on the annealing
in the
temperature
measured.
For samples
with
at midgap
on the order
of IO”’
is a linear
current
5.
14.
due
for most
states/cm2-eV,
3. 4.
for the
depends
is not the same in all
in samples
depletion
the
is in
near the minimum.
The
density
This
Lehovec
suggest that the large density
below 475°C is due to a different states
I.
anneal.
but has a strong results
REFERENCES
time
of energy
at 475°C
from
has only a small effect
inversion. states
annealed
relationship
at midgap,
is dominated
than bulk generation.
author wishes to thank Dr. W. D. Baker comments. suggestions and discussions.
in
an order of magnitude
of the minimum
samples
the
work
and does not occur exactly
6. For
carrier
a minimum
higher.
Acknowledgement-The for innumerable helpful
large generation
nitrogen
midgap
Fig.
region
model.
in this
final
of
is the
experimental
response. of
as a function
measured of
with
state
circuit
of N,,
inversion
the minority
predictions
equivalent
samples
annealed
layer
surface
the
constant
However,
that in samples
dominates
agreement
MOS
results.
in the depletion
in the course
time
in the weak
with previous
here
currents
measured
carrier
which by
between implies surface
a the
that state
15. 16. 17. 18.
L. M. Terman, SolidSI. Electron. 5. 28.5 (1962). C. N. Berglund. IEEE Trans. Efectron Deck-es ED-13, 701 (1966). M. Kuhn. Solid-St. Electron. 13, 873 (1970). E. H. Nicollian and A. Goetzberger. Bell S.wt. Tech. J. 46. 1055 (1967). G. Declerck, R. Van Overstraeten and G. Broux, Solid-St. Elecfron. 16, 1451 (1973). J. A. Cooper and R. J. Schwartz, Solid-% Electron. 17. 641 (1974). D. H. Eaton and C. T. Sah, Solid-St. Electron. 16,841 (1973). K. Lehovec and A. Slobodskoy, Solid-St. Electron. 7. 59 (1964). A. Goetzberger and E. H. Nicollian. Bell Syst. Tech. .I. 46, 513 (1967). S. R. Hofstein and G. Warfield. Solid-Sf. Elecfrom 8. 321 (196s). See, for example G. F. Amelio, Surface Science 29. 125 (1972). H. Deuling, E. Klausmann and A. Goetzberger. Solid-St. Elecfron. 15, 559 (1972). A. S. Grove, B. E. Deal. E. H. Snow and C. T. Sah. So/id-St. Electron. 8, 145 (196.0. A. Goetzherger. Proc. Int. Conf. Tech. Appl. CCD’s. (iniuersity oj Edinburgh, 25-27, Sepf. 1974. p. 47, University of Edinburgh Press (1974). E. A. Fogels and C.A.T. Salama, J. Efectrochem Sot. 118, 2002 (1971). B. E. Deal, J. Electrochem. Sac. 121, l98C (1974). H. Prier, Appl. Phys. Letters 10, 361 (1967). A. S. Grove and D. J. Fitzgerald, Solid-St. Elecfron. 9. 783
(1966). 19. W. Fahrner (1970).
and A. Goetzherger,
Appl. Phys. Letters 17. 16
Ekctnmrcs.
1975. Vol. 18. pp 737-744
Pergamon Prev.
Printed in Great Britain
LOW FREQUENCY CONDUCTANCE AND CAPACITANCE MEASUREMENTS ON MOS CAPACITORS IN WEAK INVERSION
U.S. Naval
N. S. SAKS Laboratory, Washington,
Research
(Received
23 November
D.C. 2037.5, U.S.A.
1974: in retkwdform
26 March
1975)
Abstract-The analysis of capacitance and conductance measurements as a function of frequency on MOS capacitors biased in depletion is well understood. However, little information is available on such measurements for capacitors biased in weak inversion. In this work it is shown that approximations to the theory of surface state response lead to a very simple technique for obtaining the density of fast surface states as a function of energy in the weak inversion region. Low frequency conductance and capacitance measurements have been made on a number of MOS samples and analysis of the data yields N,, as a function of energy in excellent agreement with results obtained by other techniques. As expected, experimental results show that N,, in weak inversion depends strongly on the annealing treatment given the MOS samples. However, annealing is found to have a much greater effect in reducing N,, in weak inversion than at midgap. It is also shown that the depletion layer generation current in the majority of samples measured is due to surface state generation rather than bulk generation.
samples
NOTATION surface potential reduced surface potential, = &/kT position of bulk Fermi level with respect to midgap capture cross section of surface states for capture of electrons capture cross section of surface states for capture of holes time constant for capture of electrons by surface states time constant for capture of holes by surface states thermal velocity of free carriers
concentration concentration
have developed
available (N,,)
for determining
a.c. conductance
in MOS
techniques as described static and
structures.
a.c.
Goetzberger
state parameters
midgap
Declerck,
for
Although depletion, surface
parameters
there
discussed
yields information
However,
as discussed
of
the
quasistatic
states/cm*-eV
surface
inversion.
MOS
samples
Secondly, with
very
and
in detail by
viewpoint
and
parallel
the
data
low
(3) The limiting
the
data
potentials
number
of MOS
samples
density
obtained
by low frequency
about a factor
cross
results
on a
show that the fast surface
conductance
technique
The experimental
results
be a strong
on the conditions
state
a.c. measurements
obtained
of
it is not
capture
Experimental
with results
may
from of this
However,
to obtain
states.
are
by the Nicollian and the quasistaalso show that N,,
function
of energy
of the final low-temperature
APPROXIMATE
The impedance current
A general
or
capacitor
following
by Kuhn[3],
in
Fig. l(a).
One additional
the equivalent
generation-recombination
depletion
sample
in these
were 737
MODEI.
by an MOS
flow has been considered
Slobodskoy[8].
and
presented
near flatband
Consequently,
other (2) N,,
sensitivity
technique.
to analyze
that the
equilibrium.
model,
for
anneal.
1x IO”
midgap,
than
and less data is required.
of the surface
inversion
than the
circuit
simpler
sections
depending
Of
a.c. over
rather
is about 1 x lo9 states/cm*-eV,
in weak
about
regime.
frequency advantages
over a wide range of surface
tic technique.
in
low
equivalent
is much
to inversion.
and Goetzberger
about
is biased
about
near
potentials
a large
is a complex
the series R-C equivalent
R-C
techniques,
in good agreement
only the quasistatic
as discussed
as well as
require
state Ioss[6,7]
possible
rates the ramp rate must be kept small to insure is in thermal
of
that
(1) Using
IO better than the quasistatic
et al. [5], the accuracy
potentials
they
have several
for surface
used
technique
of samples.
is at best
may be much worse for surface strong
Nicollian
little information
by Declerck
about interface
of the data
it is shown
about N,, in weak inversion.
technique
for
model
flatband
or quasi-
information
above,
utilizing
a.c. conductance
cross section
However,
measurements
is obtained
used
technique
in the weak inversion
technique
These
and analysis
work,
conductance
and disadvan-
the surface
is comparatively
state parameters
the three techniques
of
a theoretical
when
this
analysis
[2] and Kuhn [3],
on a number
there is now considerable
state
density.
the other techniques:
states
commonly
capacitance
have been compared
results
of data,
conductance
of techniques
advantages
et al. [5], both from
experimental
surface
most
technique
relative
amount
circuit
of fast surface
by Berglund
conductance [4]. The
state
results
inversion
information
such as capture
surface
In
the low-frequency
suggested
tages of these techniques from
The
by Terman[l],
technique the
are a number
are the high frequency
in weak
measurements.
to
and Schwartz[6]
and some experimental
yield considerable
commonly
the density
the theory
is small and difficult Cooper
state parameters
techniques
INTRODUCTION
there
current
Recently,
procedure.
of holes at the surface intrinsic concentration of carriers difference between midgap and the effective surface state response, defined by eqn (5b)
time
accurately.
on interface
of electrons at the surface
the present
the displacement
measure
circuit
their
equivalent
circuit
nomenclature element,
to account by Lehovec
to a.c. and
for an n-type
is presented
G,, has been added for
layer generation-recombination
not considered
capacitor
in detail by Lehovec
surface
state
currents,
and Slobodskoy.
in to and
which
N. S
738
SAKS
temperature by Goetzberger and Nicollian[9]. Thus CDs and GPDcan be neglected with respect to GP (2) G,D % G,, at all biases of interest for surface state densities less than by Hofstein and 1O’2 states/cm*-eV as shown Warfield [ IO]. Thus, G,, can be eliminated from the equivalent circuit. The resulting simplified circuit is shown in Fig. l(b). For a single level of surface states, the elements C,,, G,,,. and G,,, which describe surface state loss are given
(a)
by[81:
c,, =&TfT(I -fr)
(b)
1 T
(1)
GATE
co,
CI
GP
1
SUBSTRATE
Fig. 1. (a) General equivalent circuit for ax. response of an MOS device after Lehovec and Slobodskoy[S]. (b) Simplified equivalent circuit. Referring to Fig. l(a). the physical mechanisms of a.c. current flow in the MOS structure can be understood in terms of three parallel current paths in series with the oxide capacitance C,,, : (1) a path through CD,the depletion layer space-charge capacitance; (2) a path through GnD, G,,, and C,,, representing the conductance associated with electron flow across the depletion region, the loss mechanism due to trapping of electrons by surface states, and the capacitance due to changes in the net surface state charge as a result of electron trapping, respectively; (3) a path through GPs, Gp~, G,, and C,,, representing the conductance due to the diffusion of holes in the neutral region, the conductance due to the diffusion of holes across the depletion region, the loss mechanism due to trapping of holes by surface states, and the capacitance due to changes in the net surface state charge as a result of hole trapping, respectively. The elements of path (2) form a branch representing majority carrier capture and emission from surface states. The elements of path (3) form a branch representing minority carrier capture and emission from surface states. Holes can also be supplied to the surface by generation-recombination centers as represented by the conductance G, of Fig. l(a). The capacitance C, represents the minority carrier storage in the inversion layer at the silicon-silicon dioxide interface. The equivalent circuit of Fig. I(a) can be simplified somewhat by the following considerations: (1) In silicon diodes at room temperature the generation-recombination current usually dominates the diffusion current. This fact has been verified in the case of MOS diodes at room
where NJ is the number of surface states and fi is the Fermi function which gives the occupancy of the states. These equations must be modified to account for three effects: (I) Surface states occur in a continuum throughout the bandgap; (2) Due to the statistical distribution of fixed charge at the interface, as described by Nicollian and Goetzberger[4], the interface is not an equipotential surface; and (3) When the surface is inverted, the buildup of minority carriers in the inversion layer affects surface state response. This effect is described in detail by Cooper and Schwartz[6], and it means that surface state response is described by two separate models for depletion and weak inversion. These two regions are defined as follows: When the surface is in “depletion”, the majority carrier capture conductance G,,r is larger than the minority carrier capture conductance G,,,. Conversely, in “weak inversion”, G,,, > G,,. From eqns (2) and (3), it is straightforward to show that the ratio of G,, to G,, is given by[4]:
where & is the position of the bulk Fermi level with respect to midgap. Therefore, from (4), G,, equals G,Y when
Depletion is defined by O< 4Y < & +A4, and weak inversion by & t Ac$ < c$$< 2 &. Since AC#Jvaries as the logarithm of the ratio of the capture cross sections, the effective midgap position should not deviate from the real midgap position by more than a few kT. For surface potentials in depletion, low frequency approximations to the theory have been considered by Eaton and Sah[7] who used the series R-C equivalent
Lowfrequencymeasurementson MOScapacitors circuit model. For low frequencies such that 07. 6 1, they have shown that Cm= q Ns,
(7)
where T,, is the time constant for capture of electrons by surface states. For surface potentials in weak inversion and using a series R-C equivalent circuit model, the following expressions have been derived by Cooper and Schwartz [6]:
I
OD
c,, = 4 Nss -x
(I-f*)&)d~s
(9)
739
carrier response dominates minority carrier response and the effective time constant of the surface states is the electron time constant T.. Equations (6), (7) and (8) apply at low frequency. Region (2): In weak inversion, when the surface potential is more than a few kT below the effective midgap position, with negligible generation currents so that G, 6 G., 4 G,,. Due to the small generation current, majority carrier response still dominates surface state response, and the effective time constant of the surface states is the electron time constant T,,.Equations (8)-(11) apply. This is the assumed condition in the literature which treats the weak inversion case[4,6]. Region (3): Weak inversion with large generation currents. If G., a G,, Q G,, then minority carrier response dominates surface state response and the effective time constant is TV. If G., e G, a G,, then minority carrier response still dominates surface state response but the effective time constant of the minority carrier branch of the equivalent circuit is given by (C,, + C,)/G,. EXPERIMENTAL RESULTS
MOS samples were fabricated on (111) orientation n-type IOIl-cm epitaxial silicon wafers. The wafers were chemically cleaned and oxidized in dry 9 at 1000°Cfor a f*= [l+zexp(-2(+~-de)lkT)]-’ (11) 1OOOAoxide (nominal value). After metallization with aluminum, 30 mil diameter contact dots were defined by where P(u,) is the probability distribution function given photolithographic techniques. The wafers were then given by eqn 35in reference[4], u. is the normalized surface a final anneal in dry nitrogen. The temperature of the final potential, and T,, is the electron time constant given by anneal was varied between 200°C and 47s”C to produce eqn (7). In weak inversion f* approaches zero and from samples with different densities of surface states. Samples (9) C,, approaches qN,,. It is not possible to reduce (10) to were mounted in TO-5 headers and placed in an airtight a simpler form using the same level approximation due to shielded apparatus where all measurements were made in a dry nitrogen ambient. the exponential dependence of the electron time constant Capacitance and conductance measurements were and P(u,) on surface potential. a.c. lock-in amplifier In weak inversion if G, @GPs9 G.,, the situation is made with conventional analogous to depletion with T" replaced by TV, where TV is techniques Ill]. The measurement system was carefully the time constant for capture and emission of holes by calibrated to ? 0.1 pf ? 0.2% (reading) over the frequency range 0.2 Hz-100 kHz. Stray capacitance due to the TO-5 surface states and is given by: header and associated wiring was carefully measured and TP’= urhupn, exp I- (4, - &s)/kTl (12) subtracted from the measured capacitance. d.c. leakage in the sample apparatus, an important consideration at very low frequencies, was measured at less than lo-l5 amps. If WTp 6 1, C,, is given by (6) and from (7) we obtain All measurements presented here were made at room temperature. (13) The measured equivalent parallel capacitance (C,,,) and conductance (G,) of a typical sample as a function of applied bias with frequency as the parameter are shown in We have two important results: (1) At low frequencies, C,, is simply equal to qN,, both in depletion and weak Figs. 2 and 3, respectively. The quasistatic capacitance inversion; and (2) Using the series R-C equivalent circuit curve for this sample obtained by the method of Kuhn[3] model, from (6), (7), (IO) and (13), C,,, G,, and G,, are at a voltage ramp rate of 6.28 mV/sec is shown for frequency independent. This is a considerable simplifica- comparison in Fig. 2(d). The accumulation, depletion, tion from the more commonly used parallel R-C weak inversion, and strong inversion regions for this equivalent circuit model because the parallel elements are sample are shown in each figure. The capacitance data shows the usual high-frequency not frequency independent. These results are derived under the assumption that the surface state parameters behavior at 100kHz. At low frequencies the capacitance is strongly frequency dependent in the depletion and weak including N,,, u., and a, are independent of energy. Using equivalent circuit Fig. l(b) and the above inversion regions. It is expected that C, will approach the equations, it is possible to distinguish three different quasistatic capacitance curve at very low frequencies regions of surface state response. Region (1): In depletion, when minority carrier response dominates majority when the surface potential is more than a few kT above carrier response; i.e. when G, a oCD (refer to equivalent the effective midgap position, and G., *G,,. Majority circuit Fig. l(b)). Clearly this condition is not satisfied for
S
740
-3 5
-3.0
-2 5
DEP -,,e-ACC 1 I -20 -I 5 GATE
~ I -0.5
-I 0
0
VOLTAGE
Fig. 2. Capacitance of an MOS sample as a function of gate voltage showing low frequency dispersion effect. (a) 100~00 kHz (b) 2.0 Hz (c) 0.5 Hz (d) quasistatic results, ramp rate equals 6.28 mV/sec. The accumulation, depletion, weak inversion, and strong inversion regions of surface potential are shown at the bottom of the figure.
4 SAMPLE
6AI
SAKS 100 Hz, G, peaks in the weak inversion region and then approaches a constant non-zero value in strong inversion. The peak in the weak inversion region is due to surface state response. As discussed previously, this may be due to either majority or minority carrier response depending on the relative order of magnitude of G, with respect to G,,. In strong inversion, surface state response is negligible with respect to minority carrier response in the inversion layer (C, in series with G,), and G, approaches a bias independent value. The measured data at a given frequency and gate voltage as shown in Figs. 2 and 3 is evaluated according to the equivalent circuit Fig. I(b) as follows: (I) G, and C,, are converted to equivalent series data, the capacitance C,, is subtracted, and then the data is converted back to the equivalent parallel form. This step is performed conveniently by equations 2.15 and 2.16 in[12]. (2) The capacitance CD is subtracted from the equivalent parallel capacitance calculated in step (1). CD at the given gate voltage is obtained from high frequency capacitance measurements (100 kHz or 1.OMHz) assuming no surface state loss. This method does lead to some error in C, near flatband but gives excellent results in the weak inversion region. This step results in equivalent parallel elements G,, and C,,. (3) Finally, G, and C, are converted to equivalent series elements G, and C, which represent the net effect of the elements G.,, G,,, G,, C,,, and C, shown in Fig. l(b). The resulting G,/w, C,, G,, and C, for sample 6A1 at a surface potential in weak inversion (0.103 eV below midgap) as a function of frequency are shown in Fig. 4. Looking first at the series elements G, and C,, G, is independent of frequency as predicted previously. C, is also frequency independent except at the higher frequencies where experimental error is large. The error bars
SAMPLE +r-+B
I. I 3.5
I
I
-30
-25 GATE
I -20
. . . .
.
GA, = -0,103ev
..e*G.
I -15
VOLTAGE
Fig. 3. Measured conductance/w of MOS sample in Fig. 2 as a function of gate voltage with frequency as a parameter. (a) 100.0 kHz (b) 1.0 kHz (c) 90.0 Hz (d) 10.0 Hz (e) 2.0 Hz (f) 0.5 Hz. Tile conductance peak in depletion and weak inversion is due to surface state loss, and the bias independent region in strong inversion is due to the generation current.
this sample at the lowest measurement frequency used, 0.5 Hz. The behavior of the equivalent parallel conductance G, is also significantly different at high and low frequencies. At frequencies greater than approximately I .OkHz the conductance is non-zero only when the surface is in depletion. Surface state response is therefore characterized by majority carrier response and the data can be analyzed to yield G., and C,,. At frequencies below
FREQUENCY
( HZ 1
Fig. 4. Data points show reduced data for sample biased in weak inversion (0.103 eV below midgap) for G,/o, C,,, G,, and C,. Solid lines represent best fit of single time constant eqns (16) and (17) of [41 to G,,/o and C,. Error bars show assumed experimental error. C, and G. are frequency independent except for deviation at high frequency due to experimental error.
Lowfrequency
measurements
show the amount of error assuming f 0.1 pf 20.2% (reading) in the measured quantities C, and G,/u. The error in G, for this particular data is approximately 2 5%, which is too small to display in the figure. The error in C, is larger due to step (2) of the data analysis when CD is subtracted from the capacitance calculated in step (1). Since these two quantities are nearly equal at higher frequencies, a small error in either quantity results in a large error in C,. G,,/w and C,, in Fig. 4 represent the same data in equivalent parallel format. The dots are the experimental data points and the solid lines represent the best fit of the single time constant eqns (16) and (17) in [4] to the experimental data. Again, the fit is good except for C, at high frequency where C,, is small. G, and C, for the same sample at constant frequency (0.5 Hz) are shown in Figs. 5(a) and (b), respectively, as a function of surface potential with respect to midgap. In strong inversion G, approaches a constant value independent of surface potential which is equal to G,. In weak inversion where G, is only weakly dependent on surface potential, G, is equal to either the series combination of G,, and G, or the parallel combination of G., and G, (refer to Fig. l(b)). Because G, 2 G,, G, must be given by the parallel combination of G., and G,, and surface state loss in this sample is dominated by majority carrier response. This is in agreement with the fact that G, decreases with increasingly negative surface potential, which can only occur when surface state response is dominated by the electron time constant.
on MOS capacitors
741
From the equivalent circuit Fig. l(b), the capacitance C, should be equal to C,, in depletion and weak inversion assuming C, is negligible over this range of surface potential. Therefore, from (6) and (9), C, equals qiV,, and the surface state density can be obtained directly from C,. In order to use eqn (6) in depletion, we have assumed that WT.4 1. From (6) and (7) it can be shown that 26X,, 07” =-G”,
and using the data in Fig. 5 it is clear that the condition WT.e 1 is satisfied in depletion. It is not necessary that this condition be satisfied in weak inversion. In strong inversion where C, is large, the capacitance C, should be equal to Cl. The theoretical value for C, calculated for this sample as a function of surface potential is shown in Fig. 5(c). C, is calculated from eqn (7) in [13] with C, = dQ,/d& As shown in Fig. 5, there is good agreement between calculated and experimental C,. For sample 6Al at a measurement frequency of 0.5 Hz, C, equals qN,, both in depletion and weak inversion. N,, obtained in this manner as a function of surface potential with respect to midgap is shown in Fig. 6. Results of the quasistatic technique and of the Nicollian and Goetzberger analysis are also shown. Agreement between the three techniques is excellent. The density of states for this sample increases rapidly with surface potential in weak inversion. This probably introduces some error in the measured density of states since previously it was assumed that N,, is not a strong function of surface potential. Therefore, more accurate results could be obtained in this case by using the integral equations for C,,
SAMPLE &,
EPLETIO+
(14)
= -0.276
681 eV
WEAK ---kSTRONG INVERSION
Fig. 5. (a) Experimental G, and (b) C, at constant frequency (0.5 Hz) as a function of surface potential with respect to midgap. G, decreases from depletion to strong inversion, indicating majority carrier response dominates surface state response in weak inversion. C. equals C., in depletion and weak inversion, and closely approaches theoretically calculated C, (curve(c)) in strong inversion.
Fig. 6. Comparison of density of states as a function of surface potential with respect to midgap obtained by different techniques. A Nicollian and Goetzberger conductance analysis. - Quasistatic analysis. 0 Low frequency analysis at a measurement frequency of 0.5 Hz.
N. S.
742
and G,, [4,6] rather than the approximate equation Css = qNa.
G, and C, for another sample (16Al) as a function of surface potential with respect to midgap with the measurement frequency as a parameter are shown in Figs. 7(a) and (b), respectively. The value of G, for this sample is 9.3 X lo-” f12-‘-cm-*,a factor of more than 300 larger than the previus sample. This large generation current is believed to be a bulk property of this particular wafer because all samples fabricated from the wafer had the same large generation current. The behavior of G, as a function of surface potential is divided into three regions: (I) In depletion, the 1.0 kHz data shows that G, decreases exponentially with increasingly negative surface potential. This is in qualitative agreement with (7) and (8) (although from (14) it can be shown that the condition WT”e 1 is not satisfied at 1.OkHz in depletion), and therefore G, = G.,. (2) In weak inversion, between approximately midgap and 0.17 eV below midgap, G, increases with increasingly negative surface potential. This in in agreement with (12) and (13), and therefore G, = G,, and surface state response is dominated by the minority carrier time constant TV.As noted previously, this can occur only when G, Z+G.,, a condition which is clearly shown to be satisfied by the data in Fig. 7(a). (3) For surface potentials below 0.17 eV below midgap, G,,, > G, and so G, = GW G, is weakly dependent on surface potential as discussed by Goetzberger and Nicollian [9]. In Fig. 7(b), C, obtained at 22.5 Hz and 90. Hz is shown to be in excellent agreement with quasistatic results (solid
SAKS
curve). The data at these two frequencies shows that C, and G, are frequency independent in weak inversion. From (14) at 22.5 Hz (with T. replaced by T,, and G,, replaced by G,,), the experimental data confirms that UT,, Q 1 in weak inversion. However, this condition is not satisfied at 1.0 kHz, and in fact the 1.OkHz data for G, does not agree with the lower frequency data. Curve 7(c) shows the calculated inversion capacitance C,, and again agreement with C, is very good in strong inversion. DlSCUSSION
The behavior of the density of states N,, as a function of energy is qualitatively similar for both samples 6Al and 16A1. N,, has a minimum value of approximately 3 x 10” states/cm*-eV near midgap and increases with energy away from the minimum both in depletion and weak inversion. Similar behavior in N,, has been observed previously [4,14, 151. The increase in N,, in the weak inversion region for these two samples is much greater then the increase in the depletion region. The excellent agreement between quasistatic results and low-frequency results shows conclusively that this behavior in N,, as a function of energy is not an artifact of the measurement technique. However, not all the samples investigated in the course of this work show the same behavior of N,, as a function of energy. G, and C, obtained by low frequency measurements at 0.25 Hz for sample 3A2 are shown in Figs. 8(a) and (b), respectively. It can be deduced from the energy dependence of G, that surface state response for this sample in the weak inversion region is dominated by majority carrier response. N,, at midgap is approximately ,
to-9 -
SAMPLE +.e=-0_27’e”
SAMPLE 342 F=0.25Hz .#.s = -0.266 eV
1681
Fig. 7. (a) Experimental G, for sample 16 Al with high generation current. G, increases from midgap to 0.17 eV below midgap, indicating minority carrier response dominates surface state response in weak inversion. (b) Experimental C. as a function of surface potential with respect to midgap. -, Quasistatic results; 0, 22.5 Hz; x, 90 Hz; 0, I.0 kHz. In strong inversion C, closely approaches theoretica!ly calculated C, (curve(c)).
Fig. 8. (a) G, at a measurement frequency of 0.25 Hz as a function of surface potential with respect to midgap for a sample annealed at 475°C. (b) C, for same sample. In weak inversion Cs equals C,., so this sample shows no increase in density of surface states in weak inversion. Increase in C, in strong inversion is due to inversion capacitance.
Lowfrequency measurements on MOScapacitors 1.7 X 10” states/cm’-eV, and Fig. 8(b) shows that there is no increase in N,, in weak inversion to about 0.2 eV below midgap (at energies farther into inversion, C,, is obscured by the rise in C,). Sample 3A2 was processed in the same way as the other samples except for the temperature of the final nitrogen anneal, which is higher for sample 3A2 (475°C) than for samples 6Al (340°C)or 16A1(3OO”C).It is well known that a final nitrogen or hydrogen anneal decreases the density of surface states in MOS structures[l6]. Comparing samples 3A2 and 6A1, the higher anneal temperature of 3A2 has resulted in approximately a factor of two decrease in N,, at midgap and a factor of 10 decrease near inversion. The preferential annealing of surface states in the weak inversion region may indicate that they arise from a different physical mechanism than the states at midgap. In samples where the majority carrier time constant dominates, the time constant for surface in weak inversion is large and ranges between approximately lo-’ and 10 seconds. It has been suggested that such “slow states” in MOS devices are due to oxide traps near the interface[l4,17]. Annealing temperature is also found to affect the value of G,, the conductance associated with bulk and surface state generation currents. This is shown in Fig. 9, where G, for various samples is plotted against the density of surface states at midgap. Samples 6A1, 6B, and 6C are samples which have been scribed from a single wafer after all processing except for the final nitrogen anneal. The value of G, decreases with increasing anneal temperature. Because it seems unlikely that a low tem10-5
!
,
, ,,
,
,
, /,
,
,
, (
V
o6 -
743
perature anneal will affect the density of bulk traps in the depletion region, the generation current in these samples is apparently dominated by surface state generation. The surface state generation current is given by [18]: I,,, =
4 ni
so
so = l/2 d\/(gnuP) v,,,g kT N,,
(19 (16)
where so is the surface recombination velocity and N,, is taken at the effective midgap position for surface state response defined by (5b). From Fig. 7(a), the minimum in G, near midgap occurs when T”= TV,i.e. when (r. = a,. The experimental data shows that this is on the order of only 25 to 50 mV below midgap, confirming the validity of using N,, at midgap. The four samples with the smallest density of states at midgap in Fig. 9 show an approximately linear dependence of G, on N,,, in agreement with (15) and (16). Using the relationship Zgen= G, d$~G,(24~) and equations (15) and (16), the value of d(a.u,) determined from the straight line region of Fig. 9 is 2.5 X 1OP cm*. Sample 6C, the sample which is annealed at the lowest temperature and has the highest density of states at midgap, has a large generation conductance which does not fit the linear dependence of G, on N,, of the other samples in Fig. 9. (The generation conductance of sample 6C is so large that surface state response in weak inversion is dominated by minority carrier response.) From (15) and (16), the value of q(a. up) for sample 6C is 3.6 x 1O-‘4cm2, a factor of greater than 100larger than the annealed samples. This large capture cross section is further evidence that surface states which can be annealed by this low temperature process arise from a different physical mechanism than the states which do not anneal. Fahrner and Goetzberger[l9] have reported a similar dependence of capture cross section on N,, on samples with a high density of states (-10” - lO”/cm*eV). CONCLUSIONS
10-e0
Fig. 9. G,, conductance due to generation currents in the depletion layer, as a function of N,. at midgap for: I, Sample 3A3; 0, sample 3A2; A, sample 6B; x , sample 6Al; V, sample 6C. Anneal temperatures are 475°C. 475°C. 750°C. 34O”C, and 25OT, respectively.
The density of fast surface states in MOS structures both in the depletion and weak inversion regions can be obtained in a straightforward manner from low frequency conductance and capacitance measurements at room temperature. The technique has been shown to yield results in excellent agreement with other techniques. The low frequency measurements also yield the value of the conductance across the depletion layer due to generationrecombination currents. A self-consistency check of the technique can be made by making measurements as a function of frequency. The measured conductance and capacitance are frequency dependent but the reduced data C, and G, should be frequency independent if the analysis of the data has been performed correctly. The energy range over which N,, can be obtained by low frequency measurements is limited to the region between flatband and inversion. This is due to the fact that the surface state capacitance C,, is small compared to CD near flatband or to C, near inversion.
N. S. SAKS
744 In the majority
this
work
dominant
majority
time
agreement results
of samples
the
constant
show
constant
with
Slobodskoy The
behavior
temperature
the
below
475°C
show
with N,,? in weak inversion The position
samples states
is nearly
Annealing near
constant
the minimum, These
in weak
inversion
2.
and
on the Samples
in
at midgap
N,,
near
as shown in
the density
midgap
to
of
inversion.
on the density effect which
physical
conductance
to generation
layer also depends of the samples of surface
generation
current
generation
generation
states
there
rather
6. 7. 8. 9. IO.
of states
on N,,
near of
are annealed
mechanism
Il. 12. 13.
than
and N,,
currents
on the annealing
in the
temperature
measured.
For samples
with
at midgap
on the order
of IO”’
is a linear
current
5.
14.
due
for most
states/cm2-eV,
3. 4.
for the
depends
is not the same in all
in samples
depletion
the
is in
near the minimum.
The
density
This
Lehovec
suggest that the large density
below 475°C is due to a different states
I.
anneal.
but has a strong results
REFERENCES
time
of energy
at 475°C
from
has only a small effect
inversion. states
annealed
relationship
at midgap,
is dominated
than bulk generation.
author wishes to thank Dr. W. D. Baker comments. suggestions and discussions.
in
an order of magnitude
of the minimum
samples
the
work
and does not occur exactly
6. For
carrier
a minimum
higher.
Acknowledgement-The for innumerable helpful
large generation
nitrogen
midgap
Fig.
region
model.
in this
final
of
is the
experimental
response. of
as a function
measured of
with
state
circuit
of N,,
inversion
the minority
predictions
equivalent
samples
annealed
layer
surface
the
constant
However,
that in samples
dominates
agreement
MOS
results.
in the depletion
in the course
time
in the weak
with previous
here
currents
measured
carrier
which by
between implies surface
a the
that state
15. 16. 17. 18.
L. M. Terman, SolidSI. Electron. 5. 28.5 (1962). C. N. Berglund. IEEE Trans. Efectron Deck-es ED-13, 701 (1966). M. Kuhn. Solid-St. Electron. 13, 873 (1970). E. H. Nicollian and A. Goetzberger. Bell S.wt. Tech. J. 46. 1055 (1967). G. Declerck, R. Van Overstraeten and G. Broux, Solid-St. Elecfron. 16, 1451 (1973). J. A. Cooper and R. J. Schwartz, Solid-% Electron. 17. 641 (1974). D. H. Eaton and C. T. Sah, Solid-St. Electron. 16,841 (1973). K. Lehovec and A. Slobodskoy, Solid-St. Electron. 7. 59 (1964). A. Goetzberger and E. H. Nicollian. Bell Syst. Tech. .I. 46, 513 (1967). S. R. Hofstein and G. Warfield. Solid-Sf. Elecfrom 8. 321 (196s). See, for example G. F. Amelio, Surface Science 29. 125 (1972). H. Deuling, E. Klausmann and A. Goetzberger. Solid-St. Elecfron. 15, 559 (1972). A. S. Grove, B. E. Deal. E. H. Snow and C. T. Sah. So/id-St. Electron. 8, 145 (196.0. A. Goetzherger. Proc. Int. Conf. Tech. Appl. CCD’s. (iniuersity oj Edinburgh, 25-27, Sepf. 1974. p. 47, University of Edinburgh Press (1974). E. A. Fogels and C.A.T. Salama, J. Efectrochem Sot. 118, 2002 (1971). B. E. Deal, J. Electrochem. Sac. 121, l98C (1974). H. Prier, Appl. Phys. Letters 10, 361 (1967). A. S. Grove and D. J. Fitzgerald, Solid-St. Elecfron. 9. 783
(1966). 19. W. Fahrner (1970).
and A. Goetzherger,
Appl. Phys. Letters 17. 16