38 (1994) 81-86
Grain boundary effect in polycrystalline InP films from optical reflectance measurements P. Mitra, P. Gupta, S. ~haudhuri
and A.K. Pal
Dep~rt~~lentof ~~~uterials Science, Indian Association ,furthe ~~iiti~ution qf Science, ~ulc~ttu-~~~~O32(India) (Received October 4. 1993; accepted January 14, 1994)
Abstract Polycrystalline InP films were deposited by d.c. magnetron sputtering of an InP target on glass substrates. The effect of inter-crystalline barrier on the carrier transport in InP films has been studied critically. The grain boundary potential, the density of trap states at the boundary region and the carrier concentration in the films were obtained by utilizing an optical technique. developed on the basis of the Dow-Redfield model. The roughness (30-40 nm) of the surface of the film was determined by measuring the diffuse reflectance by a spectrophotometer while the band gap (-1.35 eV) was determined from the transmittance versus wavelength traces. The barrier height in InP films was found to be in the range 0.16 to 0.22 eV, while the corresponding density of trap states in the grain boundary region was -0.3-7.0 x 10*2cm-2. It was observed that the experimental plot of normalised absorption coefficient below the band gap showed excellent agreement with the theoretical model based on the consideration of both the electric field and the mechanical stress to be present in the film.
1. Introduction Indium phosphide is a very promising photovoltaic material for space solar cell applications [l]. This is basically due to its high radiation resistance and its potentiality for achieving high efficiency. Earlier research efforts were directed towards the preparation of the multicomponent structures like ITO/InP and CdS/InP for terrestrical applications . MBE grown thin InP films were successfully used in the fabrication of highly efficient solar cells with efficiencies greater than 18% . The electro-optical properties of InP along with the carrier recombination mechanism indicated that InP and related compound multilayers are the best candidate for optoelectronic and microwave devices. Thin layers of InP produced by MOCVD and LP-MOCVD  have become very important in the field of semiconductor quantum devices using heterojunctions, quantum wells and superlattices. Hence, preparation of InP films by different techniques were tried by different workers with a view to study the material critically in thin film form so that device properties may be understood more clearly. ~254-0584~/$~.~ Q 1994 Ekevier Science S.A. All rights reserved SSL>I ~2S4-0584(94)OI354-J
Among the different techniques, reported so far for the deposition of InP films, liquid phase epitaxy , sputtering , electrodeposition  and organic chemical vapour deposition [S] are worth mentioning. InP in thin film form is, in general, polycrystalline in nature 161. Polycrystalline films generally consist of large number of grains with intermediate high resistive grain boundary regions. As a result the electron transport properties of these films will be controlled by the grain boundary scattering phenomenon (61. Grain boundaries are, in fact, disordered regions with large number of defects arising due to the incomplete atomic bonding or due to the departure from stoichiometry in a compound semiconductor. These result in the formation of energy states (trap states) within the band gap, which act as effective carrier traps, It is evident that the grain size, which depends on the deposition condition of the film, should affect the trap states in a polycrystalline semiconductor. Thus, the determination of the trap state density and barrier height in InP films will be very important to understand the properties of devices, based on polycrystalline InP films, in general. In this communization, we evaluated the grain boun-
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Chemistry and Physics 38 (1994) 81-86
dary barrier height and related physical parameters in polycrystalline InP films from optical reflectance measurements by using the modified model of Dow and Redfield [9-121.
2. Experimental InP films were deposited on glass (Corning 7059) substrate by d.c. magnetron sputtering technique. The target (diameter - 8 cm) was a p-type InP wafer (Cambridge Instruments Ltd., U.K.) with (100) orientation. The substrate was kept at a temperature within 380-450 K for the deposition of the film and the wafer was sputtered in argon plasma at a system pressure of 10-l Pa. The films with thicknesses of 0.2-1.0 urn were deposited and were analysed by EDX for composition, which indicated the films to be nearly stoichiometric. Optical transmittance versus wavelength traces of the films were recorded by a spectrophotometer (Hitachi: U-3410). The surface morphology of the films were studied by SEM (Hitachi: S-2300), which indicated a rough surface. The roughnesses of the films were determined by recording the diffuse reflectance of the film surface .
where R, = R + Rdiffuse. The diffused part of the reflectance from the film surface is Rdirfuse and C is a constant. Thus, we can obtain the surface roughness (CT,)from the slope of the plot of In (RJR) versus l/h2 (Fig. 1). The surface roughness (0,) for the above InP films was observed to lie in the range 30-40 nm. The absorption coefficient (a) was obtained from the transmittance versus wavelength traces. The variation of a with the incident photon energy (hv) is shown in Fig. 2. When multiple transitions occur in a material, the absorption coefficent may be written as (2)
c 0.55 AL
3. Results and Discussion X-ray diffraction trace (not shown here) of InP films was similar to that reported earlier . Films deposited at a substrate temperature in the range 380-450 K, had a most intense peak at 54.7” due to (222) planes while additional smaller peaks corresponding to (400) and (331) planes at 63.7” and 69.4” respectively The lattice constant (0.58 nm), were also present. calculated from the XRD trace, was in good agreement with that reported earlier for InP bulk (0.5869 nm) with zinc blende structure . The grain size of the polycrystalline InP films, as determined from SEM studies, was - 0.2 urn. The films had a rough surface, which was suitable for capturing more light for device applications. The surface roughness of the InP films was determined from the optical reflectance measurements  and is described, in short, here.
hd (eV) Fig. 2.
Fig. 1. Plot of In (RJR) against lA2 for a representative InP film.
3.1 Optical Measurements For a rough surface, if 6, be the r.m.s. height of the surface irregularities then we can express o0 in terms of the specular reflectance (R) and the total reflectance (R,) from the film surface, so that , In (R/R,) = - (47~5, )V?G +C
Variation of (a) absorption coefficient (a) with incident photon energy, and (b) (c&v)~ versus hv for a InP film.
et al. I ~ute~u~
Chemistry and Physics 38 (~~4~
where i denotes the summation over various types of transitions present. We have obtained only direct transition in InP film. The band gap (E,) - 1.35 eV was obtained from a plot of (ahv)z versus hv plot (Fig. 2). The effect of grain boundaries with inherent space charge regions due to the interfaces result in band bending and this is reflected in the broadening of the tail end of the variation of the absorption coefficient (a) at photon energies less than the band gap. Excess absorption in a polycrystalline semiconductor at the band edges may be described by the Franz-Keldysh effect arising out of the built-in electric field in the material. The Dow-Redfield model [lo, 111 seems to be a realistic approach towards the understanding of the absorption behaviour at the band tails due to grain boundary trap states in a polycrystalline semiconductor like InP. Bujatti and Marcelja  modified the DowRedfield model by considering spherical crystallites with radius L with some distribution P(L) of the radius (L) of the spheres. They could obtain an useful expression for the normalised total absorption (Al from which the potential barriers at the grain boundaries could be obtained under some simplified assumptions. Using the subscript zero to indicate quantities at the energy gap, the normalised total absorption was expressed as :
with C=[ (~“*/6)( K6)‘-(4i3)(
where P(L) is the probability for a crystallite to have a radius L. It can be noted here that a appearing in equation (3) is a function of both photon energy and electric field in the crystallites. Simplified expressions for the two limiting cases i.e. for small crystallites and for large crystallites, were also obtained by them 1121. For large crystallites the surface states may be considered to be all occupied by the charge carriers so that the grains become partially depleted of carriers and the electric field close to the surface will decay exponentially. In such a case, considering a Gaussian distribution  of the grains as: P(L) = (L,,, - L) (L - bin) exp (-L2/s2)
so that A/A, i.e. a(v)laO can be expressed as: a( v)/a,=C-‘[(~“~/12)(K~)~I~ -(K6/3)Iz+(n”2/&)I,]
The integrals I*, I2 and I3 are given by I, =
‘)Wl W~,)(y,/~)‘/~dy/y .Iys ‘)Wl (I/&,)(Y,/Y
(I i 1,) (y, i ~)~‘~ln(y,’Y$ dy 1 Y
with y = 7’;” fqF)-“” (Eg- ftw)
and ye= (Eg - fro) 7”’ (qF$2’3 and ym= ( E, -ho
)‘I3 Y”~ ( K )-*I3
= 2m* I ti’ ,6= 0.76f. and K = 11 h, .
f, and Xdbeing the average grain size and the Debye length respectively. The integral I in equations (7), (8) and (9) may be expressed as
Ai being the Airy function and K, is a constant of the material. The electric field (F) existing in the grain is given by F, exp [ -(L-r)/&]
The preexponential factor, F,, is assumed to be independent of the crystallite size and is equal to the ratio of the surface charge density to the dielectric constant of the material. The integral in eqn. (5) reduces to zero for E,-hv=E, and y,=y,; when A/A, tends to zero value. Thus, a plot of A/A, (or clip) versus (E,-hv) would indicate a sharp change at E,-hv= E,,. So, the eqn. (5) will allow one to evaluate the electric field F, and the inverse of the Debye length K from the best fit of the experimental data of aia,with the theoretical expression (5). Fig. 3 shows such a plot for a representative InP film. It may be observed that the above theoretical fit does not tally with the experimental data, indicating that there must be additional effects which was not considered in the above theoretical model. We have considered the effect of mechanical stress in the subband gap absorption, which is described here, in short. The influence of mechanical stress in the grain boundary region of polycrystalline films has been associated to electrostatic fluctuations of the band edge by several authors [17-191. The basic idea of the above model is the existence of a finite probabili~
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Chemistry and Physics 38 (1994,I 81-86
Now, the general form of the absorption coefficient oM (ho) due to mechanical stress may be expressed as:
Eg-h+(eV) Fig. 3. Variation of ala, with (Eghv) for a representative InP films along with the best fit theoretical plot (corresponding to Eb= 0.16 eV and Q,= 3x1011/cmz): --------- : Considering electric field only, -.-.-.-. : Considering mechanical stresses only, ___ : Considering both electric field and stress.
of transitions between states lying at different sites in the polycrystalline sample. This will control the specific shape of the absorption tail in the below bandedge absorption region. Besides this indirect transitions, allowed direct transitions may also occur simultaneously in these polyc~stalline films. But the latter will predominate only in the photon energy region ho > E, EE is the average value of the fluctuating Eg in the grain and grain boundary regions. So we will not consider the contribution from the latter on the tail of the optical absorption. In order to calculate the absorption due to mechanical stress, we consider first the variation of E, in various sites of the specimen by the following distribution function, written as : -(E&f” D(E,)-exp[
where D(E,)dE, is proportional to the number of microcrystallites per unit volume and P(E) is the probability of indirect transitions within the region of the sample in which the energy gaps are between I?, and E,+dE, Assuming the form of P(E) as given by Szczyrbowski :
where E’ = ?/ [ ( b* k202 ) /6me 1 and substituting eqn. (15) ineqn. (16), thefinalformofaM (lie) aftersimplification becomes:
where a! is the value of aM (ho) at E,, E,=E,- &/2E’ and
In the photon energy region IiiwIE, which is our special interest here, the above function @(Tim) is almost constant and its explicit form may be given by: Ii2k2 @(hW=(6me)E;’
with xmin= 6me ho / Ii2k2 and x,, = 6me E, / h2k2 . In real situation, the inclusion of finite grain size distribution as given in eqn. (4) 1131 will modify the expression of aM ( fiw) i.e. eqn. (18) as:
Cr2=Eg2&’ ,A2 - a/4Lc, Lc being the characteristic length over which E, is assumed to be constant and a is the average lattice constant. For polycrystalline material Lc is approximately equal to the diameter of the microcrystallite i.e. Lc-D (= 2L). Physically, the parameter K is a relative local and thermal fluctuating dilation constant and depends on the grain size the shape of the polycrystalline film and its lattice temperature.
with Co= [ ( I&*Ei )
QiL,hw)-Q,(W) ~ % (L/a)1’3( a/L)“3 16Co( E,-ho) ,
The inclusion of the grain distribution influence on [email protected]
has a negligible
R M&-u et al. i Materials
By using eqns. (5) and (21), one can get the total below sub-band-edge absorption, a = ([email protected] [email protected]
), and hence ([email protected]
to grain boundary effects. The best fit of this simple theoretical model to the experimental data (Fig. 3) gives the values of K and F,. It may be observed that consideration of both electric field and mechanical stress in the theoretical plot (Fig. 3) shows excellent agreement with the experimental data. The values of K and F,, thus obtained, will provide meaningful informations on the grain boundary potentials, density of trap states, carrier concentration etc. of polycrystalline semiconductor films. The barrier height (Eh) and the trap state density (Q,) were obtained from the relations
and Physics 38 (1994) 8146
pare well with the value for light hole effective mass (0.078) reported in the literature . Now, the electric field in the partially depleted grains would decay exponentially so long as exp (-L/h,) << 1 i.e L > h,. Thus, for partially depleted grains Debye length h, should be much less than the average grain size L. In our InP films L - 190 nm whereas h, was 40 nm indicating that the films were partially depleted of carriers. With increasing degree of depletion (as in the case of highly resistive undoped films), h, should tend towards L so that for full depletion, the electric field inside the grain boundary region will vary linearly according to F = F, (r/L)
Q,= EF,/ q
The values of Ei, and Q, for different InP films were found to be in the range 0.16 to 0.2 eV and 0.3-7.0 x 1012/cmzrespectively. Now, the Debye length (&) may be expressed in terms of the carrier density (P) as follows : hd = [( E kT/P q2)]“2
The variation of electric field inside the crystallites was also studied. It was observed that the field at the surface of the grains are - 105 V/cm and decreased rapidly to a small value towards the center of the crystallites.
The grain boundary barrier height obtained from the optical measurements as indicated above was compared with that obtained from the electrical measurements. For this purpose the electrical conductivity (0) and the Hall mobility (p) were measured in the temperature range 180-400 K. Fig. 4 shows the plot
Thus eqn. (24) may be used to calculate the carrier density (P) in the InP films. We have obtained P in the range 0.9-1.1 x1017/cm3 in the InP films studied here. It may be noted that these values of carrier concentrations agreed well with those obtained from the C-V measurements by using a Au/InP Schottky junction. The barrier height Eb may be expressed as  Eb= 2.58 x lo7 (m*/m)1/2(L/hd1)2 (aJB)3L where m*/m is the normalised carrier and &, is given by 
(25) mass of the
Z&l= hd -I-(&3/3LZ) - (h&L)
B may be obtained (for a direct transition) from 0
(ahv)2= B2 (hv-E,)
since the absorption coefficient (a) and the band gap energy (E,) have already been obtained. The values of absorption coefficient at band gap energy (a,,), the grain size (L) and B as obtained above may be put in eqn. (25) to obtain the value of m*/m. The value of m*/m in our InP film was - 0.08 which com-
Fig. 4. Plot of (a) In d versus UT, (bf In (~Tt’*f versus l/T for a representative InP film (a in 0’ cm-l).
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Chemistry and Physics 38 (1994) 81-86
0.3-7.OxlOl*/cm*. The grain size (L), density centration (P), obtained measurements confirm depleted of carriers.
values of Debye length (1L& of traps (Q,) and carrier confor InP films from the optical that the grains were partially
Acknowledgments The authors wish to thank the DST, Govt. of India for their financial support in executing the progranIme. One of the authors (P. Gupta) wishes to thank the C.S.I.R., Govt. of India, for awarding her a fellowship during the tenure of the work.
Fig. 5. Plot of In ( pTln) versus UT for a representative (p in cm%olt-set).
of In o versus l/T. It may be observed that the activation energies at low (~300 K) and high temperature regions differ significantly producing a sharp kink in the plot at - 300K. This is due to the onset of grain boundary scattering at low temperature. The data were analysed by using Petritz model [Zl], which was later modified by Seto  and Baccarani et al. . The slopes of the plots of In (fir’*) versus l/T and In (~Tln) versus l/T at the low temperature region (Figs. 4 and 5) gives  the grain boundary barrier height (Eb). The Eb values thus determined for the InP films were in the range 0.16-0.22 eV, which indicated an excellent agreement with that obtained from the optical measurements.
4. Conclusions The grain boundary potential in d.c, sputtered InP films was determined by utilizing a modified theory of Dow and Redfield. It was observed that the theoretical plot shows an excellent agreement when in addition to the built-in electric field the mechanical stress in the film is also considered. Only direct optical transitions were observed in the InP films at 1.35 eV. The barrier height was observed to be within 0.16-0.2 eV. The density of trap states in InP was also calculated and was observed to be within
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