METASTABILITIES AT THE Si-SiOx INTERFACE

412

METASTABILITIES AT THE Si-SiO

INTERFACE

C. T. White and K. L. Ngai Naval Research Laboratory, Washington, D. C. 20375 ABSTRACT We summarize some of the results of our investigation of the effects of dangling/weaker and stronger bonds on the electronic structure of the Si-SiO« interface. These dangling bonds give rise to a new type of interfacial compensating charged state and have an interesting dynamic character with implications for device characteristics. It is pointed out how these states can be severely modified by external perturbations when they are in contact with e.g. the p-channel inversion layer (IL) which could represent a sensitive probe of their nature and distribution. INTRODUCTION At the Si-SiO interface the covalently bonded semiconductor Si is joined to the dielectric Si0~; hence, it is reasonable to expect that this interfaced electronic structure is such that not all the possible bonded states are occupied and some that are can be easily altered. Inherent in the nature of such states is their ability to mediate an effective local pairing interaction between electrons, a feature employed by Anderson (Ref. 1) in his discussion of certain amorphous glasses. Here we will primarily be concerned with perhaps the most straightforward example of a dynamic electron pairing center that might well be present at the Si-SiO interface: an Si dangling bond. We will discuss how the p-channel Si IL can be used as a probe of the nature and distribution of these states and how their metastable character could give rise to measurable alterations in the device characteristics after the external perturbations causing these changes have been removed. THE MODEL AND RESULTS To begin we envision an Si atom at the interface bonded to three neighboring silicons and/or oxygens, leaving a dangling hybrid (DH). One would then expect that the average number of electrons in this hybrid would deviate significantly from one. The origin of this effect can be understood by observing that a lowering of the system energy from what is obtained when the nonbonded hybrid is singly occupied can usually be achieved by essentially transferring (donating) an electron to (from) this hybrid from (to) one of the other available occupied (unoccupied) states of the system and simultaneously distorting the atom possessing the dangling bond so to weaken (strengthen) its associated backbonds, while concomitantly lowering (raising) the DH level. Distortions would not be advantageous if the DH were constrained to be singly occupied since, although they should produce changes in the DH and associated back levels linear in the displacement, these changes would tend to cancel leaving an elastic-like energy to dominate.

413 This situation is entirely different if the DH occupancy is allowed to vary since e.g. if the DH was essentially unoccupied, then raising its level would have little energetic consequence. To specify and quantify this picture further one can employ (Ref. 2) the following Hamiltonian

Σ

t a .V. εo nma + *-τ* / . V. . . a. . JjimJ ισ mo ^ V b mo ojm

-

Xu(n

M

+ n

b+ -

1} + c u 2 / 2 + V

a

oZ)cbaaba

CD +

«Ϊσ^)

to describe a dangling bond in contact with the IL. The first two terms on the right hand side of (1) comprise a tight binding Hamiltonian, H_ R , taken to represent the IL where a' . a „ create and annihilate electrons ~ . , i ma ma , , , + of spin σ m the Wannier state ma> centered at the site m and n =a' a „ . . . L· . . /, N mo _ mo mo is the usual number operator. The remaining terms entering (1; refer entirely to the Si atom with the DH with the exception of the last which couples the dangling hybrid to the IL. The operators c? , c, create and destroy electrons in the dangling hybrid orbital \bo> ana u represents a local displacement of the atom possessing the dangling bond from its position if this bond were singly occupied with energy E, . The fifth term appearing on the right hand side of (1) is an elastic energy while the fourth is a dehybridization energy which can be obtained (Ref. 3) by applying the valence bond theory (Ref. 4 ) . The free energy corresponding to (1) can be expressed for low temperatures as F(u)=K+*u+cu /2

(2) o o

where E f is the Fermi level, G a (E)= , E + = lim £È+is), s -> 0 Gf=s9G /9E and K is independent of u. Both experimental (Ref. 5) and theoretical results (Ref. 6) concerning freshly vacuum-cleaved Si (111) surfaces imply the existence of a split surface dangling bond band in the vicinity of the valence band edge. It is generally agreed (Refs, 3,5) that the observed splitting of this band can in effect be ascribed to a dehybridization energy mediated attractive interaction amongst the surface dangling bond band electrons similar in form to that employed here. This data leads one to expect that the centers of reconstruction, E, , of these ideal dangling bonds lie ^.15 eV above the valence band edge with typical values of λ /c of ^.15 eV. Since the coupling of the DH to the IL should not be large, one can show from (2) that those DHs with centers of reconstruction that lie not too far from E f have a very interesting property, that is for those the free energy (2) exhibits two local minima associated with distinctly different occupancy of the DH. In one instance, effectively two electrons are strongly self-trapped by one another in the DH which lies λ /c below E, , while in the^other case, the two electrons lie in the IL and the DH state appears at λ /c above E, . Grossly, if E f >Ev>> t n e system prefers to put two electrons in the DH. However, if E- <Ε^> it prefers two holes in the DH. Thus, although a pair of electrons tholes) may be strongly trapped (e.g. .1 eV) below (above) E f , this pair can be eventually broken by a small change in the chemical potential

414 Fig. 1. The behavior of F(u.) [(a), (b)] for zero temperature 2 and 2λ /ire. > 1 if the inversion layer DOS, p Q , is taken as constant. Also shown a schematic of the effective oneelectron picture of the DOS [(af),(bf)] corresponding to an absolute minimum in F and the Fermi level below [(a),(a1)] and above [(b), (b1)] the center of reconstruction ε.. Shaded areas represent occupied states. In (a), (b), ε.=0 and X./c.= .75 with λ.= 9 in units taken so that V n πρ.« χ. (e.g. 1 meV). In Fig. 1 we summarize this discussion where the results obtained there have been found in assuming that the IL density of states (DOS) is independent of energy. We have obtained essentially similar results by taking this DOS as elliptic, rectangular, etc. The above properties of these dangling hybrids when in contact with the IL leads us to suspect that application of external perturbations could result in a rearrangement of the available holes over the dangling hybrid and IL states and these rearrangements might maintain themselves after the perturbations are removed. Assuming such is the case, measurable changes in the IL behavior could result. In particular, because of the disordered nature of the interface, the IL exhibits a mobility edge (Ref. 7) which sharply separates localized from extended states. This latter feature gives rise to an activated behavior for p-channel conduction when E- lies above E and . . f c since meV changes in the activation energy, E., are detectable, one could then possibly measure metastable changes in tne number of holes in the IL at constant gate voltage by observing changes in E A · Of course for any such changes to be easily observed in this manner it is necessary that the DOS of the dangling hybrids be comparable with and overlap to some extent the IL. For vacuum cleaved Si(111) surfaces the number of dangling bond states is ^10 per cm with centers of reconstruction presumably peaked at about .15 eV above the valence band edge. How many of these states are eliminated with the formation of the interface is difficult to estimate, as is the degree of the expected spreading of the centers of reconstruction. Note though that because of the metastable character of these states one should be able to sample not only those with centers of reconstruction right at E f , but any others that can be put into improperly reconstructed states. We now detail several examples of how such changes could be produced, (a) Mechanical stress: Application of uniaxial stress will shift the IL band as well as the centers of reconstruction of the pair states and such shifts should not be too strongly correlated. Thus a redistribution of electrons and holes is expected. Upon removal of the stress this state could persist as a strongly self-trapped metastable one whose existence could be reflected in changes in the activation energy from the prestressed situation, (b) External magnetic field: At low carrier densities magnetic fields of

415 sufficient strength can be generated so that there is essentially only one spin species of IL hole states. It then becomes energetically favorable to transfer some electrons from the IL to the dangling hybrids resulting in a strong pairwise trapping of these electrons below E f . Removal of the field could thus leave the system in what then is a very low lying selftrapped excited state which will exhibit an activation energy reduced from what was found prior to application of the field· Although this example is amusing, such effects would probably not be easily observable, (c) Annealing: Heating the device and then rapidly cooling it could easily freeze in different rearrangements of the available holes. Annealing could also produce a significant reduction in the pair state DOS. (d) Negative bias stress: Under negative voltage bias at room or elevated temperatures, negatively charged electron pair states can be activated to an excited state of one electron on the Si dangling bond which is now neutral, with the other electron transferred to the Si substrate. Subsequently the remaining electron is also transferred across to the Si substrate and a positively charged hole pair state results, changing the nature of the surface charge Q and hence perhaps the energetic position of the mobility edge, (e) Radiation: Photo excitation of electrons from the IL to the unoccupied dangling bond hole band could result in a condensation of these electrons at least strongly reconstructed dangling bonds effectively producing a nonradiative recombination process eventually taking the initially photoexcited electrons below the Fermi level. Such a process could actually change the device behavior from activated to conducting. Implicit in some parts of our above discussion is the assumption that the mobility edge does not change drastically with alterations in the occupancy of the dangling hybrids. Such an assumption is quite reasonable since these hybrid states upon reconstruction should lie either far above or below the mobility edge. Indeed we have carried out calculations assuming firstly, a tight binding model of the IL, and, secondly, that the dangling hybrids randomly occupy 10% of the lattice sites and thirdly, that the one electron potentials and centers of reconstruction of the pair states both obey Anderson probability distributions of width W., W~ respectively. It is found for a physically reasonable choice of the parameters of this model, that the assumption of the essential constancy of the mobility edge is indeed verified. Furthermore, within this model we have obtained an example of a rather severe rearrangement of the holes over the system which actually changes the behavior of the device from activated to conducting but represents a low lying strongly self-trapped excitation of the system. CONCLUDING REMARKS The p-channel MOSFET was chosen here to illustrate some of the important effects that could be produced by Si dangling bonds at the Si-SiO interface. These dynamic pairing states not only contribute to Q if E,. is above or below E, but also can provide a source of interface "fast" states N , each of whicn can be thought of as lying essentially at a center of reconstruction. Other pairing states that arise from weaker and stronger (in the spirit of Anderson) Si-Si interfacial bonds have also been studied and characterized by the present authors and this work will be reported elsewhere. We propose that these pairing states when taken altogether can account partially for the interface "fast" states which are commonly observed but seldom understood. It is important to remark that irrespective of whether our identification of the pair states with N is correct or not, experiments on inversion layers have invariably been carried out with the assumption

416 that the interface states can be neglected. No one seems to have measured N inside the conduction or valence bands although as the associated band edges are approached from midgap the density of N states is rapidly rising and it is conceivable that it is sufficiently high near the subband energies that it should be accounted for especially in the localized low carrier density regime of both n and p-channel MOSFETs. In closing, we make an important prediction of the frequency dependence of the dielectric response of the interface. The density of pair states could well be smooth, continuous and occupied to E- (Ref. 1 ) . Fast hopping/ transition of interface carriers induced by an external field switches on a sudden potential followed by the emission of electron pairs across E f in transient response (Ref. 8 ) . We have discovered the existence of an infrared divergence in the pair state excitation response and predict an interface dielectric loss χ"(ω) *> ω which is exactly the "universal" Curie-von Schweidler law of dielectric response of almost all solid dielectrics correlated by Jonscher (9). We have also shown that the infrared divergence of the pair states could naturally be responsible for this "universal" dielectric behavior of solids. Details will be reported elsewhere. REFERENCES +

NRC-NRL Resident Research Associate

(1)

P. W. Anderson, Possible consequences of negative U centers in amorphous materials, J. Physique C4, 341 (1976).

(2)

C. T. White and K. L. Ngai, Random attractive electron-electron interaction in two dimensional systems, Surface Sei. 73 (to be published).

(3)

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(4)

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(5)

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(6)

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(7)

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(8)

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(9)

A. K. Jonscher, The "universal" dielectric response, Nature 267, 673 (1977).