Transport properties of polycrystalline silicon films

Transcription

1 Transport properties of polycrystalline silicon films G. Baccarani, B. Riccò, and G. Spadini Citation: Journal of Applied Physics 49, 5565 (1978); doi: 163/ View online: View Table of Contents: Published by the AIP Publishing Articles you may be interested in Charge transport in polycrystalline silicon thin-films on glass substrates J. Appl. Phys. 112, (212); 163/ Electron transport and band structure in phosphorus-doped polycrystalline silicon films J. Appl. Phys. 15, (29); 163/ Properties of tungsten silicide film on polycrystalline silicon J. Appl. Phys. 52, 535 (1981); 163/ Carrier transport in oxygen rich polycrystalline silicon films J. Appl. Phys. 49, 469 (1978); 163/ The electrical properties of polycrystalline silicon films J. Appl. Phys. 46, 5247 (1975); 163/

2 Transport properties of polycrystalline silicon films G. Baccarani and B. Ricco Istituto di Elettronica, Universita di Bologna, Italy G. Spadini a ) C.N.R.-Laboratorio LA MEL, Via Castagnoli, 1, Bologna, Italy (Received 19 September 1977; accepted for publication 4 January 1978) The transport properties of polycrystalline silicon films are examined and interpreted in terms of a modified grain-boundary trapping model. The theory has been developed on the assumption of both a 8- shaped and a uniform energy distribution of interface states. A comparison with experiments indicates that the interface states are nearly monovalent and peaked at midgap. Their density is 3.8 X 1'2 cm -2, in accordance with carrier-lifetime measurements performed on CVD films. PACS numbers: n.2.fr, n.8.cw, 73.Fw I. INTRODUCTION The electrical properties of polycrystalline silicon films have been interpreted in terms of two distinct models: the segregation theory, 1,2 according to which impurity atoms tend to segregate at the grain boundary where they are electrically inactive, and the grainboundary trapping theory3,4 assuming the presence of a large amount of trapping states at the grain boundary able to capture, and therefore immobilize, free carriers_ These charged states at the grain boundary create potential barriers, as illustrated in Fig. 1, which oppose the passage of carriers from a grain to the neighboring ones. The basic limitation of the segregation model is that it does not explain the temperature dependence of the film resistivity which is thermally activated and exhibits a negative temperature coefficient. By combining the grain-boundary trapping model with a thermionicemission mechanism through the barriers, Set 5 has recently developed a comprehensive theory of transport phenomena in polycrystalline materials which explains most of their electrical properties. However, Seto's theory, which assumes a 6-shaped density of states at the grain boundary, does not include the possibility that these are only partially filled when the depletion region does not extend throughout the entire crystallite and is, therefore, limited to the special situation where the trap energy is smaller than the Fermi level. In this work, we propose a modified version of the grain-boundary trapping model which, in our opinion, better clarifies the electrical properties of poly crystalline silicon films in the intermediate range of impurity concentrations. We consider both the case of monovalent trapping states and that of a continuous energy distribution of interface states within the band gap. Resistivity and Hall measurements have been performed on phosphorus-doped sputter-deposited polycrystalline silicon films. Comparison between theory and experiments leads to the following main conclusions: (i) Impurity segregation and carrier trapping at the grain boundary both take place in polycrystalline silicon, at least when this is phosphorus doped, and (ii) the trapalpresent address: SGS-ATES, Agrate Brianza, Milano, Italy. ping states are nearly monovalent, and peaked about at midgap. The theoretical model is derived in Secs. II-IV. Experimental details and measurements are described in Secs. V and VI, while Sees. VII and VIII are devoted to the discussion and conclusions. II. MODIFIED VERSION OF THE GRAIN-BOUNDARY TRAPPING MODEL According to Seto's theory, the dominant transport mechanism in polycrystalline silicon films is thermionic emission over the barriers. When the voltage applied to the crystallite is small, that is V kt /q, the thermionic theory leads to the following expression of the current density: where Ee is the band-gap energy, EE is the barrier height, EF is the Fermi energy referred to the intrinsic Fermi level in the neutral region, Nc is the effective density of states relative to the conduction band, and Vc = (kt /27Tm*)1 /2 is the collection velocity. 6 The conductivity of the film is then given by (a) (b) (c) GRAIN BOUNDARY \ I CRYSTALLITE I ) I FIG. 1. Sketch of the band diagram in polycrystalline silicon films J. Appl. Phys. 49(11), November American Institute of PhYSics 5565

3 putting W=tL. We find which allows one to determine N by means of an iterative procedure. The result of such a computation is shown in Fig. 2, where Nt has been represented versus the grain size L for various trapping-state concentrations and assuming E t = O. (6) L O'-6'-"-1.L--;:5-'-1"---"4'-'----L.J1O-3 GRAIN SIZE [em 1 FIG. 2. Impurity concentration values at the onset of complete depletion versus grain size, for various monovalent tra}&pingstate densities located at midgap. where L represents the grain size. Equation (2) can also be represented in terms of the electron concentration in the neutral region no, viz" which differs from the corresponding expression adopted by Seto [Eq. (14) in Ref. 5] by the factor no/na, na being the average carrier concentration within the crystallite. Equation (2) and (3) represent the starting point for interpreting the conductivity-temperature behavior. Such an interpretation, however, requires a hypothesis as to the nature of the interface states. In what follows, we shall consider two different cases: monovalent trapping states and a continuous distribution of interface states, in each of them reaching general expressions for the conductivity-vs-temperature relationship. III. MONOVALENT TRAPPING STATES AT THE GRAIN BOUNDARY Let us assume that the grain-boundary traps consist of Nt acceptor states with energy E t referred to the intrinsic Fermi level at the interface. Electrical neutrality then requires 2ND W =Nt{l + i exp[(et + EB - E F)/kT]} l, (4) Nn being the impurity concentration and W the depletion width. Correspondingly, the barrier height, obtained integrating the Poisson equation, is given by E B =q 2 W 2 N D /2E. (5) For any assigned values of L, Nt and E t, there will be an impurity concentration N such that, when ND < N the crystallites are entirely depleted. Such an impurity concentration can be derived from Eqs. (4) and (5) by (2) (3) Figure 2 clearly shows how Nt becomes proportional to L -1 and to L -2 respectively for the smaller and larger values of L and Nt. The asymptotic behavior of Nt may be derived from Eq. (4) by assuming W = L. N5 ""NtiL for EF - E t - B»}:;T; 1'15 "" (8E/q2L2)[EG - E t + kt In(2NtlNcL)] for E t + EB - Ji F» kt. For No < NIS the energy barrier B is given by EB =q2l 2 Nv /8E. F rom the charge neutrality condition NDL =Nt[l + exp(et + EB - EF)/kT]-l, the Fermi energy is given by EF =Et + EB - kt In{2[(N t /LND) - In. By substituting Eq. (1) in Eq. (2) we find the following expression for the conductivity: (7a) (7b) (8) (9) (1) r/l 2 NcNn vc ( Ea) ( ) g= 2kT{N t _ LN n ) exp C kt ' 11 where the activation energy Ea is given by Ea =EG - E t (12) F or No 'Nt, the crystallites are partially depleted. The barrier energy is obtained from Eqs. (4) and (5), eliminating the depletion width W. We find EB = EF - E t + kt ln2[qnt/(8en OEB)l /2-1] (13) E F - E IMPURITY CONCENTRATION [cm- 3 ] FIG. 3. Barrier height versus impurity concentration for a grain size of 1-5 cm. Reference is made to monovalent trapping states at midgap J. Appl. Phys. Vol. 49. No. 11. November 1978 Baccarani. Ricco. and Spadini 5566

4 ...'!'.. - C!).7 a: 4 LLJ Z LLJ z.3 '2 <t.2 '-' <t d 8 IMPURITY CONCENTRATION [cm- 3 ] 1 19 FIG. 4. Activation energy versus impurity concentration for the same case as Fig. 3. which can be solved iteratively. The barrier height is represented versus the impurity concentration for various Nt values in Fig. 3, where it has been assumed that L=1-5 cmo For ND<Nb, EB linearly increases with N D, according to Eq. (8). For N D N;, we distinguish two situations EB "'i E G - E t + kt IntqN1/2Nt/[Nc(2EEB)1/2 j} for E t + EB - EF»kT (14a) (14b) which correspond to different behaviors of the conductivity. The boundary between the regions where the two conditions of Eqs. (14) hold is represented by a dotted line in Fig. 3: in the lower Eq. (14a) is true, and the conductivity is given by with = (llnovc/1?t) exp(- Ea/kT) E =E. a B, in the upper, instead, Eq. (14b) holds, the barrier height then is no longer temperature independent, and the conductivity becomes o=qlnvc(2eni}eb)1/2(ktntt1 exp(- Ea/kT), where the activation energy is given by Ea =ieg - E t The extension of this latter region, which has been totally neglected in Seto's theory, increases as the grain size and the density of trapping states increase. (15) (16) (17) (18) Figure 4 represents the activation energy Ea for several values of Nt again assuming L = 1-5 cm. The most remarkable feature of the calculated activation energy is the abrupt transition between ieg and EB which occurs at the onset of complete depletion for the lowest values of Nt. For the larger contents of trapping states, instead, Ea is practically continuous because, when EB + E t - EF»kT, the activation energy tends to i EG - E t for both complete and incomplete depletion of the crystallites. IV. CONTINUOUS ENERGY DISTRIBUTION OF INTERFACE STATES Let us assume now that the grain-boundary traps consist of states with a uniform density (these being acceptors in the upper half of the band gap, and denors in the lower half). The charge neutrality condition then reads IiiF-E B N (E) de 2ND W = 1 where N (E) represents the constant interface-state distribution. In Eq. (19) the integration limits are referred to the intrinsic Fermi level at the grain boundary. By substituting Eq. (5) in Eq. (19), we find the following equation in W: W2+()W_=O q N.. q ND whose physically meaningful solution is given by (19) (2) W= {[I + (q2n;.ef) 1/2 -I}. (21) q N.. 2END IJ The limiting value of the impurity concentration ND corresponding to a complete depletion of the crystallites is obtained by equating Eq. (21) to il: this gives NPJ = (")(1 + q2 L) -1 kt In() (22) which may be solved iteratively. The result of such a computation is shown in Fig. 5 versus the grain size L, for various interface-state densities. In the region of smaller Land N, Nt is proportional to L -1: Nt ""(N kt/l)ln(nt/n j ) for L 8E/lN.. ; (23a) while, in the region of larger Land N, Nt is proportional to L- 2 FIG. 5. Impurity concentration values at the onset of complete depletion versus grain size, for various interface-state densities, uniformly distributed within the band gap J. Appl. Phys., Vol. 49, No. 11, November 1978 Baccarani, Ricco, and Spadini 5567

5 4 I- - ::t: -- EF <!l.3 Uj ::t:.2 U-I <: <D Nss ' 5xlO'3 / N.2xlO' IMPURITY CONCENTRATION [cm- 3 ] FIG. 6. Barrier height versus impurity concentration for a grain size of 1-5 cm. Reference is made to a continuum of interface states. (23b) When the impurity concentration Nv < N, the crystallites are completely depleted, and the barrier height is expressed by Eq. (8). The charge neutrality condition then reads LNv =N (EF - E B ) and consequently the Fermi level is given by EF =EB +LNv/N... From Eq. (2) the film conductivity is J = (q2 LNcvc/kT) exp(- Ea/kT), where the activation energy Ea is (24) (25) (26) Ea=iA'c -LNv/N... (27) For Nv N!5, the depletion width is smaller than L, and the barrier height is represented by the expression EB =E F - [(1 + q 2 N;sEF) 1/2-1J (28) q-1v;. 2ENv which asymptotically tends to EB =q2n;se/8env for Nv»q 2 N;.EF/2E (29a) EB = EF for Nv q2 N;.EF /2E. (29b) The barrier height is represented in Fig. 6 versus the impurity concentration, for several values of the interface- state density. In the field of practical values of ND and N, the asymptotic expressions (29) represent a poor approximation of Eq. (28), which must be referred to in order to derive a correct expression of the activation energy Ea. Remembering that, in the partialdepletion case, the barrier height EB can be expressed as (3) 4EN [( q 2 N 2 E ) 1/2 ] EB""Ec--.,-d!- 1+ N c -1 -ktln(nc/nv) q-1v;. 4E v The conductivity of the film is thus given by 2LN ) (N c ) _(1+q2 N ;.EC 14eNv )_1/2] (_ En) J= q ktcl'c - [( N v exp f;;t (32) (33) Figure 7 shows the activation energy versus impurity concentration for several values of the interface-state density. As for the case of monovalent trapping states, Ea tends to iec for the smaller Nv values and is proportional to Nil for the largest impurity concentrations. The transition region between these two asymptotic behaviors, however, is far more extended that in the case of monovalent trapping states, and the abrupt transition of Ea between the complete and partial depletion cases never disappears, even at the largest interfacestate densities. V. EXPERIMENTAL (l11)-oriented p-type silicon slices were thermally oxidized to a thickness of 1 Mm at 12 e. Following the oxidation, a 5-nm polycrystalline-silicon film and a Si 2 layer of the same thickness were sputter deposited onto the oxidized silicon slices, and annealed at 11 e for 15 min, to allow for an increase of the grain size. 7 Contact windows were opened in the oxide film, and a standard P predeposition was performed at lgoooe. After removing the oxide, the sample were p+ implanted at an energy of 15 kev with doses ranging from 1 14 to 3 X 1 16 cm- 2, and subsequently annealed at 11 e for 3 min in a N2 + 1(/ Oz ambient. A second masking step was performed to define the Van der Pauw geometry. Al dots were evaporated onto the diffused areas through a metal mask suitably aligned to the Hall pattern, and a final low-temperature annealing was performed to reduce the contact resistance. Resistivity and Hall measurements were performed, the former in the temperature range 3-5 OK, the latter at room temperature. Due to intrinsic limitations - <!l L 1Q-5 cm Nss14cm-2 ev-' U-I.4 z UJ z.3 EF g I- <: :::.2 l- e..: <: Nss ' 2x1 12 / '8 119 IMPURITY CONCENTRATION [cm- 3 ] x 1-1+ q2n2e)-1/1 as c. [ ( 4ENv (31) FIG. 7. Activation energy versus impurity concentration for the same case as Fig J. Appl. Phys., Vol. 49, No. 11, November 1978 Baccarani, Ricco, and Spadini 5568

6 '7 E 12C o f Z o u... c...j 1 18 /... _-A- '-' oj a; :E -oj -oj :%: o C\J cp; 3,1" o <P- 1" cp; 3 1" A cp = 1" CP=3" D cp = FIG. 8. Experimental carrier concentration and Hall mobility versus implantation dose-film thickness ratio. The dotted line represents the empirical law ncr q,1.2. of our Hall setup, we did not succeed in measuring the carrier concentration of the two most resistive samples. X-ray diffraction measurements were performed to determine the average grain size L, which turned out to be about 3 xi cm. VI. RESULTS For a composite material, such as polycrystalline silicon, the interpretation of Hall measurements is open to several doubts. Petritz 8 showed that, for the case of a sample inhomogeneous in one direction and homogeneous in the planes normal to it, provided the carrier mobility is spatially constant, the Hall coefficient is directly related to the average carrier concentration, in both cases of current normal and parallel to that direction. Our case is more complicated due to the three-dimensional nature of the inhomogeneities and, in addition, the carrier mobility is likely to decrease in the grainboundary regions, where additional scattering mechanisms are expected to take place. In the present work, however, we simply extrapolate Petritz's result, i. e., we assume that the Hall coefficient provides the average carrier concentration. Such an assumption is likely to be better fulfilled at high doping levels, where the extension of the grain-boundary region is strongly reduced. This is the case for all the samples on which we have been able to perform Hall measurements. Figure 8 shows the experimentally determined carrier concentration and Hall mobility versus the implantation dose over film thickness ratio. Even at the largest implantation dose, corresponding to an average phosphorus concentration of 6x 1 2 cm,3, the carrier concentration turns out to be three times smaller, indicating that some segregation of the phosphorus atoms occurred during the 11 C annealing step. Under these 5569 J. Appl. Phys.. Vol. 49, No. 11, November 1978 FIG. 9. Relative variation of the film resistivity versus reciprocal measuring temperature. conditions (Dt)1/2 z 5 Mm, i. e., the diffusion length turns out to be much larger than the average grain size. Figure 9 shows the relative variation of the resistivity of the film versus reciprocal measuring temperature. Except for the most resistive sample at room temperature, resistivity exhibits a linear behavior in the usual semilog plot, indicating that the transport process in polycrystalline silicon films is thermally activated. The activation energy is plotted versus the electrically active phosphorus concentration in Fig. 1. ND has been obtained from the average carrier concentration, accounting for the partial depletion of the grains, i. e., making use of the expression na =N D [1-2W / L + (21T)1/2(L D /L) erf(eb/kt)] =N D [l- (8f.E B /L2q 2 N D )1/2 + (2 1T )1/2(L D /L) erf(eb/kt)] (34) relating impurity and average carrier concentration. In Eq. (34) L D =(EkT/q2N D )1 / 2 is the extrinsic Debye length. :.7 <.:) z.4 z 9.3 : i= u N,;3.8x1Q12 em- 2 l = 3 X 1. 6 em IMPURITY CONCENTRATION [ em- 3 ] FIG. 1 Theoretical and experimental activation energy versus impurity concentration. 8accaranl, Ricco', and Spadini 5569

7 For given values of n., L, and E B, Eq. (34) enables one to determine N v' In the calculations we have assumed L = 3x 1-6 cm, as from x-ray measurements, and EB = Ea. The relationship between electrically active impurity concentration and implantation dose was found to fit the empirical law which was extrapolated to the two most resistive samples on which we could not measure the average carrier concentration. (35) The theoretical expression of the activation energy, as obtained from the monovalent trapping-states model, is represented in Fig. 1 by the solid line. The latter has been fitted to the experimental data by adjusting the interface-state density Nt, which turned out to be 3. ax 1 12 cm- 2, and by assuming E t =. The model based on a continuous interface-state distribution failed in fitting the experimental data. On the contrary, the agreement between the monovalent trapping-states model and experiments is indeed very satisfactory except for one sample, indicating that the interface states are most probably peaked at midgap. VII. DISCUSSION The segregation model 1,2 and the grain-boundary trapping mode1 3,4 have been regarded in the past as alternative explanations of the electrical properties of polycrystalline silicon films. Hall measurements performed on phosphorus-doped sputter-deposited films provide evidence of an electrically active impurity concentration inside the grains considerably smaller than the total amount of implanted phosphorus ions. This would support the hypothesis of a considerable impurity segregation at the grain boundary. On the other hand, as already pointed out, the temperature behavior of the film conductivity is well explained with the assumption that it is essentially dominated by carrier trapping at the grain boundary. In our opinion, therefore, impurity segregation and carrier trapping should not be regarded to as alternative explanations for the electrical properties of polycrystalline silicon films, but rather as phenomena both taking place inside the material and influencing its conductivity, at least when this is phosphorus doped. In the present work we have developed two different trapping models assuming a o-shaped and a continuous density of trapping states at the grain boundary, and found that the former is in good agreement with the obtained experimental data. In addition, the activation energy at the lowest impurity concentrations, which has been consistently found to be about i EG in several works 5,9 including the present, clearly indicates that the above states are located at midgap. Such a conclusion is in disagreement with Seto's result of a trapping state for holes located at.37 ev above the valence-band edge. In our opinion, this is due to an erroneous evaluation of the average carrier concentration inside the grains [Eq. (6) in Ref. 5 J which is overestimated by the factor exp(eb /IzT). An additional difficulty associated with Seto's result is that, depending on the type of impurities, the energy level of the trapping states should be located either in the upper or in the lower half of the band gap. Finally, because of 3. ax 112_cm-2 trapping states at the grain boundary with energy E t located at midgap, it is straightforward to evaluate a carrier lifetime of the order of 1 psec, in agreement with measurements performed by Kamins. 1 Assuming instead E t =9 ev, one would find a carrier lifetime far too large (::::1 nsecl. One of the most remarkable features of the present theory is the abrupt falloff of the activation energy at the onset of complete depletion. In real structures, however, the grain size is not a constant, as assumed by the theory, but is randomly distributed around some average value. These statistical fluctuations tend to smooth such a transition, leading to an activation energy which continuously decreases as Nv increases, as observed in various experiments. 5,9 VII I. CONCLUSIONS Resistivity and Hall measurements have been performed on sputter-deposited polycrystalline silicon films implanted with phosphorus. Experimental data show evidence of some impurity segregation at the grain boundary, and indicate the presence of an interface-state peak located at midgap. In accordance with previous works, it has been found that the resistivity is thermally activated with an activation energy depending on the impurity concentration inside the crystallites, and almost equal to i EG for the smallest values of Nv. At the onset of complete depletion, Ea should fall abruptly to a smaller value; it is believed, however, that the statistical distribution of the grain size smoothes such an abrupt behavior, leading to the continuous function observed experimentally. lm.e. Cower and T.O. Sedgwick, J. Electrochem. Soc. 119, 1565 (1972). 2A. L. Fripp, J. Appl. Phys. 46, 124 (1975). 3T.I. Kamins, J. Appl. Phys. 42, 4357 (1971). 4J. Y. W. Seto, J. Electrochem. Soc. 122, 71 (1975). 5J. Y. W. Seto, J. Appl. Phys. 46, 5247 (1975). GC. R. Crowell and M. Beguwala, Solid-State Electron. 14, 1149 (1971). 7G. Baccarani, G. Masetti, M. Severi, and G. Spadini, Proc. 3rd Int. Symp. Silicon Mat. Sci. and Tech., Philadelphia, 1977 (unpublished).!r.l. Petitz, Phys. Rev. 11, 1254 (1958). T.I. Kamms, IEEE Trans. Parts Hybrids Packag. VHP-1, 221 (1974), 1J. Manoliu and T. I. Kamins, Solid-State Electron. 15, 113 (1972). 557 J. Appl. Phys., Vol. 49, No. 11, November 1978 Baccarani, Ricco, and Spadini 557