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Sensitivity analysis of dipole layers at semiconductor interfaces
Journal of Electron Spectroscopy and Related Phenomena 72 (1995) 49-54
Sensitivity analysis of dipole layers at semiconductor interfaces S P Wilks and R H Williams Department of Physics and Astronomy, University of Wales, College of Cardiff, P O Box 913, Cardiff CF2 3YB The modification of semiconductor heterojunction band offsets by the inclusion of an interfacial dipole layer is addressed in this article. It is well known that the introduction of 8-layers at or near semiconductor junctions can alter the band alignment and change the band profile at interfaces (e.g. using pairs of sheet Si and Be atoms in GaAs). However, disregarding problems associated with diffusion, the relative accuracy of each doping concentration and the need for charge neutrality in these structures is a non-trivial point that needs serious consideration when designing such systems. In this paper we consider the sensitivity of the band offset control on the degree of unequal charge concentration with 8-layers pairs and comment on the practicalities involved in the introduction of a dipole induced by a binary compound (e.g. ZnSe) at an interface.
1. Introduction The electronic structure prevailing at semiconductor heterojunctions has been the subject of many scientific publications over recent years. Many models have been proposed to explain the physics of the band alignment and the subsequent magnitude of the conduction band discontinuity [16]. The majority of these models predict band offsets that are in poor agreement with experimental values. However, the model proposed by Tejedor and Flores [5], in which the interactions and resulting dipoles at the interface dominate the band line-ups, predicts band offsets in remarkable agreement with experimental observations. The degree to which each contributes to the charge transfer and the resulting band discontinuities is unclear. Over the last decade there has been an avid interest in the modification and control of these interfacial band offsets with a view to producing structures where the band profile across any semiconductor junction can be tailored or engineered to a specific task. This goal has been achieved with much success using the technique of delta doping at or near the semiconductor heterojunctions (InAs-GaAs[7]). However, this method is not suitable in all systems since the effects of diffusion at high growth temperatures can cause severe deviations in the nature and definition of the delta layer. Strain [8] and compositional grading are also known to modify the band alignment. However, the successful control of band
discontinuities using these techniques is problematic from a growth point of view and can lead to a degradation in the abruptness and structural quality of the interface. The concept of band offset control is simple since it only involves the modification of the dipole that exists between the two materials. Hence, interfacial doping has become an active research area, both theoretically and experimentally, to achieve this goal. Many systems have been studied where various materials, both metallic and semiconducting, have been successfully used to produce a change in the intrinsic band discontinui~ for particular systems. An example of such a case is that of Ge bilayers at AlAs or GaAs homojunctions and at the AlAs and GaAs heterojunction [9]. In this paper we present calculations, based on the solution of Poisson's equation across the interface, where donor/acceptor atoms are placed directly at the interface and allowed to diffuse into both semiconductor materials. In this particular study we have examined the InAs-BeGaAs heterojunction, where the Be layer is assumed to act as a p-type acceptor in both materials, similar to a delta-layer placed fight at the interface. In addition, the practicalities and errors involved in the production of a neutral dipole at an interface are considered and the effect this would have on the potential profile across an interface are addressed.
0368-2048/95 $09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0368-2048(94)02297-6
50
(a)
Co)
2
2
1
Cb
~D > 0
0
0
~.b~
J
m
0
-1
L_
-20
200
-1
400
600-20
distance (nm)
2004o06o0 distance (nm)
Figurel :- Calculated conduction and valence band profile across an InAs-GaAs heterojunction without (a) and with (b) a p-type delta-layer (8=lxl013 cm "2) placed 5 nm below the interface into the GaAs. The doping concentrations of the InAs and GaAs where lxl018 cm "3 and lxl016 cm -3 respectively.
2. Theoretical Aspects The presence of donor/acceptor dipoles at or near the interface of a semiconductor heterojunction can alter the electronic properties of that system. In order to study such an effect, the conduction band profile across the interface must be known. Hence, Poisson's equation was solved selfconsistently using a shooting method. In this method, the one-dimensional Poisson equation d2
dx 2 u(x) = -;(x)
/ c
(1)
is discretised over the region of interest and integrated (using a simple second-order method) across the interface. Here s is the dielectric constant (position dependent) and p(x) is the charge density of free and bound charges given by
p ( x ) : e ( p - n + N+ - N -)
(2)
where p and n are the number densities of free holes and electrons, respectively, and N + and Nare the number densities of ionised donors and acceptors, respectively. Each of these quantities is calculated in the standard way from the local conduction band edge value (in eV) using
51 f
~
l 0 -2
o
• o-o e 44-~o-o~o"
- ° ° ~ -
.~B [] Be~
~.t~=
d0b=0.64eV o'1¢s "
<
.o"
qbb=O.92eV~m,
D Jc° l 0 -6
a
irl¢,l tl
~
I
j i 3 "
o-----e no 5 dopinja t~---o 6(p)=lxl0r3cm-2
ir
l,
10 -8 ~, o , , . . , , ~ []
lO -10
iiB~I~B
[]
[]
B [] B B~E]~B.13q343.Bra [] B Be4~]-D4:lq]43-~13B B 1=1B~
10 -12
0
0.2
0.4
0.6
0.8
Voltage (V) Figure 2:- The I-V characteristics (forward and reverse) for the structures modelled in figure 1. This figure was taken from the work of Shen et al [7].
Ec(x)=Ec(O)-u(x)
(3)
where x=O in the neutral bulk region of one-of the semiconductors. An initial guess for du/dx is taken in the integration, and the method of bisection is used to home in on the correct value of du/dx to produce zero band bending in the bulk of the other semiconductor. The effects of quantum confinement are not considered in this model. Hence, the conduction band or valence band profile across any int.erface can be produced if the position and concentration of the donor/acceptor species are known. Within this model it is possible to allow for donor/acceptor spread or diffusion, as is often observed for delta layers, by use of a simple Gaussian or top-hat distribution. 3. R e s u l t s
Typical results of the calculation are illustrated in figure 1 for the InAs-GaAs system without (la) and with (lb) a p-type delta-layer (8 =lxl013 cm -2) 5nm below the interface into the GaAs. The InAs was chosen to be degenerate for comparison with exnerimental wnrk whero
electrical measurements were performed on molecular beam epitaxially grown (MBE) samples to obtain the barrier height/conduction band offset [7]. Under these circumstances the heterojunction behaves like a simple Schottky contact and thermionic emission theory can be applied to extract the barrier height from an I-V characteristic. The I-V characteristics that correspond to each structure are shown in figure 2. Clearly, both theory and experiment show an increase in the effective conduction band discontinuity due to the presence of the p-type delta layer. The effect of placing Be right at the interface ha~ also been studied experimentally by Shen et al [10] where 1/4 of a monolayer produced an enhancement of 0.28 eV in the effective conduction band discontinuity. This result can be interpreted in terms of either a dipole produced by the chemical bonding at the interface or as a simple delta doping effect. We have calculated the conduction band profile one would expect for a Be delta layer at the interface by allowing the delta layer to diffuse into both the InAs and the GaAs at the interface. The results are shown in figure 3
52
1.5 ~j~5 ;>
ID
1.0
- 1X 1013cm-2' spread = 10nm, AE':- 1.43eV
~'~8
~r
=lx 1013crff2,spread=lnm, A155=132eV
\\
O
no 5-aoving,,,=0.72eV
o
0.5 (D
InAs lx 1018cm-3 0
GaAs lxl016cm-3 i
i
200
400
600
Distance from interface (nm) Figure 3:- Calculated conduction band profile across an InAs-GaAs heterojunction and the effect of having a Be 8-layer right at the interface. Also shown is the effect of allowing the 8-layer to diffuse into both the InAs and the GaAs layers at the interface. where a Be delta layer, having a doping concentration of lxl013 cm 2, was allowed to diffuse either side of the interface (a Gaussian diffusion distribution was assumed). It is clear from the results that a 8-doping layer right at the interface can produce a large increase in the conduction band discontinuity. An acceptor concentration of 8=lx1013 cm "2 almost doubles the effective band offset (AE0 approaching the value of the GaAs band gap. The magnitude of this increase is not very sensitive on the spread of the delta-layer, an increase of 9 nm produces a corresponding increase of ~0.1 eV. It is evident that the agreement between theory and experiment is poor since an acceptor concentration of lxl013 cm -2 produces a barrier enhancement of ,~0.65 eV whereas experimentally this was measured to be 0.28 eV [10] for a much higher concentration of 1.6x1014 cm "2 corresponding to a thickness of 0.25 MI. Thus this interface appears to be more complicated than just a simple delta layer smeared across the interface and requires a more detailed investigation. Alternatively, it is possible to conceive of a
situation where the introduction of a monolayer of a particular material, for example ZnSe or a bilayer of a group IV atom, at the interface could induce a dipole across the interlayer compound by virtue of the chemical environment. This would modify the band offset. Under these conditions the question arises concerning the stoichiometry of the interlayer and exactly how this would change the dipole at the interface. This point can be illustrated by considering the dipole set up by a pair of n- and ptype delta layers placed in close proximity (-5 nm apart), neglecting the effects of diffusion and spread. Using these delta layer pairs it is possible to produce a top-hat conduction band profile as shown in figure 4. Also shown in figure 4 is the effect of having unequal doping concentrations within a pair of n- and p-type delta layers. A +10% deviation in the doping concentrations produces a significant deviation in the shape of the conduction band profile as compared to the case where both are equal. As expected the magnitude of the dipole changes, altering both the shape of the conduction band and the size of the barrier. Hence, these
53
0.6
>
cD
1 I I If'- ~
0.4
....
~O
-10% on n-type +10% on n-type equal
I I I ! "'~1
II
C)
0.2
t
\
0
EF
\
- ~ I undo ped',~,~
_02f 0
200
5n~
~5 n
400
600
800
1000
Distance (rim) Figure 4:- Calculated conduction band profile across a GaAs sample containing a-layers arranged as indicated by the arrows (for equal concentration, each fi-layer was doped lxl013 cm2). The central region containing the a-layers was undoped and either side of this region the GaAs was doped lxl018 cm"3. problems and their effects must be considered when using such systems to modify semiconductor interfacial barriers. 4. Conclusions
There are many problems associated with placing an abrupt and well defined dipole layers at or near a semiconductor heterojunction. The calculations presented in this article are consistent with experimental data regarding the enhancement of the conduction band discontinuity for Be acceptors placed at the InAs-GaAs heterojunction. However, the calculated increase in the conduction band offset is much greater than that observed experimentally. This suggests that the situation is more complicated, where the dipoles induced by the chemical environment of the Be atoms may need to be considered. In addition, we have examined the effect of charge excess in the dipole layer as a result of errors in the relative concentration in the dipole constituents. We have shown that a discrepancy of _+10% in the doping concentration of either the
donor or acceptor atoms forming the dipole layer, can seriously distort the band profile and magnitude of the barrier enhancement. These errors are well within those experienced experimentally with MBE growth of 8-layers and raises the question whether such dipoles could be accurately and reproducibly grown. References
[1] R L Anderson. Solid-State Electronics, 5, (1962), 341 [2] J M Langer and H Heinrich. Phys. Rev. Lett., 55, (1985), 1414 [3] W R Frensley and H Kroemer. Phys. Rev. B16, (1977), 2642 141 W A Harrison. J. Vac. Sci. Technol., 14, (1977), 1016 [5] C Tejedor and F Flores. J. Phys. C l l , L19, (1978) 16] J Tersoff. Phys. Rev. B30, (1984), 4874 [7] T-H Shen, M Elliott, R H Williams and D I Westwood. Appl. Phys. Lett. 58, (1991), 842.
54 [8] C G Van de Walle and R M Martin. Phys. Rev. B35, 8154, (1987). [9] G Bratina, L Sorba, A Antonini, G Biasiol and A Franciosi. Phys. Rev. B45, (1992), 4528.
[10] T-H Shen, S Hooper, D Westwood, R H Williams and J Lapeyre. Prodeedings of ICFS-4, (1993), 664.
Sensitivity analysis of dipole layers at semiconductor interfaces S P Wilks and R H Williams Department of Physics and Astronomy, University of Wales, College of Cardiff, P O Box 913, Cardiff CF2 3YB The modification of semiconductor heterojunction band offsets by the inclusion of an interfacial dipole layer is addressed in this article. It is well known that the introduction of 8-layers at or near semiconductor junctions can alter the band alignment and change the band profile at interfaces (e.g. using pairs of sheet Si and Be atoms in GaAs). However, disregarding problems associated with diffusion, the relative accuracy of each doping concentration and the need for charge neutrality in these structures is a non-trivial point that needs serious consideration when designing such systems. In this paper we consider the sensitivity of the band offset control on the degree of unequal charge concentration with 8-layers pairs and comment on the practicalities involved in the introduction of a dipole induced by a binary compound (e.g. ZnSe) at an interface.
1. Introduction The electronic structure prevailing at semiconductor heterojunctions has been the subject of many scientific publications over recent years. Many models have been proposed to explain the physics of the band alignment and the subsequent magnitude of the conduction band discontinuity [16]. The majority of these models predict band offsets that are in poor agreement with experimental values. However, the model proposed by Tejedor and Flores [5], in which the interactions and resulting dipoles at the interface dominate the band line-ups, predicts band offsets in remarkable agreement with experimental observations. The degree to which each contributes to the charge transfer and the resulting band discontinuities is unclear. Over the last decade there has been an avid interest in the modification and control of these interfacial band offsets with a view to producing structures where the band profile across any semiconductor junction can be tailored or engineered to a specific task. This goal has been achieved with much success using the technique of delta doping at or near the semiconductor heterojunctions (InAs-GaAs[7]). However, this method is not suitable in all systems since the effects of diffusion at high growth temperatures can cause severe deviations in the nature and definition of the delta layer. Strain [8] and compositional grading are also known to modify the band alignment. However, the successful control of band
discontinuities using these techniques is problematic from a growth point of view and can lead to a degradation in the abruptness and structural quality of the interface. The concept of band offset control is simple since it only involves the modification of the dipole that exists between the two materials. Hence, interfacial doping has become an active research area, both theoretically and experimentally, to achieve this goal. Many systems have been studied where various materials, both metallic and semiconducting, have been successfully used to produce a change in the intrinsic band discontinui~ for particular systems. An example of such a case is that of Ge bilayers at AlAs or GaAs homojunctions and at the AlAs and GaAs heterojunction [9]. In this paper we present calculations, based on the solution of Poisson's equation across the interface, where donor/acceptor atoms are placed directly at the interface and allowed to diffuse into both semiconductor materials. In this particular study we have examined the InAs-BeGaAs heterojunction, where the Be layer is assumed to act as a p-type acceptor in both materials, similar to a delta-layer placed fight at the interface. In addition, the practicalities and errors involved in the production of a neutral dipole at an interface are considered and the effect this would have on the potential profile across an interface are addressed.
0368-2048/95 $09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0368-2048(94)02297-6
50
(a)
Co)
2
2
1
Cb
~D > 0
0
0
~.b~
J
m
0
-1
L_
-20
200
-1
400
600-20
distance (nm)
2004o06o0 distance (nm)
Figurel :- Calculated conduction and valence band profile across an InAs-GaAs heterojunction without (a) and with (b) a p-type delta-layer (8=lxl013 cm "2) placed 5 nm below the interface into the GaAs. The doping concentrations of the InAs and GaAs where lxl018 cm "3 and lxl016 cm -3 respectively.
2. Theoretical Aspects The presence of donor/acceptor dipoles at or near the interface of a semiconductor heterojunction can alter the electronic properties of that system. In order to study such an effect, the conduction band profile across the interface must be known. Hence, Poisson's equation was solved selfconsistently using a shooting method. In this method, the one-dimensional Poisson equation d2
dx 2 u(x) = -;(x)
/ c
(1)
is discretised over the region of interest and integrated (using a simple second-order method) across the interface. Here s is the dielectric constant (position dependent) and p(x) is the charge density of free and bound charges given by
p ( x ) : e ( p - n + N+ - N -)
(2)
where p and n are the number densities of free holes and electrons, respectively, and N + and Nare the number densities of ionised donors and acceptors, respectively. Each of these quantities is calculated in the standard way from the local conduction band edge value (in eV) using
51 f
~
l 0 -2
o
• o-o e 44-~o-o~o"
- ° ° ~ -
.~B [] Be~
~.t~=
d0b=0.64eV o'1¢s "
<
.o"
qbb=O.92eV~m,
D Jc° l 0 -6
a
irl¢,l tl
~
I
j i 3 "
o-----e no 5 dopinja t~---o 6(p)=lxl0r3cm-2
ir
l,
10 -8 ~, o , , . . , , ~ []
lO -10
iiB~I~B
[]
[]
B [] B B~E]~B.13q343.Bra [] B Be4~]-D4:lq]43-~13B B 1=1B~
10 -12
0
0.2
0.4
0.6
0.8
Voltage (V) Figure 2:- The I-V characteristics (forward and reverse) for the structures modelled in figure 1. This figure was taken from the work of Shen et al [7].
Ec(x)=Ec(O)-u(x)
(3)
where x=O in the neutral bulk region of one-of the semiconductors. An initial guess for du/dx is taken in the integration, and the method of bisection is used to home in on the correct value of du/dx to produce zero band bending in the bulk of the other semiconductor. The effects of quantum confinement are not considered in this model. Hence, the conduction band or valence band profile across any int.erface can be produced if the position and concentration of the donor/acceptor species are known. Within this model it is possible to allow for donor/acceptor spread or diffusion, as is often observed for delta layers, by use of a simple Gaussian or top-hat distribution. 3. R e s u l t s
Typical results of the calculation are illustrated in figure 1 for the InAs-GaAs system without (la) and with (lb) a p-type delta-layer (8 =lxl013 cm -2) 5nm below the interface into the GaAs. The InAs was chosen to be degenerate for comparison with exnerimental wnrk whero
electrical measurements were performed on molecular beam epitaxially grown (MBE) samples to obtain the barrier height/conduction band offset [7]. Under these circumstances the heterojunction behaves like a simple Schottky contact and thermionic emission theory can be applied to extract the barrier height from an I-V characteristic. The I-V characteristics that correspond to each structure are shown in figure 2. Clearly, both theory and experiment show an increase in the effective conduction band discontinuity due to the presence of the p-type delta layer. The effect of placing Be right at the interface ha~ also been studied experimentally by Shen et al [10] where 1/4 of a monolayer produced an enhancement of 0.28 eV in the effective conduction band discontinuity. This result can be interpreted in terms of either a dipole produced by the chemical bonding at the interface or as a simple delta doping effect. We have calculated the conduction band profile one would expect for a Be delta layer at the interface by allowing the delta layer to diffuse into both the InAs and the GaAs at the interface. The results are shown in figure 3
52
1.5 ~j~5 ;>
ID
1.0
- 1X 1013cm-2' spread = 10nm, AE':- 1.43eV
~'~8
~r
=lx 1013crff2,spread=lnm, A155=132eV
\\
O
no 5-aoving,,,=0.72eV
o
0.5 (D
InAs lx 1018cm-3 0
GaAs lxl016cm-3 i
i
200
400
600
Distance from interface (nm) Figure 3:- Calculated conduction band profile across an InAs-GaAs heterojunction and the effect of having a Be 8-layer right at the interface. Also shown is the effect of allowing the 8-layer to diffuse into both the InAs and the GaAs layers at the interface. where a Be delta layer, having a doping concentration of lxl013 cm 2, was allowed to diffuse either side of the interface (a Gaussian diffusion distribution was assumed). It is clear from the results that a 8-doping layer right at the interface can produce a large increase in the conduction band discontinuity. An acceptor concentration of 8=lx1013 cm "2 almost doubles the effective band offset (AE0 approaching the value of the GaAs band gap. The magnitude of this increase is not very sensitive on the spread of the delta-layer, an increase of 9 nm produces a corresponding increase of ~0.1 eV. It is evident that the agreement between theory and experiment is poor since an acceptor concentration of lxl013 cm -2 produces a barrier enhancement of ,~0.65 eV whereas experimentally this was measured to be 0.28 eV [10] for a much higher concentration of 1.6x1014 cm "2 corresponding to a thickness of 0.25 MI. Thus this interface appears to be more complicated than just a simple delta layer smeared across the interface and requires a more detailed investigation. Alternatively, it is possible to conceive of a
situation where the introduction of a monolayer of a particular material, for example ZnSe or a bilayer of a group IV atom, at the interface could induce a dipole across the interlayer compound by virtue of the chemical environment. This would modify the band offset. Under these conditions the question arises concerning the stoichiometry of the interlayer and exactly how this would change the dipole at the interface. This point can be illustrated by considering the dipole set up by a pair of n- and ptype delta layers placed in close proximity (-5 nm apart), neglecting the effects of diffusion and spread. Using these delta layer pairs it is possible to produce a top-hat conduction band profile as shown in figure 4. Also shown in figure 4 is the effect of having unequal doping concentrations within a pair of n- and p-type delta layers. A +10% deviation in the doping concentrations produces a significant deviation in the shape of the conduction band profile as compared to the case where both are equal. As expected the magnitude of the dipole changes, altering both the shape of the conduction band and the size of the barrier. Hence, these
53
0.6
>
cD
1 I I If'- ~
0.4
....
~O
-10% on n-type +10% on n-type equal
I I I ! "'~1
II
C)
0.2
t
\
0
EF
\
- ~ I undo ped',~,~
_02f 0
200
5n~
~5 n
400
600
800
1000
Distance (rim) Figure 4:- Calculated conduction band profile across a GaAs sample containing a-layers arranged as indicated by the arrows (for equal concentration, each fi-layer was doped lxl013 cm2). The central region containing the a-layers was undoped and either side of this region the GaAs was doped lxl018 cm"3. problems and their effects must be considered when using such systems to modify semiconductor interfacial barriers. 4. Conclusions
There are many problems associated with placing an abrupt and well defined dipole layers at or near a semiconductor heterojunction. The calculations presented in this article are consistent with experimental data regarding the enhancement of the conduction band discontinuity for Be acceptors placed at the InAs-GaAs heterojunction. However, the calculated increase in the conduction band offset is much greater than that observed experimentally. This suggests that the situation is more complicated, where the dipoles induced by the chemical environment of the Be atoms may need to be considered. In addition, we have examined the effect of charge excess in the dipole layer as a result of errors in the relative concentration in the dipole constituents. We have shown that a discrepancy of _+10% in the doping concentration of either the
donor or acceptor atoms forming the dipole layer, can seriously distort the band profile and magnitude of the barrier enhancement. These errors are well within those experienced experimentally with MBE growth of 8-layers and raises the question whether such dipoles could be accurately and reproducibly grown. References
[1] R L Anderson. Solid-State Electronics, 5, (1962), 341 [2] J M Langer and H Heinrich. Phys. Rev. Lett., 55, (1985), 1414 [3] W R Frensley and H Kroemer. Phys. Rev. B16, (1977), 2642 141 W A Harrison. J. Vac. Sci. Technol., 14, (1977), 1016 [5] C Tejedor and F Flores. J. Phys. C l l , L19, (1978) 16] J Tersoff. Phys. Rev. B30, (1984), 4874 [7] T-H Shen, M Elliott, R H Williams and D I Westwood. Appl. Phys. Lett. 58, (1991), 842.
54 [8] C G Van de Walle and R M Martin. Phys. Rev. B35, 8154, (1987). [9] G Bratina, L Sorba, A Antonini, G Biasiol and A Franciosi. Phys. Rev. B45, (1992), 4528.
[10] T-H Shen, S Hooper, D Westwood, R H Williams and J Lapeyre. Prodeedings of ICFS-4, (1993), 664.