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Si Schottky barrier
Applied Surface Science 159–160 Ž2000. 154–160 www.elsevier.nlrlocaterapsusc
Defect causing nonideality in nearly ideal AurSi Schottky barrier Keiji Maeda) Department of Materials Science and Technology, Science UniÕersity of Tokyo, Noda, Chiba 278-8510, Japan Received 8 November 1999
Abstract Previously we have proposed a model of lattice defect, positively charged defect close to the MrS interface, which causes nonideality in nearly ideal AurSi Schottky barrier. This model is elaborated in this paper. The To anomaly is caused by the spatial inhomogeneity of Schottky barrier height ŽSBH. due to the same defect, which is expressed by a Gaussian distribution with standard deviation s . The ideality factor n is related with s 2 , which depends on applied voltage. Utilizing a relation between the local SBH lowering and the distance of defect from metal-induced gap state ŽMIGS., the defect ˚ . to the MIGS. Changes of the distribution distribution, 6 = 10 13 cmy2 in total, is obtained to be confined close Žabout 10 A with applied bias indicate that the defect is an ionized donor in an equilibrium with neutral state in a low SBH region. The defect is induced by the Au evaporation process which produces Au silicide. Si self-interstitial induced by the process has appropriate atomic and electronic properties as the defect with deep donor levels of the negative-U property. q 2000 Elsevier Science B.V. All rights reserved. PACS: 73.30.q y Schottky barriers Keywords: Schottky barrier; Silicon; Ideality factor; Defect; Si self-interstitial
1. Introduction This work is to clarify the microscopic structure of defects and mechanism which induce nonideality in nearly ideal Si Schottky barrier ŽSB. as an elaboration of our previous report w1x. Since Aurn Si SB has a large Schottky barrier height ŽSBH. and has been studied extensively w2x, it is chosen as the sample for investigation. While the characteristic of SB depends on the structure of metalrsemiconductor ŽMrS. interface, Au has been considered to have small reactivity with Si and to make simple MrS interface. For the SB prepared by a metal evaporation onto etch-cleaned Si surface, the H-atom termi)
Tel.: q81-471-24-1501r4302; fax: q81-0471-23-9362. E-mail address: [email protected] ŽK. Maeda..
nation of surface dangling bond passivates the surface against oxidation and leads effectively to the intimate contact. The activation energy of electron transport in SB, i.e., the effective SBH, can be obtained from the temperature dependence of I–V characteristics. While the near equality of the temperature dependence of effective SBH to that of the ideality factor has been known for a long time as the To anomaly w2x, the reason was attributed to a particular distribution of interface state on the implicit assumption of spatially uniform SBH. However, the spatial inhomogeneity of SBH is deduced from the temperature dependence of effective SBH w3x. When the SBH is inhomogeneous, the current flows preferentially over the low SBH region with decreasing temperature. Correlations are expected
0169-4332r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 0 0 . 0 0 0 7 0 - 2
K. Maedar Applied Surface Science 159–160 (2000) 154–160
between the To anomaly and the nonideality. The SBH inhomogeneity is demonstrated directly by the ballistic electron emission microscopyrspectroscopy ŽBEEMrBEES. observation of Aurn–Si SB w4x. As for the theoretical model of Si SB the metalinduced gap state ŽMIGS. model has been developed Ža review of MIGS is given in Ref. w5x.. The charge density in MIGS determines the SBH at MrS interface. This model successfully explains the Fermi level pinning in nonepitaxial SB. Hitherto uniform interface structure has been investigated in the studies of SBH. The distribution of SBH in epitaxial SB w6x indicates nonuniformity even in the epitaxial interface. We are interested in the nonuniform structure associated with the To anomaly in nearly ideal interface, which is closely correlated with the formation mechanism of SB. Here, the MIGS concept is applied for the first time to the analysis of local band bending due to defect in nearly ideal Si SB. We have proposed a microscopic model of a defect causing low SBH spot w1x, in which a positively charged defect at distance x from the MIGS tail induces a negative charge dQ MIGS Ž x,r . at radial distance r from the normally projected position of defect in the metallic MIGS plane. While the induced charge density dQ MIGS varies gradually with r, it can be approximated by a step function DQ MIGS s yqor2p x 2
for p r 2 F x 2 ,
for p r 2 ) x 2 as illustrated in Fig. 1Ža.. Since the Fermi level is equal with the surrounding region but the induced charge density DQ MIGS occupies the MIGS of state density D MIGS , the energy band of semiconductor locally bends downward w1x. Thus, the induced charge lowers SBH by and
DQ MIGS s 0
d f s f y F B sDQ MIGSrqD MIGS s yqor2p qx 2 D MIGS )
2
2
Ž 1.
in an area of p r s x in the MIGS as illustrated in Fig. 1Žb.. Here,F B is the normal SBH and f is the local SBH. This equation shows that the donors closer to MIGS induce larger local reduction of SBH. The magnitude of D MIGS in Si is obtained theoretically to be about 4 = 10 14 statesrcm2 eV w5x. In this paper, the experimental nonideality in Aurn–Si SB analyzed in terms of the Gaussian distribution of inhomogeneous SBH leads to a corre-
155
Fig. 1. Ža. Full line shows induced charge distribution dQ MI GS in MIGS due to ionized donor and dashed line shows its approximation DQ MI GS . Dotted lines illustrate electric line of force due to the donor, Ref. w1x. Žb. Energy band diagram illustrating local SBH lowering due to ionized donor. EC) and E V) are lowered local band edges.
lation with the To anomaly ŽSection 2.. The spatial distribution of the positive-charge defects is obtained and this defect charge is preferentially neutralized with an application of forward bias in the low SBH region ŽSection 3.. Si self-interstitial has appropriate properties as the defect causing the To anomaly ŽSection 4.. Discussion and conclusion are given in Sections 5 and 6, respectively.
2. Gaussian distribution of SBH and the To anomaly AurSi SBs were prepared using n-type Si Ž100. wafers with carrier concentration of 3 = 10 15 cmy3
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K. Maedar Applied Surface Science 159–160 (2000) 154–160
by evaporating Au electrode onto chemically cleaned and etched surface w1x. The temperature dependence of I–V and C–V characteristics of these samples was measured in a temperature range of 1608C to 408C. The thermionic emission theory gives the I–V relation with the ideality factor n and the effective SBH Feff by J s Jo exp Ž qVrnkT . y 1 4 ,
Ž 2a .
Jo s A) T 2 exp Ž yqFeffrkT . ,
Ž 2b .
where q is the electronic charge, k is the Boltzmann constant, T is the absolute temperature and A) is the effective Richardson constant. The n value is obtained at each temperature from the slope of straight line in the log J vs. V plot w1x. The n value is close to unity at room temperature and increases with decreasing temperature as shown in Fig. 2Ža..
Several other samples show quite similar characteristics. This characteristic is essentially the same as the so-called To anomaly, which is expressed by the equation w2x J s A) T 2 exp yqF B rk Ž T q To . 4 = exp qVrk Ž T q To . 4 y 1 ,
Ž 3.
where To is a parameter which is independent of temperature and voltage over a wide range of temperatures. Eq. Ž3. is equivalent to writing the ideality factor for the V dependent term n s 1 q ŽTorT . in Eq. Ž2a.. Fig. 2Žb. shows the plot of nT against T to determine the To value. Here, the To value is 34 K. The variation of ideality factor with temperature in our AurSi SB can also be expressed by the relation 1rn s 1ŽyTorT . as shown in Fig. 2Žc.. The temperature dependence of effective SBH due to the spatial inhomogeneity is experimentally expressed as F B rn w7x. Therefore, in order to explain the mechanism of To anomaly it is convenient to introduce the ideality factor n for SBH by the definition
Feff s F B r Ž 1 q TorT . s F B rnF
Ž 4.
and to prove the relation n s nF . While there is a difference between n s 1 q TorT of the To anomaly and 1rn s 1 y TorT by the inhomogeneous SBH model, the difference of n is a second order of TorT for To < T and henceforth this characteristic n s nF is called the To anomaly. A symmetric Gaussian has been used to represent the distribution of inhomogeneous SBH w3x. From a standpoint of the inhomogeneous SBH model w1x, in which defects in MrS interface cause local reduction of SBH, the normalized distribution probability of local SBH f is expected to be expressed by half of Gaussian distribution,
'2 PH Ž f , s . s s'p
½
exp y
ŽF B yf . 2s 2
y` - f F F B .
Fig. 2. Temperature dependence of ideality factor n in AurSi Schottky barrier by different plot. Ža. n vs. T, Žb. nT vs. T, and Žc. Ž1y1r n. vs. 1r T.
2
5
,
Ž 5.
By an integration of the current flow over the SBH with the distribution of Eq. Ž5., Feff has the temperature dependence given by w3,8x
FeffrF B s 1rnF s 1 y qs 2 2 kTF B .
Ž 6.
K. Maedar Applied Surface Science 159–160 (2000) 154–160
Eq. Ž6. is in good agreement with the experimental result of 1rT dependence shown in Fig. 2Žc. provided that nF is equal to n. The SBH F B is equated with the SBH F C s 0.83 eV w1x obtained by the C–V measurement at 1 MHz, since the image-force Schottky effect DSE is absent in the low SBH region of the proposed model w8x. The s value determined from experimental data is 60 mV using Eq. Ž5. w8x. When Feff varies with applied bias, n becomes w2x 1rn s 1 y EFeffrEV .
Ž 7.
The SBH inhomogeneity causing temperature dependence of n is represented fairly well by a Gaussian distribution. Then, Feff depends on s in Eq. Ž6. and we have EFeffrEV s yqs Ž EsrEV . rkT .
Ž 8.
Since n is experimentally independent of V, s ŽEsrEV . is also a constant independent of V. Then by solving a differential equation with a proper choice of an integration constant s 2 becomes
s 2 s so2 Ž F B y V . rF B ,
Ž 9.
where so is a constant which is equal to s for V s 0. Accordingly, we have 1rn s 1 y Ž qso2r2 kTF B . .
Ž 10 .
157
ture at zero bias. The N Ž x . distribution thus obtained is shown in Fig. 3 by the curve marked with circles. N Ž x . exponentially increases with x at small x values, reaches to a maximum Nmax and then gradually decreases in proportion to xy5 . The very large ˚ Since Nmax , about 1x10 21 cmy3, appears at x s 9 A. the region of large N value is only several ML in width, this large Nmax is considered to be produced by the interface reaction as discussed in Section 4. The interface defect density Nid per unit area is obtained by an integration of N Ž x ., `
Nid s
FB
H0 N Ž x . d xsHy` P 2q
s q0
'2p s D MIGS
H
Ž f ,s .
1 x2
df
Ž 12 .
Nid , being proportional to s , is 6.0 = 10 13 cmy2 for the above values of parameters. Though the Nmax is very large, the total area of low SBH region is estimated to be only a few percent from the N Ž x . distribution and is consistent with the nearly ideal SB characteristics w8x. Since s decreases with increasing forward bias, N Ž x . is calculated for two additional values of s given by Eq. Ž9. with F B s 0.83 V as shown in Fig. 3. In these N Ž x . distributions under forward bias the
Since Feff is obtained from Jo extrapolating ln J to V s 0, s in Eq. Ž6. is actually so . The relation nF s n for the To anomaly is proved by comparing Eqs. Ž6. and Ž10.. Thus the To anomaly is concluded to be a general characteristic of nearly ideal SB with SBH inhomogeneity expressed by a Gaussian distribution.
3. Spatial distribution of defects The density distribution N Ž x . of the positively charged defects inducing the SBH lowering can be obtained by the relation N Ž x . x 2 d x s PH Ž f , s . d f
Ž 11 .
2
where x is the area of low SBH spot, and f is given by Eq. Ž1.. The qo value depends on the identity of positively charged defect. Here, qo is assumed to be 2 q as explained in Section 4. The s in PH Ž f , s . is set equal to 60 mV at room tempera-
Fig. 3. Distributions of charged defect density N vs. distance x for three applied voltages, qo s 2 q. Ž`. V s 0, s s60 mV, Ž^. V s158 mV, s s 54 mV, ŽI. V s 315 mV, s s 47.2 mV.
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K. Maedar Applied Surface Science 159–160 (2000) 154–160
remarkable change is the parallel shift of the straight line portion with applied bias in the range of x where N exponentially increases with x. There is no appreciable change in the gradual decrease after passing the maximum. Therefore, this change of N Ž x . with applied bias suggests that the positively charged donor at a position of small x is preferentially neutralized with applied bias. The entity of the ideality factor n, i.e., the increase of Feff with applied bias expressed by Eq. Ž7., is interpreted to be this preferential neutralization of ionized donors. It has been considered that the deep ionized donors in a depletion layer of SB are not neutralized by an application of forward bias w2x. However, the preferential neutralization is analytically shown to occur in a local low SBH region of inhomogeneous SBH w8x. This analysis suggests that the N Ž x . in zero-bias condition is also determined by the equilibrium of the defect energy levels E D with the Fermi level EF . Here, we are concerned about the electronic property of the donor. Usually an ionized donor is neutralized when EF rises above ED . Fig. 4 illustrates the variation of qf , EC and ED with distance x of the defect from the MIGS. When the donor becomes neutralized at x o , the SBH lowering due to the ionized donor disappears. Here, the ionized donor is neutralized raising both EC and E D by yd f and E D becomes above E F . If the neutralization is assumed to occur for EC y EF - EC y ED after neutralization, a hysteresis is expected in the I–V characteristics contrarily to the observation. Therefore, stable
Fig. 4. SBH f and energy levels plotted against ionized donor position x. Neutralization of the donor at around x o is illustrated. A Gaussian shape at x o illustrates broadening of donor energy level ED .
neutralization in an ordinary donor is not a cause of the To anomaly. This situation is considered for Si self-interstitial as an example. Si self-interstitial is known as the negative-U center by theoretical calculations w9,10x, where the neutral energy level occupied by two electrons is lower than the ionized level occupied by single electron, i.e. the electron correlation energy U is negative. The charge states change between I 2q and I 0 . Iq is not a stable charge state for any value of E F . The energy level ED represents the Fermi level energy where I 2q and I 0 are in equilibrium. When x is large the self-interstitial is I 2q since its energy level E 2qrEq is above the Fermi level E F . With decreasing x, I 2q becomes I 0 at around x 0 because of the EC lowering. This is the reason why there is no ionized donor close to x s 0. While the SBH lowering disappears by this neutralization, I 0 state is stable because the relation EC y E 0 ) EC y Eqis satisfied by the negative-U property.
4. Identity of the defect The identity of the defect is considered to be a process-induced positively charged donor, because the maximum density 1 = 10 21 cmy3 is very high and the distribution is confined close to the interface. At first, Au impurity atom is examined as the process-induced defect by the Au evaporation. Substitutional Au has a large diffusion coefficient in Si w11x. While Au atom in Si has two energy levels, they are not adequate for the donor w8x. Though the reactivity of Au with Si is very small, Au silicide formation is known when Au is evaporated onto Si surface at room temperature w12x. Si–Si bonds are broken and the released Si atoms migrate into the Au film. Photoemission spectroscopy study of room-temperature-grown AurSi Ž111. interface revealed the process of Au–Si alloy formation w13x. It is plausible that a small portion of released Si atoms simultaneously diffuse into the Si interior and become self-interstitials w8x. However, they are hardly detected by their nature. A high-density Si self-interstitial is possible without lattice distortion since the covalent Si radius is small relative to the tetrahedral
K. Maedar Applied Surface Science 159–160 (2000) 154–160
interstitial cavity. They are not detected by EPR since the state with unpaired spin is unstable by the negative-U property. It is reported w14x that a large number of point defects, self-interstitial or vacancy, are generated during near-noble-metal silicide formation at low temperature Ž; 2508C. in Si near the siliciderSi interface and that the concentration of these point defects are estimated to be about 10 21 cmy3 from the enhanced diffusivity of implanted substitutional As dopant, which is the same order of magnitude as our Nmax . Since the diffusion of As dopant is enhanced by Si oxidation process, the diffusivity is using mainly self-interstitial as vehicles of diffusion w11x. The diffusivity of Si self-interstitial near room temperatures is controversial at present w11x. The high mobility of Si self-interstitial in p-Si at 4.2 K w15x is explained theoretically w9,10x to be due to small energy differences at various minimum energy positions by changing charge states under ionizing radiation. Although the products of diffusivity D i and concentration Ci of the intrinsic defect i in Si are known to have a large activation energy by a number of diffusion studies at high temperature, the determination of individual factors D i and Ci are extremely difficult w11x. Stable configurations of Si self-interstitial are the tetrahedral site for I 2q and the w110x split site for I 0 . As for the negative-U property of Si self-interstitial the deep donor level ED for the I 2qrI 0 equilibrium is E V q Ž0.6–0.7. eV w9,10x, which is in agreement with the estimates w8x when the energy level lowering of I 2q due to the image force potential w2x is taken into account. While the energy levels of Si vacancy as donor have negative-U property, they are too low in the energy gap, i.e. ED for the V 2qrV 0 equilibrium is E V q 0.13 eV w9,15x, to be consistent with the SBH value. 5. Discussion The results of BEEM experiment on Aurn-Si SB at room temperature w4x are: the density of low SBH spot is about 10 13 cmy2 and the diameter of low SBH spot is about 2 nm. The SBH distribution by the BEES experiment w4x is asymmetric Gaussian decaying gradually in the low-f side of the maximum fmax but rapidly in the high-f side. The fmax
159
and full width at half maximum ŽFWHM. of distribution are compared with the F C and sI – V of I–V characteristics for the same sample based on the half-Gaussian SBH distribution of Eq. Ž5.. The value of fmax corresponding to the normal SBH region is nearly equal to F C y DSE and s BEES obtained from the FWHM is nearly equal to sI – V w8x. All these results strongly support the validity of our model. Tung w16x proposed a model of inhomogeneous SBH in SB, in which the SBH right at MrS interface is low in circular patches of radius R. By macroscopic field calculation solving Poisson’s equation on a defect-free semiconductor except the SBH inhomogeneity as the boundary condition, a potential saddle point is obtained in the potential distribution along the normal to MrS interface and it is the current-determining SBH. The saddle point potential becomes nearly equal to the surrounding high SBH when R is very small compared with the depletion layer width W. The saddle point disappears when R is comparable to W. Therefore, the magnitude of R is critical for the model. There is a problem in applying his model to the nonepitaxial SB. The depletion layer width W of BEEMrBEES sample is an order of 1 mm, about three orders of magnitude larger than R. The calculated fmax y Feff value according to his model is too small compared with the observed values w8x. The dimension, where the macroscopic field calculation using Poisson’s equation is valid, is generally considered to be larger than several times of the average doped donor distance d. In a semiconductor of donor density 1 = 10 15 cmy3 d is equal to 1 = 10y5 cm. Thus, the R discussed here is two orders of magnitude smaller than d. These considerations indicate that Tung’s model is adequate to explain the SBH inhomogeneity in the epitaxial SB of large R dimension but is not adequate to the nonepitaxial SB. The To anomaly is observed in n-Si SB but is not observed in p-Si SB w7x. The present investigation strongly suggests that the To anomaly is caused by the process-induced deep donor in n-Si, Si self-interstitial, which has the negative-U property. When this analysis is translated into p-Si SB, a deep acceptor with the negative-U property has to be induced in p-Si by the fabrication process. Intrinsic point defects in Si do not satisfy this condition. Thus, it is understood that the To anomaly is not observed in
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K. Maedar Applied Surface Science 159–160 (2000) 154–160
p-Si SB where the same Fermi level pinning mechanism works as in n-Si SB. Therefore, it seems reasonable to conclude Si self-interstitial as the defect inducing To anomaly.
6. Conclusion The following model is proposed as a conclusion. The To anomaly in nearly ideal Aurn-Si SB is due to the spatial SBH inhomogeneity caused by the positively charged donors close to the MrS interface. The ideality factor n is related to the variance s 2 in the Gaussian distribution of SBH. The spatial distribution of ionized donor is in an equilibrium ionization of fabrication-induced defect. Si self-interstitial has appropriate properties as the defect in the proposed model. Thus, the mechanism of To anomaly in nearly ideal Aurn-Si SB is understood consistently with an absence of To anomaly in p-Si SB.
References w1x K. Maeda, E. Kitahara, Appl. Surf. Sci. 130–132 Ž1998. 925. w2x E.H. Rhoderick, R.H. Williams, Metal–Semiconductor Contacts, 2nd edn., Clarendon Press, Oxford, 1988.
w3x J.H. Werner, H.H. Guettler, J. Appl. Phys. 59 Ž1991. 1552. w4x H. Palm, M. Arbes, M. Schulz, Phys. Rev. Lett. 71 Ž1993. 2224. w5x W. Moench, Semiconductor Surfaces and Interfaces, 2nd edn., Springer, Berlin, 1995. w6x H.H. Weitering, J.P. Sullivan, R.J. Carolissen, R. PerezSandoz, W.R. Graham, R.T. Tung, J. Appl. Phys. 79 Ž1996. 7820. w7x M.O. Aboelfotoh, A. Cros, B.G. Svenson, K.N. Tu, Phys. Rev. B 41 Ž1990. 9819. w8x K. Maeda, unpublished. w9x R. Car, P.J. Kelly, A. Oshiyama, S.T. Pantelides, Phys. Rev. Lett. 52 Ž1984. 1814. w10x W.-C. Lee, S.-G. Lee, K.J. Chang, J. Phys.: Condens. Matter 10 Ž1998. 995. w11x U.M. Goesele, T.Y. Tan, in: W. Schroeter ŽEd.., Materials Science and Technology vol. 4 VCH, Weinheim, 1991, p. 197. w12x A. Hiraki, Surf. Sci. Rep. 3 Ž1984. 357. w13x J.J. Yeh, J. Hwang, K. Bertness, D.J. Friedman, R. Cao, I. Lindau, Phys. Rev. Lett. 70 Ž1993. 3768. w14x M. Wittmer, K.N. Tu, Phys. Rev. B 29 Ž1984. 2010. w15x G.D. Watkins, in: W. Schroeter ŽEd.., Materials Science and Technology vol. 4 VCH, Weinheim, 1991, p. 105. w16x R.T. Tung, Phys. Rev. B 45 Ž1992. 13509.
Defect causing nonideality in nearly ideal AurSi Schottky barrier Keiji Maeda) Department of Materials Science and Technology, Science UniÕersity of Tokyo, Noda, Chiba 278-8510, Japan Received 8 November 1999
Abstract Previously we have proposed a model of lattice defect, positively charged defect close to the MrS interface, which causes nonideality in nearly ideal AurSi Schottky barrier. This model is elaborated in this paper. The To anomaly is caused by the spatial inhomogeneity of Schottky barrier height ŽSBH. due to the same defect, which is expressed by a Gaussian distribution with standard deviation s . The ideality factor n is related with s 2 , which depends on applied voltage. Utilizing a relation between the local SBH lowering and the distance of defect from metal-induced gap state ŽMIGS., the defect ˚ . to the MIGS. Changes of the distribution distribution, 6 = 10 13 cmy2 in total, is obtained to be confined close Žabout 10 A with applied bias indicate that the defect is an ionized donor in an equilibrium with neutral state in a low SBH region. The defect is induced by the Au evaporation process which produces Au silicide. Si self-interstitial induced by the process has appropriate atomic and electronic properties as the defect with deep donor levels of the negative-U property. q 2000 Elsevier Science B.V. All rights reserved. PACS: 73.30.q y Schottky barriers Keywords: Schottky barrier; Silicon; Ideality factor; Defect; Si self-interstitial
1. Introduction This work is to clarify the microscopic structure of defects and mechanism which induce nonideality in nearly ideal Si Schottky barrier ŽSB. as an elaboration of our previous report w1x. Since Aurn Si SB has a large Schottky barrier height ŽSBH. and has been studied extensively w2x, it is chosen as the sample for investigation. While the characteristic of SB depends on the structure of metalrsemiconductor ŽMrS. interface, Au has been considered to have small reactivity with Si and to make simple MrS interface. For the SB prepared by a metal evaporation onto etch-cleaned Si surface, the H-atom termi)
Tel.: q81-471-24-1501r4302; fax: q81-0471-23-9362. E-mail address: [email protected] ŽK. Maeda..
nation of surface dangling bond passivates the surface against oxidation and leads effectively to the intimate contact. The activation energy of electron transport in SB, i.e., the effective SBH, can be obtained from the temperature dependence of I–V characteristics. While the near equality of the temperature dependence of effective SBH to that of the ideality factor has been known for a long time as the To anomaly w2x, the reason was attributed to a particular distribution of interface state on the implicit assumption of spatially uniform SBH. However, the spatial inhomogeneity of SBH is deduced from the temperature dependence of effective SBH w3x. When the SBH is inhomogeneous, the current flows preferentially over the low SBH region with decreasing temperature. Correlations are expected
0169-4332r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 0 0 . 0 0 0 7 0 - 2
K. Maedar Applied Surface Science 159–160 (2000) 154–160
between the To anomaly and the nonideality. The SBH inhomogeneity is demonstrated directly by the ballistic electron emission microscopyrspectroscopy ŽBEEMrBEES. observation of Aurn–Si SB w4x. As for the theoretical model of Si SB the metalinduced gap state ŽMIGS. model has been developed Ža review of MIGS is given in Ref. w5x.. The charge density in MIGS determines the SBH at MrS interface. This model successfully explains the Fermi level pinning in nonepitaxial SB. Hitherto uniform interface structure has been investigated in the studies of SBH. The distribution of SBH in epitaxial SB w6x indicates nonuniformity even in the epitaxial interface. We are interested in the nonuniform structure associated with the To anomaly in nearly ideal interface, which is closely correlated with the formation mechanism of SB. Here, the MIGS concept is applied for the first time to the analysis of local band bending due to defect in nearly ideal Si SB. We have proposed a microscopic model of a defect causing low SBH spot w1x, in which a positively charged defect at distance x from the MIGS tail induces a negative charge dQ MIGS Ž x,r . at radial distance r from the normally projected position of defect in the metallic MIGS plane. While the induced charge density dQ MIGS varies gradually with r, it can be approximated by a step function DQ MIGS s yqor2p x 2
for p r 2 F x 2 ,
for p r 2 ) x 2 as illustrated in Fig. 1Ža.. Since the Fermi level is equal with the surrounding region but the induced charge density DQ MIGS occupies the MIGS of state density D MIGS , the energy band of semiconductor locally bends downward w1x. Thus, the induced charge lowers SBH by and
DQ MIGS s 0
d f s f y F B sDQ MIGSrqD MIGS s yqor2p qx 2 D MIGS )
2
2
Ž 1.
in an area of p r s x in the MIGS as illustrated in Fig. 1Žb.. Here,F B is the normal SBH and f is the local SBH. This equation shows that the donors closer to MIGS induce larger local reduction of SBH. The magnitude of D MIGS in Si is obtained theoretically to be about 4 = 10 14 statesrcm2 eV w5x. In this paper, the experimental nonideality in Aurn–Si SB analyzed in terms of the Gaussian distribution of inhomogeneous SBH leads to a corre-
155
Fig. 1. Ža. Full line shows induced charge distribution dQ MI GS in MIGS due to ionized donor and dashed line shows its approximation DQ MI GS . Dotted lines illustrate electric line of force due to the donor, Ref. w1x. Žb. Energy band diagram illustrating local SBH lowering due to ionized donor. EC) and E V) are lowered local band edges.
lation with the To anomaly ŽSection 2.. The spatial distribution of the positive-charge defects is obtained and this defect charge is preferentially neutralized with an application of forward bias in the low SBH region ŽSection 3.. Si self-interstitial has appropriate properties as the defect causing the To anomaly ŽSection 4.. Discussion and conclusion are given in Sections 5 and 6, respectively.
2. Gaussian distribution of SBH and the To anomaly AurSi SBs were prepared using n-type Si Ž100. wafers with carrier concentration of 3 = 10 15 cmy3
156
K. Maedar Applied Surface Science 159–160 (2000) 154–160
by evaporating Au electrode onto chemically cleaned and etched surface w1x. The temperature dependence of I–V and C–V characteristics of these samples was measured in a temperature range of 1608C to 408C. The thermionic emission theory gives the I–V relation with the ideality factor n and the effective SBH Feff by J s Jo exp Ž qVrnkT . y 1 4 ,
Ž 2a .
Jo s A) T 2 exp Ž yqFeffrkT . ,
Ž 2b .
where q is the electronic charge, k is the Boltzmann constant, T is the absolute temperature and A) is the effective Richardson constant. The n value is obtained at each temperature from the slope of straight line in the log J vs. V plot w1x. The n value is close to unity at room temperature and increases with decreasing temperature as shown in Fig. 2Ža..
Several other samples show quite similar characteristics. This characteristic is essentially the same as the so-called To anomaly, which is expressed by the equation w2x J s A) T 2 exp yqF B rk Ž T q To . 4 = exp qVrk Ž T q To . 4 y 1 ,
Ž 3.
where To is a parameter which is independent of temperature and voltage over a wide range of temperatures. Eq. Ž3. is equivalent to writing the ideality factor for the V dependent term n s 1 q ŽTorT . in Eq. Ž2a.. Fig. 2Žb. shows the plot of nT against T to determine the To value. Here, the To value is 34 K. The variation of ideality factor with temperature in our AurSi SB can also be expressed by the relation 1rn s 1ŽyTorT . as shown in Fig. 2Žc.. The temperature dependence of effective SBH due to the spatial inhomogeneity is experimentally expressed as F B rn w7x. Therefore, in order to explain the mechanism of To anomaly it is convenient to introduce the ideality factor n for SBH by the definition
Feff s F B r Ž 1 q TorT . s F B rnF
Ž 4.
and to prove the relation n s nF . While there is a difference between n s 1 q TorT of the To anomaly and 1rn s 1 y TorT by the inhomogeneous SBH model, the difference of n is a second order of TorT for To < T and henceforth this characteristic n s nF is called the To anomaly. A symmetric Gaussian has been used to represent the distribution of inhomogeneous SBH w3x. From a standpoint of the inhomogeneous SBH model w1x, in which defects in MrS interface cause local reduction of SBH, the normalized distribution probability of local SBH f is expected to be expressed by half of Gaussian distribution,
'2 PH Ž f , s . s s'p
½
exp y
ŽF B yf . 2s 2
y` - f F F B .
Fig. 2. Temperature dependence of ideality factor n in AurSi Schottky barrier by different plot. Ža. n vs. T, Žb. nT vs. T, and Žc. Ž1y1r n. vs. 1r T.
2
5
,
Ž 5.
By an integration of the current flow over the SBH with the distribution of Eq. Ž5., Feff has the temperature dependence given by w3,8x
FeffrF B s 1rnF s 1 y qs 2 2 kTF B .
Ž 6.
K. Maedar Applied Surface Science 159–160 (2000) 154–160
Eq. Ž6. is in good agreement with the experimental result of 1rT dependence shown in Fig. 2Žc. provided that nF is equal to n. The SBH F B is equated with the SBH F C s 0.83 eV w1x obtained by the C–V measurement at 1 MHz, since the image-force Schottky effect DSE is absent in the low SBH region of the proposed model w8x. The s value determined from experimental data is 60 mV using Eq. Ž5. w8x. When Feff varies with applied bias, n becomes w2x 1rn s 1 y EFeffrEV .
Ž 7.
The SBH inhomogeneity causing temperature dependence of n is represented fairly well by a Gaussian distribution. Then, Feff depends on s in Eq. Ž6. and we have EFeffrEV s yqs Ž EsrEV . rkT .
Ž 8.
Since n is experimentally independent of V, s ŽEsrEV . is also a constant independent of V. Then by solving a differential equation with a proper choice of an integration constant s 2 becomes
s 2 s so2 Ž F B y V . rF B ,
Ž 9.
where so is a constant which is equal to s for V s 0. Accordingly, we have 1rn s 1 y Ž qso2r2 kTF B . .
Ž 10 .
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ture at zero bias. The N Ž x . distribution thus obtained is shown in Fig. 3 by the curve marked with circles. N Ž x . exponentially increases with x at small x values, reaches to a maximum Nmax and then gradually decreases in proportion to xy5 . The very large ˚ Since Nmax , about 1x10 21 cmy3, appears at x s 9 A. the region of large N value is only several ML in width, this large Nmax is considered to be produced by the interface reaction as discussed in Section 4. The interface defect density Nid per unit area is obtained by an integration of N Ž x ., `
Nid s
FB
H0 N Ž x . d xsHy` P 2q
s q0
'2p s D MIGS
H
Ž f ,s .
1 x2
df
Ž 12 .
Nid , being proportional to s , is 6.0 = 10 13 cmy2 for the above values of parameters. Though the Nmax is very large, the total area of low SBH region is estimated to be only a few percent from the N Ž x . distribution and is consistent with the nearly ideal SB characteristics w8x. Since s decreases with increasing forward bias, N Ž x . is calculated for two additional values of s given by Eq. Ž9. with F B s 0.83 V as shown in Fig. 3. In these N Ž x . distributions under forward bias the
Since Feff is obtained from Jo extrapolating ln J to V s 0, s in Eq. Ž6. is actually so . The relation nF s n for the To anomaly is proved by comparing Eqs. Ž6. and Ž10.. Thus the To anomaly is concluded to be a general characteristic of nearly ideal SB with SBH inhomogeneity expressed by a Gaussian distribution.
3. Spatial distribution of defects The density distribution N Ž x . of the positively charged defects inducing the SBH lowering can be obtained by the relation N Ž x . x 2 d x s PH Ž f , s . d f
Ž 11 .
2
where x is the area of low SBH spot, and f is given by Eq. Ž1.. The qo value depends on the identity of positively charged defect. Here, qo is assumed to be 2 q as explained in Section 4. The s in PH Ž f , s . is set equal to 60 mV at room tempera-
Fig. 3. Distributions of charged defect density N vs. distance x for three applied voltages, qo s 2 q. Ž`. V s 0, s s60 mV, Ž^. V s158 mV, s s 54 mV, ŽI. V s 315 mV, s s 47.2 mV.
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K. Maedar Applied Surface Science 159–160 (2000) 154–160
remarkable change is the parallel shift of the straight line portion with applied bias in the range of x where N exponentially increases with x. There is no appreciable change in the gradual decrease after passing the maximum. Therefore, this change of N Ž x . with applied bias suggests that the positively charged donor at a position of small x is preferentially neutralized with applied bias. The entity of the ideality factor n, i.e., the increase of Feff with applied bias expressed by Eq. Ž7., is interpreted to be this preferential neutralization of ionized donors. It has been considered that the deep ionized donors in a depletion layer of SB are not neutralized by an application of forward bias w2x. However, the preferential neutralization is analytically shown to occur in a local low SBH region of inhomogeneous SBH w8x. This analysis suggests that the N Ž x . in zero-bias condition is also determined by the equilibrium of the defect energy levels E D with the Fermi level EF . Here, we are concerned about the electronic property of the donor. Usually an ionized donor is neutralized when EF rises above ED . Fig. 4 illustrates the variation of qf , EC and ED with distance x of the defect from the MIGS. When the donor becomes neutralized at x o , the SBH lowering due to the ionized donor disappears. Here, the ionized donor is neutralized raising both EC and E D by yd f and E D becomes above E F . If the neutralization is assumed to occur for EC y EF - EC y ED after neutralization, a hysteresis is expected in the I–V characteristics contrarily to the observation. Therefore, stable
Fig. 4. SBH f and energy levels plotted against ionized donor position x. Neutralization of the donor at around x o is illustrated. A Gaussian shape at x o illustrates broadening of donor energy level ED .
neutralization in an ordinary donor is not a cause of the To anomaly. This situation is considered for Si self-interstitial as an example. Si self-interstitial is known as the negative-U center by theoretical calculations w9,10x, where the neutral energy level occupied by two electrons is lower than the ionized level occupied by single electron, i.e. the electron correlation energy U is negative. The charge states change between I 2q and I 0 . Iq is not a stable charge state for any value of E F . The energy level ED represents the Fermi level energy where I 2q and I 0 are in equilibrium. When x is large the self-interstitial is I 2q since its energy level E 2qrEq is above the Fermi level E F . With decreasing x, I 2q becomes I 0 at around x 0 because of the EC lowering. This is the reason why there is no ionized donor close to x s 0. While the SBH lowering disappears by this neutralization, I 0 state is stable because the relation EC y E 0 ) EC y Eqis satisfied by the negative-U property.
4. Identity of the defect The identity of the defect is considered to be a process-induced positively charged donor, because the maximum density 1 = 10 21 cmy3 is very high and the distribution is confined close to the interface. At first, Au impurity atom is examined as the process-induced defect by the Au evaporation. Substitutional Au has a large diffusion coefficient in Si w11x. While Au atom in Si has two energy levels, they are not adequate for the donor w8x. Though the reactivity of Au with Si is very small, Au silicide formation is known when Au is evaporated onto Si surface at room temperature w12x. Si–Si bonds are broken and the released Si atoms migrate into the Au film. Photoemission spectroscopy study of room-temperature-grown AurSi Ž111. interface revealed the process of Au–Si alloy formation w13x. It is plausible that a small portion of released Si atoms simultaneously diffuse into the Si interior and become self-interstitials w8x. However, they are hardly detected by their nature. A high-density Si self-interstitial is possible without lattice distortion since the covalent Si radius is small relative to the tetrahedral
K. Maedar Applied Surface Science 159–160 (2000) 154–160
interstitial cavity. They are not detected by EPR since the state with unpaired spin is unstable by the negative-U property. It is reported w14x that a large number of point defects, self-interstitial or vacancy, are generated during near-noble-metal silicide formation at low temperature Ž; 2508C. in Si near the siliciderSi interface and that the concentration of these point defects are estimated to be about 10 21 cmy3 from the enhanced diffusivity of implanted substitutional As dopant, which is the same order of magnitude as our Nmax . Since the diffusion of As dopant is enhanced by Si oxidation process, the diffusivity is using mainly self-interstitial as vehicles of diffusion w11x. The diffusivity of Si self-interstitial near room temperatures is controversial at present w11x. The high mobility of Si self-interstitial in p-Si at 4.2 K w15x is explained theoretically w9,10x to be due to small energy differences at various minimum energy positions by changing charge states under ionizing radiation. Although the products of diffusivity D i and concentration Ci of the intrinsic defect i in Si are known to have a large activation energy by a number of diffusion studies at high temperature, the determination of individual factors D i and Ci are extremely difficult w11x. Stable configurations of Si self-interstitial are the tetrahedral site for I 2q and the w110x split site for I 0 . As for the negative-U property of Si self-interstitial the deep donor level ED for the I 2qrI 0 equilibrium is E V q Ž0.6–0.7. eV w9,10x, which is in agreement with the estimates w8x when the energy level lowering of I 2q due to the image force potential w2x is taken into account. While the energy levels of Si vacancy as donor have negative-U property, they are too low in the energy gap, i.e. ED for the V 2qrV 0 equilibrium is E V q 0.13 eV w9,15x, to be consistent with the SBH value. 5. Discussion The results of BEEM experiment on Aurn-Si SB at room temperature w4x are: the density of low SBH spot is about 10 13 cmy2 and the diameter of low SBH spot is about 2 nm. The SBH distribution by the BEES experiment w4x is asymmetric Gaussian decaying gradually in the low-f side of the maximum fmax but rapidly in the high-f side. The fmax
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and full width at half maximum ŽFWHM. of distribution are compared with the F C and sI – V of I–V characteristics for the same sample based on the half-Gaussian SBH distribution of Eq. Ž5.. The value of fmax corresponding to the normal SBH region is nearly equal to F C y DSE and s BEES obtained from the FWHM is nearly equal to sI – V w8x. All these results strongly support the validity of our model. Tung w16x proposed a model of inhomogeneous SBH in SB, in which the SBH right at MrS interface is low in circular patches of radius R. By macroscopic field calculation solving Poisson’s equation on a defect-free semiconductor except the SBH inhomogeneity as the boundary condition, a potential saddle point is obtained in the potential distribution along the normal to MrS interface and it is the current-determining SBH. The saddle point potential becomes nearly equal to the surrounding high SBH when R is very small compared with the depletion layer width W. The saddle point disappears when R is comparable to W. Therefore, the magnitude of R is critical for the model. There is a problem in applying his model to the nonepitaxial SB. The depletion layer width W of BEEMrBEES sample is an order of 1 mm, about three orders of magnitude larger than R. The calculated fmax y Feff value according to his model is too small compared with the observed values w8x. The dimension, where the macroscopic field calculation using Poisson’s equation is valid, is generally considered to be larger than several times of the average doped donor distance d. In a semiconductor of donor density 1 = 10 15 cmy3 d is equal to 1 = 10y5 cm. Thus, the R discussed here is two orders of magnitude smaller than d. These considerations indicate that Tung’s model is adequate to explain the SBH inhomogeneity in the epitaxial SB of large R dimension but is not adequate to the nonepitaxial SB. The To anomaly is observed in n-Si SB but is not observed in p-Si SB w7x. The present investigation strongly suggests that the To anomaly is caused by the process-induced deep donor in n-Si, Si self-interstitial, which has the negative-U property. When this analysis is translated into p-Si SB, a deep acceptor with the negative-U property has to be induced in p-Si by the fabrication process. Intrinsic point defects in Si do not satisfy this condition. Thus, it is understood that the To anomaly is not observed in
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p-Si SB where the same Fermi level pinning mechanism works as in n-Si SB. Therefore, it seems reasonable to conclude Si self-interstitial as the defect inducing To anomaly.
6. Conclusion The following model is proposed as a conclusion. The To anomaly in nearly ideal Aurn-Si SB is due to the spatial SBH inhomogeneity caused by the positively charged donors close to the MrS interface. The ideality factor n is related to the variance s 2 in the Gaussian distribution of SBH. The spatial distribution of ionized donor is in an equilibrium ionization of fabrication-induced defect. Si self-interstitial has appropriate properties as the defect in the proposed model. Thus, the mechanism of To anomaly in nearly ideal Aurn-Si SB is understood consistently with an absence of To anomaly in p-Si SB.
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