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Discrimination between volume and interface traps in C (V) and photo I(V) experiments on 10-30 nm MOS
capacitors
J. Peisner, Y. Sangare, G. Lévêque
To cite this version:
J. Peisner, Y. Sangare, G. Lévêque. Discrimination between volume and interface traps in C (V) and photo I(V) experiments on 10-30 nm MOS capacitors. Journal de Physique III, EDP Sciences, 1993, 3 (11), pp.2101-2112. �10.1051/jp3:1993263�. �jpa-00249069�
J. Phys. III France 3 (1993) 2101-2112 NOVEMBER 1993, PAGE 2101
Classification
Physics Abstracts
73.60H 73.400
Discrimination between volume and interface traps in C(V)
and photo I(V) experiments on 10-30 nm MOS capacitors
J. Peisner (I), Y. Sangare (2) and G. Levdque (2)
(') Laboratoire d'Electrooptique des Couches Minces, Universitd Montpellier II, Sciences et
Techniques du Languedoc, Place Eugdne Bataillon, 34095 Montpellier Cedex 5, France (2) Laboratoire d'Etudes des Surfaces Interfaces et Composants, URA CNRS n 787, Universitd
Montpellier II, Sciences et Techniques du Languedoc, Place Eugkne Bataillon, 34095 Montpellier
Cedex 5, France
(Received 28 September J992, revised J9 July J993, accepted 6 August J993)
Rksumk, Nous discutons et comparons [es mdthodes usuelles de caractdrisation des pidges,
C (V et photo J(V), dans le cas oh la charge dans le volume et la charge d'interface sont du mdme ordre de grandeur. Cette situation est interrnddiaire entre le cas des couches trds minces
~ 5 h IQ nm) oh la densitd des charges volumiques Qvai est ndgligeable devant la densitd de charge totale des dtats d'interface Q,t et celui des oxydes dpais (~ 30 nm) oh la situation est inverse. Nous donnons une estimation quantitative de l'effet des charges de volume ou d'interface
sur [es mesures et nous montrons que pour ces dpaisseurs intermddiaires, les quantitds
Q,i et Qvoi ne peuvent pas dtre ddtermindes sans ambiguitd. La densitd d'dtats d'interface D,~ est toujours mesurable avec prdcision, mdme en prdsence de charges de volume par contre, la
mesure de la charge dans l'oxyde Qeff est fortement perturbde par la prdsence de charges
d'interfaces.
Abstract. The usual methods to characterize traps, C (V) and photo J(V) are discussed and compared in the case where the volumic charge is of the same order of magnitude as the interface charge. This is an intermediate case between very thin films
~ 5 to 10 nm) where volumic charge density Qvoi is negligible with respect to the interface charge density Q,t, and the thick oxides (~ 30 nm where the reverse situation occurs. We estimate quantitatively the effect of volume or
interface charges in the measurements and show that for these medium thickness films, the
quantities Q,t and Qvoi cannot be determined unambiguously. The interface state density
D,~ is always accurately measurable even in presence of volume charge on the contrary, the
measurement of the charge within the oxide Qeff is strongly perturbed by interface charges.
Notation.
C~~ Capacitance of the oxide (F/cm2) ;
C~~ Surface semiconductor capacitance (F/cm2) ;
D~~(E) Interface state energetic density (charges/cm2.eV) ;
D(~ Acceptor state density (charges/cm2.eV)
D( Donor state density (charges/cm2.eV)
E Energy level in the gap of the semiconductor (eV), the origin is at mid gap
E~~ Barrier height for a null field (eV)
L Oxide total thickness (nm)
Qjt Integrated total interface state density (C/cm2) ;
Qeff Effective volumic charge density (C/cm2)
= Q~~j ilL
Qf Fixed or initial charge density in the oxide (C/cm2) ;
Qot Oxide trap charge density (C/cm2)
Q( Oxide trap charge density in the interval (xi,.;() ;
Qvoi Volumic charge density in the oxide (C/cm2). Q~~j
= Q~ + Q~~ = AL
V~ Gate bias (V) ;
$r~ Surface band bending of the semiconductor (V)
4~~ Work function difference between metal and semiconductor (V).
1. Introduction.
Deviations of real MOS structures from the ideal case have a critical effect on the
performances of MOS devices. One important deviation comes from the presence of parasitic charge in the oxide layer and at the Si-SiO~ interface. This charge, created in the oxidation
process or by ionizing radiations~ disturbs the electrical properties of the device and has to be carefully corrected in MOS systems.
Many sensitive methods [1, 2] have been proposed to measure the parasitic charge :
interface density D~ is commonly obtained from quasistatic C(V) curves [3-5], from the
highflow frequency capacitance method [1, 6] from deep level transient spectroscopy (DLTS) and its variants [8-10]. Charge within the oxide Qvoi is more difficult to estimate in the case of thin oxides. The simplest and most widely used method to obtain oxide charge is to determine the flat band voltage on the C (V) curves
~~G~FB " ~m~ ) iov°'
~ ~ ~Q~t~FB ~i " ~mS ) ioeff
~ ~o't~fBi ~~~
where I is the charge barycenter in oxide. The effective charge, Q~~~, is related to the first order
moment of the volumic charge.
For thick oxides (L
~ 100 nm ), this relation can be applied to determine Q~~~, neglecting the term Q~~ because the amount of charge trapped in the oxide volume may be large. On the other hand for a thin oxide (L
~ 10 nm ), the volume of the oxide is not sufficient to accommodate
numerous charges and Qvoi is negligible, the only significant data are here the interface charge
density. For some intermediate thickness, the values of Q~~~ and Q~~ may be of the same magnitude j10~-1011 charges/cm2) and clearly the above approximation does not apply.
An independent determination of Qvoi can be obtained through photo I (V measurements [7, Ii. This method, tested for thick oxides is supposed to have a sensitivity proportional to the oxide thickness. An analysis of its applicability to thin oxides is therefore necessary.
The purpose of this article is to examine quantitatively the usual C(V) and photo
J(V) methods of D~~, Q~t and Qvoi determination~ in the case of medium thickness oxides. In order to specify the notation used in this paper, we admit the following classification of
charges and traps
a) Interface states and traps are localized at the interface Si-Si02 and in the oxide very close to the interface. This zone~ about of nm thick~ is in equilibrium with the semiconductor
N° ii VOLUME AND INTERFACE TRAPS IN MOS CAPACITOR 2103
during measurements and can be charged and discharged rapidly according to the position of
the Fermi level in the gap. The charges of these zones are characterized by D~~(E) and
Qjt.
b) Oxide charge density~ Qvoi, is located in the remaining zone of the oxide. The oxide charge can be divided in two types Qvoi ~ Qf + Qot according to the origin of the charge. The first type~ the oxide fixed charge, Q~~ is the initial charge obtained just after the MOS realization. Oxide fixed charge may be unevenly distributed in the oxide, for instance
concentrated near the interfaces. The second type, oxide trap charge density Qot, is produced in the oxide by subsequent treatment ion implantation, injection of electrons or holes~ internal
photoemission by UV excitation or exposure to ionizing radiation. Qot is then connected to the variations of Q~~j without any hypothesis on the physical state of the traps.
The discussion below has been primarily developed in the aim of testing good quality MOS
capacitor grown on oxidized wafers. Most samples show nearly ideal but translated
C(V) curves. In these condition we try to select simple relations allowing to deduce the
interface trap and the volumic charge densities, from true quasistatic C(V) and photo
I(V) measurements, performed in constant temperature, thickness and doping conditions.
2. Determination of interface state density.
Volumic charge causes a rigid shift of the C(V) curve according to expression (I). In the
absence of a precise knowledge of 4~~ or Q~~~, the quasistatic C(V) experiment gives
D~~(E) curve via a differential method Ill, assuming one correspondence between points of the ideal and real curve is known (arrow in Fig. I). On the other hand the high/low frequency C (V method is independent of the above shift and gives reliable D~~ values, at least in the
central region of the gap.
We propose below an additional check of the interface charge value, from C (V quasistatic
measurements, which is also independent of volumic charges.
C/Cox
, '
"'~
~ i~
I /
i
(V)
~~
J o -i
aCC ~
Fig. I.-Theorical quasistatic C(V) curves showing the selected points: A: point for which
C
= C~, (accumulation side). I : point for which C C~~ (inversion side). Heavy line ideal curve
2 2
for a 15 nm thick oxide on n type silicon (N~ 6 x 10'~ cm~ ~) dotted lines curves for D,~ 2 x 10"
and 5 x IQ'' cm- ~ eV- ' The arrow indicates the shift (AV~. AC ) of the mid gap point MG induced by
the trap density.
USE OF THE SLOPES OF THE C (V cuRvE. This method gives the density D~~ for two energy values situated on each side of the gap, at special points defined in figure I as A and I A point for which C
= C~~/2 (accumulation side) I point for which C
= C~~/2 (inversion side).
The method is based on the measure of the slopes at A and I (Fig, I). Actually, it is easier to determine on the graphs the inverse relative slope
dV~
~
~ ~°~ W ~~~
This quantity depends on the density of interface traps D~~, as can be seen in figure I where
quasistatic C(V) curves are calculated with different constant D~~ values. The X values deduced by numerical derivation are reported in figure 2 for different capacitances. They show
a regular increase of X versus D~~ which allows a simple numerical or graphical determination of the density.
It should be mentioned that the results obtained by this method are sensitive to the oxide thickness, semiconductor doping and temperature, moreover the experimental slope X should be recorded in true quasistatic condition. As can be seen in figure 2, the X values increase with
D~~, thickness and doping. The above method apply then more easily on thin oxide
(L ~ 30 nm), on lightly doped materials (N~ or N~ ~ 10~~ cm~ ~) and for low interface state densities (D~~ ~ 10~~ cm~ ~).
Due to the generation time of inversion layer it is preferable to sweep the gate bias V~ from an equilibrium inversion state towards accumulation. Figure 3a show several curves
obtained in these conditions with a sweep rate of 10 mV/s.
On the other hand, the numerical analysis used in figure I gives also the $r~ values
corresponding to points A and I. Then the differential Berglund method has two D~~($r~) values which can serve as initial condition in calculating the D~~(E) as reported in
figure 3b. This method applies only when D~~ varies smoothly with energy E.
~~~
30 /m /
°.8
20
/ 0.8
/~
°~~
o,6 /
lE14 lE16 lE15
o~
lE16
°'~o 5 lo '~o
II II 2 Fig. 2. Inverse relative slope X
=
~~
of the quasistatic C IV curves at the point A or I for
C~~ dV~ '
selected MOS capacitances (-) different oxide thickness for N~
=
I x IQ'~ cm- ~ (---) different doping in cm-3 for L
=
15 nm.
N° II VOLUME AND INTERFACE TRAPS IN MOS CAPACITOR 2105
c/cox
Exposure
Time
oh 0.5
lh 2h 4h
Vg v )
o.5 o -o.5 -1
~~
D~~ charges /cm~ev
4h
, /
4~1° 1[, ,1'
,
2h
i~~,_,_.I'(,,[$"
~~ ~ h
~~.ZZ.7.T.00°~."" 0h
~
-0.5 0 0.5
~ Energy (eV) '~ ~~
Fig. 3. a) Experimental set of C (V curves obtained before and after UV irradiation (A = 249 nm, times in hours), on a 15 nm MOS capacitance with semitransparent gate. b) Interface trap density deduced from Berglund method. The initial points are A and I, on each side of the calculated segment.
3. Determination of volumic charge density Q~~.
Equation (I) shows that the absolute value of V~ depends both on Qeff and Q~~. Even when the number D~~ of interface states is known from C (V) experiments, the determination of the volumic charge Qeff is difficult as we generally ignore the sign of the interface charges
Q~~ [12].
If we note as 6V~ the shift of the C (V curve relative to the ideal case we get
Qeff" ~Cm 6VG~Qa. (3)
Possible variation (during treatment) of the volume charges AQ~~~ by trapping or detrapping can'neither be determined, as we do not know the change AQ~~.
We will give below an estimation of the effect of the unknown sign of interface states in the
case of two well-known methods.
3.I QUASISTATIC C (V) EXPERIMENTS. If there is a distribution of donor and acceptor interface states~ in the gap, the interface charge results from the two densities (D(~ and
D$) and expressed at 0 K as :
4~ E~/2
Q,t(#s = q D( dE + q D( dE
E~/2
j~
where 4~ is the surface potential measured from the mid-gap at the silicon surface
(~bs " $is ~ (EF E~)/q).
If we consider the extreme case where interface state density is constant and composed of only acceptor or donor states, we obtain
qD(~(4~ + E/2 ~ Q~~ ~ qD$(E~/2 4~ (4)
As surface potential for non degenerate surface lies inside the gap E~--~ 4~~
2 E~
,
the uncertainty on Qeff determination is 2
hoeff
~ QR ~ ~~R ~g (5)
The expression used in the HF or LF experiments and neglecting Q,t may then be erroneous by
the above quantity. A slightly better approximation of Q~~~ can be obtained by considering the
displacement of the mid point M between A and I. The shift of M involves the mean value between Qn values at A and I.
By averaging the Q~t values between the A and I bias, the possible error in Qeff is given by :
AQ~~~ =
Qi +
Ql~i (6)
It is difficult in the general case to estimate how much the above value is reduced relative to
(5), but it is certainly lower than (Q( or Q)~(.
In summary, Qeff cannot be measured exactly in presence of variable interface charges. The best approximation is obtained by the shift of the center (M point) of the quasistatic
C (V curve. The measure of the CJJ~(V shifts, as usual for thick oxides [2, 13], would lead to
less accurate results.
The determination of initial charge Qf I/L is also Qit dependent, but as the initial values of interface traps are generally weak for undamaged structures (w 10' ' cm~ ~ Q~ can be obtained with a better precision than Q~~.
3.2 COMBINED EXPLOITATION OF C (V AND PHOTO I(V cuRvEs. We discuss here, the
Krawczyk [14] method, when interface charges are present. The method consists in comparing
the value of the polarization which cancels the photocurrent (V~)1
~ and the flat-band voltage (~G)FB.
(VG)i
o ~ #m~ + (4i~)1=o (~G)FB " ~bms ) [Qeff
~ (Q,t)FBI
ox
the useful experimental quantity is here
~ ~~G)1=
0 (~G~B ($i~)I
0 ~ ) [Qeff
~ (QR)FBI
ox
For1
= 0, the field through the oxide is very small. Then assuming the mean field to be zero, the electrostatic equilibrium can be expressed as :
(Q,t)1
0 ~ Qetf ~ (Qsc)1
0 "
o (~)
N° II VOLUME AND INTERFACE TRAPS IN MOS CAPACITOR 2107
To get (V~)1
~ we must take into account the equilibrium equation of MOS structures under illumination. Because radiation creates a large number of electron-hole pairs, n
= p » n,, the
equilibrium equation reduces to
Qsc(~is)
= =
) ~
(8)
where p
=
~ and L~ is the extrinsic Debye length.
kT
As $r~ is slowly variable as function of Qsc in the 10" charges/cm~ range, we obtain in
combining (7) and (8)
( 4~s)/
0 "
) A~g Ch 1
~ Qeff ~ j
(9) Qeff ~ IA (4~s)1=01Cox (Q,t)FB
~
(io)
a system of two equations easily solved by applying successively the two equations. As seen in relation (10), this method has the same inaccuracy as the previous method using the quasistatic
C (V ), due to the same unknown Q,t term. The only advantage of this method is that we do not compare C (V) with the ideal case and it gives also 4~~.
Typical application on n and p type samples are reported in table1.
Table I. -Application of the Krawczyk method for two MOS capacitances with N~ or
N~ = I x 10~~ cm~~, thickness 15 nm. D~~ at midgap is of the order of
I x 10~~ charges/cm~.eV as deduced fi.om C(V) measurements.
Type (VG)i
o (VG)FB ~~~~ ~ ~~'~~~~
~4'S~I ° ~
m'
q
p initial 0.28 0.70 + 3.8 x 1011 0.15 0.43
p irradiated 0.25 0.44 + 1.3 x 1011 0.10 0.35
n initial + 0.09 0.15 + 1.8 x 1011 0.ll 0.02
n irradiated + 0,12 0.10 + 1.6 x 1011 0.ll + 0.01
V V charges/cm2 V V
4. Determination of Q~~ from photo I( V) measurements.
The oxide trap charge density Qot can be determined indenpendently by the measurement of the
translation or deformation of photo-I(V) curves. Commonly, the oxide charge and its
barycenter is deduced from the shift AV~ of the photo I(V) curves [7, 1, 2] (Fig. 4a) by : Q4
"
C
ox
(AVt AVi (I')
y = lAVj j-' (12)
~ ~~(
a) ~ /
vc /~v~-
I(pA)
hv
= 4.88 eV
b)
loo
v~(v)
-i o i
Fig. 4.-a) The effect of charge capture in oxide on photo I(V) curves after Di Maria [7].
b) Experimental I(V) for a 15 nm oxide MOS structure. (-) before exposure to U-V- radiation (-.-) after exposure to U-V- radiation.
These formula were demonstrated to be valid for thick oxides when interface states could be
neglected. The examination of photo I (V) experimental results for 15 nm MOS capacitance (Fig. 4b) reveals curves very different from those in figure 4a. We observe, in particular, a large slope at the origin.
This leads us to re~examine the theoretical model of photoinjection in the case of thin oxides (10 to 30nm) and when interface and volume density of traps are of the same order of
magnitude. The basic expression of photocurrent [2] is
q2 P x~
I
=
A (h v h
v E~~ + q(V (x~) V (0)) + 16 exp ~ (13)
" Em Xm
where x~ is the position of the maximum of the barrier and f the mean free path of carriers. To compute this expression, we solved in parallel the electrostatic equation of MOS capacitance
to obtain V(x) and x~ without approximation.
Figures 5 and 6 display the results of I(V simulations for a MOS capacitance having 15 nm
oxide thickness, in the case of a uniform distribution of charges in the oxide and at the interface. The form of these curves are very different from those observed for thick oxides. The shifts AV] and AVj are small and :
N° II VOLUME AND INTERFACE TRAPS IN MOS CAPACITOR 2109
(PA)
12
-10
ii
-IQ
~~
II
ii
5.io
12
10
Fig. 5.- Theoretical photo-I(V) curve for a MOS structure (lsnm oxide on nsi(100) with
N~
= 6 x 101~ cm- ~). The parameters needed in expression (13) are : hv E~
= 0.8 eV, p
= 2,
f
=
4 nm. The set of curves were computed assuming an uniform charge distribution within the oxide,
units in charges/cm2. The curves are different for large V~ according to expression (11).
1 (pA)
-1/~ 100
11 -2.10
° v~(vj
-1
12
10
11
-100 ~'~°
Fig. 6. -Theoretical photo I(V) curve for the same MOS structure as in figure 5 with the same parameters, but in the presence of donor type (positive charges) on acceptor type (negative charges) at the interface oxide-silicon. A uniform trap distribution is assumed in the gap, units in charges/cm~. eV. The
curves tend towards the same limit for large V~.
I) there are two dissymetrical bends near the center of the I(V) curve. In this zone, the variation of V~ relates essentially with the variation of $r~. In the region near the origin (-1.5 ~ V~~1.5V), the photo I(V) curves depend on the oxide charge and on the interracial charge in a complex manner.
ii) On both sides of the curve, the values of $r~ saturate and the variations of
