LBIC QUANTITATIVE MAPPING

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LBIC QUANTITATIVE MAPPING

J. Boyeaux, A. Laugier

To cite this version:

J. Boyeaux, A. Laugier. LBIC QUANTITATIVE MAPPING. Journal de Physique Colloques, 1989,

50 (C6), pp.C6-111-C6-127. �10.1051/jphyscol:1989610�. �jpa-00229641�

R E W E DE PHYSIQUE APPLIQUEE

C o l l o q u e C6, S u p p l Q m e n t a u n 0 6 , Tome 24, J u i n 1989

LBIC QUANTITATIVE MAPPING

J . P . B O Y E A U X ' ~ ) and A . LAUGIER

Laboratoire de Physique d e la Matiere, CNRS UA-358, INSA de Lyon, Bat.

502, 20, Avenue A. Einstein, F-69621 Villeurbanne Cedex, France

Resume - La mithode EBIC, qui consiste B g6n6rer des porteurs excidentaires dans le matiriau par un faisceau &electrons et B exploiter les informations contenues dans le courant induit, peut Etre transpos6e en utilisant un faisceau de lumiere ce qui conduit aux methodes LBIC. Dans ce papier on donne une revue des paramhtres physiques qui peuvent ainsi Ctre CtudiCs. Comme en microscopie 6lectronique B balayage, des images peuvent Ctre rialisies permettant de mettre en evidence des dCfauts Clecmquement actifs dans les dispositifs Clectroniques. Pour une analyse et une imagerie quantitatives des difauts, les principaux mod5les theoriques sont prisentis et discutis. On dicrit les diff6rentes rialisations en analysant les limitations de la mithode. Des exemples &applications sont donn6s pour des cellules solaires et des transistors de puissance. On examine aussi les moyens d'6tudes des materiaux sans structure de collecte

.

Abstract

-

The method of electron beam induced current (EBIC) characterization has been widely used. However, many of experiments possible with the EBIC mode can be performed using a light-beam as an excitation source. The aim of this paper is to give a review of the physical parameters that may be obtained using the light-beam induced current (LBIC) method. Theoretical models involved for quantitative interpretation of LBIC signal and some typical applications are reviewed. The conditions to obtain quantitative mapping are discussed. Some examples including Schottky barriers, solar cells and bipolar transistor are given.

1

-

INTRODUCTION.

In recent years, the limits of device technology have been constantly improved, especially for the VLSI technology. In this case, the high density of fine lines has put stringent requirements on the photolithographic and etching processes. Metallization plays a major role in the fabrication of integrated circuits. Of course, several junctions are present in the device and must be locally controlled.

Independantly of fabrication steps, structural defects in semiconductor sample are known to greatly impact device performance, lifetime and reliability, so it is crucially important to be able to analyze their behaviour. Consequently, the development of suitable devices needs the use of non destructive analytical techniques with good spatial resolution for the electrical characterization of the device performances.

A localized source of excess carriers in semiconductors can be produced by a finely focused ionizing beam. With a suitable structure of collection

-

namely a pln or Schottky junction

-

the generated carrien give a current available in an external circuit. Analysis of the signal can provide important information on the local transport properties of the material under test.

Primarily, the surface probing can be carried out either by an electron-beam or by a light-beam.

The method of elecmn-beam-induced-current (EBIC) characterization has been widely used 111 and several attempts have been made /2,3,4/ to characterize the signal emitted. However, many of the experiments possible with the EBIC mode can be performed using a light-beam as an excitation source 141.

The aim of this paper is to give a review of the physical parameters that may be obtained using the LBIC method. To quantitatively interpret the induced current signal, several conditions are required, especially: (i) measurement of the beam power and a control of the low injection level in order to avoid any change in the local transport properties. (ii) measurement of the reflection coefficient at the device level.

Morever, the principle.of carrier generation by light is different from that by electrons: (i) one photon with energy greater than the band-gap of the material generates a single electron hole pair, (ii) since light absorption follows an exponential law, it is not possible to define a maximum penetration

("permanent A d d r e s s : U n i v e r s i t b Lyan I. ISIDT, B a t . 203. F-69622 V i l l e u r b a n n e Cedex, Prance

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989610

C6-112 REVUE DE PHYSIQUE APPLIQUEE

depth in the sample; (iii) recently, the finite beam cross section and divergence has also been taken into account 151. Since the LBIC mode would not add any excess charge to the specimen under test, this can be a major advantage, especially for high resistivity material.

On the other hand, a contrast mechanism is necessary to interpret quantitatiqely the LBIC signal for a specific defect. For example, Marek 151 has recently developed a theoretical model giving the photocurrent in the vicinity of grain boundaries. The diffusion length and the recombination velocity at the grain boundary are obtained by fitting the theoretical and experimental photocurrent profiles. In the next part of the paper, a description of a high spatial resolution apparatus designed for precise analysis of the local photovoltaic properties is given 161. Usually, a GaAs laser diode (780 nm in wavelength ⁾ is used in pulsed mode. This wavelength is well suited for Si material ⁽ the carriers are generated by the light down to 10 Fm ) and also for the study of the window effect and the antireflection (AR) coating behaviour in the case of 111-V solar cells. A comparison is given between the system presented and other similar commercially available devices such as Scanning Optical Microscope.

2

-

THE LIGHT BEAM INDUCED CURRENT TECHNIOUE,

Fig.1 gives classical arrangement for LBIC observations. The charge collection is due to a p-n junction. Obviously, it is possible to collect the carriers from a Schottky barrier. In this case, the front of the sample will be coated with a thin semitransparent layer of appropriate metal. The electron-hole pairs generated by the light beam are collected by the built-in-field, giving a current that can be analyzed. For a suitable current measurement, an 1.V converter is used which insures low input impedance( R a , where a, is the open-loop gain) and keeps the negative input at null potential. By

f'

scanning fine ^y focused beam over the device 17/( or bv moving the device under the stationan, beam 184, theiocal Gduced current provides an image of the analyzed-area. At defects, like grain bouidaries, the collected current is usuallv lower. because of the higher carrier recombination.

.+

Now, some important pafameters are reviewed.

2.1 Light source.

As discussed below, the following points are to be considered:

(i) in EBIC mode, the high voltage is well regulated in order to have monocinetic electrons.

Analogously, in LBIC mode, it is desirable to operate with a monochromatic wavelength source: in this case, the generation rate is the same for all the generated caniers.(ii) low powers are usually suitable in order to avoid any change in the local transport properties.(iii) using periodic light source allows a better signal treatment and a good signaynoise ratio.

Two types of light source are classicalally used: steady or periodic. A periodic source can be obtained by a mechanically chopped light source from a continous laser beam or a monochromator.

This method is used for the visible spectrum as in this range of wavelength commercially available light emitting diodes do not provide a "good light beam. However, in the IR range, several solid state emitters are available and some of them are summarized in Table 1.

Table 1- Some commercially available solid-state emitters. LD : laser diode; LED : light emitting diode. h : emitting wavelength.

...

h ( n m ) 780 870 904 940 1060

type double hetero- collimated single diode LED LED

stucture LD LD injection laser

material AlGaAs AlGaAs GaAs GaAs InGaAs

---.

Ro

Ohmic contact

Figure 1

-

Schematic classical arrangement for the LBIC measurement

The 904 nm injection laser can be used when short pulse durations are necessary ( 150 ns). The other emitters can be monitored by a pulse generator. The pulse duration and the repetition time are varying, so it is possible to obtain the steady-state current. This does not occur under very short pulsed hght excitation.

2.2 Beam characteristics.

For local analysis, the light beam must be focused. The commonly adopted definition for a laser beam is the diameter where the transverse field amplitude has fallen to a fraction l/e of its peak axial value. At this same diameter, the corresponding beam irradiance will have fallen to l/e2 ( 13.5%) of its axial value: see Fig.2(a) and (b).Then, two parameters are under consideration /9/:

(i) the minimum spot diameter : a Gaussian beam can be focused to a small area but optics must approach diffraction limited performance. For a collimated Gaussian beam ( radius wl), focused with an aberration free lens ( lens focal length f ), the diffraction limited radius is given by:

wo = hf/xwl (1)

where h i s the wavelength : see Fig.2.(c). (1) is to be compared with the classical relation:

wo = 1.22 h f P 0 (2)

where Dn is the lens diameter.

(ii) the dzpth of field d: see Fig.2.(c) , d is given by :

d = 2 R h-l( p2

-

1)lI2 w

0"

₍₃₎

were p = w /wg; w2. is the beam radius at d/2 from the focal waist. Large depth of field is necessary in L&C lmaglng when the surface of the tested sample is not plane, as in the case of a textured surface for instance.

2.3 Carrier generation and injection level.

A lot of model calculations exists in the literature about the photoinduced decay of the open-circuit voltage and the short- circuit current ⁽ transient effects: see e.g. 1100 or the photoinduced steady

-

state ( see e.g Ill/). These models are mostly one-dimensional and an analytical result can only be given for infinite geometry of the device. In this case, the effective generation rate at a depth z is given by ( see e.g. 1124

g (z) = aGoexp(-az) (4)

Figure 2

-

Beam characteristics- a ) Gaussian irradiance profile showing definition of the beam radius wg - b ) l / e 2 contour radius vs distance from Gaussian waist -c) definition of the depth offield d.

C6-114 REVUE DE PHYSIQUE APPLIQUEE

in the steady illumination case, where

Go-is

the photon flux at wavelength h and z = 0 and a(h) is the absorption coefficient. When the device is illuminated by a monochromatic light in the form of a pulse of intensity $(t), the generation rate is given by /lo/:

g (2.t) = 4(t) a exp(-az) (5)

(5) can be modified as g (z,t) = ggexp(-az) (6)

if Oc t c 6 in the case of a very short light pulse duration 6 1131. A three-dimensional calculation has been performed by Marek 151. He takes a Gaussian shape for the lateral dependence of the generation volume ( cylindrical coordinates ):

g ( r,z ) = A(z) ⁽ 2 no2 )-I exp [ $12 02(z)] (7) where o is the width of the Gaussian function at a depth z; the generation volume has the depth Minority /majority

carrier ratio

~ i n o l ' i t ~ /majority carrier- ratio

Figure 3

-

Minoritylmajority carrier ratio vs distance

ffom

junction in p n

-

a ) parameter: spot diameter- b) parameter: d ~ m i o n length-

dependence A ( z ) = aexp(-az) (8)

Low injection conditions are satisfied when the minority camer concentration is smaller that the majority c b e r concentration, namely minoritylmajority canier ratio < 10%. Several attempts have been made to evaluate the excess carrier distribution in order to calculate the LBIC signal. In stationary case, Marek 151 use the concentration of minority carriers deduced from Donolato's results 1141 (three-dimensional model). The excess carriers has been also analyzed when the steady-state carrier excitation is abruptly terminated ( transient case): /10,12,13/. This excess is calculated by Kern and Wagemann I151 with an exact-three-dimensional model: the device and spot size are considered and the excess is obtained in the form of a triple infinite series. However, the three-dimensional analysis appears to be too complicated. Thus, a rough approximation is sufficient to describe the excess carriers and to follow the parameter evolution. The minority carrier concentration is obtained from the solution of the equation of continuity ( one-dimensional case) taking into account the boundary conditions ⁽ see e.g.1161) : n ( 0 ) = 0 and n ( w ) = 0 ( w is the base thickness and the recombination velocity value at the back contact is taken to ⁰⁰ : ohmic contact). The solution is given by :

n (z) = a ~ O ~ 2 [ ~ ( a 2 ~ 2

-

l)]-l{ch (zIL) +[ exp (- aw)

-

ch ( ~ ~ ) ] . s h ( z / ~ ) . s h - ' ( w / ~ ) - e x ~ ( - a z ) I (9) where L and D are the minority diffusion length and diffusivity, respectively. Table 2 gives numerical values used in computing from Eq.(9) the results presented in Fig.3, The curves show that h and the spot diameter are parameters to be chosen carefully. For instance, Damaskinos and Dixon 1171 emphazise that the measured diffusion length varies from 150 pm to 60 pm when the power source was in the range 100 pW to l o 3 pW respectively ( Si Wacker p type, h = 632.8 nm and spot diameter 1.6 pn ). However, the values obtained in Fig.3 are overestimated, first by the used model and second because L increases the effective spot size when the carriers are generated deeply.

Minority /olajority carrier ratio

0,45 parameter :

wavelengtli

0,35

Figure 3.c)

-

Minoritylmajority carrier ratio-vs distance from junction ( in pm ⁾

+

Dopg substrate. 10

-

Numexi? #ue%used cm- ; base in the wmputation of thickness: 300 pq D the = 20 curve cm Is.

9

in Fi 3. g.

2.4 Abmption d c i e n t .

According to G d f and Fischer 1181, the experimentally determined absorption coefficient of siliwn 1191 is given by the following equation /20/ :

a @) = 0.526367

-

1.14425.h-I

+

0.585368.?~-~

+

0.039958.h~~ (10) Relation (10) with a in ( pm )'I holds for stress-relieved crystals. The following relation :

a (2,) =

-

1.06964

+

3.34982.h-I

-

3.61649.h-*

+

1.34831.h-~ (11) used for non-stress relieved silicon is usually appropriate for as grown crystals /20,21/. Equation (1 1) is limited to crystals with specifxc resistivities exceeding 0.1 a m . FigA.(a) shows the variation of a@) vs 5 according to (10 ) and (1 1). Similar variation was given by F a b /22/. We note that the 780 nrn wavelength is well suited for both as-grown and stressed crystals. In particular, a stressed region can exist in the vicinity of grain boundaries and it is important to avoid a gradient when scanning across a grain boundary. On the other hand, the absorption coefficient varies upon temperature and doping concentration: 11 a change from 10 pm (25 OC) to 5 pm (200 OC) /23k for pure and heavily doped silicon a have been determined between 268 nm and 1 pm b Jellison et al. 1241 usin polarization modulation ellipsometry. For Si: As a varies from 1 d (undoped) to 5.1@ cm-

f

(3.2.1021 ~ m - ~ ) at 780 nm. With :B ( 5.102~ cmcm4) and :P (3.2.102~ ~ m - ~ ) , small variation was obtained. FigA.(b) gives the variation of a(h) vs h for Gal,A1,As ( O<x<l; x = 0.36 corresponds to the cross-over ) in agreement with other nsults /25,26/.

Absorption Coef. ( l i p ⁾

1 0 0

1 0

Absorption Coef. (licm)

1 1 OE+5

1 OE+4

0.1 1 OE+3

1 OE+2

0.01 10E+1

I O E 4

0.001 l OE-.I

0 . 3 0 . 4 0 . 5 0 . 6 0.7 0 . 8 0 . 9 1 1 . 1 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 Wavelength (nm)

LamMa (pm )

Figure 4

-

Absorption coefficient vs wavelength- a) silicon- b) Gal,AlxAs 2.5 Reflection coefficient R.

Short

-

circuit current is proportional to (1-R). Fig.5 shows the variations of reflectance in the 400 nm-900 nm range for some materials of interest mentioned in the figure captions. We note that Si and GaAs show nearly the same variation except for the near U.V. Some problems can occur during LBIC scanning if reflectance varies along the line-scan. Experimental values of R were necessary to obtain the photovoltaic contribution. However, when the LBIC resolution is good ( small spot), the R measurement can be difficult, for instance with a textured surface having a spatial variation similar to the spot size.

3.1 Determination of the recombination velocity at grain boundaries.

Zook's 1271 calculation is based on the assumption that a portion of the minority carriers is reflected at grain boundaries and the other part is transmitted. The beam diameter was assumed to be zero and the divergence of the beam was neglected. The recombination velocity could not be determined by this method. In a further paper, Zook 1281 included the finite size of the pair generation region but gave no fitting between theoretical and experimental profiles in vicinity of grain boundary

.

Recently, Marek 151 has developed a theoretical model giving the photocurrent in the vicinity of grain boundaries. In his model, the grain boundary is considered as a semi-infinite plane of recombination centers with spatially invariable recombination velocity. On the other hand, the minority camer diffusion length is supposed to be constant throughout the material. The LBIC signal is then calculated as the difference between the background current, i.e., the current at a large distance from the grain boundary, and the recombination current due to the presence of the grain boundary. A three-dimensional calculation with a Gaussian shape of the generation volume yields a recombination current density given by the following equation :

2 2

cos (Ax)

-x

oOn 2 2

I*(x) =

-

e [exp erfc

-

exp O2 erfc ]

where a is the absorption coefficient, q the electron charge, o the laser spot diameter, D the diffusivity of the minority carriers, S the recombination.velocity at &e gain boundary, and I3 the beam divergence inside the material. Further,

Figure 5

-

Reflectance vs wavelength for Si and c ) G d s ; a ) GaAs

+

G U ~ - ~ A I ~ A S window; b) G d s

+

Gal-xAlxAs window +AR layer; d ) GaAs

+

G ~ l - ~ A I f i s etched window, without AR layer.

where p = ( h 2 + ~ * )If2 and A=1/ L

.

The background current-density is given by :

where w is the width of the denletion region, N the incident hoto on density. and R the reflection coefficient. The photocurrent fiofile cananbe calculated from thk set of equadons (12)-(14) by using Simpson's method. Figs.d(a) and (b) give typical numerical results using the values of the parameters given.

3.2 Determination of diffusion-length 3.2.1 Spectral response method

By taking the exponential term as unity in Eq. (14), it reduces to the form:

R, N and I are measured for various wavelengths around 0.8-1 pm and plotted against the penetration $epth l f a of the incident monochromatic light. Some problems can occur with this method due to the validity of a(h) values. On the other hand, the device preparation conditions also affect

!o

because of native oxide growth: according to Kipperman and Omar 1291, a 30% reduced short-circuit current was obtained by rinsing the silicon wafer in deionized water after the HF treatment. This thin interfacial oxide of SiO, can limit the transmission of the chyge carriers by the tunnel effect. In this case, the diffusion length, as given by the spectral response method, is underestimated, while the method related in the next section gives a more exact value since it depends only on the shape of the photocurrent decay curve.

3.2.2 Scanning spot method.

The value of L can be determined by a laser spot scanning away from the junction, as proposed by Ioannou et al. /30/ for EBIC , and Dixon et al. D l / for LBIC techniques. In this method, the excess minority carriers injected into the semiconductor by a focused laser beam diffuse away from the injection point. The total charge thus collected by the Schottky bamer, and measured as the sample short-circuit current, is a function of L and the barrier-beam distance x. Thus, a slow spot-scan of the surface gradually away from the Schottky bamer give the LBIC current-decay as follows:

I(x) = A exp (- XL ) /xn (17)

where n is a constant which depends on the recombination velocity at the surface, and A is a constant depending primarily on the beam intensity and the penetration depth.

In their paper Ioannou et al. take 1.5 as n exponent value. This, however, corresponds to an infimite recombination velocity at the surface 1321. According to Davidson and Dimitriadis 1321, n may vary anywhere from 0.5 to 1.5, wherein the lower limit corresponds to a recombination velocity of zero. Eq. (17) thus contains two unknown parameters, namely, n and L. In order to determine n from the experimental photocurrent profile /33/, we selected a range of set-values of x; in each set, the two

Figure 6

-

Theoretical photoresponse profile in vicinity of grain boundary with a = l d cm-l;

spot radius = 1 pm; depletion region : 0 5 pm; beam divergence: 0286- a ) recombination velocity

&ect ( in 104 cm.s-1) and L = 20 pa- b) diffusion length effect ( in pm) and S = 4.104 cm.s-1.

values of x were such that x2 = 2x

.

Denoting by I1 and I2 the photocurrents corresponding to xl and x2 respectively, from equation (17j it follows that

(Iz/ II2) = n ln (xl)

-

^ln (A)

-

n ln (2) (18) which is a straight line with a slope of n.Thus, from a plot of ln (I/ I 2, vs. In (xl). the value of n can be obtained. Once n is known, L can be calculated by modifying

4.

⁽¹⁷⁾ as follows:

In (l.xn) = (-x/L)

+

ln (A) (19) A plot of ln (I.xn) vs. x yields the value of L.

3.3 Lifetime determination.

The measurement of the short-circuit current appears as the best method to obtain the lifetime &om the response of a device to a transient excitation /10,12,13/. The experiment can be performed either with a delta pulse or with a square pulse, the latter yielding a steady-state cument

.

In this case

.

^the

decay of photocurrent vs time when light is switched off at t = 0 follows an analytical law /IS/ :

(n = 1 2 ,

...

⁾ with z,, ⁼ zdn.[l+ (nn~/w)2] (21)

where w is the thickness of the base,

z,

the lifetime in the base and z h the decay time of the nh mode ( n =1,2,

...).

An infinite recombination velocity at front and back contacts is assumed in Eq. (20). The determination of lifetime is indirect since the L ( or D ) value is needed. To obtain

z,

from a measurement of T ~ , it is necessary to verify the validity of (20) and (21). The equation of continuity for minority carriers can be solved numerically assuming (5) as a generation function. Hence the shape of the light s o m e can be analyzed. In particular the effect upon z h of the rise and fall time of the light source can be obtained.The steady state photocurrent can be fitted with the experimental one.

Fig.7.(a) and (b) show two typical cases for two wavelengths; the inset gives Ln(I ) fort >= 0. For short duration all the modes exist , but only n =1 persists. Hence the validity of

(91)

can be tested.

According to Ahrenkiel and Aharoni /34/, the junction capacitance C- , the device series resistance R, and the junction leakage resistance R, could give a time constant ktroducing discrepancies in the lifetime determination.

4

-

LBIC IMAGING.

4.1 Numerical LBIC image processing.

For precise analysis of the local photovoltaic properties, the LBIC experimental set up has been used for several applications: /35,36/. A GaAs laser diode ⁽ 780 nm ) in a pulsed mode was the light beam source (typically 10 ps in pulse duration and 1 ms in repetition time). The beam was focused by

Figure 7

-

Photocurrent response to a pulsed light beam for two wavelength

a) a =0.lpm-l;15fetime :3 p ; rise time: 0.1 p ; fall time: 0 ;plateau time: 1 p ; laser power: 200 pW.

b) a = 0.02 pm-l;lifetirne :I p ; rise time: 0.1 p ; fall time: 0 ;plateau time: 0 5 p ; laser power: 200 PW.

diffraction limited optics; the spot diameter and the depth of field of the incident beam were 8 pm and 100 pm respectively. A relatively low laser diode power was used to avoid any changes in the local transport properties. The test-device was moved under the fixed laser beam on computer-controlled X,Y translation stages ( resolution 1 pm). The numerical photocurrent value for each point was averaged in order to get a good signal / noise ratio and the associated value was transferred to the computer memory. The total image was stored in a matrix form. After computer processing of the image, the local transport properties were displayed using grey levels or arbitrady chosen colors. A grey level or false color two-dimensional topograph was obtained on the color display monitor by selecting i photocurrent intervals associated with i levels. Usually i was taken equal to 8, but values up to 255 can be used ( one color per level ). Fig.8 gives a simplified diagram of the experimental set up

.

Some applications will be presented in the next section.

rrl

^{generator sFhroTn}

Laser diode

r - 7 ^)I / - - % G k l

Ga A1 As I

I

d Converter H recorder k--~

I ^Computer

,,,LC ;;.I....';..'.

.. ,. ..;.:;<::

IBM PC

/

XT

Table Z

Table Y

Ld

^Decoder

I

L T O c o n S O ' e

I 1

Figure 8

-

Simplified diagram of the experimental set up. I--- TO plotter 4.2 Scanning Optical Mimscope.

Following Dixon et al.'s work ( see e.g /17,31/) a Scanning Laser Microscope is now available from Waterloo Scientific Inc. The system works with a single helium nwn laser and a resolution of 1.5 pm. Simultaneous reflected light and OBIC ( Optical Beam Induced Current ⁾ are possible. Green or IR HeNe lasers are optional additions. The computer and display are comparable to that describe before. In the Laser Scan Microscope developed by Carl Zeiss 1371, the laser beam is scanned by the controlled deflection of a galvanometer mirror. This apparatus uses the same optics as a conventional optical microscope. Light sources available are 633 and 1150 nm (HeNe laser), 442 nm (HeCd laser),488 and 514.5 nm ( Ar-ion laser).The spot size may be as small as 0.4 pm and the power output of the laser lies between 2 and 10 mW.

4.3 Lifetime imaging.

Minority-carrier lifetime mapping in silicon using a microprocessor-controlled flying-spot scanner is given by Nordlanger et al./38/. The results are presented by a 3D-map line-scan or by an array of -400 lifetime values.

5

-

TYPICAL EXAMPLES AND DISCUSSION, 5.1 Grain boundaries in polycrystalline silicon materials.

5.1.1 Devices under test

.

For the best fit to the theoretical model, a Schottky solar cell was fabricated with one grain

boundary. A p-type silicon bicrystal ( 1 SZ cm resistivity and 213 grain boundary) was supplied by CENG-France ( prepared by CZ process). A semi-transparent, 20 nm thick, Cr Schottky contact was obtained by vacuum (oil-free) thermal evaporation and the substrate temperature was maintained below 40' C during evaporation. A sharp and well defined Schottky contact edge was obtained by a microphotolithography technique. An aluminum grid was then deposited on a part of the Cr to minimize the series resistance. To avoid any heat treatment of the sample after the metal deposition 1391, the ohmic back-contact was formed by a thin layer of an eutectic alloy of Ga and In.

5.1.2 Electrical activity of grain boundaries from LBIC topography

Fig.B.(a) shows typical LBIC topography of the bic~ystal Schottky device. The numerical imaging was carried out using 100 lines with 100 points in each line and a step of 10 pm between each succesive point. The analysed solar cell area was lmm2. The minority carrier recombination is clearly evident: the photocurrent was reduced by nearly 25% at the grain boundary.

5.1.3 Minority carrier diffusion length in the grain and recombination velocity at the grain boundary.

The experimental data are plotted according to relation (18). A straight line was obtained with a regression coefficient of 0.98 which shows that relation (17) fits the experimental data well

.

A value of n = 0.56 was obtained which corresponds to a low surface recombination velocity. Inserting this value of n in Eq.(19) yields L = 50 pm. The above value of L was used to fit the experimental photocurrent profile with the theoretical one given by Marek's model. A typical case is shown in Fig9.(b). Curve 1 is the experimental photoresponse profile ( line no 50 in Fig.9.(a)). To take into account the presence of native oxide, which would effectively increase the tunnelling resistance of the minority carriers, the experimental photocurrent profile was multiplied by a factor of 1.89 (as discussed in /40/), for comparison with the theoretical curve. The corrected experimental curve thus obtained is shown as curve 2. For theoretical computation of the photocment profile, the following input parameters were used: w = 0.33 pm ,

P

⁼ lo0, and a,, = 7 pm

.

A fitting of the corrected experimental and theoretical profiles was carried out by varying S values in the model. The best fit thus obtained for a grain boundary recombination velocity of 2.104 cm/s ⁽ curve 3 ), gives excellent agreement between the theoretical and experimental photocurrent profiles.

5.1.4 Hydrogen passivation.

Fig.lO.(a) and (b) show the effect of hydrogen implantation by a Kaufman source on the photocurrent of a p-type polycrystalline (SILSO) solar cell. In order to obtain a passivated and an un

-

passivated zone , a central strip was protected by a silicon slice during hydrogen implantation. The main relevant information was a significant increase of the mean value of the photoresponse in the passivated zone. For the purpose of illustration, Fig.lO(a) uses 8 color levels and Fig.lO(b) uses 256 color levels. The lowering of the reflection coefficient in the passivated zone can explain a large part of the increase of the photocurrent inside the grains /41/.

5.2 ADDlication to 111-V solar cells.

5.2.1 ~ e v i c e under test.

The im~roved 111-V solar cells under test were made bv a m d e d isothermal LPE Drocess recentlv described 1421. A thin (= 70 nm ) graded band gap window was grown by isothe&ally soaking

a

n-GaAs substrate in a saturated Be doped GaAlAs melt. The A1 composition increased towards the surface up to X A l ~ s = 0. 85 and Be diffused in the GaAs substrate giving a GaAs p-n junction. The junction depth was 1.5 pm. This window allowed an increase of cell efficiency due to a decrease of reflection coefficient and, mainly, to a reduction of surface recombination velocity for minority carriers. This point will be discussed below. The front contact ( 200nm thick ) was made by Au-Be eutectic alloy ( 99-1 in weight ) after window etching by lift-off micro-photo-lithography

.

The rear ohmic contact was made with a 100 nm AuggGeMNi layer.

5.2.2 AR coating effect and GaAlAs window effect.

A study of the AR coating was performed. Two solar cells presenting nearly the same photovoltaic characteristics before the AR coating were used. One device was coated ( 123 nm of MgF2 obtained by vacuum deposition ). For each device, LBIC topography was performed with the same laser diode power (145 p W )I43 I. Each numerical image was obtained with 100 lines of 100 points, with 10 pm steps between each geometrical points; the analyzed solar cell area was lmm2. A statistical analysis of these 2 x 10000 photocurrent values was performed-. an histogram was obtained by plotting the number of points analyzed versus the photocurrent amplitude ( 256 levels ). The histogram ( Fig.

11) corresponding to the LBIC topographies gives the photocment contribution of the different zones of each solar cell : an increase of 27 % was obtained between the two maximum currents. This was mainly due to reflectance variation ; see Fig.5: curve a) without AR layer ; curve b) with AR layer ; curve c) GaAs for comparison.

Now, by means of a photoresist process, a part of the above solar cell without an AR layer was exposed to HC1. This is a selective etchant for Ga .A1 As for x> 0.4. The A1 concentration was nearly proportional to the window thickness. Then,

lbZ

thicbess of the etched zone was about the half of the window

-

around 30 nm thick 1441 and x = 0.4 on the surface. Fig.12 shows a high resolution

C6-122 REVUE DE PHYSIQUE A P P L I Q U ~ E

-

0 5 0 100

Distance x ( pm )

Figure 9.Si bicrystal a) LBIC topography ; b) Photoresponse profiles in vicinity of boundary.

Figure

1300

10.

Hydrogen passivation effect. a) 8 levels of current: b) 256 1evels.Silso solar

WITHOUT AR LAYER

84 92 100

75 80 85 90 9s I00 105 110 115 120 125 I30 135 140

cell.

PHOTOCURRENT LEVELS

Figure ll.Histogram corresponding to two 1II.V solar cells.

Figure 12.III.V solar cell with an etched window zone.

Figure 14.~ipolar transistor;a) structure of the device; b) LBIC topography ( area 4 m 2 )

a

Figure 15.S~hott.k~ device; a) structure: b) effect of series resistance ( area 1 mm2)

C6-124 REVUE DE PHYSIQUE A P P L I Q U ~ E

LBIC topograph corresponding to this GaAs solar cell .The investigated region includes the 2 zones : with window (a) and etched window (b). We can observe a drastic photocurrent decrease in the etched area. However, the measured local photocurrent was influenced by variations of both the reflectance and the local transport properties. Then reflectance experiments were performed on the two zones of the solar cell: we obtained nearly the same reflection coefficient at 780 nm (see curves a) and d) in Fig.5). Only the local transport properties can explain the large variations obtained between the 2 zones, namely 30%, as discussed now.

5.2.3 Recombination velocity at the GaAsIGaAlAs interface deduced from LBIC measurements.

The maded band-P~D window is almost transDarent at 780 nm : the contribution of this laver to the total shos circuit currzni is negligible. The normdized contribution of the base to the photore~ponse is :

This relation is based on the following approximations : i) S, --> 00 , ii) aET >> 1 , and iii) H'IL >>I

.

S is the hole surface recombination velocity on ;he back side of the cell , a the abso&tion coepficient, ITthe thickness of the base, the junction depth,

%

the hole diffusion length and w the depletion zone width.

The normalized contribution of the depletion zone is :

J d / q N = ( l - R ) [ 1 -exp(- a w ) ] exp ( - a x j ) The contribution for the front ( p-type ) is , with $ = SnLn/Dn

Jf / q N = (1-R)aLn ( a 2 ~ n 2 - l ) - 1

(

- a L n e x p ( - a x j )

+

[

^{( $ +} aLn)

-

I ( ch(xj/Ln) + sh(xj/Ln)I =P(- a xj)

I.[

^{$ sh(xjLn) +} ch(xj/Ln)l-l} (24) Sn Ln and Dp are the surface recombination velocity, the diffusion length and the diffusion coefficiht, respecuvely, for minority carriers. The total normalized photoresponse is given by :

J / q N = ( l - R ) J t (25)

where Jt stands for the internal quantum efficiency and J = Jb+ Jd

+

Jf

.

Let 1 and 2 be the indexes for the zone with window and with etched window respectively ; then :

J1 / J2 = ( I-R1 ⁾ Jtl / ⁽ 1-R2) Jo (26) Fig.12 shows that the mean photoresponse values are in the ratio : J1/J2 = 1.43. According to reflectance measurements ( Fig.5 ), we tak R1

-

^R

^.

From (22) to (26), the calculation is made with the following set of data: a = 1.7 1 J c m - l 26

1

^{x. = 1.5 pm , w = 0.1 pm , L = 3 pm , L =}

2 pm , HC 350 pm

.

^{D,, =} 25 cm2/s and SnI = l d c d ;

/45/

The value of the surfacc!recombina~on velocity obtained for the GaAsIGaAlAs interface at the etched window, is Sd = 2.34 lo5 cm/s. In a previous paper 1461, a constant band-gap window (1200 nm thick) has been analysed by LBIC mapping. In this case, a very thin transition layer ( 0 < x < 0.8 ) does exist between the p-GaAs zone and the constant concentration window with x = ($8. After etching, the etched area left a residual window around 1 nm thick 1471 with x = 0.4 at the surface. The above calculation was made with the same set of data, and a value of Sn2 = 4.57.10~ cm/s is obtained. These results suggest that the recombination velocity at the interface varies with the window thickness. When the latter decreases, the minority carriers are more affected by the free surface due to the tunneling effect.

5.2.4 Multispectral tandem solar cells

.

A promising way to improve the efficiency of concentrating type photovoltaic devices is to fabricate multibandga~ systems with two or three iunctions of different enerwgaus

-- -

^m

.

The GaAs (1.42 eV)

-

A b

3 5 ~ a 0 - 5 k ~

11.89 eV) couple represents a very efficient band gap combination. The & e - t e d a l cascade sdfar cell reauires few e~itaxial lavers ( no tunnel iunctions ⁾ and no current matching. Such a device creates two s6icked juncgons whic6 are klectri~alliinde~endent. The structure of this2evice is given in Fig. 13.(a). The first junction was formed by two GaAs layers, Sn and Ge doped, grown by LPE on a p+ Zn

-

doped substrate. Then a thick Sn

-

doped A10.35Ga0 6 5 A ~ layer ( about 10 pm thick) was subsequently fabricated. Finally a thin graded AlGaAs wndow layer was deposited by isothermal liquid phase epitaxy by contact between the solid and the Be

-

doped melt corresponding to A10 iSAs. During the contacting process, Be diffuses into the A10 35Ga0 65A~ layer to form the upper junction of the device. The homogeneity of the local p h o t o c k n t was ~nvestigated by LBIC imaging. Fig.l3.(b) and (c) show the topographies of tandem devices without and with a buffered (Ge doped) layer between the substrate and the n-GaAs layers. The images were generated using 200 lines with 200 points in each line and a step of 10 pn. The 780 nm wavelength is well suited for the present study since the window and the first junction are transparent to the incident beam thereby allowing a clear imaging of the second junction

.

Fig.l3.(b) presents a device without a buffered layer

Au-Gc-Ni contact Au-Be conwct

Figure

Q

I

^GaAs

I

With Buffer layer

13.Multispectral tandem solar ce1l.a) structure;b)without buffer;c)with

Without lay=

buffer layer.

and some growth defects are clearly evidenced. With a buffer layer ( Fig.l3.(c) ⁾ the homogeneity is good and we note the straight lines corresponding to the mesa process. For the first time, a buried active junction, at 8 pm below the surface, is electrically imaged. Of course the method is non destructive.

5.3 Control of doping in bipolar transistor.

Fig.l4.(a) gives the stucture of the NPN bipolar transistor under test. The device was used in photovoltaic mode. Fig.l4.(b) shows the corresponding topography using 200 lines with 200 points in each line and a step of 10 pm. The black color corresponds to the front metal. The emitter-base region appears with two colors: blue for the n-zone and red for the p-zone. The photocurrent of the emitter zone was reduced by 34% with respect to the base. This is due to the difference of the diffusion length between the two regions.

5.4 Series resistance of Cr layer for Schottky device.

The LBIC topograph Fig.lS.(a) corresponds to a scan between two grid fingers of the structure shown in Fig.lS.(b). Numerical imaging was obtained from 100 line scans of 100 points which are separated by 10 pm from each other. The analyzed device area was 1 mm2. Each color level corresponds to a photocurrent interval of 9 arbitrary units. However, the image is more representative of the effect of a series resistance in the Cr layer than the bulk properties of the silicon substrate. Also shown in Fig.lS.(a) is the photocurrent profile of line 50; it is clear that the current decays depend on two factors: the initial decay is due only to the effect of the series resistance whereas the later part incorporates in addition the effect of the decay due to scanning away from the Schottky edge 1481. The effect of the series resistance does not seem to play any significant role in the determination of L as long as there is a sufficient number of data points in the exponential region of the photocurrent prof~le.

In semiconductor technology, it is of great importance to be able to follow the various process steps to identify uncontrolled and undesirable changes of the final product. Consequently, the development of effective devices needs the use of non destructive analytical techniques, with suitable spatial resolution, to characterize the electrical performance of the device. Quantitative mapping by LBIC is just such a technique.

ACKNOWLEDGEMENTS: This work was supported by the CNRS (Pirsem) and AFME.

Dr. K. Masri is gratefully acknowledged.

REFERENCES

Holt, D.B.,Quantitative scanning electron microscopy , ed. Holt , D.B., Muir , M.B., Grant, P.R. and Boswarra, I.M., (Academic, London ) 1974 chap.8.

Hanoka, J.I., Solar Cells

1

(1979) 123. and references therein.

Inoue, N., Goodnick, S.M.and Wilmsen, C.W., Solar Cells.

1

(1979) 233.

Donolato, C., Proc.Int. School of Materials Science and Technology, (Springer-Verlag, Berlin) 1985 p. 138.

Marek, J., J. Appl. Phys. (1984) 318.

Chernisky, G.and Laugier, A., Poly-micro-crystalline and amorphous semiconductors , ed. Pinard, P. and Kalbitzer ,S., ( Editions de Physique, Paris) 1984 p.343.

Szedon, J.R., Temofonte, T.A.and O'Keeffe, T.W., Solar Cells.

1

(1980) 251.

Wilson, T., Osicki, W.R.,Gannaway, J.N. and Booker, G.R.J. Mat Sci.

14

(1979) 961.

Siegman, A.E.,An Introduction to Lasers and Masers , (Mc Graw Hill, N.Y) 1964 p.304.

Dhariwal, S.R., Kothari, L.S. and Jain, S.C., Solid-State Electronics. 3 (1977) 297.

Hovel, H.J., Semiconductor and Semimetals ,Vol.l 1, Solar cells, (Acad.Press, N.Y) 1975 Ioannou , D.E., IEEE Trans. Electron.Devices, E.D.-30 ,

2

(1983) 1834.

Rebiai, S. and BielIe-Daspet, D., Rev.Phys.Appl.21 (1986) 545.

Donolato, C. , Phys. Stat.Solidi (a) (1981) 649.

Kern, R. and Wagemann, H.G., Proc. 6th E.C. Photovoltaic Solar Energy Conference, (London, U.K) , ed.Palz,W. and Treble, F.C., ( Reidel, D., Dordrecht ), (1985) p. 133.

Weinberg, I., Goradia, C., Swartz, C.K. and Hermann, A.M., Proc. 15th IEEE Photovoltaic Specialists Conference, (Kissimmee, USA), ( 198 1) p.484.

Damaskinos, S. and Dixon

,

A.E., Can. J. Phys. 62 (1985) 870.

Graff, K. and Fisher, H., Topics in Applied Physics, Vo1.31, chap.5, ed. B.O.

Seraphin, (Springer

-

Verlag, Berlin ) , 1979 p. 173.

Runyan, W.R., NASA CR 93154, National Technical Infomation Se~ce,N68-16510 (1968) 1976 Annual book of ASTM Standards, Philadelphia, part 43 F 391.

Dash, C.and Newrnan, R., Phys. Rev.

B

(1955) 1151.

Fabre, E., Acta Electronics 2Q (1977) 117.

Weakliem, H.A. and Redfield, D., J. Appl. Phys. a ( 3 ) (1979) 1491.

Jellison Jr, G.E.,Modine, F.A.,White, C.W.and Young, R.T., Proc.15th IEEE Photovoltaic Specialists Conference, (Kissimmee, USA), ( 1981) p.1164.

Monemar, B., Shih, K.K:and Pettit, G.D., J. Appl. Phys. a ( 6 ) (1976) 2604.

Therez, F., Thesis, no 949, LAAS, Toulouse, France , (1980) Zook, J.D., Appl.Phys. Lett. z ( 2 ) (1980) 223.

Zook, J.D., Appl.Phys. Lett. Q(7) (1983) 602.

Kipperman , A.H.M. and Omar, M.H., Appl.Phys.Lett.2 (1976) 620.

Ioannou, D.E. and Davidson, S.M., J. Phys. D: Appl. Phys.

12

(1979) 1339.

Dixon, A.E.,Damaskinos, S.,Oliver,B.A. and Adsett, R.T.,J.Can.Ceram.Soc.~ (1984) 21.

Davidson S.M.and Didtriadis, C.A., J. Microscopy

118

(1980) 275.

Boyeaux, J.P., Masri, K., Mayet, L., Stcherbanioff, L. and Laugier, A., Ann. Chim. Fr.

2

(1987) 395.

Ahrenkiel. R.K.. Aharoni. H.. Haves. R.E. and Fardi. H., Proc.18th IEEE Photovoltaic specialists conference, &as iregas, USA), ( 1985) p.738.

Boyeaux, J.P., Laugier, A. and R. Ruckteschler, Energy Beam-Solid Interactions and Transient Thermal Processing, ed.Nguyen, V.T. and Cullis, A.G., (Editions de Physique, Paris), (1985) p. 291.

Laugier, A., Mayet, L., Boyeaux, J.P.. Gavand , M. and Montegu .B.$efect Recognition andfmage Processing in ZIZ-V Compounds , ed.Fillard. J.P. (Elsevier Science Publishers B.V.), (1985) p. 269.

Wilke, V., Scanning

1

(1985) 88.

Nordlander, E., Drugge, B. and Tapia, M., J. Phys.E : Sci. Instr.

fi

(1985) 65.

Truong, V.K., Marchand, J.J. and Nodet, H., J. Phys.

a

(1982) C1-165.

Masri, K., Boyeaux, J.P., Kumar, S.N., Mayet, L. and Laugier, A.,Polysilicon Films and Intelfaces, ed.Wong, C.Y.,Thompson, C.V. and Tu, K.N., MRS. Symposium Proc.Vo1.

106, (MRS, Pittsburgh) (1988) p.89.

Boyeaux, J.P., Laugier, A., Montegu, B., Courcelle, E., Siffert, P. and Chemisky, G., Energy Beam-Solid Interactions and Transient Thermal Processing, ed. Nguyen , V.T.

and Cullis, A.G. (Editions de Physique, Paris) , ( 1985), p. 285.

Gavand, M., Mayet, L., and Laugier , A., Proc.11 th Int.Symposium on GaAs and Related Compounds ( Biarritz, France). Inst. Phys. Conf. Ser. no. 74 : Chap. 6, (1984) p. 469.

Boyeaux,J.P., Gavand, M., Masri, K. , Mayet, L., Montegu , B. and Laugier, A.,

Proc. 19th IEEE Photovoltaic Specialists Conference, (New Orleans, USA) , ( 1987) p. 804.

Kordos, P. and Pearson, G.L., J. Appl. Phys. X ( l 1 ) (1979) 6902.

Laugier, A. and Roger, J-A., Les photopiles Soiaires , (Tchnique & Documentation , Paris), 1981

Boyeaux, J.P., Masri, K., Mayet, L., Montegu,B., Zerdoum, R. and Laugier, A.,

Proc. 7th E.C. Photovoltaic Solar Energy Conference, ( Sevilla, Spain )

.

ed.Goetzberger, A., Palz, W. and Willeke, G., ( Reidel, D., Dordrecht ), (1986) p. 1089.

Garner, C.M., Shen, Y.D., Su, C.Y., Pearson, G.L. and Spicer, W.E., J.Vac.Sci.Techn01. u ( 4 ) (1978) 1480.

Masri, K., Boyeaux, J.P., Kumar, S.N., Mayet, L., Chaussemy, G. and Laugier, A., 1988 Europ. Mat. Res. Soc. Spring Meeting, Strasbourg, to be published in Appl.Surf.Sci.