Scanning tunneling microscopy of hydrogenated amorphous silicon: high-resolution topography and local apparent barrier heights

Applied Surface Science 151 Ž1999. 73–85 www.elsevier.nlrlocaterapsusc

Scanning tunneling microscopy of hydrogenated amorphous silicon: high-resolution topography and local apparent barrier heights J. Herion

)

Institut fur D-52425, Julich, Germany ¨ Schicht- und Ionentechnik, Forschungszentrum Julich, ¨ ¨ Received 6 April 1999; accepted 7 May 1999

Abstract As-grown films of phosphorous-doped hydrogenated amorphous silicon Ža-Si:H. were investigated by scanning tunneling microscopy ŽSTM. using a combination of high-resolution constant-current imaging and apparent barrier height ŽFA . imaging. We observed a distribution of atomic scale surface structures which is characterized by a local root-mean-square ˚ to 1.8 A˚ and which is superimposed on the array of hills described previously. The roughness, d l , ranging from 0.2 A structures can be ascribed to surface phases consisting of silicon monohydride species andror adsorbed hydrogen as well as to higher hydrides, SiH x Ž x G 2.. Correlations were found between FA and cos 2w , where w is the angle between the local surface normal and the direction of tip movement perpendicular to the surface, and between FA and d l . The frequency distributions of FA , cos 2w and d l depend significantly on the tunneling voltage, Ut . The frequency distribution of FA, ˚ . and for Ut s 2.3 V, is peaked at 3.1 eV which is in reasonable agreement obtained for atomically smooth areas Ž d l f 0.3 A with a simple model of vacuum tunneling. The dependence of FA on Ut can be explained by intermediate state tunneling. q 1999 Elsevier Science B.V. All rights reserved. PACS: 61.16.Ch; 81.05.Gc; 68.35.Bs; 73.40.Gk Keywords: Scanning tunneling microscopy; Hydrogenated amorphous silicon; Surface species; Local apparent barrier height

1. Introduction Thin films of hydrogenated amorphous silicon Ža-Si:H. are materials of considerable technological interest for microelectronic and macroelectronic devices. An example of the latter application is the use of amorphous silicon for thin-film solar cells which is an active field of current research and develop)

Tel.: q49-2461-61-3923; fax: q49-2461-61-3735; E-mail: [email protected]

ment w1x. The properties of these films have been extensively studied using macroscopic probes of various types. These methods can, however, give only average information on a material which is known to be inhomogeneous on a microscopic scale. Atomic scale defects have been widely considered as being the cause of various short-comings of these materials. For example, a light-induced instability of the electronic transport properties known as Staebler– Wronski effect w2x, which, despite many efforts, is not well understood, is thought to be due to atomic

0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 9 . 0 0 2 6 0 - 3

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J. Herionr Applied Surface Science 151 (1999) 73–85

scale defects. In this situation it is hoped that local probes as, for example, scanning tunneling microscopy ŽSTM. and atomic force microscopy ŽAFM. may give more direct insight into the properties and the formation of defects. By their nature these methods are limited to surface studies, however, macroscopic measurements w3x and STM w4x have shown that surface properties are correlated with bulk properties and local imperfections of as-grown surfaces can indicate the formation of bulk defects, respectively. Moreover, surface studies with local probes may give more detailed information on interfaces of devices which, as in the case of thin-film solar cells, depend critically on interface properties. Only a short time after its invention STM has been successfully applied to various semiconductors and also to a-Si:H. The first exploratory investigations of this material were performed with samples which were exposed to air before or during STM analysis Žfor the earlier work see Ref. w4x.. It is now generally agreed, however, that experiments of this type, at least when atomic scale properties are involved, have to be performed in UHV w4–7x. This includes also the transfer of the samples between deposition and analysis. This view is supported by results from Auger electron spectroscopy which show that impurity concentrations increase from values below the detection limit up to few percent of an atomic layer during one week of storage in UHV w7x. This gives just sufficient time to perform STM measurements under well-defined conditions. In an early paper Kazmerski w8x reported atomic scale imaging by STM and AFM of a-Si:H films, that were protected in argon-sealed ampoules, and determined the chemical nature of the individual species by ‘‘spectroscopic’’ STM. To the author’s knowledge those results have not been reproduced since. Stutzin et al. w4,9,10x have studied as-grown surfaces of a-Si:H by STM in an attempt to gain a better understanding of the growth process on a microscopic scale. Important results of that work can be summarized as follows: Ž1. A major structure element of a-Si:H surfaces consists of so-called ‘‘rolling hills’’ with lateral dimensions of the order of 10 nm depending on the film thickness. Ž2. Steep-sided valleys and nanoparticles that occur at specific sites could be precursors of defects or voids in the bulk. Ž3. Surface roughness vs. thickness of

the films has been discussed in terms of continuum growth models. Ž4. Conventional constant-current imaging did not reveal individual atomic sites. Ikuta et al. w5x have studied by STM the growth of thin a-Si:H films on highly oriented pyrolytic graphite. After the coalescence of initially isolated islands they observed the formation of densely packed hills. These were covered by subnanometer structures which have been tentatively ascribed to adsorbed SiH 3 species. The topography was found to be ‘‘qualitatively independent’’ on the tunneling voltage. Already in the early days of STM the local apparent barrier height, FA , has been shown to give useful information on inhomogeneous surfaces w11x. FA is defined by "2

FA s

2

d ln It

8m

ž /

Ž 1.

dz

where w is the electron mass, It is the tunneling current and the z-coordinate corresponds to the direction of the tip movement perpendicular to the mean surface plane of the sample w12x. If the direction, s, of the local surface normal does not coincide with the z-direction, as it is generally the case with rough surfaces, we can write d s s cos w d z

Ž 2.

where w is the angle between the z-axis and the s-axis. For a simple tunneling model, which is expected to hold only for small tunneling voltages and ideal vacuum gaps, the ‘‘true’’ barrier height F can be obtained from "2

Fs

8m

d ln It

ž / ds

2

.

Ž 3.

Eqs. Ž1. – Ž3. give

FA s F cos 2w

Ž 4.

Feenstra w13x has given an approximate expression for F which holds also at higher tunneling voltages, Ut :

F f Fav y

e < Ut < 2

Ž 5.

J. Herionr Applied Surface Science 151 (1999) 73–85

75

where Fav s ŽFs q F t .r2 is the average of the work functions Fs and F t of sample and tip, respectively. According to Eqs. Ž4. and Ž5. variations of FA would reflect variations of Fs only if cos 2w f 1. Alternatively, variations of cos 2w would give rise to a varying FA even at a constant F . Both types of effects have been identified on metal and semiconductor surfaces w14x. In the case of a-Si:H variations of Fs could be due to a varying SirH ratio as the Si–H bond is known to have a considerable dipole moment w15x or to the statistical distribution of the dopant, impurity or defect concentrations w16x. No systematical measurements of FA have been made so far on as-grown a-Si:H. Stutzin et al. w4x measured at particular sites the decay length of the tunneling current in z-direction, z 0 , which, according to Eq. Ž1., is given by z 0 s "r 8 mFA Žassuming It A expŽyzrz 0 ... The authors considered val˚ corresponding to FA - 0.42 eV, ues of z 0 ) 1.5 A, to be indicative of unsatisfactory tunneling conditions Ždue to dirt or sample-related material which may have accumulated at the tip andror at the sample surface.. This criterium may be founded on practical considerations but is hardly supported by known values of the work functions of the tip and sample materials. In the present paper we give STM results for P-doped Žn-type. a-Si:H films which, during transport and analysis, remained in UHV. High-resolution constant-current images and corresponding spatial distributions of FA were measured simultaneously. Using these methods experimental conditions have been identified which allow STM to give information on atomic scale properties of a-Si:H films. Short reports of this work and of a complementary AFM study have been published elsewhere w7,17x. Here we give a more detailed account of the experimental techniques and present results of a more comprehensive treatment of the data. In particular, we consider the dependence on the tunneling voltage which turned out to be a key parameter determining the tunneling process.

hanced chemical vapor deposition ŽPECVD. in a capacitive glow discharge system operated at 13.56 MHz. The deposition chamber was built of UHV components and enabled base pressures of 10y9 mbar. Films with thicknesses of typical 0.5 mm were prepared using the following parameters: RF power f 0.1 Wrcm2 Žtotal 5 W., deposition temperaturef 2008C, gas flow f 3 sccm, deposition pressuref 0.5 mbar, dopant concentration in the gas phase f 1% PH 3 in pure silane. After deposition the samples were cooled to room temperature and transferred to the analysis chamber by means of an UHV transfer system. The analysis chamber was an UHV system with a base pressure in the low 10y1 0 mbar range. The STM was a commercial instrument ŽDelta PhirBeetle. with several home-made modifications of its control electronics as described below. Pneumatic vibration isolation elements were used to isolate the analysis chamber from external vibration sources. The samples remained in UHV until the STM investigations were completed which took typically several days. In situ Auger analyses, which were performed on samples prepared under similar conditions, showed that a carbon coverage of about 1r20 of a monolayer may have accumulated on the surface during the studies. We used tunneling tips made of polycrystalline tungsten wire ŽLongreach Scientific Resources.. Prior to use the tunneling tips and the

2. Experimental

Barrier height imaging: Data resolution Žbit. Lock-in amplifier time constant Žms. Z-modulation frequency ŽkHz.

(

Thin films of n-type a-Si:H were deposited on SiŽ100. wafers ŽP doped, 3 V cm. by plasma-en-

Table 1 Experimental parameters of the combined constant-currentr barrier height method General: Scan width Žnm. Image resolution Žpixel. ˚ . Scan velocity ŽArms Sampling frequency ŽkHz. Feed-back loop upper frequency limit ŽkHz. Constant current imaging: Data resolution Žbit. Band-pass filter lower frequency limit Žy3db; kHz. Band-pass filter upper frequency limit Žy3db; kHz.

62.5 512=512 3.4 2.8 1.5

8 0.072 1.5

12 1 24

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J. Herionr Applied Surface Science 151 (1999) 73–85

Fig. 1. Constant-current image ŽAC mode, original data.. Surface ˚ Žhigh signal area: 128=128 Žnm. 2 . Range of grey scale: 5 A intensities correspond to bright areas on the image.. Ut s 4 V, It s 0.4 nA.

silicon wafers used as substrates for the films were carefully rinsed in methanol ŽMerck, VLSI Selectipur. to remove dust particles or dirt that may have accumulated during storage in air. Separate experiments have shown that the surface roughness Žrootmean-square. of the silicon wafers, which were covered by their natural oxide layers, was lower than about 0.2 nm on an area of 100 = 100 Žnm. 2 . The principle of the method used in the present work has been described previously w11x. The sample topography was measured in a modified Žand more sensitive. constant-current mode which is described below. The basic parameters of the method are given in Table 1. To measure the local apparent barrier heights a sinusoidal modulation of the tip-sample ˚ was generated by distance of the order of 0.5–1 A applying an alternating voltage to the z piezo element. The amplitude of the resulting alternating

component of the tunneling current was measured by a specially designed broad-band preamplifier w18x followed by a two-channel lock-in amplifier ŽEG and G Princeton Applied Research, model 5210.. The output of the lock-in amplifier was recorded by a PC-based transient recorder ŽFAST ComTec, TR1202rPC. which was operated synchronously to the constant-current mode. To increase the sensitivity of the conventional constant-current mode we used a technique which has been familiar in measurements of small highfrequency Žalternating current or AC. signals which are superimposed on large low-frequency signals. In the AC mode an alternating signal consisting of frequencies in an interval Ž f 1 , f 2 . can be measured with high sensitivity by suppressing or damping signals with frequencies outside that interval. Technically this is achieved by inserting a high-pass frequency filter between the signal output of the STM and the input of the data acquisition system. In conjunction with the low-pass characteristics of the feedback system a band-pass behaviour is obtained. We note that the signal gain is proportional to f when the signal frequency f is below f 1. The experimental parameters determining the properties of the data acquisition system are given in Table 1. We obtain an interval between subsequent data samples of 0.36 ms which corresponds to a lateral resolution ˚ of 1.2 A. Frequency filters have been used previously in qualitative constant-current imaging to detect small scale structures on rough samples w19x. In the present work the band-pass filter is used in a quantitative way to damp the relatively high intensities resulting from the hills structure and, accordingly, to emphasize the atomic scale structure which is superimposed on the hills. By using the AC mode typically an increase of the sensitivity in z direction by a factor of 20 is obtained as compared to the conventional mode. We note also the advantage of the AC mode in the Žpresent. case of a relatively low data resolution Ž8 bit.. As the signal returns rapidly to a

Fig. 2. Constant-current images ŽAC mode, original data. and simultaneously measured distributions of the local apparent barrier height, FA , for various tunneling voltages. Surface area: 49 = 49 Žnm. 2 . It s 0.2 nA. The data of the FA distributions were slightly filtered to avoid artifacts due to the discrete nature of the signals. The images were corrected for drift effects. To improve the contrast the intensities of FA ˚ Žb. FA s 0.63–4.0 eV. Ut s 1.5 V: Žc. D z s 0–5 A; ˚ Žd. were limited to the intervals given below. Ut s 2.3 V: Ža. D z s 0–5 A; ˚ Žf. FA s 0.23–0.63 eV. FA s 0.41–1.6 eV. Ut s 1.0 V: Že. D z s 0–5 A;

J. Herionr Applied Surface Science 151 (1999) 73–85

77

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J. Herionr Applied Surface Science 151 (1999) 73–85

pre-determined reference level there is no need to subtract a plane as is normally required in the Žlower sensitivity. conventional mode and, inevitably, connected with a loss of z-resolution. Moreover, the high-resolution data are obtained ‘‘on-line’’ and not after time-consuming data manipulation. In the present case the time constant of the lock-in amplifier limits the lateral resolution of FA images. The minimum time constant of 1 ms which is available with the present instrument leads to a spatial ˚ This is higher than the spatial resolution of 3.4 A. resolution of the constant-current mode Žsee above. thus preventing a direct correlation of the two methods on an atomic scale. It is clear from the above discussion that variations of the parameters influencing the data acquisition may critically influence the performance of the latter. For example, a change of the scan width at constant scan rate Žtimerpixel. and resolution Žnumber of pixelsrline. would change the scan velocity ˚ . which, in conjunction with fixed parameters ŽArs of the band-pass filter, would modify the measured topography. Actually, given the basic specifications of the used equipment, there is not much freedom in selecting experimental parameters. Statistical calculations and other treatments of the data were performed on a personal computer using High Tech BASIC ŽTransEra Corporation. as a programming language. From the constant-current data we determined local distributions of cos 2w where w is the angle between the local surface normal and the z-direction and of a local root-mean-square Žrms. roughness, d l . The angle w was determined for every pixel by taking into account the four nearest neighbours of that pixel. The local roughness was obtained by adding the contributions of 5 = 5 pixels in a window and assigning the result to the centre pixel of that window. Obviously these procedures do not work near the edges of the original images. These data were not taken into account, however, because drift corrections required the selection of smaller than the original areas Žsee below..

3. Results A typical large scale constant-current image of a-Si:H obtained by the AC mode is shown in Fig. 1.

As can be explained by the differentiation effect of the band-pass filter in conjunction with the scanning direction of the tip from left to right, individual structures appear in the image as if they were illuminated from the left. While in previous work Žwith the exception of Ref. w5x. rather structureless hills were observed, inspection of Fig. 1 shows that a fine structure of various length scales is superimposed on the hills. Another feature of Fig. 1 which has been found previously by STM w5x and by AFM w7x is the existence of a ‘‘dense hills structure’’ i.e., the hills are densely packed and separated from each other by a network of thin boundary layers which appear as V-shaped trenches on the STM images. In high-resolution STM structural information generally depends on the tunneling voltage, Ut , as this parameter determines the energy window in which the electronic states are located which contribute to the tunneling process. Generally, from the dependence of the results on Ut additional conclusions relating to the nature of the structures can be drawn. To enable the comparison of images taken at different Ut Žpositive tip voltages have been used throughout this work. we corrected the images for drift effects, i.e., square areas were selected from the original images which show the same region of the surface Žaccuracyf 1 nm.. Couples of simultaneously measured high-resolution topographical images and distributions of the local apparent barrier height, FA , corresponding to different tunneling voltages are shown in Fig. 2a–f. Prominent hills are clearly visible on the topographical images close to their upper edges Žsee Fig. 2a, c and e.. The surfaces of these hills are relatively smooth for all tunneling voltages. Other areas of the constant-current images appear rough on a subnanometer scale. Qualitatively we observe the following trends: Ž1. The average roughness decreases significantly with increasing tunneling voltage. Ž2. Rough areas generally show lower FA while the opposite holds for smooth areas. Ž3. FA increases strongly with increasing tunneling voltage. In the remainder of this section we will investigate these observations more quantitatively. Histograms Žfrequency distributions. of FA as obtained from the data given in Fig. 2b, d and f, respectively, are shown in Fig. 3a. The bell-shaped distributions can be characterized by their widths and

J. Herionr Applied Surface Science 151 (1999) 73–85

79

tions become narrower and their maxima shift to higher cos 2w . Inspection of the topographies reveals that the local roughness shows significant variations and, therefore, may directly reflect the physico-chemical

Fig. 3. Histograms Žfrequency distributions. for various tunneling voltages ŽUt s 2.3 V, 1.5 V and 1.0 V.. Ža. FA . Žb. cos 2w . Žc. d l .

the positions of their maxima which both increase considerably with increasing Ut . Histograms of cos 2w for various tunneling voltages are given in Fig. 3b. We observe broad distributions which vary between cos 2w f 0.2 and 1. With increasing Ut the distribu-

Fig. 4. Local distributions of inclinedrrough and less inclinedr smooth areas corresponding to dark and bright areas, respectively, of the images Žbased on the data given in Fig. 2a.. Ut s 2.3 V. A critical angle wc s15.38 Žcos 2wc s 0.93. and a critical local rms ˚ respectively, define the border lines roughness d lc s 0.37 A, between the two types of areas. Ža. Distribution based on cos 2w ; Žb. distribution based on d l .

J. Herionr Applied Surface Science 151 (1999) 73–85

80

nature of the surface. The frequency distributions of the local rms roughness, d l , that has been determined according to the procedure given in Section 2 are shown in Fig. 3c. As before we obtain a considerable dependence on the tunneling voltage. With increasing Ut the maxima shift to lower d l . The total ˚ to 1.8 A˚ with the lowest range of d l is from 0.2 A values of d l being attained at the highest voltage. We can use the information given in Fig. 3b and c to determine the local distribution of surface elements corresponding to highrlow values of cos 2w and to lowrhigh values of d l , respectively. Results for Ut s 2.3 V based on cos 2w and d l are given in Fig. 4a and b, respectively. It is shown that less inclined or atomically smooth areas Žbright areas of the images. are generally correlated with hills appearing in the corresponding constant-current image ŽFig. 2a.. As can be explained by the different averaging procedures applied in determining cos 2w and d l Žsee Section 2. the amount of noise is different in both images while, in general, the distributions of less inclinedrsmooth and inclinedrrough areas are fairly similar. These facts reflect the correlations between FA , cos 2w and d l which are considered below more quantitatively. The choice of Ut s 2.3 V, when examples for one particular tunneling voltage are given, is explained in Section 4.

A useful statistical quantity for characterizing the ‘‘similarity’’ of two images or distributions is the coefficient of linear correlation or correlation coefficient r w20x. The values of r are restricted to the range y1 F r F 1. Complete correlation or anticorrelation corresponds to r s 1 or y1, respectively, while complete independence or absence of correlation is expressed by r s 0. The quantity 100 r 2 gives the percentage of the total variation of the data of one image which is accounted for by a relationship with the second image. In Table 2 we have compiled correlation coefficients which are based on the data of Fig. 2a–f. Correlation coefficients corresponding to the same type of measurement Že.g., topography or barrier heights. but to different tunneling voltages are small to moderately high Ž r s 0.14–0.39. with the highest values of r occurring for neighbouring values of the tunneling voltage. The correlation coefficients between simultaneously measured constant-current images and barrier height distributions are always very low Ž r F 0.02.. Fairly high correlationsranticorrelations exist, however, between FA and the quantities cos 2w and d l , respectively, which have been derived from the corresponding Ži.e., simultaneously measured. constant-current data Ž< r < s 0.23–0.53.. High anticorrelations are obtained between the distributions of cos 2w and d l

Table 2 Coefficients of linear correlation for couples of distributions of the quantities D z Žtopography., FA , cos 2w and d l , respectively. ŽMore significant correlation coefficients, i.e., those in the range 0.2 F < r < - 1, have been high-lighted by a bold type-face. Ut ŽV.

Dz

1.0 1.5 2.3

1 0.23 0.14

1.0 Dz

FA

cos 2w

dl

1.0 1.5 2.3 1.0 1.5 2.3 1.0 1.5 2.3

cos 2w

FA 1.5

2.3

1.0

1.5

2.3

0.01 1 0.22

1.0

dl 1.5

0.02 1

1.5

0.09

y0.08 I0.38 I0.45

0.33 1

I0.53

0.43 1 0.09 0.03

2.3

0.06

y0.07

0.23 1 0.39

1.0 0.08

0.02 1 0.29 0.14

2.3

y0.08

I0.64 1 0.19

I0.72 I0.80

1 1 0.21 0.06

1 0.32

1

J. Herionr Applied Surface Science 151 (1999) 73–85

obtained from the same constant-current image Ž< r < s 0.64–0.80.. For a more quantitative test of Eq. Ž4. we counted the number of data falling into small fixed intervals Ž DFA , Dcos 2w . for a simultaneously measured couple of FA and cos 2w distributions. A contour-line plot of the resulting two-dimensional frequency distribution is given in Fig. 5a. The distribution has roughly the form of a cone with a rectangular triangle as a basis and a maximum at FA f 2.8 eV and cos 2w f 0.95. This distribution implies that FA is always low on inclined surface elements Žcos 2w < 1. while the highest values of FA occur on areas for which cos 2w f 1. There are plenty of surface ele-

81

Fig. 6. Histograms of FA on rough and on smooth areas. The two types of areas were defined according to Fig. 4b.

ments, however, for which cos 2w is quite high while FA is low. A contour-line plot of the two-dimensional correlation between FA and d l is shown in Fig. 5b. The improvement of the correlation as compared to that between FA and cos 2w is obvious and corresponds to the increase of the absolute value of the correlation coefficient given in Table 2. The data given in Fig. 4a and b can be used to calculate the frequency distributions of FA on ‘‘smooth’’ and ‘‘rough’’ surface areas, respectively. The results based on the distributions of cos 2w and d l are fairly similar for the particular critical values adopted in Fig. 4a,b. Those based on d l are given in Fig. 6. On smooth areas the maximum is shifted to higher values of FA and the width of the distribution Table 3 Maxima, FA,max , and widths ŽFWHM., DFA , of the frequency distributions of FA as a function of the tunneling voltage, Ut Ut ŽV.

FA,max ŽeV.

Smooth areas: 1 0.44 1.5 1.09 2.3 3.10

Fig. 5. Two-dimensional histograms. The numbers characterizing individual contour lines give the number of pixels in an interval Ž Dcos 2w , DFA . of the cos 2w – FA plane and in an interval Ž D d l , DFA . of the d l – FA plane, respectively. Ut s 2.3 V. Ža. cos 2w vs. FA . Žb. d l vs. FA .

Rough areas: 1 0.37 1.5 0.79 2.3 2.31

DFA ŽeV.

DFA rFA,max

0.29 0.75 1.56 Average value:

0.66 0.69 0.50 0.62"0.10

0.23 0.67 2.14 Average value:

0.62 0.85 0.93 0.80"0.16

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J. Herionr Applied Surface Science 151 (1999) 73–85

is narrower as compared to rough areas. The results of a more detailed investigation, including other tunneling voltages, are given in Table 3. They show that the widths DFA Žfull width half maximum. of the frequency distributions and the locations of their maxima FA,max increase considerably with increasing Ut while the ratio DFA rFA,max shows only little change with Ut . For example, on smooth areas, FA,max increases by a factor of 7 when Ut increases from 1.0 V to 2.3 V while, in this range of tunneling voltages, DFA rFA,max s 0.62 " 0.1.

4. Discussion 4.1. General A general issue in STM concerns the proper choice of tunneling parameters, i.e., tunneling current and voltage. We have selected parameters similar to those used in a study of the adsorption of disilane ŽSi 2 H 6 . on SiŽ001. w21x. In that study some of the relevant species, i.e., –SiH 3 , 5SiH 2 and silicon dangling bonds appeared as pronounced protrusions in the constant-current images. By contrast, monohydrides and adsorbed H-atoms were less prominent features and depressions, respectively. This is due to an H-induced reduction of the local density of states near the Fermi energy and formation of bonding and antibonding Si–H states far from the Fermi energy w21,22x. Therefore it is tempting to ˚. assign the atomically smooth areas Ž d l f 0.3 A appearing in the constant-current images to a relatively dilute solution of H in Si consisting of monohydrides andror adsorbed H, while the rough areas can be assumed to be due to the presence of higher hydrides. We note that, according to recent results w23x, significant dangling bond concentrations are not likely to be present in the surface layer after the deposition of the films. The present view is in agreement with previous results from in situ Fourier-transform infrared attenuated total reflection spectroscopy which show that SiH x Ž x G 2. form a predominant fraction of the surface species during deposition w24x. A surface layer consisting of a mixture of Si–H and higher hydrides is consistent with results from in situ photoelectron spectroscopy w25x.

A general feature of the data presented above is their marked random character which is expressed by the widths of the frequency distributions. This may not be surprising for an amorphous material which is characterized by the absence of structural order except on the scale of individual atoms and their nearest neighbours. As we are dealing with surface properties we have to take into account that a ‘‘growth zone’’ may exist with properties that are significantly different from the bulk w26,27x. According to this view, growth of a-Si:H occurs by incorporation of hydrogen-rich species into a thin surface layer, while the hydrogen content of the bulk is only about 10%. During growth the surplus H is continuously removed by formation of H 2 which desorbs into the gas phase. In the resulting hydrogen-rich surface layer there is a high degree of freedom which allows the redistribution of bonds necessary both for the formation of bulk amorphous silicon and the removal of hydrogen w28x. While in this growth model only variations in the direction perpendicular to the surface are considered the present work shows that significant lateral interactions occur. 4.2. Correlations The correlation coefficients given in Table 2 for topography, D z, vs. apparent barrier height, FA , distributions are close to zero. This result can be explained by the fact that the topography consists of positive and negative deviations from the mean both having equal probabilities which cancel in their effect on the correlation coefficient. Only if a positive definite quantity is determined, as, for example, cos 2w or d l , a significant correlation or anti-correlation is obtained. While it has been shown by statistical methods that a significant correlation exists between FA and cos 2w Žor between FA and d l . the linear relationship of Eq. Ž4. is not supported by the present results. This follows from inspection of Fig. 5a and of Table 2. For the dependence on Ut we refer to Section 4.3. Numerical modeling w29x has shown that the influence of the topography on FA may be more complex than the simple geometrical effect leading to Eq. Ž4.. As has been pointed out recently by Olesen et al. w30x an atomic scale corrugation implies a variation of FA the amount of which depends on the detailed

J. Herionr Applied Surface Science 151 (1999) 73–85

nature of the corrugation. At present no quantitative predictions of the last two models relating to our case appear possible. Thus, we have to confine ourselves to smooth areas in order to obtain information on intrinsic variations of FA which are not influenced by topographical effects. One constituent of the tunneling barrier height, valid for larger tip-sample distances, is the difference between the electrical potential in vacuum just outside the surface and the Fermi level within the sample, i.e., the local work function. There is experimental evidence that the size of potential fluctuations in the bulk is of the order of 0.2 V Žrms. when characteristic lengths in the range ˚ are considered w31x. While typical lateral of 5–30 A dimensions of the variations of FA are of a similar size Žsee Fig. 2b. the potential fluctuations in the surface layer, as determined from the width of the distribution of FA in Fig. 6, are much larger. We must keep in mind, however, that we are dealing with a surface zone with properties that may be different from those of the bulk material. We note that the potential step due to a surface dipole layer consisting of a complete monolayer of Si–H bonds on a SiŽ111. –H surface is only about 0.25 eV w15x and, therefore, an inhomogeneous distribution of Si–H bonds is not likely to account for the observed variation of FA . 4.3. Dependence on the tunneling Õoltage We have found that the frequency distributions of FA , cos 2w and d l and the correlations between these quantities depend significantly on the tunneling voltage. This effect is not unexpected for STM on an atomic scale because in this case we are rather concerned with electronic than with geometrical structures. By varying Ut different electronic states may come into play. Actually, a second effect may be operative. When the tunneling current, It , is constant, an increase of the tunneling voltage is accompanied by an increase of the tip-sample distance, d. This is a consequence of the experimental fact that It increases monotonously both with increasing Ut Ž d s const.. and with decreasing d ŽUt s const... Quantum-mechanical tunneling through a thin vacuum gap depends on the voltage that is applied to that gap. For a planar junction it can be shown that the apparent barrier height decreases significantly

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with increasing tunneling voltage, independently of the polarity of the tunneling voltage w13x. Assuming Fav s 4.25 eV, calculations similar to those reported in Ref. w32x Žlower curve of Fig. 1c therein. give DFA rDUt s y0.53 eVrV for the present range of tunneling voltages. We note that this ratio is close to DFrDUt s y0.50 eVrV which is predicted by Eq. Ž5.. Actually we observe a strong effect with the opposite sign Žsee Fig. 3a and Table 3.. We will discuss here mechanisms that can, in principle, explain variations of this type. One effect that occurs only with semiconducting samples is tip-induced band bending. The system consisting of tip, vacuum gap and semiconductor may behave similar to a metal-insulator-semiconductor ŽMIS. device. At low tip-sample distances, d, the electric field, which is due to the contact potential difference between tip and sample as well as due to an external bias voltage, can penetrate to some extent into the semiconductor, thus, giving rise to ‘‘tip-induced’’ band bending. A more detailed discussion of the effect for c-Si shows that the square root of the apparent barrier height can be expressed as a difference between a tunneling term and a contribution due to the variation of the surface potential of the semiconductor with d w33x. For relatively low values of d the second term can be of the same size as the first one and, as a result, low values of FA are obtained. With increasing d the tip-induced band bending decreases and, therefore, FA increases up to the value corresponding to pure vacuum tunneling, i.e., a situation where the entire voltage drop occurs across the vacuum gap. The quantitative model of Ref. w33x cannot be applied directly to amorphous silicon because the distribution and the density of electronic states in the band gap of this material differ significantly from c-Si w1x. Previous studies using measurements of the contact potential difference ŽCPD. and the surface photovoltage ŽSPV. have shown that flat-band conditions exist at the free surfaces of highly P-doped samples w34x. This effect in conjunction with a high density of states of the order of 10 19 ŽeV cm3 .y1 at the Fermi level close to the surface may explain the absence of tip-induced band bending in the present case w35x. For a more quantitative conclusion both the density of states and the tip-sample distance would have to be known.

J. Herionr Applied Surface Science 151 (1999) 73–85

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A completely different effect may cause a qualitatively similar dependence of FA as a function of Ut . Electronic states within the vacuum gap which lead to ‘‘intermediate state tunneling’’ w32x can modify the relation between the tunneling current and tipsample distance: a uniform distribution of intermediate states in the tunnel gap leads to a decrease of the apparent barrier height. In this case, FA decreases as a function of Ut as it is observed for an ideal vacuum gap Žsee Eq. Ž5... However, intermediate states which are localized at the tip andror the sample surface can cause a different behaviour. Starting from a low value at a low tip-sample distance, FA is expected to increase as a function of d and to approach eventually the Žhigher. value corresponding to vacuum tunneling. At low Ut Žor d . the theory gives

FA s FA 0r Ž n q 1 .

2

Ž 6.

where n G 1 is the number of intermediate states in the gap and FA0 is the apparent barrier height in the absence of intermediate states w32x. At higher Ut Žor d. we expect that

FA s FA 0 .

Ž 7.

Given a variation DFA and considering the dependence on Ut we obtain from Eqs. Ž6. and Ž7.

DFA FA

( const.

Ž 8.

neglecting the relatively weak dependence on Ut according to Eq. Ž5. Ži.e., assuming e < Ut
5. Conclusions The combination of constant-current imaging in a high-resolution mode and simultaneous measurements of the local apparent barrier height, FA , yields new results concerning intrinsic properties of the surfaces of a-Si:H on an atomic scale. This method, in conjunction with variations of the tunneling voltage, enabled us to identify conditions which correspond to vacuum tunneling and, thus, helps to avoid artifacts due to less defined tip-sample interactions. Previous inconsistencies regarding atomic scale properties can be explained by the absence of vacuum tunneling in those experiments andror the use of less sensitive techniques. The details of the results can be summarized as follows: Ž1. High-resolution topography shows atomically rough and smooth regions which are superimposed on the previously described hills structure. The local ˚ rms roughness, d l , varies between 0.2 and 1.8 A. Smooth areas are correlated with prominent hills. Taking into account results from other investigations we can ascribe rough areas to the presence of higher silicon hydrides ŽSiH 2 , SiH 3 . and smooth areas to a phase consisting of silicon monohydrides andror adsorbed hydrogen atoms. Ž2. The local apparent barrier height is correlated with cos 2w and d l . The frequency distributions of FA are narrower and shifted towards higher values of FA on the less inclinedrsmooth areas Žat tunneling voltages corresponding to vacuum tunneling. as compared to inclinedrrough areas. These observations can be explained qualitatively by the influence of the topography on FA . Ž3. The frequency distributions of cos 2w , d l and FA as well as the correlations between couples of these quantities depend on Ut . The experimental result that DFA rFA,max f const. at various Ut can be explained by intermediate state tunneling. At higher Ut and on smooth areas the most frequent value of FA approaches ; 3.1 eV, i.e., a value which is in agreement with a simple model of vacuum tunneling between a tungsten tip and a-Si:H. The distribution of FA obtained under these conditions is indicative of local fluctuations of the work function of the sample.

J. Herionr Applied Surface Science 151 (1999) 73–85

Further efforts are necessary to elucidate the detailed nature of the surfaces of a-Si:H. For example, the microscopic effects of a hydrogen flux are a matter of great theoretical and practical interest. Much can be learned from previous work on hydrogenated crystalline silicon, e.g., low energy electron bombardment w38x, reaction with atomic hydrogen w22x and light-induced effects w39x have been shown to give valuable information on atomic scale surface properties. Additional understanding of local electronic properties may result from distance tunneling spectroscopy ŽDTS. and from voltage tunneling spectroscopy ŽVTS. w32x.

Acknowledgements The author would like to thank K. Szot, S. Barzen and F. Siebke for valuable contributions in the early stage of this work. Technical help of W. Hilgers, W. Klein, R. Nieveler, R. Otto, M. Teske, H.M. Schwan and C. Ulrichs as well as helpful discussions with K. Besocke, W. Beyer and Ch. Ross are gratefully acknowledged. Special thanks are due to J. Halbritter ŽForschungszentrum Karlsruhe. for drawing the author’s attention to intermediate state tunneling theory and for providing valuable experimental advice. The work was supported in part by the German Bundesministerium fur ¨ Bildung, Wissenschaft, Forschung und Technologie ŽBMBF..

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