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High pressure experiments on AlxGa1−xAs-GaAs quantum-well heterostructure lasers
Solid State Conxnunications, Vo1.42, Printed in Great Britain.
No.9,
pp.633-636,
1982.
0038-1098/82/210633-04$03.00/O Pergamon Press Ltd.
HIGH PRESSURE EXPERIMENTS ON AlxGal_xAs-GaAs QUANTUM-WELL HETEROSTRUCTURE LASERS S.W. Kirchoefer,
N. Holonyak,
Jr., and K. Hess
Electrical Engineering Research Laboratory and Materials Research Laboratory University of Illinois at Urbana-Champaign, Urbana, Illinois D.A. Gulino
and H.G. Drickamer
School of Chemical Sciences and Materials University of Illinois at Urbana-Champaign, J.J. Coleman Rockwell
Research Laboratory Urbana, Illinois 61801
and P.D. Dapkus
International, Electronics Research Anaheim, California 92803
(Received
4 January
61801
Center
1982 by A.A. Maradudin)
Hydrostatic pressure experiments on AlxGal_xAs-GaAs quantunrwell heterostructure (QWH) laser diodes are described. Data are presented giving -11.5meV/kbar for the bandgap vs. pressure coefficient at lower pressures, with a change to 8.5-9meV/kbar at higher pressures. We suggest that this behavior is caused by biaxial and shear stresses in the active region induced by doping or composition mismatch relative to the confining layers, or between the n and p confining layers themselves. A model consistent with the experimental data is presented.
For some time it has been known that the application of hydrostatic pressure to semiconductor crystals alters the relative positions of their energy band maxima and minima. This technique has been used extensively for various band-str c ure studies of bulk III-V semiconductors.Y" Since the completion of much of the early part of this work, many advances have been art of made in the semiconductor crystal In particular, growth. it is now possible to grow, via metalorganic chemical vapor deposition (MO-CVD) or molecular beam epitaxy (MBE), AlAs-AlGaAs-GaAs sophisticated quantum-well heterostructures [QWH's, L,(GaAs)yOOA] that offer new opportunities for pressure studies. re capable These thin-layer structures, which of continuous 300K laser operation, J have been especially interesting not only b cause they exhibit quant -size effects (QSE)? but alsf various phonon'$ and alloy clustering effects. The technique of applying hydrostatic pressure to these quasi-two dimensional structures, and thus further varying the band structure, has not previously been attempted and is reported here.
thick+nesses Lz=LB, and a -1 pm thick cap layer The fourth GaAs for contact purposes. of P reference or comparison sample, sample, a consists of a conventional double heterostructure (DH) with n- and p-type confining layers of x -0.3 Al,Gal_,As, and an undoped active layer of GaAs of thickness - 6008 . These samples are processed into oxidedefined stripe geometry lasers. They are metallised with Au-Cr-Au on the p-side and Au-Sn-Au on the n-side, then cleaved into bars, and sawed into dice. Each die is mounted with In solder on a copper pad affixed to a TO-18 header, and is contacted on the opposite side with a Ni lead attached with In solder. To apply pres ure the diode is placed in a high pressure cell s/ with a sapphire window and standard Bridgman electric seals. Pressure is applied using an intensifier calibrated against a manganin gauge. The dielectric fluid in the cell and intensifier consists of 10% isooctane and 90% methylcyclohexane. The apparatus is operable to -12kbar. The diodes are driven pulsed to avoid any likelihood of heating, and emission spectra (3OCK) are recorded at various pressures.
The samples chosen for these experiments consist of four different heterostructures. All of the crystals have been grown (by MO-CVD)6 as p-n junctions (with undoped active regions) for use in laser diodes. Three of these samples have 6 coupled GaAs quantum wells with differing well and barrier layer thicknesses (L,,LB-120, All three are identical in other 80, and 50A). Each has a bottom n- and a top p-type respects. bulk confining layer (-1~ thick) composed of undoped quantum-well (GaAs) x=0.4 Al,Gal_,As, and barrier layers (x-O.3 Al,Gal_,As) of equal
The data collected for the four samples of interest here are shown in Fig.1. The data points correspond to the laser mode of highest intensity. The diodes are typically driven as near to threshold as possible to avoid bandfilling, and yet high enough to provide for linewidth narrowing to as few modes as possible. The data points are fitted by the 633
AlxGal_xAs-GaAs
634
QUANTUM-WELL
band minimum and heavy-hole maxima
1.62 AI,Ga,_,As-GaAs
HRTEROSTRUCTURF
p-n QWH
LASERS the degenerate of Fig.a(a).
Vol. 42, No. J k=O
light-
and
To explain the lesser slope (Fig.1, curve a, a') of 8.5-9 meV/kbar measured for the laser diode with the 600A GaAs active layer and for the 6-well QWH diodes (b, c, c', d) beyond each corner or kink marked with an arrow (+), we suggest a model in which the light- and heavyhole subbands move differently with pressure
a), a’) L, - 600 A 120
b) 1.46
I 2
I
4
I 6
cl. c’)
80
dl
50
I
I
8
10
Pressure (kbar)
Photon energy (laser) vs. pressure for Fig.1 QWH's and DH's operated under hydra;;;:;; DH's with bulk active pressure. [us-6008, (a) and (a')] exhibit linear energy in the range p=O-10 vs. pressure characteristics QWH's (L,,LR-120, kbar. Six-well, five-barrier 80, 50A) exhibit similar linear dependence of photon energy vs. pressure in the high pressure range, and a steeper linear dependence .in the The pressure at which the low pressure range. "corner" or kink (+) occurs is size-dependent smaller Ls). Slight (higher pressure for absolute energy occur for variations in different diodes of the same type [(a), (a') and (c), (cl)], but the locations of the kinks and In each the slopes of the lines do not vary. case, data points are for the diode-laser mode of highest intensity.
To provide a good fit, method of least-squares. the experimental curves are bent (two straight lines) at the locations marked by the arrows (for Lx-120, 80, and 50&). To understand the data presented here, it is important to note that the existence of thin layers (L&,5008) in a semiconductor crystal imposes boundary conditions that break the bulk Electrons and holes, symmetry of the crystal. which occupy energy states "down" to the band are constrained and edge of a bulk crystal, confined-particle behavior exhibit pronounced Of particular for the case L,(GaAs)yOO8. interest here is the effect of size on the Due to the subbands. heavy- and light-hole difference in effective masses, the degeneracy of heavy and light holes [Fig.Z(a)] is broken as The shift with pressure of shown in Fig.Z(c). ap for bulk GaAs is known to be the direct-band This is somewhat larger but -12.5 meV/kbar. 5 still near the steeper low-pressure slopes of This behavior corresponds the curves in Fig.1. to the gap as measured between the P conduction
because of shear effects introduced by the two, n and p, confining-layers.' We consider first the 600-A GaAs heterostructure with its valence band modeled as shown by (a) and (b) of Fig.2. At zero applied pressure, p=O, the hole bands are degenerate at k=O as shown in (a). As pressure is applied, the heavy-hole ba moves "4 at -12.5 meV/kbar (or a little less) and, because of the shear effects in the active region introduced by any mismatch (doping, composition, etc.) between the n and p confining themselves or relative to the active layers the light-hole band moves region, ("faster") at -8.5 meV/kbar measured relative to the P conduction band edge." for noThus, allowing crossing rules, we obtain the valence band configuration shown in (b) of Fig.2. The measured energy shift in the laser radiation meV/kbar of -8.5 at higher pressures corresponds, in this model, to the relative shift between the light-hole band and the P conduction band. For the case of the 6-well QWH diodes 80, and the behavior is 5OA), (LZ -120, essentially the same except that the hole bands zero applied exhibit a sizeat pressure dependent splitting at k=O that plays a role. This splitting [Fig.Z(c)] is larger for thinner the light-hole band located layers Lx, with below the heavy-hole band until, as pressure is corresponding applied, the point of degeneracy to p=pl in Fig.Z(d) is reached. At this pressure, we will observe a corner or kink (+) in the pressure data (Fig.1) and a change in -8.5 meV/kbar as the hole bands slope to "cross" with increasing pressure and assume the configuration of Fig.Z(e), which is the effect of the shear on the active region. Since the initial light-hole splitting is heavy-hole, greater for smaller layer thicknesses L,, we find that the change in slope of the pressure data, marked with arrows (+), occurs at higher pressures for smaller quantum-well sizes. A quantitative treatment of the above model is difficult since neither the elastic moduli of the ternary compound nor of the active region are very well known. It is also difficult to how much shear is introduced by the assess formation of the p-n junction. However, we will generally have nonvanishing uniaxial (actually biaxial) and shear components of the strain sij (i.e., Eii# Ejj and sij $0 for i#j) in addition to the hydrostatic deformation, even if purely hydrostatic pressure is applied externally to the heterostructure. The active-region valence-band structure IS especially sensitive to uniaxial and shear components since the degeneracy of heavy- and light-hole bands at P is removed by uniaxial and
vol.
42, No.
9
AlxGa,_xAs-GaAs
QUANTUM-WELL
HETEROSTRUCTURE effective mass heterolayers.
is the mass
We can d Pikus and Bi$ of the heavygiven by
uce from the equations given by that the energy of the maximum and of the light-hole bands are
p=o
p=o (a)
m P=Pl>o
P=Pl>o
(4
b)
k
perpendicular
Et = (a* + c*)p
(c)
fi
635
LASERS
(1)
,
where p is the hydrostatic pressure applied to the heterostructure and c* and a* are effective deformation potentials with c* I 0 and a* I a homogeneous material (i.e., no bulk for confining or contact layers). The upper sign is for light holes (1) and the lower sign for heavy holes (h). The splitting between the heavy- and light-hole bands is equal to 2c*p. If as mentioned above we assume that the "corners" or kinks (C) in the experimental curves of Fig.1 of heavy- and are a consequence of the crossing light-hole bands under pressure as shown in (c), (d), and (e) of Fig.2, we have BE h,ll = 2 c*p.
‘h P=P2>Pl (4
bands under the Heavy- and light-hole Fig.2 simultaneous constraints of layer size (Ls>500A, L,$SODA) and pressure-induced change in built-in Thin layer shear stresses in the active layer. size (L,$~CCA) breaks the degeneracy (p=O) of light and heavy holes at k=O [cf., (a) and With hydrostatic pressure p>O and changes (c)l. in the mismatch shear stresses in the active band, moving to higher region, the light-hole than the heavy-hole band (see energy faster text), is degenerate with the heavy-hole band at This is the pressure (pl) P=P~ IL,~500;;e (d) I. kinks (+) of Fig.1 occur. which at Increasing the pressure beyond pl causes the light-hole band to move through the heavy-hole band in the thin-layer case [L,yOO& (e)], thus producing an increase in laser photon energy to the thick-layer case equal with pressure [L,>500A, (b)]. A typical example is shown shear deformation. in (c), (d) and (e) of Fig.2 (L,yOp{) where, we have based on the results of Pikus and Bir, sketched the heavy- and light-hole bands for the case the of in compression
to the
(2)
Here AEh 1 is the difference in the energy of heavy- 2nd light-hole bands at b0 caused by that is, in the effective size quantisation; mass approximation (and a "deep" well)
AEh,R
= ?ti2/(2L~){l/m~
- l/m:),
(3)
where are the light- and heavy-hole masses ri "p=""o miespectively. Equations (2) and (3) indicate ihat the kinks (+) in Fig.1 should shift to higher pressures (pl in Fig.2) with To fit the experimental data we decreasing Le. obtain c* = 2.03 & 0.15 meV/kbar.
(4)
This value suggests a slope of -7 meV/kbar for the pressure data in the range above the kinks. Although this is smaller than the experimental value of meV/kbar, the 8.5-9 difference can easily arise from changes in the band edges of the confining layers under pressure, which have been not considered above. We that the p-n mention finally heterostructure itself (its p and n confining layers) introduces anisotropies and consequently shear and uniaxial of the strain, comuonents which appear in the active region and make it a sensitive shear "detector". The authors are grateful to K. Meehan, Yuri S. Moroz, R.D. Fults, B.L. Marshall, and B.L. The work of Payne for technical contributions. the Illinois group has been supported by NSF Grant DMR 8C-20250, U.S. Department of Energy Contract DE-AC02-76ER01198, and Navy Contract The work of the Rockwell N00014-76-C-0708. has been partially supported by ONR group Contract N00014-78-C-0711.
636
AlxGa
1
-x
As-GaAs
QUANTUM-WELL
HETEROSTRUCTURE
Vol. 42, No. 3
LASERS
REFERENCES 1. A.L. Edwards, T.E. Slykhouse, and H.G. Drickamer, J. Phys. Chem. Solids 2, 140 (1959).
7. D.A. Gulino, Illinois (1982).
2. R.W. Keyes, in R.W. Willardson and A.C. Beer, eds, SEMICONDUCTORS AND SBMIMETALS, Vol. 4, (Academic Press, N.Y., 1968), pp.327-342.
8. B. Welker, M. Cardona, C.K. Kim, and S. Rodriguez, Phys. Rev. B 12, 5729 (1975). See also J. Lagowski, A. Iller, and A. Swiatek, Surface Sci. 49, 1 (1975), and A.K. Saxena, J. Phys. Cz, 4323 (1980).
3. N. Holonyak, Jr., R.M. Kolbas, R.D. Dupuis, and P.D. Dapkus, IEEE J. Quantum Electron. QE2, 170 (1980). 4. N. Holonyak, Jr., R.M. Kolbas, W.D. Laidig, B.A. Vojak, K. Hess, R.D. Dupuis, and P.D. Dapkus, J. Appl. Phys. 2, 1328 (1980). See also K. Hess and N. Holonyak, Jr., Comments Solid State Phys. 2, 67 (1981). 5. N. Holonyak, Jr., W.D. Laidig, B.A. Vojak, Coleman, P.D. Dapkus, and J. K. Hess, J.J. Bardeen, Phys. Rev. Lett. 5, 1703 (1980). 6. H.M. Manasevit, J. Electrochem. Sot. 118, See also the entire issue of J. 647 (1971). Crystal Growth=, (i/l, Ott, 1981), pp.l-262.
MS
Thesis,
University
of
9. This is concluded from absorption measurements on superlattice samples free of confining layers exhibit no that anomalous behavior. (Unpublished data of the authors. See also J.J. Coleman, D.R. Clarke, M.D. Camras, and N. Holonyak, Jr., Appl. Phys. Lett. 2, 864 (1981).) 10. Actually the heavy-hole bands become hybridized.
and
light-hole
11. G.E. Pikus and G.L. Bir, Fizz. Tver. Tela 1, 1642 (1959) [Sov. Phys.-Solid State l_, 1502 (1960)]. 12.
See Ref.11,
Eqs. 14-17.
No.9,
pp.633-636,
1982.
0038-1098/82/210633-04$03.00/O Pergamon Press Ltd.
HIGH PRESSURE EXPERIMENTS ON AlxGal_xAs-GaAs QUANTUM-WELL HETEROSTRUCTURE LASERS S.W. Kirchoefer,
N. Holonyak,
Jr., and K. Hess
Electrical Engineering Research Laboratory and Materials Research Laboratory University of Illinois at Urbana-Champaign, Urbana, Illinois D.A. Gulino
and H.G. Drickamer
School of Chemical Sciences and Materials University of Illinois at Urbana-Champaign, J.J. Coleman Rockwell
Research Laboratory Urbana, Illinois 61801
and P.D. Dapkus
International, Electronics Research Anaheim, California 92803
(Received
4 January
61801
Center
1982 by A.A. Maradudin)
Hydrostatic pressure experiments on AlxGal_xAs-GaAs quantunrwell heterostructure (QWH) laser diodes are described. Data are presented giving -11.5meV/kbar for the bandgap vs. pressure coefficient at lower pressures, with a change to 8.5-9meV/kbar at higher pressures. We suggest that this behavior is caused by biaxial and shear stresses in the active region induced by doping or composition mismatch relative to the confining layers, or between the n and p confining layers themselves. A model consistent with the experimental data is presented.
For some time it has been known that the application of hydrostatic pressure to semiconductor crystals alters the relative positions of their energy band maxima and minima. This technique has been used extensively for various band-str c ure studies of bulk III-V semiconductors.Y" Since the completion of much of the early part of this work, many advances have been art of made in the semiconductor crystal In particular, growth. it is now possible to grow, via metalorganic chemical vapor deposition (MO-CVD) or molecular beam epitaxy (MBE), AlAs-AlGaAs-GaAs sophisticated quantum-well heterostructures [QWH's, L,(GaAs)yOOA] that offer new opportunities for pressure studies. re capable These thin-layer structures, which of continuous 300K laser operation, J have been especially interesting not only b cause they exhibit quant -size effects (QSE)? but alsf various phonon'$ and alloy clustering effects. The technique of applying hydrostatic pressure to these quasi-two dimensional structures, and thus further varying the band structure, has not previously been attempted and is reported here.
thick+nesses Lz=LB, and a -1 pm thick cap layer The fourth GaAs for contact purposes. of P reference or comparison sample, sample, a consists of a conventional double heterostructure (DH) with n- and p-type confining layers of x -0.3 Al,Gal_,As, and an undoped active layer of GaAs of thickness - 6008 . These samples are processed into oxidedefined stripe geometry lasers. They are metallised with Au-Cr-Au on the p-side and Au-Sn-Au on the n-side, then cleaved into bars, and sawed into dice. Each die is mounted with In solder on a copper pad affixed to a TO-18 header, and is contacted on the opposite side with a Ni lead attached with In solder. To apply pres ure the diode is placed in a high pressure cell s/ with a sapphire window and standard Bridgman electric seals. Pressure is applied using an intensifier calibrated against a manganin gauge. The dielectric fluid in the cell and intensifier consists of 10% isooctane and 90% methylcyclohexane. The apparatus is operable to -12kbar. The diodes are driven pulsed to avoid any likelihood of heating, and emission spectra (3OCK) are recorded at various pressures.
The samples chosen for these experiments consist of four different heterostructures. All of the crystals have been grown (by MO-CVD)6 as p-n junctions (with undoped active regions) for use in laser diodes. Three of these samples have 6 coupled GaAs quantum wells with differing well and barrier layer thicknesses (L,,LB-120, All three are identical in other 80, and 50A). Each has a bottom n- and a top p-type respects. bulk confining layer (-1~ thick) composed of undoped quantum-well (GaAs) x=0.4 Al,Gal_,As, and barrier layers (x-O.3 Al,Gal_,As) of equal
The data collected for the four samples of interest here are shown in Fig.1. The data points correspond to the laser mode of highest intensity. The diodes are typically driven as near to threshold as possible to avoid bandfilling, and yet high enough to provide for linewidth narrowing to as few modes as possible. The data points are fitted by the 633
AlxGal_xAs-GaAs
634
QUANTUM-WELL
band minimum and heavy-hole maxima
1.62 AI,Ga,_,As-GaAs
HRTEROSTRUCTURF
p-n QWH
LASERS the degenerate of Fig.a(a).
Vol. 42, No. J k=O
light-
and
To explain the lesser slope (Fig.1, curve a, a') of 8.5-9 meV/kbar measured for the laser diode with the 600A GaAs active layer and for the 6-well QWH diodes (b, c, c', d) beyond each corner or kink marked with an arrow (+), we suggest a model in which the light- and heavyhole subbands move differently with pressure
a), a’) L, - 600 A 120
b) 1.46
I 2
I
4
I 6
cl. c’)
80
dl
50
I
I
8
10
Pressure (kbar)
Photon energy (laser) vs. pressure for Fig.1 QWH's and DH's operated under hydra;;;:;; DH's with bulk active pressure. [us-6008, (a) and (a')] exhibit linear energy in the range p=O-10 vs. pressure characteristics QWH's (L,,LR-120, kbar. Six-well, five-barrier 80, 50A) exhibit similar linear dependence of photon energy vs. pressure in the high pressure range, and a steeper linear dependence .in the The pressure at which the low pressure range. "corner" or kink (+) occurs is size-dependent smaller Ls). Slight (higher pressure for absolute energy occur for variations in different diodes of the same type [(a), (a') and (c), (cl)], but the locations of the kinks and In each the slopes of the lines do not vary. case, data points are for the diode-laser mode of highest intensity.
To provide a good fit, method of least-squares. the experimental curves are bent (two straight lines) at the locations marked by the arrows (for Lx-120, 80, and 50&). To understand the data presented here, it is important to note that the existence of thin layers (L&,5008) in a semiconductor crystal imposes boundary conditions that break the bulk Electrons and holes, symmetry of the crystal. which occupy energy states "down" to the band are constrained and edge of a bulk crystal, confined-particle behavior exhibit pronounced Of particular for the case L,(GaAs)yOO8. interest here is the effect of size on the Due to the subbands. heavy- and light-hole difference in effective masses, the degeneracy of heavy and light holes [Fig.Z(a)] is broken as The shift with pressure of shown in Fig.Z(c). ap for bulk GaAs is known to be the direct-band This is somewhat larger but -12.5 meV/kbar. 5 still near the steeper low-pressure slopes of This behavior corresponds the curves in Fig.1. to the gap as measured between the P conduction
because of shear effects introduced by the two, n and p, confining-layers.' We consider first the 600-A GaAs heterostructure with its valence band modeled as shown by (a) and (b) of Fig.2. At zero applied pressure, p=O, the hole bands are degenerate at k=O as shown in (a). As pressure is applied, the heavy-hole ba moves "4 at -12.5 meV/kbar (or a little less) and, because of the shear effects in the active region introduced by any mismatch (doping, composition, etc.) between the n and p confining themselves or relative to the active layers the light-hole band moves region, ("faster") at -8.5 meV/kbar measured relative to the P conduction band edge." for noThus, allowing crossing rules, we obtain the valence band configuration shown in (b) of Fig.2. The measured energy shift in the laser radiation meV/kbar of -8.5 at higher pressures corresponds, in this model, to the relative shift between the light-hole band and the P conduction band. For the case of the 6-well QWH diodes 80, and the behavior is 5OA), (LZ -120, essentially the same except that the hole bands zero applied exhibit a sizeat pressure dependent splitting at k=O that plays a role. This splitting [Fig.Z(c)] is larger for thinner the light-hole band located layers Lx, with below the heavy-hole band until, as pressure is corresponding applied, the point of degeneracy to p=pl in Fig.Z(d) is reached. At this pressure, we will observe a corner or kink (+) in the pressure data (Fig.1) and a change in -8.5 meV/kbar as the hole bands slope to "cross" with increasing pressure and assume the configuration of Fig.Z(e), which is the effect of the shear on the active region. Since the initial light-hole splitting is heavy-hole, greater for smaller layer thicknesses L,, we find that the change in slope of the pressure data, marked with arrows (+), occurs at higher pressures for smaller quantum-well sizes. A quantitative treatment of the above model is difficult since neither the elastic moduli of the ternary compound nor of the active region are very well known. It is also difficult to how much shear is introduced by the assess formation of the p-n junction. However, we will generally have nonvanishing uniaxial (actually biaxial) and shear components of the strain sij (i.e., Eii# Ejj and sij $0 for i#j) in addition to the hydrostatic deformation, even if purely hydrostatic pressure is applied externally to the heterostructure. The active-region valence-band structure IS especially sensitive to uniaxial and shear components since the degeneracy of heavy- and light-hole bands at P is removed by uniaxial and
vol.
42, No.
9
AlxGa,_xAs-GaAs
QUANTUM-WELL
HETEROSTRUCTURE effective mass heterolayers.
is the mass
We can d Pikus and Bi$ of the heavygiven by
uce from the equations given by that the energy of the maximum and of the light-hole bands are
p=o
p=o (a)
m P=Pl>o
P=Pl>o
(4
b)
k
perpendicular
Et = (a* + c*)p
(c)
fi
635
LASERS
(1)
,
where p is the hydrostatic pressure applied to the heterostructure and c* and a* are effective deformation potentials with c* I 0 and a* I a homogeneous material (i.e., no bulk for confining or contact layers). The upper sign is for light holes (1) and the lower sign for heavy holes (h). The splitting between the heavy- and light-hole bands is equal to 2c*p. If as mentioned above we assume that the "corners" or kinks (C) in the experimental curves of Fig.1 of heavy- and are a consequence of the crossing light-hole bands under pressure as shown in (c), (d), and (e) of Fig.2, we have BE h,ll = 2 c*p.
‘h P=P2>Pl (4
bands under the Heavy- and light-hole Fig.2 simultaneous constraints of layer size (Ls>500A, L,$SODA) and pressure-induced change in built-in Thin layer shear stresses in the active layer. size (L,$~CCA) breaks the degeneracy (p=O) of light and heavy holes at k=O [cf., (a) and With hydrostatic pressure p>O and changes (c)l. in the mismatch shear stresses in the active band, moving to higher region, the light-hole than the heavy-hole band (see energy faster text), is degenerate with the heavy-hole band at This is the pressure (pl) P=P~ IL,~500;;e (d) I. kinks (+) of Fig.1 occur. which at Increasing the pressure beyond pl causes the light-hole band to move through the heavy-hole band in the thin-layer case [L,yOO& (e)], thus producing an increase in laser photon energy to the thick-layer case equal with pressure [L,>500A, (b)]. A typical example is shown shear deformation. in (c), (d) and (e) of Fig.2 (L,yOp{) where, we have based on the results of Pikus and Bir, sketched the heavy- and light-hole bands for the case the of in compression
to the
(2)
Here AEh 1 is the difference in the energy of heavy- 2nd light-hole bands at b0 caused by that is, in the effective size quantisation; mass approximation (and a "deep" well)
AEh,R
= ?ti2/(2L~){l/m~
- l/m:),
(3)
where are the light- and heavy-hole masses ri "p=""o miespectively. Equations (2) and (3) indicate ihat the kinks (+) in Fig.1 should shift to higher pressures (pl in Fig.2) with To fit the experimental data we decreasing Le. obtain c* = 2.03 & 0.15 meV/kbar.
(4)
This value suggests a slope of -7 meV/kbar for the pressure data in the range above the kinks. Although this is smaller than the experimental value of meV/kbar, the 8.5-9 difference can easily arise from changes in the band edges of the confining layers under pressure, which have been not considered above. We that the p-n mention finally heterostructure itself (its p and n confining layers) introduces anisotropies and consequently shear and uniaxial of the strain, comuonents which appear in the active region and make it a sensitive shear "detector". The authors are grateful to K. Meehan, Yuri S. Moroz, R.D. Fults, B.L. Marshall, and B.L. The work of Payne for technical contributions. the Illinois group has been supported by NSF Grant DMR 8C-20250, U.S. Department of Energy Contract DE-AC02-76ER01198, and Navy Contract The work of the Rockwell N00014-76-C-0708. has been partially supported by ONR group Contract N00014-78-C-0711.
636
AlxGa
1
-x
As-GaAs
QUANTUM-WELL
HETEROSTRUCTURE
Vol. 42, No. 3
LASERS
REFERENCES 1. A.L. Edwards, T.E. Slykhouse, and H.G. Drickamer, J. Phys. Chem. Solids 2, 140 (1959).
7. D.A. Gulino, Illinois (1982).
2. R.W. Keyes, in R.W. Willardson and A.C. Beer, eds, SEMICONDUCTORS AND SBMIMETALS, Vol. 4, (Academic Press, N.Y., 1968), pp.327-342.
8. B. Welker, M. Cardona, C.K. Kim, and S. Rodriguez, Phys. Rev. B 12, 5729 (1975). See also J. Lagowski, A. Iller, and A. Swiatek, Surface Sci. 49, 1 (1975), and A.K. Saxena, J. Phys. Cz, 4323 (1980).
3. N. Holonyak, Jr., R.M. Kolbas, R.D. Dupuis, and P.D. Dapkus, IEEE J. Quantum Electron. QE2, 170 (1980). 4. N. Holonyak, Jr., R.M. Kolbas, W.D. Laidig, B.A. Vojak, K. Hess, R.D. Dupuis, and P.D. Dapkus, J. Appl. Phys. 2, 1328 (1980). See also K. Hess and N. Holonyak, Jr., Comments Solid State Phys. 2, 67 (1981). 5. N. Holonyak, Jr., W.D. Laidig, B.A. Vojak, Coleman, P.D. Dapkus, and J. K. Hess, J.J. Bardeen, Phys. Rev. Lett. 5, 1703 (1980). 6. H.M. Manasevit, J. Electrochem. Sot. 118, See also the entire issue of J. 647 (1971). Crystal Growth=, (i/l, Ott, 1981), pp.l-262.
MS
Thesis,
University
of
9. This is concluded from absorption measurements on superlattice samples free of confining layers exhibit no that anomalous behavior. (Unpublished data of the authors. See also J.J. Coleman, D.R. Clarke, M.D. Camras, and N. Holonyak, Jr., Appl. Phys. Lett. 2, 864 (1981).) 10. Actually the heavy-hole bands become hybridized.
and
light-hole
11. G.E. Pikus and G.L. Bir, Fizz. Tver. Tela 1, 1642 (1959) [Sov. Phys.-Solid State l_, 1502 (1960)]. 12.
See Ref.11,
Eqs. 14-17.