Determination of the density of gap states: field effect and surface adsorption

Solar Cells, 2 (!980) 289 - 300 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

289

D E T E R M I N A T I O N OF THE DENSITY OF GAP STATES: F I E L D E F F E C T AND SURFACE ADSORPTION*

H. FRITZSCHE James Franck Institute and Department of Physics, The University of Chicago, Chicago, Ill. 60637 (U.S.A.)

Summary Can the conductivity, the t h e r m o p o w e r or the p h o t o c o n d u c t i v i t y of an a m o r p h o u s silicon film be determined? Does the field effect measure the density of gap states? What is the magnitude of the mobility gap? These questions do n o t have a simple answer. High quality films contain space charge layers adjacent to the substrate interface and near the top surface. These layers can strongly influence the electronic properties of the film, and changes may occur during the course of measurements as charges are exchanged with adsorbates, with the surface oxide or with traps in the insulating substrate. Other causes for change are light, thermal treatments and high transverse electric fields. A t t e m pt s to remove or fix these space charges or at least to understand their origin and effects are discussed. The validity of several assumptions needed for interpreting field effect measurements is questioned.

1. I n t r o d u c t i o n H y d r o g e n a t e d am or phous silicon (a-Si:H) and fluorinated hydrogenat ed a m o r p h o u s silicon (a-Si:H:F) alloys are of particular interest for use in amorphous s e m i c o n d u c t o r solar cells because t he y have a very low density N ( E ) o f localized states [ 1 ] in the mobility gap and therefore can be d o p e d both n t y p e and p ty pe [1, 2] . The remaining localized gap states act as traps and r e c o m b i n a t i o n centers, and the question naturally arises how the preparation conditions can be improved in order to reduce N ( E ) even further. T o achieve this, we need reliable measurements of N ( E ) as well as of the basic parameters which characterize the bulk electronic properties o f the material. Despite the wealth of data taken and published during the past few years [3] we have little i nf or m a t i on a b o u t the bulk properties. The reason for this dilemma is that we are dealing with thin films (between 0.5 and 3 pm *Paper presented at the Photovoltaic Material and Device Measurements Workshop, "Focus on Amorphous Silicon", San Diego, California, U.S.A., January 3 - 4, 1980.

290 thick) and that space charge layers adjacent to the surface and substrate interface play an important role in the electronic transport [ 4 - 6 ]. The problem is aggravated by the fact that these space charge layers depend on a n u m be r of parameters which characterize the substrate, the surface oxide, surface adsorbates and overlayers; they change with thermal treatments and illumination [7] and are subject to diffusion of protons and other mobile ions [ 6] . Moreover, long equilibration times are often encountered because of deep traps as well as ion diffusion in the substrate, the a m o r p h o u s semiconductor and the surface overlayers. In this paper we shall illustrate a number of these effects and then discuss some problems associated with the determination of N(E) from field effect measurements.

2. Conductivity Figure 1 shows the temperature dependence of the dark conductivity o of an n-type a-Si:H layer 1.2 /am thick (10 ppm PHa in the Sill 4 of the plasma) deposited on Coming 7059 glass at 300 °C. These and the following measurements [8] were carried out in an oil-free vacuum (10 a . 10 6 Torr) with a planar electrode geometry. Nichrome or carbon electrodes were used either on top of or below the amorphous film. The resistances scaled with the electrode separation which indicates that c o n t a c t effects are negligible. The heating and cooling rates used were approximately 4 °C min 1. Below 100 °C the temp er a t ur e dependence follows o = o0 exp -- ~T-

(1)

After heating, a high conductance state is established with o0 = 0.66 g~ ~ cm and AE = 0.2 eV. After exposing the sample at r o o m t em perat ure for 1 h to a bo u t 10 mW cm 2 white light, we reach a low c o n d u c t a n c e state and find t h a t o 0 = 1 . 3 × 104~z 1 cm-1 a n d A E = 0 . 6 6 e V . This effect was first discovered by Staebler and Wronski [7] and interpreted in terms of light-induced changes of N(E) in the bulk [ 9]. Although we can n o t exclude the possibility of some changes in N(E), we suspect that most of the effect arises from changes in conducting space charge layers. Evidence for an electron accumulation layer at the top surface is obtained by changing the conduct ance of the sample with exposure to H 2 0 or NH3 ambients [4, 6 ] , which act as donors, or by depositing an overlayer of selenium, which acts as an acceptor [ 6] . More evidence is provided by the following example [ 8 ] . Figure 2 shows the c o n d u c t a n c e curves of two films (100 ppm PH3 in the Sill 4 of the plasma and deposited at 260 °C) which are identical except that one is covered by an SiO layer 1/xm thick. The covered sample has a higher conductance. The SiO layer is thick enough to p r o t e c t the a-Si:H film from any influence of ambient gases. Figure 3 shows the conduct ance changes of these

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two films during and after exposure to white light. The photoconductivity is approximately the same but the subsequent decrease in the dark conductance is greatly diminished for the covered sample. The surface potential of the covered sample is apparently more stable than that of the open sample which has a natural oxide layer only a few ~ngstr6ms thick. When these samples are exposed to UV light (~ = 350 -+ 50 nm), the dark conductance is increased by a factor of 1.6 for the covered sample and it remains unchanged for the open sample. No change in dark conductance is observed by exposing the samples to blue light (X = 488 nm) through the substrate. We suspect that there is an insulating space charge layer adjacent to the substrate as observed by Ast and Brodsky [10]. Using either electron donor or acceptor adsorbates or overlayers, we can determine whether the top surface of a given sample has an n-type or p-type accumulation layer by measuring the increase or decrease in the sample's conductance. We observe either one or the other and rarely find a film with a natural flat-band surface. This means that special surface treatments are required before the bulk conductivity can be obtained from the measured conductance. This problem becomes less severe with strongly doped films with high conductivities. Although discussed already elsewhere [6], we show in Fig. 4 the decrease in conductance of an undoped a-Si:H film 1.14 pm thick as a selenium overlayer was deposited. At various selenium thicknesses the activation energy AE was measured and moisture was admitted for a short time in order to test whether the surface space charge layer was n type or p type. After Fig. 4, curve A, was taken, the selenium layer was removed by evaporation

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in vacuum and curve B was obtained subsequently by depositing selenium for a second time. This experiment established that an electron accumulation layer with a surface potential of --0.21 eV exists at the origin of curve A (AE = 0.71 eV) and that the surface becomes intrinsic (AE = 0.92 eV) after deposition of a selenium layer 1000 h thick for curve A and 260 A thick for curve B. The space charge layer of curve B is p type for selenium thicknesses larger than 260 h . The effect of an insulating layer on the surface potential depends on the thickness of the insulator because of its finite screening length. In contrast, less than a monolayer of a metal suffices to establish the interface potential. Space charge layers adjacent to the substrate may be detected and altered by ion diffusion in the substrate as discussed by Solomon e t al. [5]. In Section 5, which deals with the field effect, we present an example of a conducting space charge layer at the substrate interface. Whenever the conductance is dominated by space charge layers we find, instead of o0 ~- 3 × 104 ~2 1 cm-1, anomalously small values for this preexponential factor. It is reduced by a factor t e f 6 d where d is the film thickness and teff is that fraction of the space charge layer which carries most of the current. The magnitude of te~ is much less than the space charge width because the local conductivity increases exponentially with band bending. Figure 5 shows [11] the activation energy of the conductance and the reduction of the pre-exponential factor as functions of the surface potential for a sample 1 gm thick which in the absence of band bending has AE = 0.77 eV. The calculations are based on the density of states function N ( E ) of Spear e t al. [12]. The broken line represents the energy separation E,: - - EF at the surface. The agreement of the full symbols with the broken line shows that AE is reduced by an a m o u n t equal to the surface potential

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leVol (eV) Fig. 5. C o n d u c t a n c e a c t i v a t i o n energy A E a n d v a r i a t i o n in o 0 s h o w n as log(O0v/O0o) vs. p o t e n t i a l V0 at t h e i n t e r f a c e : o, V0 < 0; ~3, V0 > 0. Calculations are based o n t h e d e n s i t y of states of Spear e t al. [ 1 2 ] . ( A f t e r ref. 11.)

except for small band bending. The squares apply to electron accumulation layers and the circles to hole accumulation layers. The conductivity (or, better, conductance) curves of Figs. 1 and 2, which we believe are governed by space charge conduction, all have unusually small values of %. We realize of course that small o0 values can occur for other reasons: (i) if the Fermi energy lies on an exponentially increasing slope of N(E), then Ec - - E F has a linear temperature coefficient ~ which reduces Oo by a factor exp(--/3/k) or (ii) conduction may take place by hopping in localized states below the mobility edge. These cases are likely to be found in strongly doped samples. A small Oo value cannot therefore be taken as a proof for the presence of space charge conduction.

3. Photoconductivity It is n o t surprising to find that band bending at the surface and substrate interface strongly affects the photoconductivity. Figure 6 shows [ 13] the spectral dependence of the room temperature photoconductance of an undoped a-Si:H film 2 pm thick illuminated from the top surface. The ordinate is normalized by the number of incident photons. The photocurrent is very nearly proportional to the light intensity at all p h o t o n energies. Curve A was measured in vacuum. Its dark conductance was very low even though some band bending was present. We observe a sharp decrease in the normalized photocurrent at high p h o t o n energies where ~d >> 1 (~ is the absorption coefficient). Curve B is the same sample measured in an ambient of N 2 with 20% relative humidity. The adsorbed water produced an electron accumulation layer and increased the dark conductance by a factor of 400. This nearly eliminated the drop in photocurrent in the high absorption region and caused an overall increase in the photoconductance. This effect is reversible and

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curves between curves A and B are obtained for surface treatments which yield intermediate values of n-type surface band bending. In Fig. 7 we compare the normalized photocurrent of the same sample illuminated from the top (curve A) and through the glass substrate (curve C). The photocurrent drops even more rapidly for the back-lit sample (curve C) than for curve A in the high absorption regime hv > 1.5 eV. Extrapolating the trend from curve B to curve A and then to curve C we might conclude that the surface potential is closer to the flat-band position at the substrate interface than at the surface, or perhaps even on the p-type side. The dependence of the photocurrent on band bending may be caused by a change in surface recombination as the occupation of surface states changes with the position of the surface Fermi level. These band bending and surface treatment effects influence the photoresponse within a considerable depth from the surface or interface. For films [6] which are less than 0.6 ~m thick they dominate the photoresponse at all photon energies.

4. The mobility gap It is surprising that fundamental quantities such as the mobility gap Ec --Ev are not well known in a-Si:H as a function of hydrogen concentration or preparation conditions. Spear and LeComber [ 1] use Ec --Ev = 1.54 eV for presenting their N(E) values obtained from field effect measurements.

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Since the gap depends on temperature it is not a trivial matter to determine its value at room temperature and a number of assumptions have to be made. It seems reasonable to assume that the mobility gap has the same temperature dependence as the optical gap shown in Fig. 8. Near 300 K we may use the linear approximation Ec --Ev = (Ec --Ev)o - - T T

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296 5. Field effect Measuring the energy distribution N(E) of the density of gap states as a function of composition and preparation conditions would be one of the best ways to unravel the origin of the localized states. The knowledge of this can help us to improve the quality of the material. Unfortunately, N(E) is very difficult to measure. Attempts are being made to obtain it by transient deep level spectroscopy [15], by electron tunneling [16] and from capacitance-woltage characteristics [17]. The field effect [18] appeared for a while to be the easiest m e t h o d and it was the first one which demonstrated the dramatic decrease in N(E) achieved by the plasma deposition technique. In this section we give some field effect results obtained [19] with an undoped a-Si:H sample which was subjected to the Staebler Wronski cycle [7] of illumination and annealing. We then discuss some limitations of the field effect method of determining the bulk density of states N(E). Figure 9 shows the field effect of an a-Si:H sample 0.5 pm thick deposited at 260 °C onto a quartz plate 165 t~m thick which acts as the insulator between the sample and the gate electrode. The measurements were taken at 60 °C in vacuum. The sequence of treatments is explained in the figure caption After curve D was taken, the sample was again annealed at 160 °C and remeasured at 60 °C. This reproduced curve C so well that no separate curve could be drawn. For positive field voltages VF the conduction band edge E,: is bent toward EF at the quartz interface (electron accumulation). It should be noted that the Staebler-Wronski effect, which is the conductance change at VF = 0 after illumination, is small in this nearly intrinsic sample. The light-induced conductance change is essentially the result of a decrease in the band bending at VF = 0. The interface starts out to be slightly p type (curve A), approaches the flat-band condition after 4 days (curve B) and is slightly n type after annealing at 160 °C (curve C). Changes in the absolute magnitude of the conductance arise also from changes in band bending at the top surface. The curves drawn in Fig. 9 are the computer fits [19] to the experimental points which yield the N(E) curves shown in Fig. 10. We were able to swing the surface potential by 0.5 eV toward both the p-type and the n-type side. In contrast with Spear and coworkers [1, 12] we obtain a lower N(E) below the gap center than above. At first sight these results look very pleasing; they reveal interesting structure in N(E) and subtle changes after various treatments. However, in order to make sure that the structure in N(E) was indeed needed to fit the data, we constructed [ 19] by hand the smoothed average N(E) curve for case D as shown in Fig. 11. Recalculation of G(V~) yielded the computer fit to the data points shown in the same figure. Even though the fit is less perfect than that shown in Fig. 9, the deviations are within the experimental error of the data. Moreover, there are not sufficient data points to justify N(E) curves with the detailed structure shown in Fig. 10. However, the true N(E) may have an even more pronounced structure than that shown in Fig. 10,

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N(E) corresponding to the c o m p u t e r fits shown with the

approaching a situation with states in quite discrete energy regions, without significantly altering the field effect curve G(VF). This was shown to be true by enhancing the structure in N{E) and still finding satisfactory agreement with the measured G(VF) data. This structure gets lost because of the s m o o t h ing effect of integrating Poisson's equation and the kT broadening of the Fermi function. We now discuss some of the limitations of the field effect m e t h o d for determining the bulk density of states. For that purpose we show in Fig. 12 the field effect current integrated to a distance x from the interface for various surface potentials produced by the field voltage [11]. Except near the flat-band voltage, most of the field effect current flows in a narrow channel less than 50 A thick near the interface. This is because the bands are closest to EF at the surface and the band bending potential appears in the exponent of the conductance integral [ 11]. Consequently teff is much less than the space charge width as discussed in Section 2 which leads to the large reduction in the pre-exponential factor o0 illustrated in Fig. 5. The narrowness of the field effect current channel raises the question whether the structure and the composition of the initial 50 A layer are the same as those of the bulk. Effects of the substrate on the interface matching and the plasma deposition chemistry make this unlikely. Moreover, diffusion of protons [20] and mobile ions in the high fields of the space charge layers may occur and change the interface region. Heterogeneities and lateral in-

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homogeneities also become increasingly important when conduction in such a thin layer is considered. We essentially deal with two-dimensional conduction in a narrow potential well as illustrated in Fig. 13 which shows the electron potential V(x) as a function of the distance from the insulator. The quantum states in the well are strongly affected by the boundary conditions as in silicon inversion layers. It is therefore unlikely that the mobility edge follows V(x) up to the surface. We presume that states will remain localized in the potential trough up to higher energies and that the mobility edge will remain above V(x) and probably meet the interface x = 0 with zero slope. This places the mobility edge further than EF -- V(x) away from EF. Random potentials due to ions in the insulator will also tend to push the mobility edge further away from EF. Since we assumed V(x) to be the spatial dependence of the mobility

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299 edge in our analysis, we overestimated N(E), particularly in the range where IE -- E~I and the band bending are large. This may account for the fact that N ( E ) deduced from the field effect usually rises too rapidly at large IE --EF] to extrapolate smoothly to the expected value of about 1021 cm 3 eV 1 at E,: and Ev. All arguments presented so far, as well as the allowance for the presence of interface states, suggest that the true density of gap states is lower than N ( E ) calculated from the field effect data. We also cannot exclude the possibility that the localized gap states are limited to more discrete energy regimes instead of forming a continuous and quite smooth N { E ) distribution.

6. Conclusions The field effect is a valuable tool for determining the value of and changes in the interface potential. It provides an upper estimate of the localized state density N { E ) in a layer 50 - 100 A thick adjacent to the interface. N ( E ) determined by the field effect is smoothed out and is not able to reveal the presence of all sharp structures. In view of the low density of localized gap states it is not surprising that electron and hole accumulation layers adjacent to the surface and substrate interface strongly influence the transport properties of high resistivity glow discharge a-Si:H films. These space charge layers are affected by exposure to light and annealing. The surface space charge layer is strongly influenced by surface treatments and can be neutralized by an appropriate choice of an insulating overlayer.

Acknowledgments The author is deeply indebted to his capable students and associates, Nancy B. Goodman, M. Tanielian, P. D. Persans and Masaaki Yamaguchi, who did all the work. This research was supported in part by the U.S. Department of Energy under Contract DOE03o79-ET-23034, National Science Foundation Grant DMR77-11683, and the Materials Research Program of the National Science Foundation at the University of Chicago.

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353.

300 5 !. S o l o m o n , T. Dietl and I). Kaplan, d. Phys., 719 ( 1 9 7 8 ) 121!. 6 M. Tanielian, M. Chatani, It. Fritzsehe, V. Staid a n d P. D. Persans, Proc. 8th Int. Con/'. on Amorphous and Liquid Semiconductors, Cambridge, Massachusetts, August 27 - 31, 1979, in d. Non-Cryst. Solids, 35 - 36 ( 1 9 8 0 ) 575. 7 D. 1,. Staebler and C. R. Wronski, Appl. Phys. Lett., 31 ( 1 9 7 7 ) 2 9 2 ; J . Appl. Phys., 5 l ( 1 9 8 0 ) 3262. 8 M. Tanielian a n d H. I*'rilzsehe, Bull. American Physical Society March Meet.. New York, i980. 9 S. R. Elliott, Philos. Mag. B, 39 ( 1 9 7 9 ) 349. 10 D..Ast a n d M. H. B r o d s k y , Proc. 8th Int. Conf. on Amorphous and Liquid Semiconductors, Cambridge, Massachusetts, August 27 -31, 1979, in d. Non-Cryst. Solids, 35 - 36, Part I ( 1 9 8 0 ) 611;Philos. Mag. B, 41 ( 1 9 8 0 ) 273. 11 N. B. G o o d m a n a n d H. Fritzsche, Philos. Mag. B, 42 ( 1 9 8 0 ) 149. 12 W. E. Spear, P. G. L e C o m b e r a n d A. J. Snell,Philos. Mat. B, 38 ( 1 9 7 8 ) 303. 13 P. Persans a n d H. F r i t z s e h e , Bull. Am. Phys. Sot., 24 ( 1 9 7 9 ) 399;Bull. Am . Phys. Soe., 25 ( 1 9 8 0 ) 330. 14 N. F. Mott, Philos. Mat., 22 ( 1 9 7 0 ) 7;26 ( 1 9 7 2 ) 1015. 15 ,l. D. C o h e n , D. V. Lang, a. P. H a r b i s o n a n d d. C. Bean, Sol. Cells, 2 ( 1 9 8 0 ) 331. 16 I. Balberg a n d D. E. Carlson, Phys. Rev. Lett., 43 ( 1 9 7 9 ) 58. 17 M. Hirose, T. Suzuki a n d D. H. D6hler, Appl. Phys. Letl., 34 ( 1 9 7 9 ) 334. 18 A. Madan, P. G. L e C o m b e r a n d W. E. Spear, d. Non-Crysl. Solids, 20 ( 1 9 7 6 ) 289, a n d references therein. 19 N. B. G o o d m a n , I-t. F r i t z s e h e a n d H. Ozaki, Proc. 8th Int. C o n f o n Amorphous and Liquid Semiconductors, Cambridge, Massachusetts, August 27 - 31, 1979, in d. NonCryst. Solids, 35 - 36, Part I ( 1 9 8 0 ) 599. 20 W. A. L a n f o r d a n d R. Golub, Phys. Rev. Left., 39 ( 1 9 7 7 ) 1509.