Technical Physics, Vol. 50, No. 1, 2005, pp. 139–140. Translated from Zhurnal Tekhnichesko

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Fiziki, Vol. 75, No. 1, 2005, pp. 141–142.Original Russian Text Copyright © 2005 by Davydov.

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Hydrogen Adsorption on SiliconS. Yu. Davydov

Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia

Received June 16, 2004

Abstract—Change ∆φ(Θ) in work function versus surface coverage Θ for the Si(100) surface is determined interms of a model that includes not only the dipole–dipole interaction of hydrogen adatoms but also an elonga-tion of the adsorption length with increasing Θ. The charge of the adatoms as a function of Θ is calculated, andthe variation of the surface conductivity of the substrate is estimated. © 2005 Pleiades Publishing, Inc.

Until recently, theoretical investigation of gasadsorption has received little attention. In [1], modelsof atomic hydrogen adsorption on germanium weresuggested. It turned out that the experimental data forhydrogen adsorption on Ge(111) [2] can be describedadequately if the Anderson–Newns standard model[3, 4] assumes the dependence of adsorption bondlength a on degree of coverage Θ = N/NML (where N andNML are the particle concentrations in an adlayer andmonolayer, respectively):

(1)

where a0 is the adsorption bond length at zero coverageand α is a dimensionless coefficient.

In the H/Ge(111) system, the value of ∆φ(Θ) is neg-ative at small Θ (charge Z of an adatom is positive),vanishes at Θ = 0.15, and then becomes positive (theadatom takes a negative charge) and grows. In goingfrom Z > 0 to Z = 0, shell occupation number n = 1 – Zof the adatom rises and shell radius a increases from avalue close to ionic radius ri to a value close to atomicradius ra. Below, we will analyze the experimental datafor the H/Ge(100) system [5].

For hydrogen adsorption on Si(100), the depen-dence ∆φ(Θ) is in a sense inverse to this dependence forGe(100): the work function of the system does notchange up to ≈ 0.1 (that is, ∆φ(Θ) = 0) and then, at

Θ > , function ∆φ(Θ) becomes negative.1 Generallyspeaking, it is unclear why the work function of theH/Ge(100) system remains constant in the coverageinterval (0, 0.1). Conversely, the work function ofadsorption systems (such as metal-on-metal [4], metal-on-semiconductor [6], and gas-on-semiconductor [2, 7]systems) usually varies most significantly in this range,according to observations. Moreover, it was shown [5]that, when a submonolayer germanium film is applied

1 When analyzing the data in [5], we assume that an exposure of10L corresponds to θ = 0.1. It is also assumed for simplicity thatthe coverage is a linear function of exposure.

a a0 1 αΘ+( ),=

ΘΘ

1063-7842/05/5001- $26.00 0139

on the silicon substrate (i.e., in the H/Ge/Si(100) sys-tem), there appears a range of coverages (0, Θ*) where∆φ(Θ) is positive and reaches a maximum at Θ ≈ 0.05.As the adatom concentration grows, Θ* increases. Thisallows us to expect a positive correction to the workfunction in the coverage interval (0, 0.1) for the uncov-ered Si(100) surface too. Subsequently, we will proceedfrom this assumption.

As was shown in [1], charge Z of an adatom andchange ∆φ in the work function can be calculated withregard to dipole–dipole interaction in an adsorbed layeras follows:

(2)

Z = 2π---

Ω0 1 x–( )/ 1 α x+( ) x3/2ξ0Z 1 α x+( )2–Γ

---------------------------------------------------------------------------------------- ,arctan

∆φ Φ0x 1 α x+( )Z ,–=

0.2

0.1

0

–0.1

–0.2

–0.30 0.1 0.2 0.3 0.4 0.5

Θ

∆φ, eV

Fig. 1. Change ∆φ in the work function of the silicon surfacevs. coverage Θ by hydrogen atoms.

© 2005 Pleiades Publishing, Inc.

140

DAVYDOV

where

(3)

Here, Ω0 is the energy of the adatom quasi-level relativeto the Fermi level of the substrate, ξ0 is the constant ofdipole–dipole repulsion between adatoms, A ~ 10 is adimensionless coefficient that weakly depends on theadatom lattice configuration, Γ is the half-width of theisolated adatom quasi-level, I is the energy of ioniza-tion of the adatom, φ is the work function of silicon, and∆0 is the Coulomb shift of the adatom quasi-level (thisshift arises when the electron of an adatom interactswith electrons of the substrate).

To calculate the adsorption, we took the followingvalues of the parameters: a0 = 1.5 Å, NML = 6.78 ×10−14 cm–2, = 0.1, ξ0 = 11.44 eV, Φ0 = 18.4 eV, Ω0 =–0.1 eV, Γ = 0.1 eV, ∆0 = 2.4 eV, and α = –0.1. Note thathere α < 0; that is, the adsorption bond shortens and theadatom quasi-level shifts upward, passing from its ini-tial position under the Fermi level (Ω0 ≡ Ω(Θ = 0) < 0)to a position above the Fermi level (Ω(Θ) = Ω0 –∆0[αΘ/(1 + αΘ)]).

The analytical dependence ∆φ(Θ) is given in Fig. 1.Good agreement with the experimental data is observedfor coverages between 0.1 and 0.3. A slight discrepancyat Θ > 0.3 is related to the neglect of exchange pro-cesses, which cause adatom depolarization [4]. Figure 2

zΘΘ----, ξ0 ξ0Θ

3/2, Φ0 Φ0Θ,= = =

α αΘΩ0

I φ–-----------, ξ0 2e2a0

2NML3/2 A,= = =

Ω0 φ I– ∆0, ∆0+e2

4a0--------, α

Ω0

I φ–-----------.= = =

Θ

0.2

0

–0.2

–0.4

–0.60 0.1 0.2 0.3 0.4 0.5

Θ

Z

Fig. 2. Charge Z of a hydrogen adatom on the silicon surfacevs. coverage Θ.

shows the variation of charge Z with Θ. Note that thescale in Fig. 2 shades the fine structure of the depen-dence Z(Θ): namely, charge Z first vanishes at ; thentakes a positive value, growing in magnitude up to Θ =0.4 (Z(0.4) ≈ 0.029); and finally declines slowly.

Since hydrogen accepts the electrons of the sub-strate at Θ ≤ 0.1 and donates them at higher coverages,surface conductivity σ first declines relative to the con-ductivity of the uncovered surface and then exceeds it.Figure 3 shows the Θ dependence of product µ ≡|Z(Θ)|Θ, which varies in proportion to relative change∆σ/σ0 in the surface conductivity, where σ0 is the con-ductivity of the uncovered Si(100) surface.

Thus, the simple model adopted in this work, whichwas initially proposed for sodium atom adsorption oncesium [8], can also be applied to hydrogen adsorptionon germanium and silicon.

REFERENCES1. S. Yu. Davydov, Zh. Tekh. Fiz. 75, 112 (2005) [Tech.

Phys. 50, 110 (2005)].2. L. Surnev and M. Tikhov, Surf. Sci. 138, 40 (1984).3. Theory of Chemisorption, Ed. by J. R. Smith (Springer-

Verlag, Berlin, 1980; Mir, Moscow, 1983).4. O. M. Braun and V. K. Medvedev, Usp. Fiz. Nauk 157,

631 (1989) [Sov. Phys. Usp. 32, 328 (1989)].5. G. Boishin and L. Surnev, Surf. Sci. 345, 64 (1996).6. Physics and Chemistry of Alkali Metal Adsorption, Ed.

by H. P. Bonzel, A. M. Bradshow, and G. Ertl (Elsevier,Amsterdam, 1989).

7. V. E. Heinrich and V. E. Cox, The Surface Science ofMetal Oxides (Cambridge Univ. Press, Cambridge,1994).

8. S. Y. Davydov, Appl. Surf. Sci. 140, 52 (1999).

Translated by V. Isaakyan

Θ

1.5

1.0

0.5

0

–0.5

–1.00 0.1 0.2 0.3 0.4 0.5

Θ

µ × 102

Fig. 3. Θ dependence of product µ ≡ |Z(Θ)|Θ, which variesin proportion to relative change ∆σ/σ0 in the surface con-ductivity.

TECHNICAL PHYSICS Vol. 50 No. 1 2005