Selfconsistency and selfsufficiency of the photocarrier grating techniqueI. Balberg, A. E. Delahoy, and H. A. Weakliem Citation: Applied Physics Letters 53, 992 (1988); doi: 10.1063/1.100051 View online: http://dx.doi.org/10.1063/1.100051 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/53/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Comparison of self-consistent field convergence acceleration techniques J. Chem. Phys. 137, 054110 (2012); 10.1063/1.4740249 A self-consistent, integral-equation technique for the analysis of ICRF antennas AIP Conf. Proc. 403, 421 (1997); 10.1063/1.53366 Selfconsistent proximity effect correction technique for resist exposure (SPECTRE) J. Vac. Sci. Technol. 15, 931 (1978); 10.1116/1.569678 New Techniques for the Computation of Multiconfiguration SelfConsistent Field (MCSCF) Wavefunctions J. Chem. Phys. 56, 1769 (1972); 10.1063/1.1677438 Simple steps to energy self-sufficiency Phys. Today

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Seif .. consistency and selfasufficiency of the photocarrier grating technique I. Salberg The Racah Institute a/Physics, The Hebrew University. Jerusalem 91904, Israel

A. E. Delahoy and H. A. Weakliem Chronar Corporation, P. O. Box 177, Princeton, New Jersey 08542

(Received 4 April 1988; accepted for publiction 11 July 1988)

The recently suggested photocarrier grating technique appears to be the most reliable method available for the determination of the ambipolar diffusion length in hydrogenated amorphous silicon. We show that the technique can be made simpier than originally suggested, and that it is self-sufficient in the sense that all the required parameters can be determined by the same experimental setup. It is demonstrated that the various results obtained by the technique are self-consistent and that extremely accurate values of the ambipolar diffusion length can be determined.

It is wel! known I that the solar cell operation param­eters are determined by the minority-carrier diffusion length (MCDL), and its role in determining photovoltaic device properties made from crystalline I and amorphous2

,.1 semi­conductors has been the subject of numerous investigations. Knowledgc of accurate values of the MeDL secms to be of particular importance in devices made from amorphous semiconductors.1

•3 The surt~\ce photovoltage technique has

become commonly used in recent years4•7 for the determina­

tion of the ambipolar diffusion length L, and its relationship to MCDI" is known.4 Recently it was shown' that this meth­od, while applicable to crystalline semiconductors, yields ex­aggerated values for L in amorphous semiconductors and that the measured values are not related to the MCDL in a simple manner.

A new method to determine L was suggested two years ago by Ritter and co-workers:J-

" The method is based on

the establishment of a photocarrier grating in the sample, followed by measurement of the photoconductivities in the presence and the absence of a photocarrier grating. TIle mea­surements are easier to make and the results are easier to interpret theoretically than those of the surface photovoltage technique. In particular, the theoretical analysis II of the method shows that as long as the dielectric relaxation time is shorter than the recombination time (which is equivalent to the absence of space-charge effects) the experimental results indeed yield the ambipolar diffusion length. Since we are concerned here mainly with the experimental improvement of the method and following the conclusions of Ref. 11, we assume throughout this letter that under the present experi­mental conditions of applied light intensities and dectric fields we are in the ambipolar diffusion regime. A more de­tailed and quantitative consideration of data under various experimental conditions wiB be reported later.

The object of this letter is thus twofold: to demonstrate some self-consistency checks which support the interpreta­tion of the measured quantities, and to suggest additional simplifications whkh may be applied to the measurement technique. We believe that these suggested procedures can make the method practical for routine characterization of solar cell materials.

The photocarrier grating method utilizes a coplanar ge-

ometry of a photoconductor on which a spatially modulated light intensity produces a "grating" of photocarrier genera­tionY"! This grating becomes blurred due to carrier diffu­sion, Since the two length parameters which determine the blurring in this configuration are the ambipolar diffusion length L and the known grating period A it is expected that the macroscopic transport parameters such as the photocon­ductivity {Ig transverse to the grating "fringes" will depend on the ratio L I A. The procedure which enables the deriva­tion of the magnitude of L I A is based on a comparison of 0-K

and (J, where the latter quantity is the photoconductivity for uniform illumination. The grating is created by two coherent light beams FI and F] which interfere at the photoconductor surface." If a small electric field (see below) is applied, the experimental ratio

{3= (O'g -a(FI)JI[u(FI +l~) -(T(FI )]

can be shown9 to be related to L I A by

, 2yra

/3= > - (l + rf~/F,Hl + C21TLIA)2F

0)

(2)

The parameter r characterizes the light intensity depen­dence of the photoconductivity according to the well-known dependence, 12

(3)

while the parameter Yo (,;;; 1) is an experimental quality fac­torY -Ii For small Fj F J ratios the value of L was originally derived from the fit of the experimental data to Eg. (2) using both rt~ and L I A as the fitting parameters." The relation given by Eq. (2) can be presented, however, in a more explic­it manner which yields the value of L without the knowledge of the val.ue of Yn, This can be done by rewriting Eq. (2) as

(2y) I i2Yo/[ {I - (3) (1 + yFj Pi)] 1/2 - 1

(217'L)2 (4)

Hence for small F21 FI ratios, the presentation of the data as a 1/ A 2 vs (1 - (3) -1/2 plot, directly yields the value of L by the intercept which is - 1/(217'L)2, If rand FzIF, are known (see below) one gets a more accurate result by using t (1 -~ (3) (I -t-- yF2/ F i ) 1- 1/2 as the experimental variable.

To demonstrate the use of Eq. (4) let us turn to our experimental measurements. As in Ref. 9 we determine first

992 Appl. Phys. Lett 53 (1 i). 12 September 1988 0003-6951/88/370992-03$01.00 @ 1988 American Institute of Physics 992

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the ratio f3 by measuring the ac photocurrent which is ob­tained by keeping F, as a de bias illumination and having a superimposed coherent chopped-light beam of intensity Fl' The light source was a 10 mW He-Ne laser, and the ac photo­current was monitored by a lock-in amplifier. The numera­tor of Eq. (1) is proportional then to the lock-in reading when FI and }; have the same polarization, while the de­nominator ofEq. (1) is proportional to the reading when the polarization of FI is rotated by 90° with respect to that of F2•

Typical results of such a measurement, which was car­ried out on an intrinsic hydrogenated amorphous silicon (a­Si:H) layer (prepared by a method described previouslyll), are shown by the experimental points of the "ac measure­ment" in Fig. 1. The thickness of the sample was 1 fim, the electrode separation was 1.4 mm, the bias light intensity, F J ,

was 3 mW lem2, and the chopped (350 Hz) light beam had

an intensity f; = O.lFt • Note that in order to determine L with high accuracy, one has to use the value of l' (see below). It is clearly seen that the corresponding data points can be fitted by a straight line, such that the 1/ A 2 axis intercept yields the value of L, as indicated in the figure.

The measurement procedure described above, while be­ing quite simple, can be simplified even further. For exam­ple, one can perform a direct dc measurement of the photo­conductivities listed in Eg. (1). Hence f3 can be determined without using a chopped light and a lock-in amplifier. Under typical conditions, applicable to a-Si:H, this does not cause too much loss of accuracy as demonstrated by the "de mea­surement" data points which are shown in Fig. 1-

A more significant simplification can be accomplished by removing the relianceY on the light polarization when comparing the photoconductivity under spatially modula­ted and spatially unmodulated illumination [the numerator and denominator of Eq. ( 1 ) ] . This simplification is based on rotating the sample, rather than the polarization, by 90°. The

N ,

2 r-: ~c-'~~;~~~~~~ r-'- T -

I !J. de measurement I 0 sample rotation

l-

l

~ I

-1

J '"Y

1121'o/(2nL)2=0.45 I'

~ 0 '"Y'"Yo2=O.~1

'[1/2nLl'·O.5 * L'2250"ooA j -1 ,_,,- L -,_,-,- _1_1..-1_ L...l,_ L,...l_J

o 1 234 5 6 [2/(1-(3)(1+1'F2/F1)]1I2

FIG. 1. Experimental dependence of the measured quantity fJ on the grat­ing period A as obtained by the present experimental procedures. All the measurements were carried out using a small applied field of 140 V /crn.

993 Appl. Phys. Lett, Vol. 53, No. 11,12 September 1988

numerator in Eq. (1) is then proportional to the ac photo­current which is obtained when the interference fringes are parallel to the coplanar electrodes, while the denominator in Eq. (1) is proportional to the ac current which is obtained when the interference fringes are perpendicular to the elec­trodes. Indeed, as is shown in Fig. 1, the results obtained using sample rotation rather than the light polarization rota­tion confirm this suggestion. Of course, one can combine the two simplifications described above noting the somewhat lower accuracy as well as a somewhat lower vaiue of L.

As we pointed out above, the knowledge of y is quite important for the determination of an accurate and rellable value for L. The traditional way to determine y is to vary the light intensity and use relation (3). Such a procedure for the sample whose results are shown in Fig. 1, yielded a value of y = 0.83 for the incident light intensity range 0.1 <FI + F2 <100 mW/cm2

• In the present setup one can derive, however, the value of r by measuring a( F,), a( F2 ), and a(F, + F~). For F2~Fl' Eq. (3) implies that

[a(F, +F2 ) -.(T(Ft)]/a(Fz) =r(F2IF, )! Y (5)

Since the range of y is known' 2 (0.5 < y< 1 ) , it is easy to find its value from these measurements and Eq. (5). In the pres­ent case, we found from the measurements that for F21 F\ = 0.1 the quantity given in the left side of Eq. (5) is 0.54, yielding a y value of 0.82. As expected, this is in excellent agreement with the result mentioned above.

Having determined y we can turn now to self-consisten­cy checks of the results. First let us consider the slope ob­tained in Fig. 1. This slope is expected, according to Eq. (4), to yield the value of yJ/2yO' One also expects'! (see above) that the value of Yo win be smaller than, but very dose to, unity. Hence, if the yl12 Yn value, which is obtained from the slope, is found to be larger than the yl /2 value which is deter­mined independently, one must conclude that the data are inconsistent with the interpretation suggested by Eqs. (2) and (4). On the other hand, if the value of Yo is found to be less than, say, 0.8, it means that the grating is poor and the L values are oflow accuracy. In the example shown in Fig. 1, the slope yields a yti value of 0, 81 which, combined with the above value of y = 0.82, yields the reasona.b!e9

.1

! valu.e of Yo = 0.99.

As mentioned above, the accuracy of the L value ob­tained is of importance and thus we have also devised a cor­responding self-consistency check for the value derived for 1,. We have analyzed the.8( A) dependence when the blur­ring of the grating is due to both the drift and the diffusion of the minority carriers. Following the analysis of Ref. 10, the effective drift length of the minority carriers, Le (the net contribution due to the applied electric field E), can be ob­tained from the above-described measurements by using the relation:

A { 2yri; [(21TL \ 2121112 L=- -1+--, 21T (I-PHI + yFzIF, ) A ) .1

(6)

Since y, Yo, and L (for the E -> 0 case) were determined above, one can find 10 the electric field dependence of L" by just measuring the field dependence of f3 for a given A and using Eq. (6). Considering the linear dependence Iil:

Salberg, Delahay, and Weakliem 993

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I ~ I

?OOO~ 1

I r I

1 (\C)I) 1_ J\.,\ __

I ~ i

0 1

o

J\~2.5 IJm Fl=3 mW/cm2

F2/Fl=O.1 ,,(,),.2=0.81

o

~ L=2225±10A o L=220OA ... L=225OA o L=200OA -j

I _J ____ L__ __ L __ .1. __ .J

1000 2000 3000 E (V/cm]

FIG. 2. Experimental dependence of the minority-carri<!r effective drift length on the applied electric field. The different sets of the data points arc associated with different values assumed for the ambipolar diffusion length I..

(7)

where fir is an effective pr product, one expects that for E _'""C 0 olle should get L" = O. We can then derive the Le values from the experimental,8(E) data and choose the val­ue of L as a parameter, The desired value of L is the one which will force the linear extrapolation fEq. (7) 1 of the data points in an L" vs E plot. Such a plot of data points, which were obtained with a A = 2.5 pm grating and under the conditions described in relation to Fig. 1, is shown in rig. 2. It is seen that the value of L = 2225 A yields an excellent fit to the linear dependence given by Eq. (7). The value of pT derived from the slope is in agreement with values previously obtained l.i for intrinsic a-Si:H. The important point made here is, however, the high sensitivity of the L" (E) depen­dence to the value assumed for L. As is dearly seen in Fig. 2, a deviation of more than 10 A (i.e., 0.5%) is enough to yield a disagreement with the behavior expected from Eq. (7).

994 Appl. Phys, Lett, Vol. 53, No, ii, i 2 September 1988

The fact that the value of L derived here (Fig. 2) is in excel­lent agreement with that derived from the data of Fig. 1 is a convincing proof for the self-consistency of the method.

In conclusion, we have shown that the photocarrier grating technique ca.n be simplified by using a dc measure­ment and a sample rotation. We have further shown that the value of the photoconductivity exponent can be easily de­rived in the experimental setup used for the determination of the ambipolar diffusion length. This determination, as well as the field dependence of the measured p, enables a self­consistency check of the value and the accuracy of the ambi­polar diffusion length L.

This work was supported by the Solar Energy Research Institute (SERl) under subcontract No. ZB-7-060031.

'See. for example, S. J. Fonash. Solar Cel! Device Physics (Academic. New York, 1981); H. ], Hovel. Solar Cells, Vol. 11 of SemicoNductors and Se­mil1lPtals, edited by R. K. WiHardson and A. C. Beer (Academic, New York, 1975)' p, 1; see also references therein,

"R, S, CrandaH, j, App\. Phys, 54, 7176 (1983), 'M. Hack and M. Shur, J, App!. Phys, 58, 997 (1985). and references therein,

'A. R. Moore, in Semiconductors and Semimetals, edited by J. 1. Pankove (Academic, New York, 1984), Vol. 21, PI. C, Chap, 7,

'R, Schwartz, D, Slobodin, and S. Wagner, App!. Phys. Lett. 47, 740 (1985),

"!, Sakata, T. Ishida, S. Okazaki, T. Saitoh, M, Yamanaka, and Y. Haya­saki, J, Apr!. Phys, 61,1916 (1987),

7S, R. Kurtz, ], Proscia, and R. Gordon, }, App\. Phys. 59, 243 (1986). 'I'. J. McElheny,}, K. Arch, and S. J, f'ollash, App!. Phys. Lett. 51, 1611 (l9R7); R. Schwarz, S. Goldeckcr, T. Muschik, N. Wyrsch, A, V, Saha, and H. Curtins. j, Non-Cryst. Solids 97&98.759 (1987).

"D. Ritter, E. Zeldov, and K. Weiser, AppJ. Phys, Lett. 49. 791 (1986), ,oD, Ritter and K. Weiser, Phys. Rev. B 34, 9031 (19g6), "Preliminary accounts of the theoretical analysis have been reported by D.

Ritter, E. ZeJdov, and K. Weiser, }, Nun-Cryst. Solids 97&98, 619 (! 9(7), A [!1orecomprehensive account of the theory is given in D, Ritter, E. Zeldov. and K, Weisel', Phys, Rev, B 15 (in press),

'~'A. Rose, Concepts in Photoconductivity and Allied Problems (Wiley, New York, 19(3),

uS, C. Gan, H. Volltrauer, F. Faras, A, E, Delahoy, E. Escr, and Z, Kiss, AppL Phys, Lett. 47,1317 (1985),

'.R. A. Street. J, Zesch, and M, J, Thompsoll, AppL Phys, Lett. 43, 672 (1983).

Salberg, Delahoy, and Weakliem 994

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