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Broad band spectroscopic ellipsometry for the characterization of photovoltaic materials
Solar Cells, 30 (1991) 473-485
473
Broad band spectroscopic ellipsometry for the characterization of photovoltaic materials F. A. A b o u - E l f o t o u h , G. S. Horner, T. J. C o u t t s and M. W. W a n l a s s Solar Energy Research Institute, 1517 Cole Bd., Golden, CO 80401 (U.S.A.)
(Received October 25, 1990)
Abstract The availability of commercial spectroscopic ellipsometers (SE) has been restricted to the UV-visible range from 250-900 nm. Although this is useful for many applications, it must be extended to the near IR region (up to 1700 nm) for the study of the optical behavior of most photovoltaic materials. This paper discusses the development of a broad band (300-1700 nm) SE which has been used to measure the optical characteristics of various materials. Among these are the polycrystalline thin film materials, CuInSe2 and CdTe (for which single crystal samples have also been investigated), and materials for high efficiency cascade solar cells including InP, InGaAs and InGaAsP. Most of these data are not presently available over such a wide spectral range. Experimentally, a rotating polarizer-fixed analyzer ellipsometer with an a.c. detection system has been developed for accurate measurement of $ and A, the relevant eliipsometric parameters, in the near IR. This approach has certain advantages over the rotating analyzer-fixed polarizer systems including reduced sensitivity to room light. The analytical methods include the use of a specially developed computer modeling program which gives $ and A for a given set of values related to the film thickness (which may be finite or zero) and to the optical properties of the substrate.
1. I n t r o d u c t i o n N o n - d e s t r u c t i v e analytical t e c h n i q u e s to m o n i t o r the t h i c k n e s s a n d c o m p o s i t i o n of individual layers in multilayer devices are an i n c r e a s i n g r e q u i r e m e n t for the f a b r i c a t i o n o f w e l l - e n g i n e e r e d o p t o e l e c t r o n i c devices. The optical p r o p e r t i e s o f the materials involved in s u c h devices c a n be d e t e r m i n e d a c c u r a t e l y using s p e c t r o s c o p i c e l l i p s o m e t r y b y m e a s u r i n g the ratio of c o m p l e x r e f l e c t a n c e s of the s- a n d p - p o l a r i z e d light. Since the state of polarization o f light reflected f r o m a s u r f a c e is sensitive to surface irregularities o n a m i c r o s c o p i c scale, a n d to the p r e s e n c e o f native c o m p o u n d s , this t e c h n i q u e is v e r y valuable for the d e t e r m i n a t i o n of s u r f a c e a n d interface properties. P r o p e r u n d e r s t a n d i n g a n d m o d e l i n g of solar cell p e r f o r m a n c e is i m p o s s i b l e w i t h o u t a t h o r o u g h k n o w l e d g e o f the f u n d a m e n t a l optical p r o p e r t i e s o f the materials involved in the device c o n s t r u c t i o n as a f u n c t i o n o f their c o m p o s i t i o n , s t r u c t u r e a n d f a b r i c a t i o n p a r a m e t e r s . Local c h a n g e s in p r o p e r t i e s due to interfacial effects m a y also be vitally i m p o r t a n t . T h e s e m a y all be m o n i t o r e d using p r e c i s e m e a s u r e m e n t s of the optical c o n s t a n t s N a n d k (the real a n d
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474 imaginary parts of the refractive index) that determine the extent to which incident light is absorbed and reflected. The availability of commercial spectroscopic ellipsometers (SE) has been restricted to the UV-visible range from 2 5 0 - 9 0 0 nm. Although this is useful for many applications, it must be extended to the near infrared (NIR) region (up to 700 nm) for the study of the optical behavior of certain types of materials and structures. A typical application is to low bandgap materials and solar cells, the spectral responses of which extend into the NIR region of the spectrum. For these, it is required to evaluate the interband electron contribution to the dielectric function in the lower energy part of the spectrum. In addition, a detailed description of optical effects and band edge transmission of optical systems consisting of some metals, semimetals and silicides is only possible if ellipsometric measurements are made at wavelengths greater than 850 nm. Because of the dependence of optical penetration depth on wavelength, the SE is capable of performing high resolution, non-destructive depth profiling on multilayer devices to obtain structural information on each layer, whether crystalline or amorphous. Information on the layer thicknesses, possible existence of a native oxide layer, microroughness and porosity may also be obtained. This, together with the wavelength dependence of the optical constants over a broad range of wavelengths, is crucial for the design and optimization of several optoelectronic devices, including solar cells. In this paper, the capability of an SE, developed at SERI to monitor the optical characteristics of various materials and structures, is demonstrated. The materials include the polycrystalline thin film materials, CuInSe2 and CdTe (for which single crystal samples have also been investigated), and materials for high efficiency cascade solar cells including InP, InGaAs and InGaAsP. Data for most of these are not presently available. The data are necessary for: (a) modeling of solar cell performance, (b) design of antireflection coatings, (c) control over the device fabrication process and surface oxidation, (d) quality assessment of the material produced in-house and by SERI subcontractors.
2. D e s i g n f e a t u r e s o f t h e SE
The design is based on a stepper-motor-controlled polarizer, fixed analyzer ellipsometer and this configuration exhibits several advantages over rotating analyzer systems (Fig. 1). In particular, the position of the monochromator reduces sensitivity to room light, the system is mechanically stable and the computer interface makes efficient use of readily available high speed analogto-digital (A/D) microcomputer boards. It operates in an a.c. mode using a light chopper to improve the signal-to-noise ratio in the NIR. The light from a 100 W tungsten halogen lamp is polarized by a rotating prism after first being collimated. After reflection from the sample surface (and the associated changes in amplitude and phase), the polarized beam is directed to the fixed analyzer, and then to the monochromator. The monochromator uses three
475 Broadband light source. Beam collimation / reduction optics JlIL~ ~ J ~ " ~ j Light chopper " ~ / Computer controlled polarizer plate v"~tl / with optical encoder.
1/4 m computercontrolled monochromator
I
Lock-in Amp. I
I
-I m
PMT gain controller PMT signal amplifier PMT high volt. source Analog//O Digital I/0
Computer Electronic interface box
Fig. 1. Schematic diagram of the SE. separate gratings (blazed at 250, 600 and 1000 nm) to maintain high throughput over the entire wavelength operating range. The polarizer assembly consists of a hollow shaft carrying the analyzer prism mounted in a singie-race, sealed ball-bearing shaft, which in turn is mounted in the analyzer/motor housing assembly. The rotating prism assembly is driven with a small flexible chain by a high resolution stepper motor (12 800 steps per revolution). This allows precise positioning of the polarizer plate via an RS232 interface for integrated measurements. An optical encoder provides an 'absolute' position reference (i.e. one that will not drift) for the polarizer positioning system. In its present configuration, the system is able to collect and average 24 000 data points at each wavelength, perform a Fourier analysis on the resulting intensity curves, and present real-time plots in less than 20 s. The Fourier coefficients are then used to calculate the standard ellipsometric parameters 0 and A. 3. S o f t w a r e The information from an ellipsometric measurement at a given wavelength and angle of incidence is the complex reflectance ratio r, which is often expressed by the differential amplitude ratio tan ~ and the differential phase shift A. Contained in these parameters is all of the available information regarding surface interactions and the optical properties of layers within the sample, r is defined as: rffi rp - - = t a n ~#e~ rs
(1)
476 where
IrplZ = (I~i) =Rpandlr~12 = (~i) =Rs p
s
F o r practical use o f this technique, it was n e c e s s a r y to develop software for data collection, r e d u c t i o n and modeling. A b r i e f outline of the data acquisition software is given below.
3.1. Data acquisition software The SERI SE has b e e n designed for use in the rotating polarizer configuration. This t y p e of SE exhibits low sensitivity to r o o m light, but a u t o m a t i c b a c k g r o u n d s u b t r a c t i o n has b e e n i m p l e m e n t e d to e n h a n c e the m e a s u r e m e n t accuracy. A m e a s u r e m e n t at one w a v e l e n g t h m a y be b e t w e e n 20 and 30 s, one half of which is d e v o t e d to b a c k g r o u n d and dark c u r r e n t collection. Data are a c q u i r e d with p h o t o m u l t i p l i e r t u b e (PMT) in the r a n g e 3 0 0 - 8 0 0 nm, and a liquid-nitrogen-cooled g e r m a n i u m d e t e c t o r is u s e d b e t w e e n 800 and 1700 nm. Sixty reflected intensity m e a s u r e m e n t s are m a d e during o n e revolution of the polarizer. The quantities P and A are defined as the polarizer and analyzer angles with r e s p e c t to the plane of incidence. The f o r m o f the resultant intensity curve (after b a c k g r o u n d s u b t r a c t i o n ) in a rotating polarizer s y s t e m is [ 1 ]: Icc a c o s ( 2 P ) + b sin(2P) = c
(2)
The coefficients a, b and c are calculated with a F o u r i e r series least-squares routine. T h e s e p a r a m e t e r s allow solution for functions o f the eUipsometric p a r a m e t e r s 0 and A (defined in eqn. (1)):
,
/(c+a)
tan ~ = V ~
b cos A = - -
tan A
(3) (4)
The wavelength, 0, A, a, b, c and F o u r i e r fit variance are s t o r e d o n a h a r d disk for data reduction. Commercially available 12-bit A/D c o n v e r t e r s are u s e d to interface the d e t e c t i o n s y s t e m s to the c o m p u t e r . The T u r b o P a s c a l p r o g r a m m i n g language is u s e d to achieve 10 kHz sampling r a t e s for high s p e e d data averaging. The PMT gain is optimized at e a c h w a v e l e n g t h so that the full input r a n g e ( 0 - 1 0 V) of the c o m p u t e r A/D c o n v e r t e r s is utilized. This minimizes digitization effects o f low voltage signals. The light s o u r c e is c h o p p e d in the NIR, and the g e r m a n i u m d e t e c t o r signal is r o u t e d t h r o u g h a lock-in amplifier b e f o r e input to the c o m p u t e r . C o m m u n i c a t i o n s with the lock-in are i m p l e m e n t e d with a s t a n d a r d I E E E - 4 8 8 interface. R e m o t e control o f the sensitivity o f the
477 lock-in amplifier allows automatic signal size (again, near 10 V peak) optimization in the infrared. Real-time graphics have been developed to display current system settings, intensity and background curves, and the resultant Fourier fit. Separate graphs are continuously updated to display all of the relevant parameters (~b, A, a, b, c, etc.) as a function of wavelength. A larger variance in the Fourier fit or non-optimal gain settings trigger an automatic repeat of the measurement at any wavelength. 4. E l l i p s o m e t r i c m e a s u r e m e n t s
4.1. Optical constants of semiconductors In order to undertake adequate modeling, it is necessary to have a sound knowledge of the optical constants of the various materials involved in the solar cells to be studied. Typically, the properties of these materials depend upon the details of their fabrication, and whether they are in thin film form or they are single crystals. Whether transparent or in bulk form, correlation between the optical constants of the material is very important for an understanding of the material behavior and optimized device design. Figure 2 shows the optical constants of two single-crystal samples of CuInSe2 of different chemical compositions. N and k are used to calculate the absorption coefficients of the two samples and the data are shown in Fig. 3. These results are shown simply to illustrate the capability of the SE. A complete
Effective Optical Constants for Single Crystal CIS 3.0"
N (X1 2.5-
N (X2) 2.0'
1.5"
k (X2) 1.0.
k (Xl)
. . . . . . . . . . . . . . .
0.5"
0.0 200
4;0
600
800
1000
1200
Wavelength (nm) Fig. 2. Effective o p t i c a l c o n s t a n t s o f t w o C u I n S e 2 s i n g l e c r y s t a l s o f different c o m p o s i t i o n .
478
Single Crystal CIS Absorption Coefficients 0.5
"7 < E
04,
~9 <
,,..z 0.3.
.N ~
0.2"
O O ,~
<
0.1
0.0 300
|
!
i
!
500
700
g00
1100
1300
Wavelength (nm) Fig. 3. T h e a b s o r p t i o n coefficients o f t h e s a m e CuInSe2 s a m p l e s a s c a l c u l a t e d f r o m t h e m e a s u r e d optical c o n s t a n t s .
discussion of the data and correlation with other material properties will be given elsewhere [2]. The optical constants of copper-doped CdTe polycrystalline thin film has also been determined ellipsometrically (Fig. 4) and its absorption coefficient is calculated and shown in Fig. 5. The optical properties of Ino.~sGao.47As (i.e. lattice matched to InP), have been measured in the 3 5 0 - 1 6 5 0 nm wavelength range (Fig. 6), and the results are in excellent agreement with previous data published by Aspnes [3]. The optical constants of the quarternary semiconductor compound Gao.z~Ino.75Aso.54Po.46 are shown in Fig. 7. This composition has a bandgap of 0.95 eV and it is lattice matched to InP. This is the first time that these data have been obtained over such a wide spectral range but, in the visible, they agree well with the data of Aspnes [3]. The N and k values have been used to model the reflectance, and this is found to agree with the measured reflectance to within 2.5% (Fig. 8).
4.2. Modeling of short circuit current density One of the advantages of these measurements is that they can be used for the optimization of anti-reflection coatings (ARCs) and in the modeling of the quantity of light actually being transmitted into the absorber of solar cells, in order to maximize the current output Js¢. This depends upon the incident spectrum, external quantum efficiency, reflectance, and the thicknesses and optical constants of all materials in the cell. The current relation
479
Effective Optical Constants of Cu-doped CdTe Thin Film 6.0
2.5
N •.
7
.
.
.
.
.
.
.
5.5
--Z..
'5.0
2.0
'4.5
N
k ,4.0
1.5
~3.5
1.0 400
i
I
I
I
l
I
I
500
600
700
800
900
1000
1100
3.0 1200
Wavelength (nm) Fig. 4. Effective optical constants of copper-doped CdTe polycrystalline thin film.
is given by [4 ]: J~¢ _- e I~ I(A) × QEe~(A) x (1 - R'(A))dA (1 -R(A))
(5)
o
J~
short circuit current (A em -2) incident spectrum (photons nm -~ em -2 s - i ) h wavelength (nm) e electronic charge (A s) QE(A) external quantum efficiency (electrons per photon) R(A) cell reflectance before ARC application (dimensionless) R '(h) calculated cell reflectance for specific ARG geometry (dimensionless) Two-layer ARCs a r e often used on solar cells. Hence, J~c is a function of the thickness of both materials and its variation must be presented in a contour graph format. In this, the y-axis represents the thickness of the coating with the larger index (i.e. the ZnS) and the x-axis indicates the thickness of the lower index material (i.e. the MgF2). The data are represented in the form of curves of equal J,c and the maximum current, together with the thicknesses of the two materials may easily be determined. The N, k data for each layer in the structure are used in the calculation of R '(h). A 2 × 2 complex matrix method [5] has been implemented which calculates reflectance from an n-layer optical stack, given N and k of every layer, as a function of the angle of incidence and incident light polarization state. In this paper, normal incidence is assumed.
I(h)
480 Data from "E15 CdTe.crk"
| I []
[]
3 ¸
[] w [] w w []
[]
Alpha
m [] w
%
2-
l
1
•
200
i
•
!
400
-
600
i
!
800
1000
1200
Lambda
Fig. 5. The calculated absorption coefficient of the CdTe thin film. InGaAs 4.5 4
["\
N
3.53 /
_~2.5 f 1.5 ~k 0.5
~
. . . .
0
Wavelength (nm)
Fig. 6. The optical properties of Ino.5~Gao.47Aslattice matched to InP. Figure 9 s h o w s Jsc c o n t o u r plots for GaAs h o m o j u n c t i o n with a doublelayer MgF2/ZnS ARC. A n u c l e a t i n g layer of MgF2, 2 n m in t h i c k n e s s was used a n d this has b e e n included in the model; this layer is often d e p o s i t e d to e n h a n c e g r o w t h c h a r a c t e r i s t i c s o f ZnS on I I I - V c o m p o u n d s . Figure 10
481
InGaAsP
B
0
•
200
•
i
•
•
400
i
-
600
i
•
i
800
•
1000
.
i
•
1200
,
i
m
n
•
k
•
1400
1600
Lambda
Fig. 7. The optical constants of the quaternary compound Gao.25Ino.75ASo.54Po.4a.
Ga(0.25)l n(O.75)AS(O.54)P(0.46) 0.7 0.6
0.5
Elltpsometry / C a l c u l a t e d
n.zt
~
,
O.3
~
-
_/"
0.2
,
--""'I':"----
-
, ....
Measured O.t 0.0
3oo
J
5oo
i
7oo
,
to
9o0
~~ o
~3oo
Wavelength (nm) Fig. 8, The modeled and measured refleetanees of Gao.25Ino.75Aso.54Po.46 agree within 2.5%.
482
120
Global : MgF2 / ZnS / MgF2 (2 nm)/ GaAs
Jsc (mA/cmA2)
11028,5
10090E
8O-
U)
70-
28.25 28
27.75
= 60.L2 .c I- 50a 40-
27.5 27.25 27 26.75 26.5 MgF2 Thickness (rim)
Fig. 9. J,c contour plots for GaAs homojunction with a double-layer MgF2/ZnS ARC.
Global : M g F 2 / I T O / I n P
Jsc (mA/cm^2)
110-
28
100-
27.5
~- 9 0 -
¢.-
80-
27
70-
26.5
._o 60tI- Kn.
26 25.5 25 24.5 24 MgF 2 Thickness (rim)
Fig. 10. Jsc contour plots for ITO/InP cell with a MgF2 layer.
483
Global : Entech / MgF2 / ZnS / MgF2 (2nm) / GaAs
120-
Jsc (mNcmA2)
11028.5
100-
E
90-
28.25
8O-
28
¢n 70-
27.75
¢/)
c
60-
27.5
._o z: 50pN
27.25
40-
27
30-
26.75 26.5 26.25 M g F 2 T h i c k n e s s (nm) Fig. 11. The effect of a non-coherent cover on the Jsc contour plots for the GaAs homojunction.
Global : Entech / MgF2 / ITO/InP
Jsc (mNcm^2)
28
27.5 A
E
27
U) G) ¢.-
26.5
.to tF-
26 25.5 25 24.5
oooooo T¢~1 03
~
t43
ooo8ooo I~¢O O'J
24 ~--
04
03
MgF2 Thickness (nm) Fig. 12. The effect of a non-coherent cover on the J ~ contour plots of the ITO/InP cell.
484 shows a similar calculation for an indium tin oxide (ITO)/InP cell. In this case, the ITO acts .as one of the ARCs, while MgF2 is used as the top ARC. This particular application requires several approximations, since the ITO is an integral (conducting) part of the solar cell. It is assumed that the quantum efficiency is independent of ITO thickness (an assumption which will certainly fail for significantly thinner ITO). The results are, however, valid for a broad range of ITO thicknesses centered on 60 nm, since the external quantum efficiency and reflectance data (R(A)) were obtained from such a device. Recently, Entech prismatic covers have been used to enhance solar cell performance by diverting light from above grid fingers to active areas of the device. The geometric concentration effects have been studied in some detail [6], but the change in optimal ARC thicknesses due to application of such a cover has not been investigated. For concent rat or measurements, the incident spectrum is normally incident upon the prismatic cover. The curvature of the cover determines the angle of incidence at the front surface of the cell. The extreme values of angle of incidence may reach 30° -60 ° [6], while the majority of light is much closer to normal incidence. The materials which are used in Entech plastic covers are quite thick (on the order of 100 ~Lm) and non-planar. An important optical property, then, is that these materials do not interfere constructively or destructively. To avoid repetitive integrations over incident angle, the cover has been treated as a non-coherent material with an index of refraction N = 1.4, k = 0, under normally incident light. The effect of a non-coherent cover on the previous two-layer ARCs is shown in Fig. 11 and Fig. 12, respectively. Note that the optimum ARC thicknesses have shifted significantly from their original values. The current will rise substantially due to the elimination of shadow losses (an effect which is not included in these graphs), but these results indicate that performance may be increased even further with the use of properly designed ARCs.
5. C o n c l u s i o n In summary, the development of a broad band ( 3 0 0 - 1 7 0 0 nm) SE (a rotating polarizer-fixed analyzer configuration with an a.c. detection system) has been discussed. The instrument has been used to measure the optical characteristics of various materials. Among these are the CdTe polycrystalline thin film, CuInSe2 single crystal samples, and materials for high efficiency cascade solar cells including InP, InGaAs and InGaAsP. Most of these data are not presently available over such a wide spectral range. These measurements have also been used for the optimization of ARCs and in the modeling of the quantity of light actually being transmitted into the absorber of solar cells, in order to maximize the current output Jsc.
Acknowledgment This work was per f or m ed by the Solar Energy Research Institute under contract DE-AC 02-83 CH 10093 to the U.S. Department of Energy.
485
References 1 M. E r m a n a n d J. B. Theeten, Surf. Sci., 135 (1983) 3 5 3 - 3 7 3 . 2 F. A. Abou elfotouh, G. S. H o m e r and T. J. Coutts, Solar Cells, in the press. 3 S. M. Kelso, D. E. Aspnes, M. A. Pollack and R. E. Nahoory, Phys. Rev. B, 26 (12) (1982) 6669. 4 H. J. Hovel, Semiconductors and Semimetals, Vol. 11, 1975. 5 Azzam and Bashara, Ellipsometry and Polarized Light, North-Holland. 6 J. Zhao, A. W a n g and M. A. Green, J. Appl. Phys., 68 (3) (1990).
473
Broad band spectroscopic ellipsometry for the characterization of photovoltaic materials F. A. A b o u - E l f o t o u h , G. S. Horner, T. J. C o u t t s and M. W. W a n l a s s Solar Energy Research Institute, 1517 Cole Bd., Golden, CO 80401 (U.S.A.)
(Received October 25, 1990)
Abstract The availability of commercial spectroscopic ellipsometers (SE) has been restricted to the UV-visible range from 250-900 nm. Although this is useful for many applications, it must be extended to the near IR region (up to 1700 nm) for the study of the optical behavior of most photovoltaic materials. This paper discusses the development of a broad band (300-1700 nm) SE which has been used to measure the optical characteristics of various materials. Among these are the polycrystalline thin film materials, CuInSe2 and CdTe (for which single crystal samples have also been investigated), and materials for high efficiency cascade solar cells including InP, InGaAs and InGaAsP. Most of these data are not presently available over such a wide spectral range. Experimentally, a rotating polarizer-fixed analyzer ellipsometer with an a.c. detection system has been developed for accurate measurement of $ and A, the relevant eliipsometric parameters, in the near IR. This approach has certain advantages over the rotating analyzer-fixed polarizer systems including reduced sensitivity to room light. The analytical methods include the use of a specially developed computer modeling program which gives $ and A for a given set of values related to the film thickness (which may be finite or zero) and to the optical properties of the substrate.
1. I n t r o d u c t i o n N o n - d e s t r u c t i v e analytical t e c h n i q u e s to m o n i t o r the t h i c k n e s s a n d c o m p o s i t i o n of individual layers in multilayer devices are an i n c r e a s i n g r e q u i r e m e n t for the f a b r i c a t i o n o f w e l l - e n g i n e e r e d o p t o e l e c t r o n i c devices. The optical p r o p e r t i e s o f the materials involved in s u c h devices c a n be d e t e r m i n e d a c c u r a t e l y using s p e c t r o s c o p i c e l l i p s o m e t r y b y m e a s u r i n g the ratio of c o m p l e x r e f l e c t a n c e s of the s- a n d p - p o l a r i z e d light. Since the state of polarization o f light reflected f r o m a s u r f a c e is sensitive to surface irregularities o n a m i c r o s c o p i c scale, a n d to the p r e s e n c e o f native c o m p o u n d s , this t e c h n i q u e is v e r y valuable for the d e t e r m i n a t i o n of s u r f a c e a n d interface properties. P r o p e r u n d e r s t a n d i n g a n d m o d e l i n g of solar cell p e r f o r m a n c e is i m p o s s i b l e w i t h o u t a t h o r o u g h k n o w l e d g e o f the f u n d a m e n t a l optical p r o p e r t i e s o f the materials involved in the device c o n s t r u c t i o n as a f u n c t i o n o f their c o m p o s i t i o n , s t r u c t u r e a n d f a b r i c a t i o n p a r a m e t e r s . Local c h a n g e s in p r o p e r t i e s due to interfacial effects m a y also be vitally i m p o r t a n t . T h e s e m a y all be m o n i t o r e d using p r e c i s e m e a s u r e m e n t s of the optical c o n s t a n t s N a n d k (the real a n d
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474 imaginary parts of the refractive index) that determine the extent to which incident light is absorbed and reflected. The availability of commercial spectroscopic ellipsometers (SE) has been restricted to the UV-visible range from 2 5 0 - 9 0 0 nm. Although this is useful for many applications, it must be extended to the near infrared (NIR) region (up to 700 nm) for the study of the optical behavior of certain types of materials and structures. A typical application is to low bandgap materials and solar cells, the spectral responses of which extend into the NIR region of the spectrum. For these, it is required to evaluate the interband electron contribution to the dielectric function in the lower energy part of the spectrum. In addition, a detailed description of optical effects and band edge transmission of optical systems consisting of some metals, semimetals and silicides is only possible if ellipsometric measurements are made at wavelengths greater than 850 nm. Because of the dependence of optical penetration depth on wavelength, the SE is capable of performing high resolution, non-destructive depth profiling on multilayer devices to obtain structural information on each layer, whether crystalline or amorphous. Information on the layer thicknesses, possible existence of a native oxide layer, microroughness and porosity may also be obtained. This, together with the wavelength dependence of the optical constants over a broad range of wavelengths, is crucial for the design and optimization of several optoelectronic devices, including solar cells. In this paper, the capability of an SE, developed at SERI to monitor the optical characteristics of various materials and structures, is demonstrated. The materials include the polycrystalline thin film materials, CuInSe2 and CdTe (for which single crystal samples have also been investigated), and materials for high efficiency cascade solar cells including InP, InGaAs and InGaAsP. Data for most of these are not presently available. The data are necessary for: (a) modeling of solar cell performance, (b) design of antireflection coatings, (c) control over the device fabrication process and surface oxidation, (d) quality assessment of the material produced in-house and by SERI subcontractors.
2. D e s i g n f e a t u r e s o f t h e SE
The design is based on a stepper-motor-controlled polarizer, fixed analyzer ellipsometer and this configuration exhibits several advantages over rotating analyzer systems (Fig. 1). In particular, the position of the monochromator reduces sensitivity to room light, the system is mechanically stable and the computer interface makes efficient use of readily available high speed analogto-digital (A/D) microcomputer boards. It operates in an a.c. mode using a light chopper to improve the signal-to-noise ratio in the NIR. The light from a 100 W tungsten halogen lamp is polarized by a rotating prism after first being collimated. After reflection from the sample surface (and the associated changes in amplitude and phase), the polarized beam is directed to the fixed analyzer, and then to the monochromator. The monochromator uses three
475 Broadband light source. Beam collimation / reduction optics JlIL~ ~ J ~ " ~ j Light chopper " ~ / Computer controlled polarizer plate v"~tl / with optical encoder.
1/4 m computercontrolled monochromator
I
Lock-in Amp. I
I
-I m
PMT gain controller PMT signal amplifier PMT high volt. source Analog//O Digital I/0
Computer Electronic interface box
Fig. 1. Schematic diagram of the SE. separate gratings (blazed at 250, 600 and 1000 nm) to maintain high throughput over the entire wavelength operating range. The polarizer assembly consists of a hollow shaft carrying the analyzer prism mounted in a singie-race, sealed ball-bearing shaft, which in turn is mounted in the analyzer/motor housing assembly. The rotating prism assembly is driven with a small flexible chain by a high resolution stepper motor (12 800 steps per revolution). This allows precise positioning of the polarizer plate via an RS232 interface for integrated measurements. An optical encoder provides an 'absolute' position reference (i.e. one that will not drift) for the polarizer positioning system. In its present configuration, the system is able to collect and average 24 000 data points at each wavelength, perform a Fourier analysis on the resulting intensity curves, and present real-time plots in less than 20 s. The Fourier coefficients are then used to calculate the standard ellipsometric parameters 0 and A. 3. S o f t w a r e The information from an ellipsometric measurement at a given wavelength and angle of incidence is the complex reflectance ratio r, which is often expressed by the differential amplitude ratio tan ~ and the differential phase shift A. Contained in these parameters is all of the available information regarding surface interactions and the optical properties of layers within the sample, r is defined as: rffi rp - - = t a n ~#e~ rs
(1)
476 where
IrplZ = (I~i) =Rpandlr~12 = (~i) =Rs p
s
F o r practical use o f this technique, it was n e c e s s a r y to develop software for data collection, r e d u c t i o n and modeling. A b r i e f outline of the data acquisition software is given below.
3.1. Data acquisition software The SERI SE has b e e n designed for use in the rotating polarizer configuration. This t y p e of SE exhibits low sensitivity to r o o m light, but a u t o m a t i c b a c k g r o u n d s u b t r a c t i o n has b e e n i m p l e m e n t e d to e n h a n c e the m e a s u r e m e n t accuracy. A m e a s u r e m e n t at one w a v e l e n g t h m a y be b e t w e e n 20 and 30 s, one half of which is d e v o t e d to b a c k g r o u n d and dark c u r r e n t collection. Data are a c q u i r e d with p h o t o m u l t i p l i e r t u b e (PMT) in the r a n g e 3 0 0 - 8 0 0 nm, and a liquid-nitrogen-cooled g e r m a n i u m d e t e c t o r is u s e d b e t w e e n 800 and 1700 nm. Sixty reflected intensity m e a s u r e m e n t s are m a d e during o n e revolution of the polarizer. The quantities P and A are defined as the polarizer and analyzer angles with r e s p e c t to the plane of incidence. The f o r m o f the resultant intensity curve (after b a c k g r o u n d s u b t r a c t i o n ) in a rotating polarizer s y s t e m is [ 1 ]: Icc a c o s ( 2 P ) + b sin(2P) = c
(2)
The coefficients a, b and c are calculated with a F o u r i e r series least-squares routine. T h e s e p a r a m e t e r s allow solution for functions o f the eUipsometric p a r a m e t e r s 0 and A (defined in eqn. (1)):
,
/(c+a)
tan ~ = V ~
b cos A = - -
tan A
(3) (4)
The wavelength, 0, A, a, b, c and F o u r i e r fit variance are s t o r e d o n a h a r d disk for data reduction. Commercially available 12-bit A/D c o n v e r t e r s are u s e d to interface the d e t e c t i o n s y s t e m s to the c o m p u t e r . The T u r b o P a s c a l p r o g r a m m i n g language is u s e d to achieve 10 kHz sampling r a t e s for high s p e e d data averaging. The PMT gain is optimized at e a c h w a v e l e n g t h so that the full input r a n g e ( 0 - 1 0 V) of the c o m p u t e r A/D c o n v e r t e r s is utilized. This minimizes digitization effects o f low voltage signals. The light s o u r c e is c h o p p e d in the NIR, and the g e r m a n i u m d e t e c t o r signal is r o u t e d t h r o u g h a lock-in amplifier b e f o r e input to the c o m p u t e r . C o m m u n i c a t i o n s with the lock-in are i m p l e m e n t e d with a s t a n d a r d I E E E - 4 8 8 interface. R e m o t e control o f the sensitivity o f the
477 lock-in amplifier allows automatic signal size (again, near 10 V peak) optimization in the infrared. Real-time graphics have been developed to display current system settings, intensity and background curves, and the resultant Fourier fit. Separate graphs are continuously updated to display all of the relevant parameters (~b, A, a, b, c, etc.) as a function of wavelength. A larger variance in the Fourier fit or non-optimal gain settings trigger an automatic repeat of the measurement at any wavelength. 4. E l l i p s o m e t r i c m e a s u r e m e n t s
4.1. Optical constants of semiconductors In order to undertake adequate modeling, it is necessary to have a sound knowledge of the optical constants of the various materials involved in the solar cells to be studied. Typically, the properties of these materials depend upon the details of their fabrication, and whether they are in thin film form or they are single crystals. Whether transparent or in bulk form, correlation between the optical constants of the material is very important for an understanding of the material behavior and optimized device design. Figure 2 shows the optical constants of two single-crystal samples of CuInSe2 of different chemical compositions. N and k are used to calculate the absorption coefficients of the two samples and the data are shown in Fig. 3. These results are shown simply to illustrate the capability of the SE. A complete
Effective Optical Constants for Single Crystal CIS 3.0"
N (X1 2.5-
N (X2) 2.0'
1.5"
k (X2) 1.0.
k (Xl)
. . . . . . . . . . . . . . .
0.5"
0.0 200
4;0
600
800
1000
1200
Wavelength (nm) Fig. 2. Effective o p t i c a l c o n s t a n t s o f t w o C u I n S e 2 s i n g l e c r y s t a l s o f different c o m p o s i t i o n .
478
Single Crystal CIS Absorption Coefficients 0.5
"7 < E
04,
~9 <
,,..z 0.3.
.N ~
0.2"
O O ,~
<
0.1
0.0 300
|
!
i
!
500
700
g00
1100
1300
Wavelength (nm) Fig. 3. T h e a b s o r p t i o n coefficients o f t h e s a m e CuInSe2 s a m p l e s a s c a l c u l a t e d f r o m t h e m e a s u r e d optical c o n s t a n t s .
discussion of the data and correlation with other material properties will be given elsewhere [2]. The optical constants of copper-doped CdTe polycrystalline thin film has also been determined ellipsometrically (Fig. 4) and its absorption coefficient is calculated and shown in Fig. 5. The optical properties of Ino.~sGao.47As (i.e. lattice matched to InP), have been measured in the 3 5 0 - 1 6 5 0 nm wavelength range (Fig. 6), and the results are in excellent agreement with previous data published by Aspnes [3]. The optical constants of the quarternary semiconductor compound Gao.z~Ino.75Aso.54Po.46 are shown in Fig. 7. This composition has a bandgap of 0.95 eV and it is lattice matched to InP. This is the first time that these data have been obtained over such a wide spectral range but, in the visible, they agree well with the data of Aspnes [3]. The N and k values have been used to model the reflectance, and this is found to agree with the measured reflectance to within 2.5% (Fig. 8).
4.2. Modeling of short circuit current density One of the advantages of these measurements is that they can be used for the optimization of anti-reflection coatings (ARCs) and in the modeling of the quantity of light actually being transmitted into the absorber of solar cells, in order to maximize the current output Js¢. This depends upon the incident spectrum, external quantum efficiency, reflectance, and the thicknesses and optical constants of all materials in the cell. The current relation
479
Effective Optical Constants of Cu-doped CdTe Thin Film 6.0
2.5
N •.
7
.
.
.
.
.
.
.
5.5
--Z..
'5.0
2.0
'4.5
N
k ,4.0
1.5
~3.5
1.0 400
i
I
I
I
l
I
I
500
600
700
800
900
1000
1100
3.0 1200
Wavelength (nm) Fig. 4. Effective optical constants of copper-doped CdTe polycrystalline thin film.
is given by [4 ]: J~¢ _- e I~ I(A) × QEe~(A) x (1 - R'(A))dA (1 -R(A))
(5)
o
J~
short circuit current (A em -2) incident spectrum (photons nm -~ em -2 s - i ) h wavelength (nm) e electronic charge (A s) QE(A) external quantum efficiency (electrons per photon) R(A) cell reflectance before ARC application (dimensionless) R '(h) calculated cell reflectance for specific ARG geometry (dimensionless) Two-layer ARCs a r e often used on solar cells. Hence, J~c is a function of the thickness of both materials and its variation must be presented in a contour graph format. In this, the y-axis represents the thickness of the coating with the larger index (i.e. the ZnS) and the x-axis indicates the thickness of the lower index material (i.e. the MgF2). The data are represented in the form of curves of equal J,c and the maximum current, together with the thicknesses of the two materials may easily be determined. The N, k data for each layer in the structure are used in the calculation of R '(h). A 2 × 2 complex matrix method [5] has been implemented which calculates reflectance from an n-layer optical stack, given N and k of every layer, as a function of the angle of incidence and incident light polarization state. In this paper, normal incidence is assumed.
I(h)
480 Data from "E15 CdTe.crk"
| I []
[]
3 ¸
[] w [] w w []
[]
Alpha
m [] w
%
2-
l
1
•
200
i
•
!
400
-
600
i
!
800
1000
1200
Lambda
Fig. 5. The calculated absorption coefficient of the CdTe thin film. InGaAs 4.5 4
["\
N
3.53 /
_~2.5 f 1.5 ~k 0.5
~
. . . .
0
Wavelength (nm)
Fig. 6. The optical properties of Ino.5~Gao.47Aslattice matched to InP. Figure 9 s h o w s Jsc c o n t o u r plots for GaAs h o m o j u n c t i o n with a doublelayer MgF2/ZnS ARC. A n u c l e a t i n g layer of MgF2, 2 n m in t h i c k n e s s was used a n d this has b e e n included in the model; this layer is often d e p o s i t e d to e n h a n c e g r o w t h c h a r a c t e r i s t i c s o f ZnS on I I I - V c o m p o u n d s . Figure 10
481
InGaAsP
B
0
•
200
•
i
•
•
400
i
-
600
i
•
i
800
•
1000
.
i
•
1200
,
i
m
n
•
k
•
1400
1600
Lambda
Fig. 7. The optical constants of the quaternary compound Gao.25Ino.75ASo.54Po.4a.
Ga(0.25)l n(O.75)AS(O.54)P(0.46) 0.7 0.6
0.5
Elltpsometry / C a l c u l a t e d
n.zt
~
,
O.3
~
-
_/"
0.2
,
--""'I':"----
-
, ....
Measured O.t 0.0
3oo
J
5oo
i
7oo
,
to
9o0
~~ o
~3oo
Wavelength (nm) Fig. 8, The modeled and measured refleetanees of Gao.25Ino.75Aso.54Po.46 agree within 2.5%.
482
120
Global : MgF2 / ZnS / MgF2 (2 nm)/ GaAs
Jsc (mA/cmA2)
11028,5
10090E
8O-
U)
70-
28.25 28
27.75
= 60.L2 .c I- 50a 40-
27.5 27.25 27 26.75 26.5 MgF2 Thickness (rim)
Fig. 9. J,c contour plots for GaAs homojunction with a double-layer MgF2/ZnS ARC.
Global : M g F 2 / I T O / I n P
Jsc (mA/cm^2)
110-
28
100-
27.5
~- 9 0 -
¢.-
80-
27
70-
26.5
._o 60tI- Kn.
26 25.5 25 24.5 24 MgF 2 Thickness (rim)
Fig. 10. Jsc contour plots for ITO/InP cell with a MgF2 layer.
483
Global : Entech / MgF2 / ZnS / MgF2 (2nm) / GaAs
120-
Jsc (mNcmA2)
11028.5
100-
E
90-
28.25
8O-
28
¢n 70-
27.75
¢/)
c
60-
27.5
._o z: 50pN
27.25
40-
27
30-
26.75 26.5 26.25 M g F 2 T h i c k n e s s (nm) Fig. 11. The effect of a non-coherent cover on the Jsc contour plots for the GaAs homojunction.
Global : Entech / MgF2 / ITO/InP
Jsc (mNcm^2)
28
27.5 A
E
27
U) G) ¢.-
26.5
.to tF-
26 25.5 25 24.5
oooooo T¢~1 03
~
t43
ooo8ooo I~¢O O'J
24 ~--
04
03
MgF2 Thickness (nm) Fig. 12. The effect of a non-coherent cover on the J ~ contour plots of the ITO/InP cell.
484 shows a similar calculation for an indium tin oxide (ITO)/InP cell. In this case, the ITO acts .as one of the ARCs, while MgF2 is used as the top ARC. This particular application requires several approximations, since the ITO is an integral (conducting) part of the solar cell. It is assumed that the quantum efficiency is independent of ITO thickness (an assumption which will certainly fail for significantly thinner ITO). The results are, however, valid for a broad range of ITO thicknesses centered on 60 nm, since the external quantum efficiency and reflectance data (R(A)) were obtained from such a device. Recently, Entech prismatic covers have been used to enhance solar cell performance by diverting light from above grid fingers to active areas of the device. The geometric concentration effects have been studied in some detail [6], but the change in optimal ARC thicknesses due to application of such a cover has not been investigated. For concent rat or measurements, the incident spectrum is normally incident upon the prismatic cover. The curvature of the cover determines the angle of incidence at the front surface of the cell. The extreme values of angle of incidence may reach 30° -60 ° [6], while the majority of light is much closer to normal incidence. The materials which are used in Entech plastic covers are quite thick (on the order of 100 ~Lm) and non-planar. An important optical property, then, is that these materials do not interfere constructively or destructively. To avoid repetitive integrations over incident angle, the cover has been treated as a non-coherent material with an index of refraction N = 1.4, k = 0, under normally incident light. The effect of a non-coherent cover on the previous two-layer ARCs is shown in Fig. 11 and Fig. 12, respectively. Note that the optimum ARC thicknesses have shifted significantly from their original values. The current will rise substantially due to the elimination of shadow losses (an effect which is not included in these graphs), but these results indicate that performance may be increased even further with the use of properly designed ARCs.
5. C o n c l u s i o n In summary, the development of a broad band ( 3 0 0 - 1 7 0 0 nm) SE (a rotating polarizer-fixed analyzer configuration with an a.c. detection system) has been discussed. The instrument has been used to measure the optical characteristics of various materials. Among these are the CdTe polycrystalline thin film, CuInSe2 single crystal samples, and materials for high efficiency cascade solar cells including InP, InGaAs and InGaAsP. Most of these data are not presently available over such a wide spectral range. These measurements have also been used for the optimization of ARCs and in the modeling of the quantity of light actually being transmitted into the absorber of solar cells, in order to maximize the current output Jsc.
Acknowledgment This work was per f or m ed by the Solar Energy Research Institute under contract DE-AC 02-83 CH 10093 to the U.S. Department of Energy.
485
References 1 M. E r m a n a n d J. B. Theeten, Surf. Sci., 135 (1983) 3 5 3 - 3 7 3 . 2 F. A. Abou elfotouh, G. S. H o m e r and T. J. Coutts, Solar Cells, in the press. 3 S. M. Kelso, D. E. Aspnes, M. A. Pollack and R. E. Nahoory, Phys. Rev. B, 26 (12) (1982) 6669. 4 H. J. Hovel, Semiconductors and Semimetals, Vol. 11, 1975. 5 Azzam and Bashara, Ellipsometry and Polarized Light, North-Holland. 6 J. Zhao, A. W a n g and M. A. Green, J. Appl. Phys., 68 (3) (1990).