GaAlAs multi-quantum-well structures grown by molecular beam epitaxy

(

HIGH-RESOLUTION

1986

Pergamon

Prrss Ltd

PHOTOLUMINESCENCE

K. K. BAJAJ, D. C. REYNOLDS and C. W. LITTON Air Force Wright Aeronautical Laboratories, Avionics Laboratory, AFWAL/AADR, Wright-Patterson Air Force Base, OH 45433. U.S.A.

and JASPRIT SINGH Universal

Energy

Systems. Inc., 4401 Dayton-Xenia

Rd., Dayton,

OH 45432, U.S.A.

and P. w. Yu University

Research

Center, Wright

State University,

Dayton,

OH 45435, U.S.A.

and W. T. MASSELINK Department of Physics and Coordinated Science Laboratory, University of Illinois, Urbana, IL 61801. U.S.A.

and R. FISCHER and H. MORKOC Department

of Electrical Engineering and Coordinated Science Laboratory, University of Illinois, Urbana, IL 61801. U.S.A.

(Received

12 Fehruur?, 1985; in revisedform14 June 1985)

Abstract-Recent developments in the studies of GaAs/GaAlAs multi-quantum-well (MQW) structures using high-resolution photoluminescence spectroscopy are reviewed. Results discussed in this paper are all obtained in quantum wells grown using molecular-beam epitaxy (MBE). The observed linewidths of the excitonic transitions are very small (in many cases < 0.2 meV), thus indicating a high quality of the quantum wells. Theories of crystal growth by MBE using Monte Carlo techniques and of excitonic lineshape in quantum wells are reviewed. Based on the observed linewidths of the excitonic transitions, a microscopic model for the GaAs/GaAlAs interface is proposed. Variations of the energies of the various transitions in MQW structures as a function of the well size are presented and are compared with the available calculations. The behavior of the excitonic transitions as a function of temperature and applied electric field is also reviewed.

1. INTRODUCTION

The last decade has seen an evolution of a new semiconductor technology based on ultra-thin heterostructures[l-31. The backbone of this technology is the ability to change the composition (chemical) or doping properties of a semiconductor structure over a few monolayers. This has been made possible due to the development of novel epitaxialcrystal-growth techniques such as molecular-beam epitaxy (MBE) [4,5] and metal-organic chemical vapor deposition (MOCVD) [6]. Under carefully selected growth conditions MBE has proved its ability to fabricate interfaces between two semiconductors that are abrupt to a monolayer [7,8]. This has led to the conception and realization of numerous device structures whose optical and electronic properties can be tailored for specific purposes. In this

paper we review our recent work on the properties of MBE-grown GaAs-GaAlAs multi-quantum-well (MQW) structures as revealed by high-resolution photoluminescence (PL) spectroscopy. Due to limitations of space, it is not possible for us to review work of other investigators on the optical properties of these structures. The reader is, however, referred to excellent review articles by Bastard [9], Chemla[lO] and Miller and Kleinman [ll]. The study of quantum-well structures has played an important role in the advancement of the thin heterostructure technology. Some of the motivations for these studies are: 1) fabrication of new heterostructure lasers with tailored emission lines, 2) exploration of new physics in quasi-2-dimensional systems, and 3) the use of quantum wells as a characterization tool for the study of the quality of 215

216

K. K. BAJAJet 01.

interfaces. We will devote this paper to 2) and 3) and present theoretical and experimental observations of exciton-related phenomena in quantum-well structures. As noted earlier, the key ingredient in the success of the heterostructure technology is the ability to reproducibly fabricate abrupt, high-quality interfaces between two materials. This has required an interactive program between understanding the details of the MBE crystal grown process and characterization techniques capable of giving microscopic details about the quality of an interface. High-resolution photoluminescence (PL) spectroscopy is an important experimental technique capable of studying both the new physics of quasi-2-dimensional systems as well as probing the microscopic details of interfaces and will be the experimental tool for the studies reported here [12-141. In the next section we briefly discuss some features of the MBE growth and the theoretical understanding of crystal growth and interfacial structure. In Section 3 we discuss the physics of excitons in quantum wells as well as the theory of the effects of the quality of the quantum wells on the linewidth of excitonic emission lines. In Section 4 we present experimental results obtained using high resolution photoluminescence spectroscopy. A discussion of the comparison between theoretical and experimental results is given in Section 5. Section 6 contains the concluding remarks. 2.

MBE GROWTH

Since several excellent review articles on experimental aspects of MBE growth are available[l-41, here we will discuss only those aspects of MBE growth that are important in understanding the formation of interfaces. The results reported in this paper are all on GaAs/GaAlAs quantum well-structures grown by MBE. To understand the formation of the interfaces related to this system (and to other common-anion systems) one must recognize that the heterostructure is grown by allowing the Ga and arsenic (AS? + As,) beams to continuously impinge on the growing substrate during growth. The Al flux is shut off during the formation of the well and is allowed to impinge during the growth of the barrier. It is clear that if a quantum well or a MQW structure with a well size lVa is to be grown, a very accurate calibration of the growth rate is required to form a perfect well with perfect interfaces. We define a perfect interface formed on a cation layer ‘i’ as one in which the layer ‘i’ is pure Ga and the layer ‘i - 1’ (or ‘i + 1’) is Ga, ~, Al., where n is the Al composition in the barrier region. Several sources of error, both extrinsic and intrinsic, can cause an “imperfect” quantum-well. Extrinsic sources of error are in principle controllable, although in practice it may be very difficult to eliminate them. These include: a) delays in opening/ closing the shutters, b) uncertainties in calibration of Ga and Al fluxes, c) time-dependent variations in Ga

and Al fluxes during the growth time (generally - 1 hr). It appears that b) may be the dominant source of extrinsically caused fluctuations. We note that the calibration of flux is usually done by growing a certain thickness of film. An error of only 5 x 10 4 can cause - 2 monolayer variation in well sizes grown over a micron of MQW structure. It is also clear that it is impossible to close or open a shutter at the precise moment that the surface layer is completely full. The significance of this uncertainty will become clear when we discuss the microscopics of MBE growth next. The problem of modeling MBE growth is quite complicated. Computer simulations based on Monte Carlo techniques have been found to be essential for understanding the atomic details of growth[l5--191. We will briefly discuss the essence of the theoretical work based on these studies and their implications for interfaces. A key feature emerging from these studies is that the surface/interface quality for (100) growth is controlled by cation kinetics in normally employed growth conditions[lS, 191. If the growth conditions are such that cation migration rate is low, the growing surface starts to become rough due to the growth occurring simultaneously at many diffcrent surface layers, as shown in Fig. l(a). Under conditions such that cation interlayer and intralayer migration rates are high (2 lo4 hops S I), growth occurs by the layer-by-layer mechanism [Fig. l(b)]. The experimental studies reported in this paper were carried out on structures grown under optimized conditions so that growth occurred by the layer-bylayer mode. Computer simulations give semi-quantitative information on the microstructure of a growing layer and in Fig. 2 we display this information

GROWTH

TIME

(set)

Fig. 1. Plots of coverage differentials dO,/dO,,, for direrent layers as a function of growth time when the growth starts from a flat surface. 0,, is the coverage on the ,I th layer and &,, is the total coverage on all layers. (a) Results for the case when cation intra- and inter-layer migration rate is 0.5 hops s- ‘. (b) Results for the case when cation intra- and inter-layer migration rate is 3000 hops s ’

211

High-resolution photoluminescence studies

Bi - 50%

ICI

8,“70%

Id1

u

t-l

u

l-r

@,‘90%

(el

u

Ll

Fig. 2. A schematic representation of the microstructure of a surface growing by the layer by layer growth mode. r, and r, are the distances associated with the clusters on layers ‘i’ and ‘i - 1’. The various cases shown correspond to the coverage 19, on layer ‘I’ given by: (a) 6’,- 10%; (b) 0, - 20%; (C) 0, - 50%; (d) 0, - 70% and t?,- 90%.

schematically. We have shown the surface clusters on the layer i at various coverages 0,. The physical interpretation of Fig. 2 is as follows. Fig. 2(a) shows the surface when 0, < 10%. In the early stages of growth, nucleation centers are formed randomly due to cation migration and formation of 2-D clusters. The average size of the 2-D clusters (r,,) is small and they are separated by large distances (r,). In Fig. 2(b) we show the surface when the coverage is 8, 20%. At this point r,, has increased slightly while r, has decreased. At 0, - 5O’%r,, and r, become comparable as shown in Fig. 2(c). At higher coverages we have the case shown in Fig. 2(d) where r, > r,. Finally at 0, > 9O%r, > r, as shown in Fig. 2(e). We emphasize that due to the complex interplay between the surface energetics and kinetics, the arrangement of atoms during the growth of a monolayer is not random but has the well-defined correlated behavior described above. The exact size of r,, and r, as a function of 0, will depend upon the precise growth conditions. For interfaces formed in (100) MBE growth, the surface microstructure is expected to be frozen in during the formation of the interfacial layer. Thus r,, r, and 6, will determine the interfacial quality when the growth mode is layer by layer. In the next section we discuss the effect of interface roughness on PL linewidths and also present the theory of excitonic effects in quantum wells. 3.

THEORETICAL

STUDIES

IN QUANTUM

WELLS

3.1 Theory of PL Linewidth As discussed above, if the interface is formed during a layer-by-layer growth mode, the interfacial cation layer will contain Ga islands (size ru) and Al I.Ga, ~, islands (size r,). These islands are expected to be distributed randomly at the interface layer. We denote the Ga islands by the symbol A and the Al,Ga, x islands by the symbol B. We will

also use the symbol A to denote Ga atoms and B to denote the entity Al,Ga, _ x which will be referred to as “atom” in these two islands. We will now derive an expression for the photoluminescence linewidth for any distribution of r,,, r, and 8,. To derive this expression, one needs to calculate the structural fluctuations seen by an exciton with a radius R,,. This is a simple problem of statistics and can be derived as follows: C,O, C,O = mean concentration of A and B type atoms (C,O = 0, ), respectively. n;, ng = mean number of atoms in A and B type clusters, respectively. NT, Ni = mean number of A and B type clusters, per unit area, respectively. 0j’, 0; = mean concentration of A and B type clusters (0; + 0; = l), respectively. NT0, = mean number of (A + B) clusters probed by the exciton. The same symbols without the superscript “’ denote the quantities representing fluctuations. One immediately sees that

Let P( NA, NR) denote the probability that over the exciton size, the number of A and B type clusters are NA and Na, (NA + NB = NT”,). It is then straightforward to show that [21]

P(N,,N,)

The corresponding

concentration

of A type atoms is

(3) resulting in a concentration ton probe size, sc,=c,-c,o=c~-c,.

fluctuation

over the exci-

(4)

A full width at half-maximum (FWHM) AC for the concentration distribution of eqn (2) can be determined numerically from eqns (3) and (4). However, on purely physical grounds it is easy to see the following properties of the distribution given by eqn (2). If r,, B r, and r, > R,, (corresponding to 0; - 0.0 and 19; - l.O), the exciton sees mostly flat and uniform interface and the concentration fluctuations are negligible leading to an FWHM which is quite narrow. This situation may correspond to Fig. 2(a) as well as to the inverse case shown in Fig. 2(e). Also if r, - r, and ru K R,,, the exciton will not be able to “see” the structural fluctuations at the interface. Thus under these conditions also, the FWHM of the distribution in eqn (2) will be narrow. With

218

K. K. BAJAJet ~1.

the growth taking place in the layer by layer mode, this may correspond to the case (c) of Fig. 2. On the other hand, if 0; - 0.2 (not neghgible) and Nf),, 1.0, i.e. average 2-D-island is comparable to exciton size, the exciton will see a full measure of the structural fluctuations and FWHM will be large. This is expected to correspond to the cases (b) and (d) of Fig. 2. From the above discussion it is clear that in the layer by layer growth mode the FWHM of the distribution given by eqn (2) may be narrow when Ci 0.0; c,o - 0.5 and C,o - 1.0. The FWHM of the concentration fluctuations discussed above have a direct impact on the excitonic linewidth as will be clear from the following discussion. A quantum well has two interfaces, each of which has a certain interface roughness. The two interfaces are expected to be independent in a statistical sense so that the total linewidth is a sum of the contributions from each interface. To calculate the linewidth we assume that one of the interfaces is perfect while the other has imperfections leading to a FWHM in concentration variations equal to AC. If W, is the well size for the perfect well and x, is the extra Al composition at the interface, then to the first order the effective well size is W(x,)=

ll-;.s

(5)

where 6 is a monolayer distance (= 2.83 A for GaAs) and x the Al composition in the barrier. The peak position of the excitonic lines will then correspond to the well size W( x,), and the linewidth will be 0(x,>

= AC(x,>

.AE( M/;,)

(6)

where A E( 4)) is the shift in exciton emission energy when the well size changes by a monolayer. Thus a( x, ) will exhibit the same behavior as a function of x, as AC. For interfaces formed by the layer by layer growth mode, it is thus conceivable that one will get sharplines(o(x,)~AE(W,))whenx,-O,orx,-x and broad lines (u(x,) - AE( &)) and x, - x/2 when these conditions are not met. In MQW structures as well as in single well structures x, can be expected to vary randomly from 0 to x over different regions of the interfaces. Thus the convoluted excitonic spectra may be expected to contain sharp lines (0 < A E( W,)) riding over a broad background ( - A E( I$&)). The separation of the sharp lines may be - AE/2( W,) according to the discussion presented above. Of course, if this is indeed the case in a given sample depends upon the growth conditions and whether or not the cluster distributions discussed above are present at the interface. 3.2 Excitons in Quantum Wells The study of the behavior of Wannier excitons in a quantum-well structure consisting of a single layer of GaAs sandwiched between two semi-infinite (gener-

ally greater than 100 A in practice) layers of Ga, x Al, As has attracted considerable attention in recent years. The conductionand the valence-band discontinuities at the interface between the two semiconductors at the r point were shown to be about 85% and 15%, respectively, of the total energy-bandgap difference [22]. More recent experimental work[23] suggests a value of 60% and 408, respectively, for these discontinuities. Owing to a reduction in symmetry along the axis of growth of this quantum-well structure and the presence of energy-band discontinuities, degeneracy of the valence band of GaAs is removed, leading to the formation of two exciton systems, namely, the heavy-hole exciton and the light-hole exciton. In this section we briefly review a calculation of the energy levels of heavy- and light-hole excitons associated with the lowest electron and hole subbands in this quantum-well structure for finite values of the potential barrier heights. This calculation was first done by Greene and his co-workers[24] who followed a variational approach and calculated the energy levels as a function of GaAs layer thickness for several different values of the potential barriers. Calculations for the case of an infinite potential barrier have been done by several groups and are referred to in [ll] and [24]. The Hamiltonian of an exciton associated with either the heavy-hole or the light-hole band in a GaAs slab sandwiched between two semi-infinite layers of Ga, _, Al, As grown along the (001) direction can be expressed (within the framework of an effective-mass approximation) using cylindrical coordinates as [25] H=

-A? I a a I a2 PapPG+T$ 2P, _[--

h* a2 ______ 2 ,$,,+ 2m i a2,?

12m, h2 a2

azj

Kw(z,>+ v,,.(Zh).

(7) Here m, is the effective mass of the conduction m k is electron, co is the static dielectric constant, the heavy ( + ) or light (-) hole mass along the z direction and p + is the reduced mass corresponding to heavy ( + ) or light (- ) hole bands in the plane perpendicular to the z-axis. Both p* and m + can be expressed in terms of well known KohnLuttinger[26] band parameters yi and y2 as[25]

(8) and

(9) where

m,

is the free-electron

mass. In these equa-

High-resolution

photoluminescence

tions the upper sign refers to the Jz = i 3/2 (heavy hole) band and the lower sign to the JL = k l/2 (light hole) band. The positions of the electron and the hole are designated by c and T,, respectively, and p, + and I are the relative electron-hole coordinates in the cylindrical coordinate system. In this expression for the Hamiltonian the same values for the conductionand the valence-band-mass parameters in GaAs and Ga, mXAl, As are used. In addition, the same values for the static dielectric constant in the two semiconductors are used, thus neglecting the effects of the image charges. For most practical quantum-well structures these should be good approximations as for most commonly used values of x these physical parameters are not too different in the two materials[27]. The potential wells for the conduction electron, Kw(ze) and for the holes, vh,,,(z,) are assumed to be square wells of width L

Kw(ze>=

(“; e,

Iz,I < L/2 IZeI’ L/2

(104

and

(lob) The values of V, and V, are determined from the Al concentration in Ga, _XAIX As,using the following recently proposed expression[27] for the total energy-band-gap discontinuity AEg = 1.155~ + 0.37~’ eV.

tion of the well-size L for three different values of the potential-barrier heights are displayed in Fig. 3. The values of the various physical parameters pertaining to GaAs[29] used in this calculation are m, = 0.067mo,c, = 12.5, yi = 7.36 and y2 = 2.57. The reduced mass associated with the heavy-hole band is smaller than that associated with the light-hole band. This is due to the anisotropic nature of the kinetic energy expression in the diagonal terms of Kohn-Luttinger Hamiltonian for an exciton [25]. There are several interesting features to be noted in Fig. 3. We find that for a given value of x, the value of E,,(h) increases as L is reduced until it reaches a maximum, and then drops quite rapidly. The value of L at which E,,(h) reaches a maximum is smaller for larger x. Essentially the same behavior is exhibited by E,,(I). The reason for this is quite simple. As L is reduced the exciton wave function is compressed in the quantum well leading to increased binding. However, beyond a certain value of L the spread of the exciton wave function into the surrounding Ga, -, Al,As layers becomes more important. This makes the binding energy go over to the Ga, _ x Al, As value for infinite thickness for that exciton system as L is reduced further. It should be pointed out that for a given value of x, E,,( /) is larger than E,,(h) for L greater than a certain critical value L, at which they become equal. For values below L,, E,,(I) is smaller than E,,(h). The value of L,., of course, depends on the magni-

I

(11)

\ \

The values of V, and Vh are assumed to be about 85 and 15% of AE,, respectively. An exact solution of the Schrodinger equation corresponding to the exciton Hamiltonian eqn (7) is clearly not possible. Greene et al. [24] therefore follow a variational approach and use the following form of the trial wave function #: ~+f,(z,)fh(zh)g(P,z,cp)

219

studies

\ \ \

1

I

I

I

~

HEAVY

HOLE

EXCITON

---

LIGHT

HOLE

EXCITON

I

I

(12)

where fr(z,) and f,,(zh) are the well-known groundstate solutions[28] for the finite square-well potentials, and the functions g( p, z, $J) describe the internal states of the exciton. To calculate the ground-state energy El of the Hamiltonian [eqn (7)], Greene et nf. [24] expand g(p, z, +) in terms of an appropriate basis set. The binding energy of the ground state of an exciton E,, is then obtained by subtracting El from the sum of the lowest electron and hole subband energies (E, + E,,). These subband energies are, of course, determined by numerically solving the well known transcendental equations[28] for finite square-wells. The binding energies of the excited states of an exciton are obtained in a similar fashion. The variation of the binding energy of the ground state of a heavy-hole exciton E,,(h) (solid lines) and a light-hole exciton E,.(I) (dashed lines) as a func-

Fig. 3. E13, of exciton size (L)

Variation of the binding energy of the ground state a heavy-hole exciton (solid lines) and light-hole (dashed lines) as a function of GaAs quantum-well for Al concentrations x = 0.15 and 0.3, and for an infinite potential well

K. K. BAJAJet ul.

220

tude of x; the larger x the smaller is the value of L, For x = 0.3, for instance, L,. = 50 A. The reason for this behavior is fairly easy to understand. The value of E,,(I) is greater than that of E,,(h) for large L. Both of them increase as L is reduced, E,,(I) less rapidly than E,,(h) as proportionally more of the light-hole exciton wave function tends to spill over into the surrounding Ga, _ x Al ~As layers thus reducing the increase in E,,(I). For a certain value of L, which depends on x, the two values become equal and then Els( I) becomes smaller as L is reduced further. This is in contrast to the behavior of E,,(h) and E,, (I) for infinite potential barriers where E,, (/) is always larger than E,,(h). It should be pointed out that Greene et ul. also did their calculations using the 60-40 rule for the band-edge discontinuities. The exciton binding energies were found to be rather insensitive (within 0.5 meV) to this change from 85-to-60% rule. For more details concerning this calculation the reader should consult [24]. Comparison of these results with the available experimental data has been done by Miller and Kleinman[ll]. 4. HIGH RESOLUTION PHOTOLUMINESCENCE STUDIES

In this section we briefly review some of our recent high-resolution photoluminescence measurements made on GaAs/GaAlAs quantum-well structures. 4.1 Experimental Details The samples used in this study were MQW structures which consisted 0 of Ga, 75Al, 25As barrier layers of thickness 100 A and GaAs well thicknesses vary ing from 87 A to 400 A. The total number of cycles varied from 20 in the thickest MQW to 50 in the thinnest wells. For the highest resolution photoluminescent measurements the samples were mounted in a strain-free manner on one end of a sample holder which was, in turn, immersed in the tip of a glass helium Dewar containing a superfluid liquid-He bath whose temperature was maintained below 2.1 K. For magnetic-field measurements the Dewar tip was inserted in the air gap of a conventional dc electromagnet the pole tips of which were separated by 5/16 in. The maximum field strength of this magnet was 45000 G. A krypton-ion laser was employed to pump the luminescence and spectral analysis of the photoluminescence was achieved with a modified Bausch & Lomb 4.m grating spectrograph, equipped with a large 10 cm square high-resolution diffraction grating ruled to 2160 grooves mm-’ and blazed at 5000 A to first order. This instrument is capable of producing a first-order reciprocal dispersion of approximately 0.54 A mm-’ in the intrinsic region of GaAs. The photoluminescence spectra were photographically recorded on Kodak type 1N spectroscopic plates. Wavelength calibration of the plates was achieved by nonlinearly interpolating the luminescence spectral lines with respect to well-known interferometrically measured neon spectral lines using

the grating equation, the known geometry of the instrument, and the dispersion of the grating. The photoluminescence for temperature and electric field dependent experiments was also excited 0 with the 6471 A line of a Kr ion laser. The excitation intensity used ranged from 0.015 to 1.5 W/cm’. For temperature-dependent measurements an excitation intensity of 3 X 10 ’ W/cm’ was usually used. The emission spectra were analyzed by a 1.26 m Spex spectrometer. A lock-in amplifier was used for the standard synchronous detection with a cooled RCA C31034 or RCA 7102 photomultiplier tube. The sample was mounted in a Janis variable-temperature (T = 2-300 K) optical dewar for temperature-dependent measurements and was directly immersed in liquid helium for the electric-field-dependent measurements. An electric field was applied perpendicular to the crystal-growth direction by using a Schottky-barrier configuration formed by evaporating a semi-transparent Au film (area - 2 X 10 ’ cm”). The average built-in field was estimated to be - lo4 V/cm and the space-charge-width - 1 pm. 4.2 High Resolution PL Results The excitonic transitions have been investigated in (MQW) structures as a function of well thickness. The samples used in this study were (MQW) structures which consisted of Ga,, 75Al, 25As barrier layers of thickness 100 A and GaAs well thickness of 100, 200. 300 and 400 A. The total number of cycles in the 300- and 400 A thick (MQW) samples was 20. whereas the 200 and 100 A MQW samples had 33 and 50 cycles, respectively. In general, the sharpest transitions are observed in those wells with the largest well thickness (L,); however, the heavy-hole donor bound exciton ( D”X) transition in the 100 A well was 0.2 meV FWHM. The photoluminescence for the 400 A well is shown in Fig. 4 as this structure exhibits all of the relevant transitions. In this sample both the light-and heavy-hole free excitons can be seen. Several extrinsic transitions are also observed: some of them occur in the same spectral region as some of the bulk GaAs transitions. The identification of the MQW transitions is aided by their diamagnetic shifts in a magnetic field. The GaAs transitions have larger diamagnetic shifts than the MQW transitions. The variations of the MQW transitions as a function of L, are shown in Fig. 5. It is seen that the free and bound excitons extrapolate to the analogous transitions in bulk GaAs. The light-hole free exciton is only observed in the 400 A well; the exciton energy is calculated for the other wells as described in Section 3. The free-to-bound transitions were all calculated using the following expression: E,Pl, =E,-E,P

+E,-E,,

(13)

transiwhere E,,, is the energy of the free-to-bound tion, EC is the electron subband energy, E,, is the

High-resolution

I51238

I51388

photoluminescence

I.51538

ENERGY

Fig. 4. Photoluminescence

spectrum

221

studies

I.51838

I.51688

I.51

(aV)

of GaA-Ga, 75A1,, 25As quantum-well size of 400 A.

hole subband energy, Z$ is the band gap, and Ez is the neutral-donor binding energy. The energies E,, E,, and Es are theoretical values from Greene and co-workers [24,30]. The appropriate values are taken for both the light-and-heavy-hole exciton and are plotted as the x’s in Fig. 5. The solid dots are the experimental values. The heavy-hole D”h is observed for all of the wells’ the light-hole D’h transitions come close to the heavy-hole free exciton transitions for the 400 and 300 A wells and occur on the high-energy-side of the heavy-hole free exciton for smaller L,. The remaining free-exciton and boundexciton transitions are appropriately labeled in Fig. 5. It should be pointed out that in the interpretation of the data it was assumed that the donor-impurity ion is located at the center of the well. It is known[31,32] that the binding energy of a donor depends on its location in the well. For donors located at the interface the binding energy is smaller by as much as 5 meV. The density of states per unit binding energy has a maximum for donors at the center and a smaller maximum at the interface [31,32]. The strongest transitions are therefore associated with donors at the center. The impurities observed in the above study were all residual impurities. The energy levels in the valence band of the quantum well are also modified. In bulk GaAs the lightand heavy-hole valence bands are degenerate at k = 0. The layered MQW structure reduces the cubic symmetry of bulk GaAs to uniaxial symmetry. The optical transitions thus become nondegenerate. The light-and heavy-hole free-exciton transitions were observed to split in an applied magnetic field. The light-hole transition showed a larger splitting than the heavy-hole transition. Assuming that the transitions are analogous to the nondegenerate semiconductor case, it would be expected that the lighthole exciton would split as the sum of the electron

structure

X-Calculated l -Experimental

‘bo

with GaAs

well

Points Points

II

200

WELL

300

THICKNESS

400

L,

6,

Fig. 5. Variations of the emission energies of free light-hole exciton (X,), free heavy-hole exciton (X,,), light-hole exciton bound to a neutral donor (D”X,), heavy-hole exciton bound to a neutral donor (Do, X,,), heavy-hole exciton bound to a neutral acceptor (AOX,,), neutral-donor-lighthole (DO/t,), and neutral-donor-heavy-hole (DO/t,,) transitions as a function of GaAs well thickness ( L,).

and hole g-values and the heavy-hole exciton would split as the difference of the electron and hole g-values. It is reasonable to assume that the electron g-value is essentially the same as the free-electron g-value in GaAs. With those assumptions a light-hole g-value of 1.3 and a heavy-hole g-value of 0.46 was obtained. The quality of the interface between two semiconducting layers in MQW structure is important to the performance of devices made from such structures. To gain a better understanding of these effects, electronic [33-351 and optical [8,36] properties associated with the interfaces have been studied. In one of the investigations[14] the low-temperature ( - 1.6 K) high-resolution photoluminescence

222

K. K.

ENERGY

BAJAJ

et ul.

(A’)

Fig. 6. Fine structure in the heavy-hole-free exciton transition for the various well sizes shown as well as fine structure in the heavy-hole-donor-bound exciton transition for the 115 A well. In the 115 A well the A series shows the fine structure for the free exciton transition and the B series shows the same structure for the donor-bound exciton transition.

(PL) properties of seven different MQW structures were studied. Transitions associated with both the heavy-hole free excitons and the heavy-hole-donorbound excitons were clearly observed. Each of the transitions exhibited fine structure. The observed linewidths were much narrower than had previously been reported, some as narrow as 0.1 meV, indicating excellent sample quality. The samples used in the study were grown by MBE, and consisted of MQW structures with seven GaAs/Al, 25Ga,,,SAs GaAs well thicknesses varying from 87 to 192 A. The barrier thicknesses were the same for all of the samples -100 A. The number of cycles varied from 50 in the narrowest wells to 33 in the widest wells. The PL spectra observed in the 108, 115 and 192 A wells are shown in Fig. 6. In MQW, if the energy shifts due to systematic fluctuations in the well size are appreciably greater than the photoluminescence linewidth, then the size fluctuation will result in multiple peaks. This is the case for the reported transitions, reflecting the very narrow linewidths that were observed. Four peaks separated in energy from each other by only 0.26 meV were observed in the heavyhole free exciton transition region for the 192 A well. The spectra for the 115 A well show additional structure, both the heavy-hole free exciton and the heavy-hole-donor-bound exciton transition show additional structure due to well size fluctuations. The energy separation between the peaks is approximately 0.5 meV. The calculated energy separation between adjacent peaks for one monolayer change in well thickness for this well size is 1.15 meV. The observed separation corresponds to an effective l/2 monolayer change in thickness. The PL spectra from

all seven of the MQW structures investigated showed line structure due to well size fluctuations. The structure in all of the samples corresponded to integral multiples of l/2 monolayer changes in well thickness. The calculated energy separations for a monolayer and half-monolayer fluctuations in well sizes for the seven different well thicknesses are given in Table 1. Also given are the experimentally observed values of the energy separations. All of the observed energy separations correlate quite well with an effective l/2 monolayer well size Auctuation. The origin of the narrow line widths and the l/2 half monolayer fluctuations have been discussed in previous sections. The quality of the interface is reflected in the sharpness of the optical transition, the sharper the transition the more perfect the interface as described in Section 3.

Table 1. Monolayer

and half-monolayer

fluctuation

energies

High-resolution

photoluminescence

I

I

I 1.5460

1.5460

ENERGY

223

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1.5500

I.!

(eV)

Fig. 7. Fine structure in the optical transitions for the 92 A MQW. The low intensity transitions are due to the heavy-hole-free-exciton, the higher intensity transitions are due to the heavy hole donor bound exciton

ENERGY

Fig. 8. High resolution

spectra

(eV)

from the 87 A MQW. The lines are broadened, still observed.

The PL spectra from a 92 A MQW is shown in Fig. 7. In this sample both the heavy-hole free exciton and the heavy-hole-donor-bound exciton are observed, as was the case for the 115 A MQW shown in Fig. 6. From these samples the binding energy of the heavy-hole exciton to the donor is determined to be 2.3 meV and 2.4 meV, respectively, which is qualitative agreement with the calculations of Kleinman [37]. The binding energy of the exciton to the donor in bulk GaAs is 1.3 meV. The PL spectra for the 87 A sample is shown in Fig. 8. In this sample the transitions are considerably broadened, reflecting a degraded quality of the interface. Structure can still be resolved from which one again obtains l/2 monolayer well size fluctuations.

however

fine structure

ia

These results clearly demonstrate the capability of optical characterization for analyzing heterostructure interfaces. 4.3 Temperature Dependent Efects An increase of the exciton binding energy due to the confinement of the carriers in MQW structures makes it possible to observe the excitomc structure even at room temperature in contrast with the case of bulk GaAs. As shown in Fig. 4 the MQW structures used in our experiment show very sharp optical transitions compared with earlier work. Thus, temperature-dependent measurements of the optical transitions were carried out. The analogous optical transitions observed in Fig. 4 are also present in the

224

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structures of L, = 100, 200 and 300 0A. Our discussion will be focused on the L, = 400 A well structure initially and then will be extended to narrower wells. The temperature-dependent photoluminescence spectra obtained in a 400 A well are shown in Fig. 9 with the proposed identification of each transition being listed. As temperature increases the emission intensity of the n = 1 light-hole exciton increases relative to the n = 1 heavy-hole exciton from 2 to 80 K, as shown in Fig. 9(b) and (c). With further increase of temperature, higher-energy emissions than the n = 1 light-hole exciton appear since the additional excitonic transitions become available with the higher-energy levels being thermally populated. Two weak structures in the higher-energy region are designated as Fi and F2 as shown in Fig. 9(c). (d) and (e). The transitions Xi,,, D”X,,, and PX,, remain as dominant radiative recombinations at T = 2-296 K whereas the emissions due to AoX,,, and D” h quench down at T = 30 K. The photoluminescence in the peak region at T = 80 K evidently consists of the superposition of the above three thermally broadened emissions. At T = 80 K, the X,, transition also contributes to the peak-region photoluminescence. However, the dominant contribution of the peak-region photoluminescence was found to come from the D’X,,, transition. Calculation was made in order to identify the transitions Fl and F2 with the consideration of the conduction-band and valence-band energy-gap discontinuities of 57-43% as well as the 85-15% rule[22,23]. The calculation shows that the transitions F, and F, can be identified as the so-called forbidden transrtion E,,,, (with E,,,) and EZ4,,, berespectively. Here, En,rih means the transitions tween the n th electron and rn th heavy-hole levels. It is assumed in the calculation that the exciton has the same binding energy for these transitions. Thus, the temperature-dependence of luminescence in the 400 k well shows that i) the peak-region luminescence at high temperatures consists of several thermally broadened optical transitions and that ii) the so-called forbidden transitions are strongly present over the allowed transitions. These characteristics were observed to be a general trend in narrower well structures. The 296 K photoluminescence charactere istics of the 100, 200, 300 and 400 A wells are shown in Fig. 10. The forbidden transitions are clearly shown in the 200 and 300 A well samples. The appearance of such forbidden transitions was discussed[38] in terms of significant mixing of light and heavy hole states away from the zone center. Consequently, our study differs from many previous investigations[39-421, where the double-peak structures in MQW were attributed to the n = 1 heavy and light-hole excitons. Another fact is that even the peak-region luminescence at T-80 K is not due to a single optical transition of the n = 1 heavy hole exciton but is due to the combination of several thermally broadened transitions. The peak-region

E

(eV)

(h) Fig. 9. Tempefature dependence of various transitions present in a 400 A well sample. In (d), (e) and (f) the peak-region photoluminescence consists of the superposition of the D”X,, and X,,. However, the transitions X,,, D”XIh, dominant contribution comes from the D”k’,, transition.

luminescence has a large contribution from transitions associated with n = 1 heavy-hole excitons bound to neutral donors and a considerably smaller contribution from transitions associated with n = 1 heavy-hole excitons. For instance, the peak-region luminescence of the 100 A well structure has contri-

High-resolution photoluminescence studies

225

/

E (ev)

Fig. 10. The 298 K photoluminescence characteristics of the wells of LL = 100, 200, 300 and 400 A. The peak-region photoluminescence consists mainly of transitions such as D”X,,, D”X,,, X,, and Xi,. Possible transitions corresponding to higher-energy structures than the peak are given.

butions associated with the n = 1 heavy hole exciton and the n = 1 heavy-hole exciton bound to a neutral donor. In the 200, 300 and 400 A well structures, even the n = 1 light-hole exciton contributes to the peak-region luminescence. A large contribution of the donor-bound-exciton complex at room temperature may be attributed to the several orders of magnitude larger oscillator strength[43] of the boundexciton transition compared to that of n = 1 heavyhole free exciton.

4.4 Electric Field Effect When an electric field is applied to bulk GaAs crystals, excitonic transitions quench at very low field strengths. However, this situation changes [44,45] drastically in MQW due to the confinement of electric carriers. Electric-field effects on the low temperature (4.2 K) photoluminescence of 200, 300 and 400 A well structures have been investigated. Details of our study will only be described for a 400 A well structure since the characteristics found in a 400 A well are generally observed in narrower wells. Figure 11 shows the effect of the electric field on the photoluminescence of a 400 A MQW. The photoluminescence characteristics of an as-grown sample were given in Fig. 4. The electric field in the well was varied by changing the applied bias V,,, of the Au electrode with respect to the %-doped GaAs substrate. A significant photovoltage was produced by

Fig.

11.

4.2 K photoluminescence spectra as a function of various applied biases for 400 A MQW sample.

the laser excitation. The most interesting result is the shift of the photoluminescence peak-energy position with the decrease of the applied bias V,,, (which corresponds to an increase of electric field). For V,,, from 0.91 to 0.55 V, the peak photoluminescence intensity shifts from the transition D”X,, to D’h and an additional photoluminescence feature appears on the lower energy side of D”h emission. With a further decrease of V,,, two broad bands A and B appear near 1.509 and 1.500 eV, respectively. The new peaks could be ascribed to the transitions of the n = 1 electron to neutral acceptors at the interfaces e-AD(I). Since the electric field tends to concentrate the electrons at the interfaces the field enhances the e-A”(I) over the e-A’(C) transition, the latter being the e-A” transition at the center of the well. The unique feature of the peak shift from one transition to another at the lower energy is a phenomenon common to all the wells studied for decreasing V,,, . Other interesting features in Fig. 11 concern the peak position of the emission and the decrease of overall photoluminescence intensity. The free and donor-bound excitons and D”h transitions do not show any discernible peak shift with a change of V,,, However, the e-A0 (I) transitions tend to show some shift to lower energies with a decrease of V&,. Mendez et a/.[441 observed a large peak shift of 30 meV/V under a negative bias for e-A” transition in MQW structures. However, in our case, the peak shift is less than 1 meV/V. The reason for this difference is not clear. A reduction of photoluminescence intensity by a factor of 300 is seen for the

226

K. K. BAJAJ et ~1.

transition. However, the presence of the free exciton is clear even at V,, = -2.0 V. A variational calculation of the excitonic emission energies in the presence of an electric field in these systems has recently been done by Brum and Bastard[46]. An impact-ionization mechanism is responsible [47] for the photoluminescence quenching of exciton transition in bulk GaAs. However, the quenching occurs at relatively low fields of l-5 V/m. In MQW the carrier confinement in the well is an important factor to be considered. The change in peak enhancement from intrinsic to lower energy emission with increasing field in our experiment may suggest that an impact-ionization mechanism is a favorable process in the well. The persistent presence of intrinsic emission at a high field of 104V/cm shows a feature due to the carrier confinement. D”X,,

5. CONCLUSIONS

Very sharp (0.2 meV FWHM) optical transitions have been observed in MQW structures. The very narrow linewidths are unique among published MQW transitions, reflecting the very high quality of these structures. The observed linewidths correlate with a theoretical model for the photoluminescence line shape due to the nonideal nature of the interfaces of a quantum well. Well-size fluctuations were observed in many of the MQW structures that were studied. It was concluded that the observed structure in the PL spectra is due to inter-layer rather than intra-layer fluctuations. The difference in well-size fluctuations that were observed correlate with an effective l/2 monolayer change in well thickness. In addition the observed narrow linewidths correlate very well with the model of the microscopic structure of the interfaces proposed here. These interfacial characteristics are very well explained on the basis of the theoretical model for MBE crystal growth in conjunction with the theoretical model for PL linewidths. The very narrow PL linewidths were helpful to the temperature dependence studies. The temperature dependent behavior for the intrinsic and near-intrinsic optical transitions in the MQW structures was determined. The position of the free and bound exciton transitions were determined as a function of electric field. As the electric field is increased the intensity shifts from the donor bound exciton to the free to bound transition D”h and additional PL features appear on the lower energy side of the D”h emission. REFERENCES 1. A. Y. Cho and J. R. Arthur, in Progress rn Solid State Chemistry, G. Somarjai and J. McCaldin, Eds., Vol. 10, p. 175, Pergamon, New York 1975. 2. R. Dinale. H. R. Stormer, A. C. Gossard, and W. Wiegm&n, Appl. Phys. Lett. 33, 655 (1978). 3. T. Mimura. K. Joshin. S. Hivamizu. K. Kikusaka. and M. Abe, Japan. J. Appl. Ph&. 20, L598 (1981). 4. C. E. Wood, in Ph_vsrcs of Thin Films, George Haas and M. H. Francombe. Eds., Vol. 11, p. 35, Academic, New York (1980). 5. See for example, articles published in Proceedings of the

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