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Electron states of the silicon-aluminum interface
Surface Science 165 (1986) L67-L72 North-Holland, Amsterdam
L67
S U R F A C E SCIENCE L E T I ' E R S
E L E C T R O N S T A T E S OF T H E S I L I C O N - A L U M I N U M I N T E R F A C E Yu.H. VEKILOV, V.D. V E R N E R and T.I. E G O R O V A Moscow Institute of Electron Technology, 103498 Moscow, USSR
Received 12 March 1985; accepted for publication 18 June 1985 The nature of the extra states of a silicon-aluminum interface has been studied by the pseudopotential method. The role of micro- and macro-interactions between the metal and semiconductor in the formation of the Schottky barrier is discussed.
Quantum-mechanical calculations of the metal-semiconductor interface (MSI) describe differently the nature of electron states in the interface region. The electronic structure of the semiconductor surface with an absorbed metal monolayer (SAMM) was studied in refs. [1 3]. The surface has revealed the spectrum of localized states formed due to chemical bonds between the metal and semiconductor. However, allowance for the bulk properties of the metal layer [4] has shown that the surface states disappear within the whole metal conduction band. The purpose of this work is to study the nature of the interface states with allowance for microscopic (interatomic) and macroscopic (the effect of bulk metal layer) interactions between the metal and semiconductor. To this end, the electron structure of the S i ( l l l ) - A I ( l l 0 ) interface was calculated by the pseudopotential method [5] for the following model. A crystal semiconductor with an adsorbed metal monolayer (as in ref. [1]) is connected to the bulk (multilayer) metal film. The parameters of the bulk metal film (crystal potential and charge density) in two directions ( X and Y), which are parallel to the interface plane, remain constant and equal to their average value for this plane. Unlike ref. [4], the crystal structure of the metal is taken into account for the Z-direction perpendicular to the interface plane [6]. The crystal potential plane and charge density varied only in the Z-direction. The adsorbed metal monolayer is intermediate between the metal and semiconductor films. Its structure was chosen the same as in ref. [1]. The distance between the adsorbed monolayer and the first atom layer of the bulk metal film was chosen to be equal to that between the crystallographic AL(110) planes, i.e. 2.7 a.u. Calculation was performed with the self-consistent A n i m a l u - H e i n e - A b o r e n k o v pseudopotential. To exclude the influence of parameters other than in ref. [1] (the pseudopotential) the SAMM electron states were calculated again. The results confirmed the data of ref. [1]. 0039-6028/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L68
Yu.H. Vekilot, et al. / Electron states of Si-A1 interface
Averaging of parameters of the metal bulk film in the X and Y directions results in a metal energy spectrum consisting of two independent spectra: a continuous one ( k , v ) and a discrete one (k:). The density of states in the continuous spectrum depends on two parameters. It rises with energy and with the distance from the Brillouin zone (BZ) centre. At the centre of the BZ ( k , , = 0) the density of metal states is low. The interface states at the BZ
Ae
a
| /
I
\ \
/1
/
I
\l
#g
b
I L I I I I .
l
Fig. 1. Charge density contours (arbitrary units) for the interface states at point I" of the two-dimensional Brillouin zone: (a) 1,7 eV higher than the bottom of the Si valence band; (b) 12.6 eV higher than the bottom of the Si valence band. The plane of the figure corresponds to the Si(ll0) plane, which is perpendicular to the S i ( l l l ) plane. Crystallographic AI(I10) planes are indicated by dashed lines.
Yu.H. Vekiloo et al. / Electron states of S i - A l interface
L69
~qe I I
/~ #e
b
/
SL
I
/8
Fig. 2. Charge density contours for the interface states at point K of the two-dimentional Brillouin zone: (a) 5.0 eV higher than the bottom of the valence band; (b) 5.6 eV higher than the bottom of the valence band. The notation is the same as in fig. 1.
centre (fig. 1) and on the BZ boundary near the bottom of the metal conduction band (fig. 2) are similar to the SAMM surface states. Their electron density is shifted a little toward the interface, which is explained by a decrease in the potential barrier on the metal-semiconductor interface in comparison with the barrier on the semiconductor-vacuum interface. Far from the BZ centre the density of metal states increases with energy. Thus, in the bulk metal layer the interface states remain similar to the SAMM
L70
Yu.H. Vekilot, et al. / Electron states of S i - A l interface
,qe
i
a
i
(
Si
L
6
t+~
j+
12
1o
b
I
SL
f
I I
I I
6
I I.~
/2
io
Fig. 3. Charge density contours for the interface states at point K of the two-dimensional Brillouin zone: (a) 9+9 eV higher than the bottom of the valence band; (b) 12.3 eV higher than the bottom of the valence band. The notation is the same as in fig. 1.
surface states in the area of the s e m i c o n d u c t o r a n d i n t e r m e d i a t e m e t a l layer, b u t are either a t t e n u a t e d slowly (fig. 3) or are t r a n s f o r m e d into metal resonances (fig. 4) as the energy increases. T h e energy of interface states in the M S I m o d e l is ~ I eV lower t h a n in the S A M M model. A n e x c e p t i o n is the interface state d e s c r i b i n g the d a n g l i n g b o n d of a n A1 a t o m in S A M M . I n M S I the c o r r e s p o n d i n g state is t r a n s f o r m e d into the state d e s c r i b i n g the A I - A 1 b o n d (fig. 3b). T h e energy shift of this is a b o u t 3 eV. This state is t r a n s f o r m e d f r o m an u n o c c u p i e d state in the S A M M m o d e l
Yu.H. Vekilov et al. / Electron states of Si-A1 interface
L71
~g
/
I
f
Fig. 4. Charge density contours for the interface state located 14.6 eV higher than the bottom of the valence band at point M of the two-dimensional Brillouin zone; the notation is the same as in fig. 1.
into an occupied state in the MSI model. Quantum-mechanical considerations do not reveal A1-A1 bonds for a monolayer covering, metal atom bonds can be found only for thick layers. In real MS structures, because of the thermal motion of adsorbed atoms, mutual bonds of metal atoms are formed for metal layers thinner than one monolayer. We obtained a Schottky barrier height of 0.75 eV for SAM and 0.8 eV for MSI. These results are in fair agreement with the experimental value of 0.7 eV [7]. For SAMM and MSI the barrier heights differ very slightly. Thus, as a result of microscopic interaction between the metal and semiconductor, the intrinsic surface states of the semiconductor are replaced by new extra states which stabilize the Fermi level [7]. As the thickness of the metal layer increases and it acquires bulk metal properties, the extra states do not disappear from the continuous energy spectrum of metal states. In the regions of reciprocal space where the density of metal states is low (gaps in the metal band structure), the extra states remain localized at the interface. In a general case, the localized states are slowly attenuated on the metal side or are transformed into states with a maximum near the interface and an undamped metal tail. The effect of the bulk metal layer is revealed as a decrease in the energy of the surface states, but it does not influence the total density of the extra states and, therefore, the stabilization of the Fermi level. As for the state produced by an A1-A1 bond, it is revealed when the layer thickness is sufficient for the formation of metal bonds. The Fermi level is finally stabilized when the formation of this state ceases [8].
L72
Yu.H. Vekilov et a L / Electron states of S i - A l interface
References [1] [2] [3] [4] [5]
J.R. Chelikovsky, Phys. Rev, B16 (1977) 3618. H.I. Zhang and M. Schluter, Phys. Rev. B18 (1978) 1923. J.E. Northrup, Phys. Rev. Letters 53 (1984) 683. S.G. gouie and M.L. Cohen, Phys. Rev, B13 (1976) 2461. A.M. Altshuler, S.N. Besrjadin, Yu. H. Vekilov, V.D. Verner and M.B, Samsonova. Dokl. Akad. Nauk 254 (1980) 336. [6] S.N. Besrjadim V.D. Verner and T.I. Egorova, Poverkhnost 6 (t984) 43. [7] G. Margaritondo, J.E. Rowe and S.G. Christman, Phys. Rev. B14 (1976) 5396. [8] P. Chen, D. Bolmont and C.A. S6benne, J. Phys. C17 (1984) 4897,
L67
S U R F A C E SCIENCE L E T I ' E R S
E L E C T R O N S T A T E S OF T H E S I L I C O N - A L U M I N U M I N T E R F A C E Yu.H. VEKILOV, V.D. V E R N E R and T.I. E G O R O V A Moscow Institute of Electron Technology, 103498 Moscow, USSR
Received 12 March 1985; accepted for publication 18 June 1985 The nature of the extra states of a silicon-aluminum interface has been studied by the pseudopotential method. The role of micro- and macro-interactions between the metal and semiconductor in the formation of the Schottky barrier is discussed.
Quantum-mechanical calculations of the metal-semiconductor interface (MSI) describe differently the nature of electron states in the interface region. The electronic structure of the semiconductor surface with an absorbed metal monolayer (SAMM) was studied in refs. [1 3]. The surface has revealed the spectrum of localized states formed due to chemical bonds between the metal and semiconductor. However, allowance for the bulk properties of the metal layer [4] has shown that the surface states disappear within the whole metal conduction band. The purpose of this work is to study the nature of the interface states with allowance for microscopic (interatomic) and macroscopic (the effect of bulk metal layer) interactions between the metal and semiconductor. To this end, the electron structure of the S i ( l l l ) - A I ( l l 0 ) interface was calculated by the pseudopotential method [5] for the following model. A crystal semiconductor with an adsorbed metal monolayer (as in ref. [1]) is connected to the bulk (multilayer) metal film. The parameters of the bulk metal film (crystal potential and charge density) in two directions ( X and Y), which are parallel to the interface plane, remain constant and equal to their average value for this plane. Unlike ref. [4], the crystal structure of the metal is taken into account for the Z-direction perpendicular to the interface plane [6]. The crystal potential plane and charge density varied only in the Z-direction. The adsorbed metal monolayer is intermediate between the metal and semiconductor films. Its structure was chosen the same as in ref. [1]. The distance between the adsorbed monolayer and the first atom layer of the bulk metal film was chosen to be equal to that between the crystallographic AL(110) planes, i.e. 2.7 a.u. Calculation was performed with the self-consistent A n i m a l u - H e i n e - A b o r e n k o v pseudopotential. To exclude the influence of parameters other than in ref. [1] (the pseudopotential) the SAMM electron states were calculated again. The results confirmed the data of ref. [1]. 0039-6028/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L68
Yu.H. Vekilot, et al. / Electron states of Si-A1 interface
Averaging of parameters of the metal bulk film in the X and Y directions results in a metal energy spectrum consisting of two independent spectra: a continuous one ( k , v ) and a discrete one (k:). The density of states in the continuous spectrum depends on two parameters. It rises with energy and with the distance from the Brillouin zone (BZ) centre. At the centre of the BZ ( k , , = 0) the density of metal states is low. The interface states at the BZ
Ae
a
| /
I
\ \
/1
/
I
\l
#g
b
I L I I I I .
l
Fig. 1. Charge density contours (arbitrary units) for the interface states at point I" of the two-dimensional Brillouin zone: (a) 1,7 eV higher than the bottom of the Si valence band; (b) 12.6 eV higher than the bottom of the Si valence band. The plane of the figure corresponds to the Si(ll0) plane, which is perpendicular to the S i ( l l l ) plane. Crystallographic AI(I10) planes are indicated by dashed lines.
Yu.H. Vekiloo et al. / Electron states of S i - A l interface
L69
~qe I I
/~ #e
b
/
SL
I
/8
Fig. 2. Charge density contours for the interface states at point K of the two-dimentional Brillouin zone: (a) 5.0 eV higher than the bottom of the valence band; (b) 5.6 eV higher than the bottom of the valence band. The notation is the same as in fig. 1.
centre (fig. 1) and on the BZ boundary near the bottom of the metal conduction band (fig. 2) are similar to the SAMM surface states. Their electron density is shifted a little toward the interface, which is explained by a decrease in the potential barrier on the metal-semiconductor interface in comparison with the barrier on the semiconductor-vacuum interface. Far from the BZ centre the density of metal states increases with energy. Thus, in the bulk metal layer the interface states remain similar to the SAMM
L70
Yu.H. Vekilot, et al. / Electron states of S i - A l interface
,qe
i
a
i
(
Si
L
6
t+~
j+
12
1o
b
I
SL
f
I I
I I
6
I I.~
/2
io
Fig. 3. Charge density contours for the interface states at point K of the two-dimensional Brillouin zone: (a) 9+9 eV higher than the bottom of the valence band; (b) 12.3 eV higher than the bottom of the valence band. The notation is the same as in fig. 1.
surface states in the area of the s e m i c o n d u c t o r a n d i n t e r m e d i a t e m e t a l layer, b u t are either a t t e n u a t e d slowly (fig. 3) or are t r a n s f o r m e d into metal resonances (fig. 4) as the energy increases. T h e energy of interface states in the M S I m o d e l is ~ I eV lower t h a n in the S A M M model. A n e x c e p t i o n is the interface state d e s c r i b i n g the d a n g l i n g b o n d of a n A1 a t o m in S A M M . I n M S I the c o r r e s p o n d i n g state is t r a n s f o r m e d into the state d e s c r i b i n g the A I - A 1 b o n d (fig. 3b). T h e energy shift of this is a b o u t 3 eV. This state is t r a n s f o r m e d f r o m an u n o c c u p i e d state in the S A M M m o d e l
Yu.H. Vekilov et al. / Electron states of Si-A1 interface
L71
~g
/
I
f
Fig. 4. Charge density contours for the interface state located 14.6 eV higher than the bottom of the valence band at point M of the two-dimensional Brillouin zone; the notation is the same as in fig. 1.
into an occupied state in the MSI model. Quantum-mechanical considerations do not reveal A1-A1 bonds for a monolayer covering, metal atom bonds can be found only for thick layers. In real MS structures, because of the thermal motion of adsorbed atoms, mutual bonds of metal atoms are formed for metal layers thinner than one monolayer. We obtained a Schottky barrier height of 0.75 eV for SAM and 0.8 eV for MSI. These results are in fair agreement with the experimental value of 0.7 eV [7]. For SAMM and MSI the barrier heights differ very slightly. Thus, as a result of microscopic interaction between the metal and semiconductor, the intrinsic surface states of the semiconductor are replaced by new extra states which stabilize the Fermi level [7]. As the thickness of the metal layer increases and it acquires bulk metal properties, the extra states do not disappear from the continuous energy spectrum of metal states. In the regions of reciprocal space where the density of metal states is low (gaps in the metal band structure), the extra states remain localized at the interface. In a general case, the localized states are slowly attenuated on the metal side or are transformed into states with a maximum near the interface and an undamped metal tail. The effect of the bulk metal layer is revealed as a decrease in the energy of the surface states, but it does not influence the total density of the extra states and, therefore, the stabilization of the Fermi level. As for the state produced by an A1-A1 bond, it is revealed when the layer thickness is sufficient for the formation of metal bonds. The Fermi level is finally stabilized when the formation of this state ceases [8].
L72
Yu.H. Vekilov et a L / Electron states of S i - A l interface
References [1] [2] [3] [4] [5]
J.R. Chelikovsky, Phys. Rev, B16 (1977) 3618. H.I. Zhang and M. Schluter, Phys. Rev. B18 (1978) 1923. J.E. Northrup, Phys. Rev. Letters 53 (1984) 683. S.G. gouie and M.L. Cohen, Phys. Rev, B13 (1976) 2461. A.M. Altshuler, S.N. Besrjadin, Yu. H. Vekilov, V.D. Verner and M.B, Samsonova. Dokl. Akad. Nauk 254 (1980) 336. [6] S.N. Besrjadim V.D. Verner and T.I. Egorova, Poverkhnost 6 (t984) 43. [7] G. Margaritondo, J.E. Rowe and S.G. Christman, Phys. Rev. B14 (1976) 5396. [8] P. Chen, D. Bolmont and C.A. S6benne, J. Phys. C17 (1984) 4897,