Variable angle spectroscopic ellipsometry (VASE) has been used to characterize Si(x)Ge(1-x)/Ge superlattices (SLs) grown on Ge substrates and thick Si(x)Ge(1-x)/Ge heterostructures grown on Si substrates. Our VASE analysis yielded the thicknesses and alloy compositions of all layers within the optical penetration depth of the surface. In addition, strain effects were observed in the VASE results for layers under both compressive and tensile strain. Results for the SL structures were found to be in close agreement with high resolution x-ray diffraction measurements made on the same samples. The VASE analysis has been upgraded to characterize linearly graded Si(x)Ge(1-x) buffer layers. The algorithm has been used to determine the total thickness of the buffer layer along with the start and end alloy composition by breaking the total thickness into many (typically more than 20) equal layers. Our ellipsometric results for 1 (mu)m buffer layers graded in the ranges 0.7 less than or = x less than or = 1.0, and 0.5 less than or = x less than or = 1.0 are presented, and compare favorably with the nominal values

Alterovitz, S. A.

Croke, E. T.

Heyd, A. R.

Lee, C. H.

Wang, K. L.

English

NASA Technical Reports Server

NASA-TM-111685
L¸
Characterization of SiGe/Ge Heterostructures and Graded Layers
Using Variable Angle Spectroscopic Ellipsometry
A. R, Heyd* and S. A. Alterovitz
NASA Lewis Research Center, 21000 Brook'park Road, MS 54-5, Cleveland, Ohio 44135
E. T. Croke
Hughes Research Laboratories, Malibu, California 90265
K. L. Wang and C. H. Lee
University of California, Los Angeles, California 99024
Variable angle spectroscopic ellipeometry (VASE) has been used to characterize SixGel-z/Ge superlattices (SLe) grown
on Ge substrates and thick SixGel_x/Ge heterostructures grown on Si substrates. Our VASE analysis yielded the thicknesses
and alloy compositions of all layers within the optical penetration depth of the surface. In addition, strain effects were
observed in the VASE results for layers under both compressive and tensile strain. Results for the SL structures were found
to be in close agreement with high re_lutlon x-ray diffraction measurements made on the same samples.
The VASE analysis has been upgraded to characterize linearly graded SixGel-z buffer layers. The algorithm has been
used to determine the total thickness of the buffer layer along with the start and end alloy composition by breaking the
total thickness into many (typically > 20) equal layers. Our ellipsometric results for 1/_m buffer layers graded in the ranges
0.7 < x < 1.0 and 0.5 < x < 1.0 are presented, and compare favorably with the nominal values.
INTRODUCTION
Characterization of semiconductor superlattice (SL)
structures is typically done by x-ray diffraction (XRD)
and transmission electron microscopy (TEM). Both
XRD and TEM can be used to quantify SL ordering
and periodicity. In addition, XRD can give the average
value of the composition. Both techniques have lim-
itations; TEM is destructive, XRD requires relatively
thick samples (,-,1000 A), and neither technique can
be used to quantify individual interfaces or quantum
wells. Recently, variable angle spectroscopic ellipsom-
etry (VASE) has been shown to be a powerful, non-
destructive technique for the post-deposition character-
ization of SixGel-x/Si SLs and other multilayer het-
erostructures [1,2]. In these studies VASE has been used
to determine layer thicknesses, alloy composition, oxide
thickness, number of superlattice periods, and sample
homogeneity. In this current work we will concentrate
on Ge rich Si=Gel_x/Ge SLs and heterostructures.
Graded composition SixGel_= layers are used in
the base of SixGel__/Si heterojunction bipolar tran-
sistors to increase device speed. Graded composition
Si=Gel__ layers (graded to achieve x _ 0.3) are also
*This work was performed while the author held a National
Research Council-NASA Research Associateshlp.
used as buffers to relieve strain in the growth of n-type
SixGel-x/Si modulation doped field effect transistors
(MODFET) structures. In previous VASE analysis of
MODFETs, only the high energy portion of the ellip-
sometric spectra was used. Thus, a graded composi-
tion layer analysis was avoided, since the graded layer
was buried below the optical penetration depth of the
probing light at these energies. In this work a simple
algorithm for the calculation of the Fresnel reflection co-
efficients of a linearly graded SizGel__ layer has been
developed. This allowed a graded SizGel_x layer to be
characterized in terms of its thickness, and Si content
at the substrate and ambient surfaces.
BACKGROUND
To determine the properties of multilayer struc-
tures the measured ellipsometric angles, {tan kO(_),
cos A()_)}, must be compared to results calculated from
well defined models. Linear regression analysis (LRA)
is used to minimize the unbiased estimator, a:
a2 - 1 _ {(tan _ _ tan _c) 2
n-m--1
i= 1
+ (cosA_-cosAf) 2} (1)
© 1996 American Inslitute of Physics
428
https://ntrs.nasa.gov/search.jsp?R=19960038261 2020-06-16T04:27:25+00:00Z
3.5
3.0
2.5
2.0
0 20 40 60 80 100
x (%)
Figure 1:E1 (long dash) and E1 + A1 (short dash) critical point
energies for relaxed and strained Si=Gel_ = layers. The relaxed
curves (Ref. 6) are shown as solid lines. The strain induced split-
ting (dashed lines) was calculated using Eqs. 2 and 3. For z > 0.5
the substrate is Si and the strain is compressive, and for z < 0.5
the substrate is Ge and the strain is tensile.
where n is the number of observed data points and m is
the number of free parameters used in the model. The
superscripts e and c refer to the experimentally observed
data and the corresponding results calculated by the
model, respectively. In order to construct a model, the
dielectric function of all the constituent materials must
be known. The dielectric function of composite lay-
ers can be determined using effective medium approxi-
mations (EMAs) [3]. The energy shift algorithm [4] is
used to interpolate between SixGel_x dielectric func-
tions published at discrete alloy compositions [5]. The
algorithm requires a knowledge of the functional depen-
dence of the critical point (CP) energies with the alloy
composition, usually the Eo(x), Et(x), and E2(x) CP
energies. To improve the analysis of Ge rich Si_Gel_x
materials the energy shift algorithm has been modified
to include the effects of the E1 + Al CP energy [6].
Fig. 1 shows the EI and E1 + A1 CP energies for
strained and relaxed SixGel-x layers. The in-plane
strain, c, in the strained SixGel__ layer results from
the lattice mismatch between the layer and the sub-
strate. The shifts in the El and E1 + A1 CP energies
for a biaxial (001) strain are given by [7]:
AE1- +AI 1 (A12 +4E_)1/2
- + E. - (2)
-A1 1
A(EI+A,)=T+EH+_(A2+4E2s)I/2 (3)
where the hydrostatic shift, EH, and uniaxiai shear, Es,
are given by:
EH = 2_¢1(1 -C12/Cll)e (4)
Es = (2/3) 1/2 D_3 (1 + 2Ct2/Ctl)e (5)
Table I: Comparison of target sample structure with that deter-
mined by HRXRD and VASE. The period is the sum of the Ge
and SIGe layer thicknesses, and z(avg) is the average silicon con-
tent in one period. The parameters of the VASE analysis are the
oxide, Ge and SiGe layer thicknesses, and the silicon content, z,
of the SIGe layer.
Sample Source Period x(avg) d(Ge) d(SiGe) z
(A) (%) (A) (A) (%)
HA57 target 178 6.2a 128 50 22.0
HA57 HRXRD 201.1 8.0 141.8 b 59.3 b 26.6 b
HA57 VASE ¢ 202.8 8.41 127.5 75.3 22.7
4-3.9 4-3.5 +1.6
HA58 target 201 7.8 _ 142 59 26.6
HA58 HRXRD 202.1 8.3 141.8 b 60.3 b 27.5 b
HA58 VASE d 204.5 8.4 a 126.9 77.6 22.1
4-4.7 4-4.4 4-2.0
aCalculatedfrom d(Ge),d(SiGe),and x.
bEstimated from the period,x(avg),and shutteropening/
closingtimes.
ca = 0.0137,d(oxide)= 17.9A + 0.4A.
da = 0.0167,d(oxide)= 25.5A 4-0.6A.
C O. are the elastic stiffness constants, £1 is the hydro-
static deformation potential, and D 3 is an intraband de-
formation potential for the A3 valence band for a [001]
uniaxial strain. The energy shift algorithm assumes the
functional dependence of the relaxed E1 and El + A1
CP energies shown in Fig. 1. Therefore, when modeling
strained SixGel__ layers the strain induced shifts in the
El and E1 + At will cause the value of the Si content,
x, to be over- or under-estimated for a compressive or
tensile strain, respectively.
SiGe/Ge SUPERLATTICE STRUCTURES
ON Ge SUBSTRATES
Two fifty period SixGel__/Ge SL structures, HA57
and HA58, were grown by Si molecular beam epitaxy
(MBE) on Ge (100) substrates at Hughes Research Lab-
oratories. The samples were first characterized by high
resolution x-ray diffraction (HRXRD) [8], the results
are shown in Table I along with the target structures.
Each sample was then measured by VASE at several
angles of incidence (69 °, 73 °, and 77 °) which were cho-
sen to increase the sensitivity of the ellipsometric angles
to the sample structure parameters [9]. The measured
{tan _, cos A} spectra for sample HA57 are shown in
Fig. 2 along with the spectra generated from the best fit
model. Due to the strong absorption in the low wave-
length region, discrepancies between the measured and
calculated spectra in this region are a result of devia-
429
0.6
0.4
0.2
0
0.0 I- .... ' .... i .... i .... i',,I -'I°
-0.4 . _ --a---77 ° |
-0.8
-1.0
300 400 500 600 700 800
Wavelength (nm)
Figure 2: Comparison of measured VASE data (symbols) with
that determined from the best fit model (lines) for the SizCrel-=/
Ge SL sample HA57. Sample HA58 shows similar fitting. The
structure parameters found from the best fit model are shown in
Table I.
tions in the model that occur near the surface. Simi-
larly, discrepancies in the fitting in the long wavelength
region are most likely due to problems in the model
which occur deeper in the structure. In this case the
model assmnes that each period of the SL is identical.
Some slight oscillations can be seen in the long wave-
length region of the cos A spectra which are not repro-
duced by the model. This indicates that the periods
of the sample are not identical and that the thickness
and/or x(avg) of each period may be fluctuating about
some average value.
The agreement between the HRXRD and VASE re-
suits is quite good, especially when comparing the pe-
riod and x(avg). There is, however, a substantial dif-
ference between the individual layer thicknesses and x.
The SixGel_x layer is under a tensile strain as a result of
being sandwiched between the thicker Ge layers. This
tensile strain accounts for the lower x value obtained
by VASE. The differences in the layer thicknesses may
be a result of interracial layers which are not currently
accounted for in the model.
Nominal VASE
Oxide Six Gel_ x (49%) 36.5
+6.5A
GeO (51% + 11%)
200A Si0.3Geo. 7 SixGel_x 206.1 ,/_
+ lo.IA
x = 29.9% ± 0.8%
40A Ge Ge 34.1A
± 10.7 A
1 _tm Stepped SiyGel.y Substrate
SiGe
Buffer Y = 25.1% ± 5.2%
c = 0.0284
Si S ubstrate
Figure 3: Structure of sample CL141 showing the target structure
parameters and those determined from the VASE analysis.
SiGe/Ge HETEROSTRUCTURES
ON Si SUBSTRATES
Two Si_Gel_x/Ge heterostructures, CL141 and
CL171, were grown on Si substrates at the University
of California at Los Angeles. The nominal structures
for sample CL141 and CL171 are shown in Fig. 3 and
Fig. 4, respectively. The Si content of the stepp_t
buffer was changed from 100% to 20% or 30% in ap-
proximate steps of 25%. Therefore, it would require six
parameters to completely characterize the buffer layer.
Characterization of the buffer layer is further compli-
cated by the fact that it is buried deep in the structure.
As a result sample CL141 was modeled over the range
300 nm to 550 nm to ensure that the top step of the
buffer would act as the substrate. Over this range the
maximum penetration depth is -_1000 A and _200 /_
in Si0.3Ge0.r and Ge, respectively. The oxide has been
modeled as a mixture of Si_Gel__ (x same as in under-
lying layer) and GeO2 using the Bruggeman EMA; this
mixture simulates a surface roughness. The surface of
these samples is expected to be rough due to the large
lattice mismatch between the Ge layer and the under-
lying Si substrate (_4%). The VASE results, shown in
Fig. 3, agree with in the 90% confidence limits with the
nominal structure.
The second sample, CL171, was modeled over the
spectral range 300 nm to 760 nm. Over this range
the SixGel_z layer will act as the substrate due to the
increased thicknesses of both the Ce and SiCe layers
The measured VASE data is shown in Fig. 5 along with
spectra generated from the best fit model; the resulting
structure parameters are shown in Fig. 4. Modeling the
430
Nominal VASE
Oxide
10o0A Ge
Ge (38%)/
GeO:] (62% _+ 9%)
SiyGq_y
y = 5.8% + 0.3%
1200A Si0.2Ge 0. 8
1 lxm Stepped
SiGe
Buffer
SixGel_x Substrate
x = 16.5% :t: 1.5%
a = 0.0269
Si S ubstrate
Table II: Results of VASE analysis of graded SizGel-x layers on
Si substrates. The nomimal thickness of all samples is 1 pra. The
samples were linearly graded from 100% Sl at the substrate to
xn(nom) at the surface. The parameters of the VASE analysis
are the oxide thickness, buffer layer thickness (D), and the Si
content at the surface (Xn). The SI content at the substrate was
held constant at 100%. A value of n = 30 was used to model all
three samples.
Sample a d(oxide) D xn x, (nom)
(A) (pm) (%) (%)
HA82 0.0522 44.8 + 0.9 1.04 4- 0.04 76.7 4- 0.6 70
HA83 0.0524 59.3 4- 1.1 1.02 4- 0.03 66.7 + 0.6 50
HA17 0.0202 43.0 4- 0.4 0.97 4- 0.01 58.7 4- 0.3 50
Figure 4: Structure of sample CL171 showing the target structure
parameters and those determined from the VASE analysis.
0.6
0.4
0.2
0.0
1.0
0.5
''''1''''1''''1'''' ''''
70 °
-- _ - 75 °
_ . _ - _ 78 °
3_ 4_ 5_ 600 7_ 8_
Waveleng_(nm)
Figure 5: Comparison of measured VASE data (symbok) with
that generated from the best fit model (lines) for the thick
SlffiGel-z/Ge heteroatructure sample CL171. The beat fit model
is shown in Fig. 4 along with the resulting values of the _¢_ructure
parameters.
Ge layer as SixGel-x resulted in a _25% decrease in
a. Since the Si content of this layer should in fact be
0%_ the value of 5.8% can be attributed to a compres-
sive strain which results in an over-estimate of the Si
content.
SiGe GRADED LAYERS
Three continuously, linearly graded Si_Gel_x layers
were grown by Si MBE on Si (100) substrates at Hughes
Research Laboratories; the nominal structures are de-
scribed in Table II. Graded layers are simulated in the
VASE model by breaking the layer in to n+ 1 sub layers.
The thickness of the i-th sub layer is:
D/2n i=O,n (6)di = Di l <_ i < n
where D is the total layer thickness. For a linearly
graded layer the Si content of the i-th layer is given by:
(n - i)xo + ix,,
x, = (7)
n
where x0 and xn are the Si content at the substrate
and surface, respectively. As n --* oo this model will
more closely approximate a continuously graded layer.
However, values of n > 20 were found to yield nearly
identical results in the VASE analysis for the graded
samples used in this study.
The graded samples were measured by VASE at
three angles of incidence: 70 °, 75 °, and 77 °. Fig. 6
shows the experimental data for sample HA17 along
with the ellipsometric angles generated from the best
fit model. The fitting is nearly perfect in the cos A
speotrum and in the long wavelength region of the tan _P
spectrum. The poor fitting in the low wavelength region
of the tan _P spectrum is most likely due to poor surface
431
0.6
0.4
0.2
0.0
300 400 500 600 700 800
Wavelength (rim)
Figure 6: Comparison of measured {tan ko, cosA} spectra (sym-
bole) for the graded SizGel_z sample HAl7 with that determined
from the best fit model (lines). The structure parameters deter-
mined from the model are shown in Table II.
quality. Because the graded layers are uncapped, the
surface region of the graded layers are expected to be
strained which can cause the surface to become rough.
Table II summarizes the results of the VASE analysis.
It can be seen from this table that the thickness values
are very close to the nominal values. The values for
the Si content at the surface (xn), however, are con-
sistently much higher than the nominal values. These
discrepancies can be caused by the compressive strain
in the surface region of the layer which would result in
an overestimate of x. The growth log notes that the
surface morphology of sample HA83 is poor when com-
pared with sample HA82. This may be the cause of the
larger discrepancy in xn for sample HA83.
CONCLUSIONS
VASE has been used to characterize SixGel__/Ge
SL structures grown on Ge substrates. The values of
the period and x(avg) determined by VASE show excel-
lent agreement with those same values determined by
HRXRD. Due to strain effects or interfacial layers not
accounted for in the VASE models, the individual layer
thicknesses and x determined by the two methods do
not agree as closely. Thick SixGel__/Ge heterostruc-
tures grown on Si substrates have also been character-
ized by VASE. Results show close agreement with the
nominal structure. In addition VASE analysis provides
a qualitative assessment of the surface roughness and
strain in the various layers of the structures. Finally,
VASE has been used to characterize continuously, lin-
early graded SixGel__ layers in terms of the layer thick-
ness and Si content at the surfaces. Results agree ex-
tremely well with the target structure, especially when
strain in the surface region of these uncaped graded lay-
ers is taken in to account.
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Characterization of SiGe/Ge heterostructures and graded layers using variable angle spectroscopic ellipsometry

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