- Email: [email protected]
GaAs quantum wells
ARTICLE IN PRESS Physica E 42 (2010) 2131–2133
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Reconfirmation of the band offsets of InGaP/GaAs quantum wells Sanjib Kabi n, Tapas Das, Dipankar Biswas Institute of Radio Physics and Electronics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India
a r t i c l e in fo
abstract
Article history: Received 15 February 2010 Received in revised form 5 April 2010 Accepted 7 April 2010 Available online 11 April 2010
The InGaP/GaAs interface is gaining importance for the fabrication of electronic and optoelectronic devices .The major advantages are it has got a large valence band offset and use of Al can be avoided, which introduces deep levels, etc. that work as recombination centers. In our pioneering experimental work we made an accurate measurement of the band offsets of the lattice matched InGaP/GaAs interface using deep level transient spectroscopic (DLTS) technique. The conduction band offset and the valence band offset were measured independently; the estimated values were DEc ¼ 0.198 eV and DEv ¼ 0.285 eV. Till date various values of band offsets have been reported, which have been derived from different experimental and theoretical models. In this paper we present appropriate theoretical calculations, which reconfirm our previously obtained values of the band offsets. Relations for computing the band line-up and band offsets of InxGa1 xP/GaAs based heterostructures have been developed, which co-relates the mole fractions, strain, band positions and energy levels of both lattice matched and strained InGaP/GaAs heterointerfaces. Results obtained re-establish our experimental results. The theoretical calculations have also been crosschecked with reported experimental photoluminescence (PL) data for reconfirmation. & 2010 Elsevier B.V. All rights reserved.
Keywords: Strain Band offsets Heterostructures Band line-up
1. Introduction InGaP/GaAs heterostructures have potential applications in the field of modulation doped field effect transistor and heterojunction bipolar transistor, in particular, Al can be avoided for high quality quantum devices, using this heteointerface. The heterojunction band offset is an important parameter for the design of heterostructure based electronic and optoelectronic devices. The band offset governs carrier confinement in the heterostructures. The total band discontinuity distributed over the conduction and valence bands, as DEc and DEv, depends on the semiconductors and the amount of mismatch strain at the interface. The ratio of DEc:DEv is not constant for different heterointerfaces, so, a detailed knowledge of the band offset ratio for a particular heterointerface is essential. The measured and computed band discontinuities at the InGaP/ GaAs interface are spread over a wide range. Reported values of DEc and DEv range from 30 to 220 meV and from 240 to 400 meV, respectively [1–4]. Such a wide spread of data is often ascribed to different growth methods and growth conditions or different measurement techniques. Recently Ghezzi et al. [5] reported the values of DEc and DEv for lattice matched InGaP/GaAs interface as 356 and 119 meV, respectively, using admittance spectroscopy. These are quite different from our estimated values [6]
where the band offset was estimated independently from the DLTS signals resulting from thermal emission of electrons from the conduction and optical DLTS signals from the valence band. In this work, an appropriate theoretical determination of the band discontinuities at the interface of the lattice matched InGaP/GaAs heterostructure is made through suitable calculations where the indium mole fraction is varied around the lattice match value x ¼0.48 to find how the band offset changes due to the introduction of strain. It is found that at the lattice matched condition the theoretical computations are in close match with our previously obtained experimental data. This paper presents details of the theoretical calculation, which co-relates the mole fractions, strain, band positions and energy levels. The strains are calculated from the In mole fractions and lattice constants. The parameters implicitly involved are the elastic stiffness constants (C11 and C12), the hydrostatic deformation potential of the conduction band (a0 ), the hydrostatic deformation potential (a) and shear deformation potential (b) for the valence band. The theoretical results obtained for lattice matched In0.48Ga0.51P/GaAs interface for valence band and conduction band offsets reconfirm our previously, experimentally determined band offsets.
2. Experimental and theoretical details n
Corresponding author. Tel.: + 91 9434383736; fax: +91 33 2351 5828. E-mail address: [email protected] (S. Kabi).
1386-9477/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2010.04.009
We have considered a InxGa1 xP/GaAs QW system for our model calculations, the composition of In has been varied on
ARTICLE IN PRESS 2132
S. Kabi et al. / Physica E 42 (2010) 2131–2133
either side of the lattice matched composition x ¼0.48 to change the strain. The band gap of InGaP changes with change in the In mole fraction and is given by the equation as Eg ðxÞ ¼ xEg,InP þ ð1-xÞEg,GaP
ð1Þ
where x is the mole fraction of indium, Eg(x) represents the band gap energy of InGaP, Eg,InP and Eg,GaP represent the band gap energies of the compounds InP and GaP, which are considered to be 1.35 eV and 2.74 eV, respectively. The strain of InxGa1 xP/GaAs is calculated from the equation [7]:
e ¼ ðde db Þ=db
ð2Þ
where de and db are the lattice constants of the epitaxial layer and the barrier, respectively. The variation of strain with indium mole fraction is shown in Fig. 1. The strain varies almost linearly with mole fraction of indium. The energy correction for the conduction band and valence band due to strain is given by the formulae [8]:
Fig. 1. Variation of strain with indium mole fraction in an InxGa1 xP/GaAs system.
DEsrt,c ¼ 2a0 ½ðC11 C12 Þ=C11 e
ð3Þ
DEsrt,v ¼ 2a½ðC11 C12 Þ=C11 e þ b½ðC11 þ2C12 Þ=C11 e
ð4Þ
where a0 is the hydrostatic deformation potential of the conduction band, C11 and C12 are the elastic stiffness constants and a and b are the hydrostatic deformation potential and shear deformation potential for the valence band, respectively. To investigate the effect of strain on the band line-up we have to include the energy correction terms as represented in Eqs. (3) and (4) for the well and the barrier. The parameters used for GaAs and InGaP are taken from Ishikawa [7]. Linear interpolation has been used to calculate de, a0 , a and b for the ternary materials and the interpolation has been weighted by the lattice constant for calculating C11 and C12 of ternary materials.
3. Results and discussion Fig. 2 shows the variation of the band gap energies for GaAs due to the strain when we include the energy correction terms in the well, as well as in the barrier for the GaAs/InGaP system. It is seen that the inclusion of strain has modified the band gap energy and hence the band positions. Fig. 3(a) and (b) shows the variation of the conduction band line-up and valence band line-up with strain, respectively. From Fig. 3 we have extracted suitable expressions for calculation of conduction and valence band positions of GaAs/ InGaP with strain, as expressed below: Fig. 2. Variation of the band gap energy with indium mole fraction for GaAs quantum well. The continuous curves show the variation without considering strain and the dash curves show the variation considering strain.
Ec ¼ 1:70394 þ0:19382e þ 0:00334e2
ð5Þ
Ev ¼ 0:1891þ0:06581e þ 0:01058e2
ð6Þ
0.6 Valance band position (eV)
Conduction band position (eV)
2.6 2.4 2.2 2.0 1.8 1.6 1.4
0.5 0.4 0.3 0.2 0.1
-1
0
1
Strain (in %)
2
3
-1
0
1
2
Strain (in %)
Fig. 3. Variation of the (a) conduction band position and (b) valence band position with strain.
3
ARTICLE IN PRESS S. Kabi et al. / Physica E 42 (2010) 2131–2133
2133
1.70
PL peak energy (eV)
1.65 1.60 1.55 1.50 1.45 1.40 0.45 Fig. 4. Variations of the (a) valence band offset ratio and (b) conduction band offset ratio with indium mole fraction.
0.46
0.47 0.48 0.49 Indium mole fraction (x)
0.50
0.51
Fig. 5. Variations of PL peak energy with indium mole fraction for 6 nm well. The dash curve represents the experimental points as given by Martinez-Pastor et al. [9] and the continuous curves show the theoretical calculation using Eq. (4).
where Ec is the conduction band position and Ev is the valence band position. The strain e is expressed in percentage (%). With this equation we have calculated the band position of the GaAs/InGaP system, hence we have determined the conduction and valence band offsets DEc and DEv. The variations of conduction and valence band offsets DEc and DEv with indium mole fraction (x) are shown in Fig. 4. It is clear from the variation that the conduction band offset increases and the valence band offset decreases with the indium mole fraction. It has been estimated that the conduction and valence band offsets, DEc ¼ 0.1902 eV and DEv ¼0.2898 eV, at the lattice matched point for In mole fraction x ¼048. This is within 2.5% error of our experimentally determined band offsets [6]. For further establishment of the reliability of the theoretical procedures we have compared our computed PL results with experimental PL data given by Martinez-Pastor et al. [9], where they have changed the In mole fraction and the measurements were carried out at low temperatures. The experimental and theoretical curves of PL peak energies against mole fraction (x) are shown in Fig. 5. The match is very close within 1%, which further establishes the proposed method for the computations of band offsets and this reconfirms the band offset values for lattice matched InGaP/ GaAs QWs. It is also observed from Fig. 5 that due to a small change in the mole fraction there is no significant change in the PL energy.
4. Conclusions We have presented appropriate theoretical procedures for computing the band offset of InGaP/GaAs quantum wells. These reconfirm our previously experimentally determined values of the band offsets for lattice matched InGaP/GaAs interface. Experimental PL data of GaAs/InGaP QWs have been matched for further corroboration. This strongly reconfirms that the band offset ratio at the InGaP/GaAs interface at the lattice matched point is (40:60)71.5%.
References [1] M. Feng, N. Holonyak Jr., R. Chen, Appl. Phys. Lett. 87 (2005) 131103. [2] E. Gombia, R. Mosca, D. Pal, S. Busi, L. Tarricone, P.G. Fuochi, M. Lavalle, Mater. Sci. Eng. B 97 (2003) 39. [3] N.H. Karam, R.R. King, M. Haddad, J.H. Ermer, H. Yoon, H.L. Cotal, R. Sudharsanan, J.W. Eldredge, K. Edmondson, D.E. Joslin, D.D. Krut, M. Takabashi, W. Nishikawa, M. Gillanders, J. Granata, P. Hebert, B.T. Cavicchi, D.R. Lillington, Sol. Energy Mater. Sol. Cells 66 (2001) 453. ¨ [4] E. Greger, P. Riel, M. Moser, T. Kippenberg, P. Kiesel, G.H. Dohler, Appl. Phys. Lett. 71 (1997) 3245. [5] C. Ghezzi, R. Magnanini, A. Parisini, L. Tarricone, E. Gombai, M. Longo, Phy. Rev. B. 77 (2008) 125317. [6] D. Biswas, N. Debbar, P. Bhattacharya, Appl. Phys. Lett. 56 (9) (1989) 833. [7] T. Ishikawa, IEEE J. Quant. Electron. 30 (1994) 562. [8] H. Nagai, S. Aadachi, T. Fukui, III–V Mixed crystal, Corona, Tokyo, Japan, 1998. [9] Juan Martinez-Pastor, Luisa Gonzalez, Philippe Roussignol, Appl. Phys. Lett. 68 (15) (1996) 2111.
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Reconfirmation of the band offsets of InGaP/GaAs quantum wells Sanjib Kabi n, Tapas Das, Dipankar Biswas Institute of Radio Physics and Electronics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India
a r t i c l e in fo
abstract
Article history: Received 15 February 2010 Received in revised form 5 April 2010 Accepted 7 April 2010 Available online 11 April 2010
The InGaP/GaAs interface is gaining importance for the fabrication of electronic and optoelectronic devices .The major advantages are it has got a large valence band offset and use of Al can be avoided, which introduces deep levels, etc. that work as recombination centers. In our pioneering experimental work we made an accurate measurement of the band offsets of the lattice matched InGaP/GaAs interface using deep level transient spectroscopic (DLTS) technique. The conduction band offset and the valence band offset were measured independently; the estimated values were DEc ¼ 0.198 eV and DEv ¼ 0.285 eV. Till date various values of band offsets have been reported, which have been derived from different experimental and theoretical models. In this paper we present appropriate theoretical calculations, which reconfirm our previously obtained values of the band offsets. Relations for computing the band line-up and band offsets of InxGa1 xP/GaAs based heterostructures have been developed, which co-relates the mole fractions, strain, band positions and energy levels of both lattice matched and strained InGaP/GaAs heterointerfaces. Results obtained re-establish our experimental results. The theoretical calculations have also been crosschecked with reported experimental photoluminescence (PL) data for reconfirmation. & 2010 Elsevier B.V. All rights reserved.
Keywords: Strain Band offsets Heterostructures Band line-up
1. Introduction InGaP/GaAs heterostructures have potential applications in the field of modulation doped field effect transistor and heterojunction bipolar transistor, in particular, Al can be avoided for high quality quantum devices, using this heteointerface. The heterojunction band offset is an important parameter for the design of heterostructure based electronic and optoelectronic devices. The band offset governs carrier confinement in the heterostructures. The total band discontinuity distributed over the conduction and valence bands, as DEc and DEv, depends on the semiconductors and the amount of mismatch strain at the interface. The ratio of DEc:DEv is not constant for different heterointerfaces, so, a detailed knowledge of the band offset ratio for a particular heterointerface is essential. The measured and computed band discontinuities at the InGaP/ GaAs interface are spread over a wide range. Reported values of DEc and DEv range from 30 to 220 meV and from 240 to 400 meV, respectively [1–4]. Such a wide spread of data is often ascribed to different growth methods and growth conditions or different measurement techniques. Recently Ghezzi et al. [5] reported the values of DEc and DEv for lattice matched InGaP/GaAs interface as 356 and 119 meV, respectively, using admittance spectroscopy. These are quite different from our estimated values [6]
where the band offset was estimated independently from the DLTS signals resulting from thermal emission of electrons from the conduction and optical DLTS signals from the valence band. In this work, an appropriate theoretical determination of the band discontinuities at the interface of the lattice matched InGaP/GaAs heterostructure is made through suitable calculations where the indium mole fraction is varied around the lattice match value x ¼0.48 to find how the band offset changes due to the introduction of strain. It is found that at the lattice matched condition the theoretical computations are in close match with our previously obtained experimental data. This paper presents details of the theoretical calculation, which co-relates the mole fractions, strain, band positions and energy levels. The strains are calculated from the In mole fractions and lattice constants. The parameters implicitly involved are the elastic stiffness constants (C11 and C12), the hydrostatic deformation potential of the conduction band (a0 ), the hydrostatic deformation potential (a) and shear deformation potential (b) for the valence band. The theoretical results obtained for lattice matched In0.48Ga0.51P/GaAs interface for valence band and conduction band offsets reconfirm our previously, experimentally determined band offsets.
2. Experimental and theoretical details n
Corresponding author. Tel.: + 91 9434383736; fax: +91 33 2351 5828. E-mail address: [email protected] (S. Kabi).
1386-9477/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2010.04.009
We have considered a InxGa1 xP/GaAs QW system for our model calculations, the composition of In has been varied on
ARTICLE IN PRESS 2132
S. Kabi et al. / Physica E 42 (2010) 2131–2133
either side of the lattice matched composition x ¼0.48 to change the strain. The band gap of InGaP changes with change in the In mole fraction and is given by the equation as Eg ðxÞ ¼ xEg,InP þ ð1-xÞEg,GaP
ð1Þ
where x is the mole fraction of indium, Eg(x) represents the band gap energy of InGaP, Eg,InP and Eg,GaP represent the band gap energies of the compounds InP and GaP, which are considered to be 1.35 eV and 2.74 eV, respectively. The strain of InxGa1 xP/GaAs is calculated from the equation [7]:
e ¼ ðde db Þ=db
ð2Þ
where de and db are the lattice constants of the epitaxial layer and the barrier, respectively. The variation of strain with indium mole fraction is shown in Fig. 1. The strain varies almost linearly with mole fraction of indium. The energy correction for the conduction band and valence band due to strain is given by the formulae [8]:
Fig. 1. Variation of strain with indium mole fraction in an InxGa1 xP/GaAs system.
DEsrt,c ¼ 2a0 ½ðC11 C12 Þ=C11 e
ð3Þ
DEsrt,v ¼ 2a½ðC11 C12 Þ=C11 e þ b½ðC11 þ2C12 Þ=C11 e
ð4Þ
where a0 is the hydrostatic deformation potential of the conduction band, C11 and C12 are the elastic stiffness constants and a and b are the hydrostatic deformation potential and shear deformation potential for the valence band, respectively. To investigate the effect of strain on the band line-up we have to include the energy correction terms as represented in Eqs. (3) and (4) for the well and the barrier. The parameters used for GaAs and InGaP are taken from Ishikawa [7]. Linear interpolation has been used to calculate de, a0 , a and b for the ternary materials and the interpolation has been weighted by the lattice constant for calculating C11 and C12 of ternary materials.
3. Results and discussion Fig. 2 shows the variation of the band gap energies for GaAs due to the strain when we include the energy correction terms in the well, as well as in the barrier for the GaAs/InGaP system. It is seen that the inclusion of strain has modified the band gap energy and hence the band positions. Fig. 3(a) and (b) shows the variation of the conduction band line-up and valence band line-up with strain, respectively. From Fig. 3 we have extracted suitable expressions for calculation of conduction and valence band positions of GaAs/ InGaP with strain, as expressed below: Fig. 2. Variation of the band gap energy with indium mole fraction for GaAs quantum well. The continuous curves show the variation without considering strain and the dash curves show the variation considering strain.
Ec ¼ 1:70394 þ0:19382e þ 0:00334e2
ð5Þ
Ev ¼ 0:1891þ0:06581e þ 0:01058e2
ð6Þ
0.6 Valance band position (eV)
Conduction band position (eV)
2.6 2.4 2.2 2.0 1.8 1.6 1.4
0.5 0.4 0.3 0.2 0.1
-1
0
1
Strain (in %)
2
3
-1
0
1
2
Strain (in %)
Fig. 3. Variation of the (a) conduction band position and (b) valence band position with strain.
3
ARTICLE IN PRESS S. Kabi et al. / Physica E 42 (2010) 2131–2133
2133
1.70
PL peak energy (eV)
1.65 1.60 1.55 1.50 1.45 1.40 0.45 Fig. 4. Variations of the (a) valence band offset ratio and (b) conduction band offset ratio with indium mole fraction.
0.46
0.47 0.48 0.49 Indium mole fraction (x)
0.50
0.51
Fig. 5. Variations of PL peak energy with indium mole fraction for 6 nm well. The dash curve represents the experimental points as given by Martinez-Pastor et al. [9] and the continuous curves show the theoretical calculation using Eq. (4).
where Ec is the conduction band position and Ev is the valence band position. The strain e is expressed in percentage (%). With this equation we have calculated the band position of the GaAs/InGaP system, hence we have determined the conduction and valence band offsets DEc and DEv. The variations of conduction and valence band offsets DEc and DEv with indium mole fraction (x) are shown in Fig. 4. It is clear from the variation that the conduction band offset increases and the valence band offset decreases with the indium mole fraction. It has been estimated that the conduction and valence band offsets, DEc ¼ 0.1902 eV and DEv ¼0.2898 eV, at the lattice matched point for In mole fraction x ¼048. This is within 2.5% error of our experimentally determined band offsets [6]. For further establishment of the reliability of the theoretical procedures we have compared our computed PL results with experimental PL data given by Martinez-Pastor et al. [9], where they have changed the In mole fraction and the measurements were carried out at low temperatures. The experimental and theoretical curves of PL peak energies against mole fraction (x) are shown in Fig. 5. The match is very close within 1%, which further establishes the proposed method for the computations of band offsets and this reconfirms the band offset values for lattice matched InGaP/ GaAs QWs. It is also observed from Fig. 5 that due to a small change in the mole fraction there is no significant change in the PL energy.
4. Conclusions We have presented appropriate theoretical procedures for computing the band offset of InGaP/GaAs quantum wells. These reconfirm our previously experimentally determined values of the band offsets for lattice matched InGaP/GaAs interface. Experimental PL data of GaAs/InGaP QWs have been matched for further corroboration. This strongly reconfirms that the band offset ratio at the InGaP/GaAs interface at the lattice matched point is (40:60)71.5%.
References [1] M. Feng, N. Holonyak Jr., R. Chen, Appl. Phys. Lett. 87 (2005) 131103. [2] E. Gombia, R. Mosca, D. Pal, S. Busi, L. Tarricone, P.G. Fuochi, M. Lavalle, Mater. Sci. Eng. B 97 (2003) 39. [3] N.H. Karam, R.R. King, M. Haddad, J.H. Ermer, H. Yoon, H.L. Cotal, R. Sudharsanan, J.W. Eldredge, K. Edmondson, D.E. Joslin, D.D. Krut, M. Takabashi, W. Nishikawa, M. Gillanders, J. Granata, P. Hebert, B.T. Cavicchi, D.R. Lillington, Sol. Energy Mater. Sol. Cells 66 (2001) 453. ¨ [4] E. Greger, P. Riel, M. Moser, T. Kippenberg, P. Kiesel, G.H. Dohler, Appl. Phys. Lett. 71 (1997) 3245. [5] C. Ghezzi, R. Magnanini, A. Parisini, L. Tarricone, E. Gombai, M. Longo, Phy. Rev. B. 77 (2008) 125317. [6] D. Biswas, N. Debbar, P. Bhattacharya, Appl. Phys. Lett. 56 (9) (1989) 833. [7] T. Ishikawa, IEEE J. Quant. Electron. 30 (1994) 562. [8] H. Nagai, S. Aadachi, T. Fukui, III–V Mixed crystal, Corona, Tokyo, Japan, 1998. [9] Juan Martinez-Pastor, Luisa Gonzalez, Philippe Roussignol, Appl. Phys. Lett. 68 (15) (1996) 2111.