Properties and electroluminescence of the GaAs1−xPx ternary system

2 PROPERTIES A N D E L E C T R O L U M I N E S C E N C E OF THE GaAsl-xPx T E R N A R Y SYSTEM M . GEORGE CRAFORD Monsanto Company, St. Louis, Missouri 63166

CONTENTS 1. Introduction

128

2. Energy Band Structure and Transport Properties

128

2.1. Basic energy band structure 2.2. Hall mobility 2.3. Hall carder concentration vs. total carrier concentration 3. Crystal Growth and p--n Junction Formation 3.1. Vapor phase epitaxial growth technique 3.2. Impurity incorporation 3.2.1. Selection of n-type impurities 3.2.2. Nitrogen doping 3.3. Zn diffusion of the p-n junction 4. Device Optimization

128 131 132 134 134 137 137 137 137 138

4.1. Device performance results 4.2. Discussion 4.2.1. Performance of GaAs vs. GaAso.6Po.4 4.2.2. Optimum diffusion profile 4.2.3. Optimum donor concentration and the effect of the direct-indirect transition 5. Electroluminescence as a Function of Alloy Composition 5.1. Electroluminescence at 77°K without nitrogen doping 5.2. Electroluminescence at 77°K with nitrogen doping 5.3. Electroluminescence at 300°K 6. Summary

138 142 142 143 145 147 147 153 157 163

127

128

M . G . CRAFOVO 1. INTRODUCTION

THE single-crystal form of the ternary alloy GaAsl _xPx has achieved commercial importance in the manufacture of light-emitting diodes. These light-emitting diodes (LED's) are used as discrete lamps and in a wide variety of alpha numeric and graphic display applications. At the present time GaAsl _xP~ crystal growth and device fabrication processes are more highly developed than those of competitive LED material and device processes. This has allowed GaAsl-xPx light-emitting diodes to dominate the mass-production oriented commercial market. Considerable research has been done on the crystal growth and device processing of GaAs1_xP~ since it was initiated in 1960 and reported in 1961-2.t1-1°) In general GaAsl_xP~ is grown epitaxially on GaAs or GaP single-crystal substrates by a chemical vapor deposition process. The commercially available GaAsl_~P~ epitaxial wafers are large (up to 3 in2), single crystal, and suitable for planar processing, t 11.12) The formation of the light-emitting p--n junction is accomplished by means of a Zn diffusion. The binary compounds, GaAs and particularly GaP, have been extensively discussed in the literature and a number of review articles have been written concerning them. o 3,,4~ These compounds will not be discussed here except as is necessary to identify and understand the electron-hole recombination mechanisms in the GaAs,_~P~ ternary alloys. It will be shown that the GaAs,_~Px ternary system is well behaved in the sense that the radiative mechanisms can be readily correlated with those of GaAs for alloy compositions in the direct energy bandgap region, x < 0.49 at 300°K, and with GaP for alloy compositions in the indirect energy bandgap region, x > 0.49. The energy bandgap, which determines the color of the emitted radiation, increases from 1.44 eV in GaAs, which yields infrared emission with a peak wavelength of 9000/~, to 1.91 eV for x ~ 0.4 which yields red emission with a peak wavelength of 6500 ,~. It is this alloy composition which yields maximum brightness diodes/~ 5) and is widely used commercially to fabricate red emitting LED's. For x > 0.4 the energy bandgap continues to increase, reaching a value of 2.26 eV in GaP which yields ~ 5600 A green emission. Within the past year the isoelectronic impurity nitrogen has been introduced into GaAs,_~P~, diodes and has been found to yield a marked improvement in the device eflficiencyfor x > 0.49. t16) This has resulted in the commercial availability of yellow and green LED's in addition to the conventional red devices. In this review, the vapor phase growth technique and some of the properties of epitaxial GaAsl _~Px wafers, which are relevant to electroluminescence, will be described. Following this the optimization of material and fabrication parameters necessary to yield high device performance will be discussed. Finally, the recombination mechanisms responsible for electroluminescence (EL) in the GaAs, _ ~P~ devices and the resulting device performance as a function of alloy composition will be described.

2. ENERGY BAND STRUCTURE AND TRANSPORT PROPERTIES

2.1. Basic Energy Band Structure In this section, only the lowest energy direct and indirect energy gaps which are relevant to electrolumineseence in the GaAst -~Px alloys are discussed. For a more complete description of the band structure the reader is referred to refs. 17 and 18.

Properties and electroluminescence of the GaAst -xPx ternary system

129

The GaAst_xP, alloys are direct energy gap semiconductors for alloy compositions x < xc, and indirect for alloy compositions x > x~, where xc is the composition where the direct and indirect minima become equal in energy, t 19) At temperatures of 300°K and 77°K, x~ = 0.49 and 0.46 respectively.(2°) A schematic diagram of the energy band structure for direct and indirect energy gap GaAst_xP~ is shown in Fig. 1. Figure l(a) shows the band structure for alloys in the direct bandgap region where the energy of the direct minimum E r is less than the energy of the indirect minima, Ex. The position of the conduction band, E o and the valence band, Ev, are shown as a function of momentum, k. The position of the donor, ED and acceptor, E A, levels are shown with donor levels indicated beneath both the direct and the indirect minima. The binding energy of the donor beneath the direct minimum is typically ~ 6 meV, (2z) whereas the binding energy of the donor beneath the indirect minima is typically ~ 100 meV/TM The larger binding energy associated with the indirect

E

E Er
Er>Ex

EC

~

E Er>Ex

Er

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Er

l )'-t-' V - -I E X E I

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Direct

Indirect

Indirect with N

(o)

(b)

(c)

)K

FIG. I. Schematic energy band structure for GaAs~-xPx. minima is due to the large conductivity effective mass of these minima m f f = 0.31 mo, (1 s) as compared to the effective mass for the direct minimum which is ml* = 0.065 m o in GaAs. T M The mass m* increases as a function of alloy composition according to the relationship ml* ,,~ 0.065 rn0(1 +?x) (1) where 7 is of the order of 0.5 and mo is the free electron mass. (z3) As the alloy composition is increased beyond xc the energy of the indirect minima becomes lower than the direct minimum. The energy band diagram for alloy compositions in the indirect bandgap region is shown in Fig. l(b). The EL efficiency is generally much lower for alloy compositions in the indirect energy gap region than for direct energy gap alloys due to momentum conservation requirements. ( ~4) The momentum of the emitted photon is nearly zero. Thus only vertical transitions from the

130

M . G . CRAFORD

conduction band to the valence band are allowed since the momentum of the electron and hole must be equal to the momentum of the photon. The majority of electrons will be located at the lowest energy position of the conduction band and the majority of holes will be located at the maximum energy position of the valence band. Thus, in direct bandgap alloys the electrons will be located directly above the holes and the recombination can proceed with momentum conserved. In indirect alloys, however, the electrons will be located at Ex with momentum kx in the (100) direction in momentum space. In order for a radiative transition to occur, an impurity or a phonon must become involved in order for momentum to be conserved. These "three-particle" processes are generally less probable than the simpler "two-particle" electron-hole recombination with the result that indirect alloys usually have much lower EL efficiency.(14) When nitrogen is added to the crystal, the situation is changed and efficient radiative recombination associated with the nitrogen states dominates the EL emission. Thus in Fig. l(c), where we have shown an indirect bandgap alloy with heavy nitrogen doping, we have omitted the donor and acceptor levels since for material of this type they do not contribute appreciably to the luminescence. The nitrogen level, shown in Fig. l(c), is drawn differently than the donor and acceptor levels shown in Fig. l(a) and (b). This is done in order to indicate the unique character of the nitrogen recombination center. The normal donor and acceptor levels, in which the electrons and holes are bound by long-range Coulombic forces, are widely distributed in real space and are therefore shown as localized in k space. The nitrogen atom, on the other hand, is an isoelectronic impurity which contributes no net charge to the crystal and does not bind a carrier by coulombic binding as does a donor or acceptor, t24'25) Instead the nitrogen atom traps an electron due to the difference in electronegativity between the nitrogen atom and the host phosphorous atom it replaces. (24'25) The potential energy "well" associated with the nitrogen atom has an extremely short range. Thus an electron bound at the nitrogen atom is highly localized in real space and, as a consequence of the Heisenberg uncertainty principal, is widely distributed in momentum or k space. Furthermore, due to the proximity of the Er conduction band minimum there is a relatively high probability that an electron bound at a nitrogen atom will be located at k ~ 0 in momentum space as indicated by the shaded region beneath the direct conduction band minimum in Fig. l(c). (26~ When AE decreases, the probability that an electron trapped at a nitrogen atom will be located at k ~ 0 increases, since AE appears in the denominator of the matrix element for the radiative transition. (25) Thus the efficiency of radiative transitions associated with the nitrogen centers is expected to be a maximum for alloy compositions near x c. A summary of the energies of the direct and indirect energy bandgaps for GaAst_xPx as a function of alloy composition as well as the composition of the direct-indirect transitions at 300°K and 77°K is shown in Table 1. The position of the direct energy bandgap at 300°K was taken from the electroreflectance data of Thompson e t aL (17) The position of the direct bandgap at 77°K was obtained by adjusting the 300°K electroreflectance data as described in ref. 15. The position of the indirect energy bandgap has been determined by means of the electroluminescence spectra, (2°~ and will be discussed in Section 5. Two equations are given for the indirect bandgap corresponding to two different end points in GaAs. Balslev(27) found that AE(0) = 0.43 at 77°K. More recently Onton (2a) has determined AE(0) to be 0.467 at 6°K. It is assumed in Table 1 that AE(0) is temperature independent. Onton has also measured the position of Ex as a function of alloy composition at 6°K and his results, when corrected to 77°K, are in reasonable agreement with the data

Properties and electroluminescence of the GaAsl_xPx ternary system

131

TABLE1. SU~t~RY of ENERGY BANDGAPPARAMETERSFOR GaAs l_xpx T = 300°K

T = 77°K

Direct energy bandgap (Er)

1.44+ 1.091x+0.210xz

1.51 + 1.153x+0.210x2

Indirect energy bandgap ( E x )

1.923+0.099x+0.241x 2ta) 1.87 +0.248x+0.143x2tb)

1.993 +0.099x+0.241x 2~') 1.94+0.248X+0.143X2tb~

Separation AE = Ex- Er

0.483 -0.992x+0.031x 2ta) 0.43 -0.843x-O.O67x ztb)

0.483 - 1.054x+0.031x2<~ 0.43 - 0.905x-0.067x 2tb)

0.49

0.46

Direct-indirect transition (xc) <")Assumes AE in GaAs = 0.483.t2s)

tu) Assumes AE in GaAs = 0.43.t27>

obtained from the EL spectra, t2 o) The position of Ex as a function of alloy composition has also been recently studied at 4.2°K by Pikhtin e t a / . t29) In that work the data extrapolate to AE(0) < 0.375, a value significantly smaller than the values obtained by Balslev t2~) and Onton.t 2s

2.2. Hall Mobility The Hall mobility as a function of alloy composition for GaAs t -~Px samples with low donor concentrations, n __<2 x 1016/cm3, has been determined by Tietgen and Weisberg, ~3o~ Groves,Ca 1) and Stewart, whose unpublished data are cited by Lees. (32) It can be seen that the mobility decreases from ,,~7000 cm2/V-sec in GaAs to ~ 3000 cm2/V-sec for x = 0.3. Likewise in the indirect bandgap region the mobility decreases from ,,, 190 cm2/V-sec in GaP to ~ 100 cm2/V-sec for x = 0.55. Between x = 0.3 and x = 0.55 there is a sharp drop in the mobility which is due to the transition from a direct to an indirect semiconductor. The mobility is high for alloy compositions where x < 0.30 since the energy gap is direct and the conduction band effective mass is relatively small, similar to GaAs. The mobility is lower for alloys with x > 0.49 since these alloys have a larger effective mass and the low mobility characteristic of GaP. For alloy compositions 0.3 < x < 0.49, AE, the separation between the direct and indirect conduction band minima becomes comparable to the thermal energy, k T . As a result an increasing number of electrons are transferred into the indirect minima. If the validity of Boltzmann statistics and a simple two-band model are assumed, the fraction of electrons which remain in the direct minimum can be expressed: n1 f = n 1 + n-----2-

1 1 + N2/NI exp(- AE/kT)'

(2)

where n I and n 2 are the electron concentrations in the direct and indirect minima, respectively, and N 2 / N 1 is the density of states ratio which is proportional to (m'~a/rn*a) a/z, where m*d and m~'d are the density of states effective masses for the direct and indirect minima respectively. The density of states effective mass for the indirect minima is a function of the number of equivalent indirect minima which may be 3 or 6 depending upon whether the minima are located at, or inside, the edge of the first Brillouin zone respectively, ta3) As a consequence, estimates of m~'a range from 0.85 mo (33) to 1.25 mo° s) resulting in density of

132

M . G . Cv.AronD

states ratios of from 45(1 +yx)- 3/2 to 84(1 +yx)- 3/2 where m~d is taken from eq. (1). When two types of carriers are involved in the conduction process the mobility can be written:

I-t. = nxl~ +n2#~ = (1~1'~f(b 2-1)+ 1 nl/-q +n2/~2 ~ b ] ' f ( b - 1) + I

(3)

w h e r e / h and ~/2 are the mobilities in the direct and indirect conduction bands and b = p~//z 2. The mobility ratio is generally taken to be ~30, as a result of comparing the mobilities in GaAs and GaP. However, if a transition from 3 to 6 equivalent minima occurs in the vicinity of the direct-indirect transition, the actual mobility ratio may be ,~ 10:3 a. a 4) In any case, the sharp drop in mobility between x = 0.3 and x = 0.49 is expected based on eqs. (2) and (3). However, the decrease in mobility between x = 0 and x = 0.3 exceeds the decrease expected due to the increasing effective mass, (a2) and the increase between x = 0.5 and x = 1.0 is totally unaccounted for on the basis of the simple two-band model. Other mechanisms such as alloy scattering must be considered. However, it has been estimated by Tietjen and Wiesberg (a o) that, due to the relatively small values of the effective mass, alloy scattering is expected to contribute only a ~ l0 ~o reduction in mobility between x = 0 and x = 0.3. It can similarly be shown that only a ~50~o reduction between x = 0.5 and x = 1.0 would be expected. Thus in order to account for the data an additional scattering mechanism is required. It has been suggested that clustering of As and p atoms which is not taken into account by the basic alloy scattering theory may account for the additional variation in mobility. ( a o) Recent carrier lifetime measurements (a 0a) indicate the presence of residual defects that are assumed also to be A s P clusters. The Hall mobility obtained by Groves (a ~) for samples with a variety of carrier concentrations is shown in Fig. 2(b). It can be seen that the mobility for the more heavily doped samples decreases more rapidly with increasing carrier concentration than does the mobility of the lightly doped samples. This can, in part, be attributed to the fact that in the case of the heavily doped samples band filling occurs in the low effective mass direct minimum, with the result that the Fermi level is pushed up into the conduction band causing an increased number of electrons to transfer into the low mobility indirect minima. ( ~o) In order to obtain Hall mobility data such as that shown in Fig. 2 it is necessary to grow epitaxial layers which are thick enough to allow the substrates and graded region to be removed. If Hall measurements are carried out on samples in which the graded region has not been removed a significant error in the measured Hall mobility can result. This is a result of the fact that the mobility in the graded region, particularly in the region near the GaAs substrate, is high, whereas the mobility in the constant composition region, particularly for alloy compositions x > 0.4, is low. The resulting measurement error is a function of layer thickness and alloy composition. For thick layers with small x the error is small, but for thin layers with large x a large error can result. 2.3. Hall Carrier Concentration vs. Total Carrier Concentration The carrier concentrations of the samples shown in Fig. 2 were determined by Hall measurements and for alloy compositions near the direct-indirect transition are not the total carrier concentrations in the crystal. The total carrier concentration is the sum of the carrier concentrations in the direct and the indirect minima na +n2. However, the carrier concentration, nn, measured via a Hall measurement, is an "effective" carrier concentration

104

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134

M . G . CgAFOgD

which from eqn. (2) can be expressed as a function of n 1 and t/2 by the equation:

__= = ~ nlb2 +n2 q 1 - e R n = epl~n ](nlb+n2)~ j • nH

(4)

The ratio of the total carrier concentration, nr, to the concentration as determined by Hall measurements can be written:

nr F(nlb2+n2)(nl+n2!l f(b2-1)+l n==~= k (ntb +n2) 2 J = [j ( b - I) + I] ~"

(5)

Thus we see that when f = I or 0, which is the case for alloy compositions far from the direct-indirect transition, nr/nH = I as expected. However, near the transition, where f = I/(b+ I), the ratio nr/n n reaches a maximum of (b+ I)2/4b. Thus, according to this simple model, the Hall carrier concentration could be in error by a factor of 8 assuming b = 30. In reality, of course, the situation is much more complicated and such factors as the effect of donor levels associated with the indirect minima must be considered. (3s) As a result the observed disparity between Hall measurements and the total carrier concen= tration is typically a factor of 3. (36) Since alloy compositions in the vicinity of x = 0,4 are widely used for red=emitting GaAs1_xP~ diodes, one must specify the measurement technique when discussing carrier concentration. For materials in this alloy composition region capacitance-voltage measure= ments and avalanche breakdown measurements give a measurement of the total carrier concentration, whereas Hall measurements give the effective concentration which may be a factor of several times lower. 3. CRYSTAL GROWTH AND p-n JUNCTION FORMATION

3.1. Vapor Phase Epitaxial Growth Technique A variety of closed tube and open tube techniques have been reported for the growth of GaAs 1_xpx.(2-7,9,11,12) Open tube techniques are used almost exclusively today since they are more versatile and they allow precise control of the relevant growth parameters. Furthermore, it has been possible to scale up the open tube chemical vapor deposition process into large reactors capable of producing commercial quantities of single crystal GaAs I _xPx.( 1i, t 2) The basic GaAs 1_~Px growth process involves: (I) the transport of Ga by means of a reaction with a suitable transport agent, generally HCl, (2) the addition of As and P in the form of gaseous hydrides or chlorides, (3) the addition of the desired dopant gas, and (4) de= position on a suitable substrate in the form of the single crystal epitaxial layer. The most widely used growth method is illustrated in Fig. 3 which shows a schematic diagram of a vertical multi=wafer reactor of the type used for the commercial production of GaASl _~P, epitaxial layers. Phosphorus and arsenic in the form of PH 3 and AsH3 diluted with hydrogen are added to the reaction zone of the reactor along with the desired dopant gas. If the dopant is Se, S, or Te, the dopant gas can be H2Se, H2S, or diethyl telluride, respectively. A mixture of HCI and H2 is introduced into the Ga reservoir section of the reactor in order to form gallium chloride and is swept into the reaction zone of the reactor by a second stream of hydrogen. The mixed gases then pass into the deposition zone of the reactor which houses an octagonal quartz pyramid which supports the GaAs substrates.

.~

PH:~+ A=Ha+ Hz + DOPANT H z + HCI

'~H z

FURNACE ZONE I

Ga RESERVOIR

/~

ZONE 2 - -

///

,/

ZONE~ I

~

ZONE 4

~

S/

ROTATING WAFER HOLDER ~

REACTOR SEAL (SS.)

.... VENT

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i i i i!~i,i!i i ,li i i i,~,;:,i,;i ',', ~i,~,:,i,, ~i~i!i~i:iii~i~ii~,i,i!~,!,iii!i!~ii i ~i~i~i i i i~i!~!i!i !i~i i !!!!~i~i i i !~i~i i~i!!ii~i ~:~:~:~;~~ .......

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iilii, !!,~ii~!!i!!!i

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,

FIG. 4. Photograph of a G a A s j - ~ P x epitaxial wafer. The area of the wafer is ~ 3 in 2. A reflection of the camera can be seen in the surface of the wafer. (The wafer was provided by J. W. Burd.)

Properties and electroluminescence of the GaASl_xP~ ternary system

135

The substrate temperature is typically 800--825°C and growth rates of ~ 1 micron per minute are typically obtained for GaAs. (11) The growth rate generally decreases with increasing phosphorus concentrations, and for x = 0.4, the composition used for GaAsx_xP~ light emitting diodes, the growth rate is typically only 0.4 micron per minute. However, even for a given As/P ratio, the growth rate as well as the alloy composition are dependent upon other growth parameters such as the deposition temperature. (aT) The reactor shown in Fig. 3 was designed to accommodate eight 20-mm diameter substrates.(11) Modifications in the reactor system, coupled with the development of larger area GaAs substrates, have resulted in a greatly increased capacity for the modern vapor phase epitaxial reactors used to produce commercial quantities of GaASl_~P~. A wafer which illustrates the size and surface quality of commercial GaASl _xP~ wafers is shown in Fig. 4. The diameter of the wafer is greater than 2 in. as can be seen by comparison with the ruler, and the area is greater than ,,~3 in2. (a s) The surface quality of the wafer is satisfactory for ~20/=m

GoAsI,..xP x : N,Te

T •~ IOOvm

GoAsj_xP X : Te

N25prn GoAsI_xPx :Te (X Vorioble)

T ,-,~OOFm

1

GoAs or

GoP

CONSTANT COMPOSITION GoAsI_xPX EPITAXIAL LAYER

~

t

GRADED ALLOY COMPOSITION EPI LAYER

/ BULK SINGLE I" CRYSTAL SUBSTRATE

!

J

Fio. 5. Schematic cross-sectional view of a typical GaAsl -xPx epitaxial structure.

the use of planar impurity-diffusion processing similar to that used in the conventional silicon technology. The layer thickness uniformity is typically constant to within ~ 10 ~o and the alloy composition is constant to within ~ 1 ~ across the surface of the wafers. (11) The cross-hatch pattern which is visible on the surface of the wafer shown in Fig. 4 is typical of GaAsl _xPx wafers and is believed to be due to an array of misfit dislocations which are formed during the growth of the initial graded alloy composition portion of the epitaxial layer.(39-42) A typical composition profile of GaAsP epitaxial layer is shown in Fig. 5. The graded region, in which the alloy composition is continuously graded from x = 0 or x = 1.0, depending upon the substrate material, to the final desired alloy composition, typically has a thickness of 25 microns, and the final constant composition layer typically has a thickness of 75-125 microns. It is necessary to grow the graded region to reduce strains and crystal imperfections due to lattice mismatch between the GaASl _xP~ layer and the substrate. (a 9) The dislocation density in the grown layer is believed to be proportional to the maximum

136

M . G . CXAFORD

alloy composition gradient in the graded region, t4°) Thus, if the graded region is too thin and hence too steeply graded, a high dislocation density in the constant composition layer will result. It has been found that layers of this type have low luminescence efficiency,ta9'.1'.2) The epitaxial layers are generally grown on GaAs wafers with a (100) crystallographic orientation since this orientation has been found to result in relatively low background impurity concentrations, t43~ and, further, since the cleavage planes are in the 110 direction, the wafers are easily scribed or diced into square or rectangular chips. When alloy compositions with x > 0.5 are desired, GaP is generally used as the substrate instead of GaAs. ~~6~ For alloys with x > 0.5 it has been found that the luminescence efficiency is greatly enhanced by the addition of nitrogen doping. ~16) This can be accomplished by the addition of ammonia to the dopant gas shown in Fig. 3. The ammonia is generally added only during the growth of the last ,~ 20 microns of the epitaxial layer, as shown in Fig. 5. The nitrogen doping is restricted to the relatively thin surface re#on in order to minimize internal reabsorption in the crystal since, in addition to efficiently generating the light, the nitrogen atoms also strongly absorb the light. ~24~ TABLE2. IMPURITIES IN

A TYPICAL G a A s l _ x P x SAMPLE BY MASS SPECTROMETRY(4*)

Elements

ppm atomic

C N Si S ci

1.I 0.2 0.9 0.04 0.04 0.05 0.06

K

0.03

O A1

Ca Fe Cr

0.03 <0.01 < 0.01

The growth technique described here yields epitaxial layers with typical dislocation densities of 104-10 5 cm-2. The crystals are of high purity as indicated in Table 2 where the trace impurities in parts per million are shown for a typical GaAsl -xPx layer. ~44~The crystal purity is a critical parameter in the growth of these layers since significant trace concentrations of certain impurities can result in poor device performance. Copper and oxygen, in particular, are undesirable. These impurities are believed to give rise to a low-energy infrared emission band and to reduce the intensity of the near band edge red emission in GaAst _xP~ devices. (s) In addition to minimizing undesirable background impurities, the crystal growth conditions must be adjusted to minimize native defects. For example, it has been suggested by Stewart (45) that Ga vacancies and Ga vacancy-donor complexes give rise to an infrared emission band, occurring at ,,~ 1.3 eV, and reduce the near band edge emission. The vacancy concentration can be reduced by increasing the Ga to group V ratio in the gas from which the crystals are grown. (45)

Properties and electroluminescence of the GaAst_xP x ternary system 3.2.

137

Impurity Incorporation

3.2.1. Selection of n-type impurities. Since none of the available n-type impurities can be readily diffused into the crystal, due to their low diffusion coefficients and tendency to react with the crystal, the epitaxial layers must be grown with the desired concentrations of n-type impurities. The three n-type impurities which have been most widely used in the GaAs 1-xPx system are the group VI elements Te, Se, and S. The group IV elements Si, Ge, and Sn have been used extensively in GaAs. However, attempts to use these elements in the growth of GaAs I _ ~P~ alloys have generally resulted in compensated layers which yielded low-efficiency devices. (46) The use of S as a dopant in GaAsl_~P~ has also been restricted although S is widely used in GaAs, and in GaP has been reported by Logan et al. to be the preferred dopant for the fabrication of high brightness emitters.(47~ For GaAsl_ xP~ alloy compositions near x = 0.4, the alloy composition most widely used in the fabrication of light emitting diodes, S exhibits undesirable properties. Trap states, apparently associated with the higher energy indirect minima, have a strong effect on the electrical transport and device properties of GaAsl_~Px for alloy compositions x > 0.3. (35,48) The properties of these trap states associated with S have been studied as a function of temperature and pressure. (35) The states do not appear to be strongly dependent either upon growth technique or on sulfur concentrations since similar effects on the electrical transport properties have been observed in closed-tube vapor transport-grown crystals with sulfur concentrations of ~ 1018/cm2~a5) and in open tube vapor transport crystals with carrier concentrations of ~ 1016/cm3.(49~ As a result of the difficulties associated with S and the group IV elements, Se and Te have been used almost exclusively in the growth of GaAs l_xPx crystals for light-emitting diode applications. These two elements have similar properties with regard to EL efficiency,c15) 3.2.2. Nitrogen doping. The fabrication of high-efficiency emitters for alloy compositions in the indirect bandgap regions, x > 0.49, requires the addition of nitrogen as discussed in Section 2.1. Nitrogen is incorporated into the lattice substitutionally for the group V elements. Since nitrogen is also a group V element it is an isoelectronic impurity and has no effect on the density of free carriers. The function of the nitrogen is to introduce into the crystal an efficient center for radiative recombination. It has been known for several years that nitrogen introduces efficient radiative recombination centers in GaP t 24,47) but only recently was discovered to work equally well in the GaAsl_xPx alloy system. (16~ Nitrogen, like the group VI donor elements Te and Se, cannot readily be diffused into GaAs l_~Px and must be incorporated into the crystal during the growth of the epitaxial layer. 3.3.

Zn Diffusion of the p-n Junction

The p--n junction is formed by the in-diffusion of a group II acceptor impurity into the crystal. Zn has been used almost exclusively in the fabrication of LED's since it is inexpensive, easy to handle, and has a large diffusion coefficient in GaAs t_xP~. Junctions suitable for the fabrication of light-emitting diodes can be diffused in less than an hour at temperatures in the vicinity of 800-900°C. Both dosed-tube and open-tube diffusions have been employed for LED fabrication.t ~6,50) In the case of a closed-tube diffusion the diffusion source, which might be Zn, ZnAs2, ZnP2, or Zn diluted in Ga, is placed in a quartz ampoule along with the wafers to be diffused. The ampoule is then evacuated, sealed, and placed in

138

M . G . CRAFORD

the diffusion furnace. In the case of an open-tube diffusion the crystals are placed into a diffusion tube and gas with the desired concentration of Zn is allowed to flow over the crystal during the diffusion.(5 o) Alternatively an open-tube diffusion can be carried out by coating the crystal with zinc doped film and placing the crystal thus coated into the diffusion furnace. (51) A closed-tube diffusion with ZnAs 2 as a source has been widely used to fabricate fight-emitting diodes in GaAs and GaAs l_xP,,.(16) When the proper diffusion time and temperature are used, this technique results in high performance devices. However, a disadvantage of this technique is that, during the diffusion, an optically absorptive surface layer is developed on the crystal. This surface layer must be removed by chemical etching techniques before high-performance devices can be fabricated. The etching step is critical since the device performance is a strong function of the etch duration. Insufficient etching results in low device efficiency due to excessive internal absorption in the heavily doped p+ surface skin. Excess etching causes a thin p-type layer with a high sheet resistivity which results in current crowding and nonuniform brightness across the surface of the finished device. Improved diffusions have been developed which involve diffusion through a modulating oxide film. Typically a SiO2 film ,~2000 tlt thick is placed on the surface of the crystal prior to the diffusion. The film serves both to reduce the Zn surface concentration, thus minimizing internal absorption, and to prevent the out diffusion of As which damages the crystal surface. The open tube Zn diffusion, recently reported by Shih and Blum, (5°) involves a 1-hour diffusion at 800°C through a 2000 ,/~ SiO 2 film. This diffusion reportedly yields devices with performance equivalent to that obtained by the ZnAs2 diffusion technique, but requires no post-diffusion etching of the surface.

4. DEVICE OPTIMIZATION 4.1. Device Performance Results In order to fabricate devices with the maximum external quantum efficiency and brightness, it is necessary to maximize the internal quantum efficiency, the ratio of photons generated within the device to electrons injected into the device, and to design the device epitaxial layer geometry and device package so that the maximum number of photons are extracted from the device. We will be primarily concerned here with the maximization of the internal quantum efficiency. Assuming that the concentrations of crystal defects and unintentional background impurities remain constant, the internal quantum efficiency will be a function of donor concentration, Zn diffusion profile, and alloy composition. In this discussion we will be mainly concerned with the standard GaAs0.ePo.( lightemitting diode without nitrogen doping. Devices of this type have a peak emission wavelength of approximately 6500 A and are in the direct energy bandgap region. The external quantum efficiency as a function of donor concentration is shown in Fig. 6. For devices fabricated by means of a ZnAs 2 diffusion the peak efficiencies are obtained for donor concentrations from 1016/cm3 to 1017/cm3 where n is determined by Hall measurements.(15) The actual carrier concentration according to capacitance-voltage measurements could be ,,~3 times higher as discussed in Section 2.3. The optimum junction profile has been found to be an abrupt junction with a junction depth of ~1-2/1m. (15) The optimum donor concentration for vapor-grown junctions obtained by Nuese et aL is also shown in Fig. 6. (52) In this case the optimum donor con-

Properties and electroluminescence of the GaAsl_xPx ternary system

139

centration is ~ 3 x 101 s. However, for the grown junctions the acceptor concentration on the p-type side of the junction was fixed at ~ 3 x 10 s 9/cm3. This high acceptor concentration in the immediate vicinity of the junction may explain the fact that the observed optimum donor concentration is ~ 3 x l0 s S/cm3 instead of ~ l0 s T/cm3 as found for diffused junctions. Hole injection into the n-type region may prevail for lower donor concentrations, as suggested by Nuese et al., (52) and the data can be explained if we assume that the hole injection is largely nonradiative or that the luminescence resulting from hole injection is reabsorbed internally since it is high-energy emission corresponding to bandgap energies.

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In the case of diffused junctions the hole concentration in the immediate vicinity of the junction is roughly equivalent to the donor concentration, but it increases sharply as one moves further from the junction. Thus the hole concentration within a diffusion length of the junction for the diffused junctions may be lower than for the grown junctions shown in Fig. 6. Heath and Stewart(Sa) performed cathodoluminescence measurements on GaAsx_xP x samples and found, as shown in Fig. 7, that in the case of cathodoluminescence the efficiency

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Properties and electroluminescence of the GaAs~_xPx ternary system

141

continued to increase with increasing donor concentrations to concentrations of > 5 + 1017[ cm a. This behavior is similar to that observed in GaAs by Cusano. (s 4) However, Heath and Stewart found, in reasonable agreement with Fig. 6, that the EL efficiency was optimized for n ~ 101 ?/cm a. Neither the observed decrease in device quantum efficiency with increasing donor concentrations nor the difference in behavior between the EL and cathodoluminescence efficiency are fully understood. However, the cathodoluminescence measurements I000

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were carried out on n-type samples, whereas in the case of EL the recombination is believed to occur largely in the p-type region. Consequently, one might expect significant differences between the behavior of EL and cathodoluminescence. The efficiency as a function of alloy composition for diodes with donor concentrations of n =< 2 x l0 t 7/cm3 and with donor concentrations of 2 - 3 x 1018/cm3 is shown in Fig. 8. It can be seen that the heavily doped diodes, which were diffused and heat treated so as to

142

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have graded junctions, are more efficient for GaAs, (x -- 0), with external efficiencies o f ~ 2 ~o. However, with increasing x the efficiency drops sharply so that for x --- 0.4 external quantum efficiencies of only ~ 0.05 ~o are obtained. ~55~The results obtained on the diffused and heat treated diodes are in good agreement with the vapor-grown junction diodes which have a similar donor concentration. For the case of the lightly doped diodes with n ~ l0 s 7/ cm 3, it can be seen that the efficiency for x = 0.0 is considerably lower than for the heavily doped devices. However, the diodes with n ~ 10:7/cm 3 do not decrease as rapidly in efficiency with increasing x for x < 0.3 with the result that at x = 0.4 external efficiencies of ,~ 0.2 ~o are obtained. The fact that, at 300°K, the efficiency for ZnAs2 diffused diodes remains nearly constant, for alloy compositions x < 0.3 may be partially fortuitous. Actually the crystal quality and hence the inherent device efficiency may be decreasing with increasing x due to such factors as increasing stoichiometric inhomogeneity. The ZnAs2 diffusion is optimized for GaAso:6P0.4 which has a low mobility and, consequently, a short minority carrier diffusion length. However, for devices with small x, the minority cartier diffusion length is longer, with the result that a significant fraction of the injected electrons traverse the p-type region and recombine nonradiatively in the p÷ surface region. Thus, the performance of devices with small x may be, in part, diffusion limited. If proper diffusions were employed for alloys with small x, it is likely that the efficiencies would decrease somewhat more rapidly with increasing alloy composition between x = 0 and x = 0.3. This is consistent with the observed behavior of the same diodes at 77°K where the diffusivity is lower due to the reduced temperature. In this case fewer electrons penetrate to the p+ region and the efficiency increases with decreasing x. The dashed curves shown in Fig. 8 are theoretical calculations which are discussed in Section 4.2.3. The optimum alloy composition for high brightness diodes is determined by combining the data for device efficiency vs. alloy composition with the response of the human eye as a function of wavelength. Since the eye response increases sharply with increasing x (decreasing wavelength) the resulting curve of brightness vs. alloy composition is sharply peaked with an optimum composition of x ~ 0.4. This can be seen in Fig. 9 where the relative eye response, the relative quantum efficiency and the resulting relative brightness as a function of alloy composition are plotted, and can be compared with the measured brightness vs. alloy composition for a series of GaAst_~Px diodes.~ 5)

4.2. Discussion 4.2.1. Performance o f GaAs vs. GaAso.rPo.4. In order to better understand the interrelationship between material parameters and device performance, it is useful to compare the GaAsl _xPx device optimization results with GaAs results. Since the energy gap for GaAso.6Po.4 is direct, and since the band structure is similar to that of GaAs except that the bandgap is somewhat larger, ,-, 1.9 eV instead of ,~ 1.4 eV, one might assume that the device optimization parameters would be similar for GaAs and GaAsl_xPx. This is not the case as shown in Table 3. For high-quality GaAs the optimum device performance is obtained when a graded junction with a junction depth of ,-~ 15/zm is employed, cs6~ The optimum donor concentration has been found to be the maximum concentration which can be achieved consistent with good crystal quality. ¢56) In GaAs this concentration is typically ,-, 2 x 10 ~S/cm3, limited by solubility considerations and the onset of structural disorder. ~56~

Properties and electroluminescenee of the GaAst-~Px ternary system

143

TAeLe3 Device characteristics Junction profile Junction depth

Donor concentration (ND) External efficiency(r/e,t)

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However, in GaAs1_xPx, as discussed above, abrupt junctions with carrier concentrations of < 1017/cm3 are required.

4.2.2. Optimum diffusion profile. It is not surprising that the optimum diffusion profiles for GaAsl_xP~ and high quality GaAs are markedly different, since the nonradiative lifetime in GaAsx_xP~ is much shorter due to the comparatively high concentration of dislocations, strain, and other defects. In order to maximize the internal efficiency, ~/i,t, the Zn diffusion profile must minimize nonradiative recombination. The effect of the diffusion profile can be understood by considering the relationship between internal efficiency (r/i,t) and the radiative (ZR) and nonradiative (~NR) minority carrier lifetimes. In this discussion only electron injection will be considered. The internal efficiency is equal to the radiative recombination divided by the total recombination, which can be expressed: 1/'OR __

~/i.t =

1/x

1/~'R = ( l "JVTR/TNR) - 1 1/"OR+ I/TNR

(6)

where z is the total minority carrier lifetime. In order to increase the device efficiency one would like to increase ~NR and reduce xR. However, ~NR is determined by the number of nonradiative centers associated with background impurities and structural disorder in the n-type crystal. For a given GaAs or GaAsl_xP~ crystal, ~NR cannot be increased although it can be sharply reduced if an improper diffusion technique is employed. Thus, in order to increase the efficiency, the Zn profile must be adjusted to reduce ~R without affecting ~NRQualitative values for the various radiative and nonradiative lifetimes involved in determining ~int are shown in Fig. 10 plotted as a function of acceptor concentration. For electrons injected into the p-type region of a diode, ~R is expected to be inversely proportional to the hole concentration if we assume that near conduction band to acceptor transitions are the dominant radiative process. In Fig. 10 it is assumed that Za = 101°/P which is in qualitative agreement with diode decay time for GaAs and other direct III-V semiconductors. (57) The background nonradiative lifetime for high-quality GaAs is taken to be 60 nsec. (56) This figure is conservative since lifetimes in excess of 100 nsec are commonly observed for high efficiency GaAs amphoterically doped devices. (Ss) The nonradiative lifetime associated with Z n , ZNrt (Zn), is a qualitative estimate based on the fact that in GaAs, ~r~(Zn) completely dominates for p >~ 3 x 1019/cm 3, but for p < 5x 10~S/cm 3 device performance is strongly dependent on the n-type material parameters. (56) In the case of GaAso.6Po.4, nonradiative hole injection may also contribute to zN~(Zn) since, as described in Section 4.2.3, the electron injection efficiency decreases markedly as the direct-

144

M . G . CRAFORD

indirect transition is approached. The total nonradiative lifetime T~R obtained by combining the r~R (GaAs) and ZNR (Zn) is also shown. For comparison, background and total nonradiative lifetimes, Z~R (GaAsP) and Tr~R respectively, are shown for a GaAsP sample where it is assumed Z~R (GaAsP) = 1 nsec. Short background lifetimes can occur as a result of defects such as strain and high dislocation densities and 1 nsec lifetimes have been observed for GaAs 1_xPx .ta o~, 57) However, I

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ACCEPTOR CONCENTRATION (carriers/crn 3 ) FIG. 10. Qualitative radiative and nonradiative minority carrier lifetimes for p-type GaAs and GaAsl_xP~. Background nonradiative lifetimes are shown for high-quality Gabs where ~' (GaAs) ~ 60 nsec and for a GaAsl-xP~ sample where ~ (GaAsP) ,,, 1 nsec has been assumed. Estimated values for the radiative zR(Zn),and nonradiative, rr~R(Zn), lifetimes associated with the Zn concentration as well as the total nonradiative lifetimes, T'NRand znse, are shown. GaAs 1_xPx diodes have also been studied with radiative decay times of ,,, 50 nsec, (59) Since trapping effects may be important in these diodes, z~a (GaAsP) is uncertain. Nevertheless, we can be reasonably confident that T~R (GaAs) > T~R (GaAsP) so that the general considerations outlined here are valid. The nature of the nonradiative recombination centers associated with Zn and the dependence of the nonradiative lifetime, ZNR (Zn), on the Zn concentration, have not been experimentally determined. It may be true that ZNR(Zn) depends as strongly on the gradient of the Zn concentration as on the absolute concentration itself. For example, the Zn

Properties and electroluminescence of the GaAs I -xPx ternary system

145

concentration gradient causes internal stresses which, if the stresses exceed the yield stress, can introduce an array of dislocations into the region of highest gradient. ~6°'61) However, the concept of ZNR (Zn) decreasing with increasing Zn concentrations is still qualitatively correct, at least for diffused junctions, because the maximum Zn concentration gradients generally occur at high Zn concentrations. From the preceding discussion and Fig. 10 it can be seen that the optimum Zn profile for a given GaAs or GaAs~_xP~ crystal can be strongly dependent on TNR for that crystal. If high-quality crystal is used such that ZNR is long, then a graded junction with a low Zn concentration gradient and a relatively low net acceptor concentration of 2 - 10 x 101 a/cm3 in the recombination region should and does result in a large ratio of ZNR/ZRand high device efficiencies. Furthermore, the low Zn concentration minimizes free carrier absorption. If GaAs or GaAsl -xP~ with a short XNRis used, a junction with a higher Zn concentration near the junction is required in order to give optimum performance. In the case of GaAso.6Po. 4, however, the maximum Zn concentration may be limited by the onset of nonradiative hole injection. For material with short background nonradiative lifetimes it may no longer be possible to obtain rR < ZNR,but a higher Zn concentration and concentration gradient should be used in order to reduce the ratio ZR/Zr~Rto its lowest possible value. This is consistent with the results generally observed for GaASl -~Px where an abrupt junction with a high Zn surface concentration and a junction depth of only 1-3/am is found to yield high performance devices. ~15) The junction depth should be only deep enough to prevent excessive nonradiative recombination which can result if the minority carrier diffusion length is long enough so that an appreciable fraction of the injected electrons traverse the p-type region and reach the crystal surface. 4.2.3.

Optimum donor concentration and the effect of the direct-indirect

transition. High donor concentrations are desirable in GaAs, both because internal reabsorption is minimized and because the radiative decay time is reduced since there is an increased hole concentration in the immediate vicinity of the junction. ~56) In the case of GaAso.6Po.4, however, the situation is complicated by the proximity of the direct-indirect energy gap transition. The decrease in the device quantum efficiency with increasing alloy composition as the direct-indirect transition is approached is due to the fact that the vast majority of electrons which are thermally excited or injected into the indirect minima recombine nonradiatively.~57) A theory which describes the efficiency as a function of alloy composition for ternary alloys has been formulated by Hakki. ~57a) This theory takes into account the intervalley scattering lifetimes. However, assuming that the intervalley scattering lifetime is short compared to the minority carrier lifetimes in the direct and indirect minima, that the minority carrier lifetimes are equal, and that the radiative efficiency in the indirect minima is negligible, then the quantum efficiency is simply proportional to f, the fraction of electrons in the direct minimum. The preceding assumptions are all reasonable for GaAs I _~Px since the minority carrier lifetimes are dominated by nonradiative recombination and as a result are probably equal for the direct and indirect minima. Further, the intervalley scattering lifetime is expected to be shorter than the __>1 nsec minority carrier lifetimes, particularly at 300OK.(57a) The decrease in efficiency with increasing x can be readily accounted for by this model as seen in Fig. 8. The dashed lines were calculated on the basis of the equation, r/,xt(X) = t/cxt(0) t/int(x) = t/,~t(0)f

(7)

146

M . G . CRAFORD

where ~/~xtand ~h,t are the external and internal quantum efficiencies,f i s determined from eqn. (2), assuming N2/N l = 84 (I +0.Sx)-3/2 and ~/cxt(0) is equal to the external quantum efficiency of GaAs. Although this model accounts reasonably well for the decrease in quantum efficiency with increasing alloy compositions, it does not account for the effect of donor concentration on EL and cathodoluminescence efficiency. It has been shown that at thermal equilibrium, in n-type material, the ratio of the electron concentration in the indirect minima to the electron concentration in the direct minima increases with increasing donor concentrations.( ao) This is due to the fact that as the donor concentration is increased, Fermi statistics must be employed and the Fermi level moves progressively higher into the conduction band with the result that an increasingly large fraction of the conduction band electrons are transferred into the indirect minima. Thus, if the electrons in the indirect minima recombine nonradiatively then one would expect to observe a decrease in luminescent efficiency for increasing donor concentrations in n-type material. This is in direct disagreement with the cathodoluminescence data shown in Fig. 7. Further, it is not clear why the device efficiency would decrease with increasing donor concentrations even if the indirect minima do give rise to nonradiative recombination. If EL emission is due to electron injection and recombination on the p-type side of the junction, then one would expect that the donor concentration on the n-side of the junction would have very little effect on device performance.(1 o) Since it is not obvious how the proximity of the indirect minima can account for the decrease in quantum efficiency with increasing donor concentrations, we can ask what other factors associated with the direct-indirect transition might be important. Two factors which can be considered are the lattice parameter and the mobility. We know that the lattice parameter decreases from 5.654 in GaAs to 5.572 in GaAso.6Po.4. It is conceivable that, as a result of the change in the lattice parameter, and since the tetrabedral covalent radii of Se and Te are larger than that of p,(62) the donor atoms have a more disruptive effect on the GaAso.6Po.4 lattice than on that of GaAs. If this were true it would give rise to a lower degree of crystal perfection for the heavily doped GaAso.6Po.4 crystals. The mobility of GaAso.6Po. 4 crystals does drop rapidly with increasing carrier concentration giving some credence to this argument as seen in Fig. 2(b). (a a) However, this argument is in disagreement with the cathodoluminescence data since a low degree of crystal perfection would be expected to imply a low cathodoluminescence efficiency. The electron mobility changes markedly with increasing alloy composition as seen in Fig. 2, due to the transfer of electrons into the low mobility (100) indirect minima. The electron injection efficiency for the (100) electrons is much lower than for the (000) electrons since the injection efficiency can be written :(63)

l

(8)

k # . / \ p/\n] where/~, and #p are the electron and hole mobilities, L. and Lp are the electron and hole minority carrier diffusion lengths, and n and p are the electron and hole carrier concentrations in the vicinity of the junction. Thus, if the electron mobility is low enough and if the hole concentration in the vicinity of the junction is high enough, significant space charge recombination and/or hole injection could result. Furthermore, for GaAs diffused junctions the net hole concentration in the vicinity of the junction has been observed to increase with

Properties and electroluminescence of the GaAs~_xPx ternary system

147

increasing donor concentrations, resulting in shorter radiative decay times.(56) Also, as seen in Fig. 2(b), the electron mobility is known to decrease markedly with increasing donor concentrations.(3 ~) Thus increased hole injection or nonradiative space charge recombination could, on a qualitative basis, account for the decrease in device efficiency with increasing donor concentrations and, at least partially, for the decrease in efficiency with increasing alloy composition for x < 0.49. However, additional experimental work must be carried out before this issue is settled. For example, it has not been clearly demonstrated that hole in= jection results in nonradiative recombination. Also, although it is known that diffusion currents dominate the recombination in devices with low donor concentrations,(15) a careful study of the effect of donor concentration on the magnitude of the space charge recombination current has not been reported. 5. ELECTROLUMINESCENCE AS A FUNCTION OF ALLOY COMPOSITION

5.1. Eleetroluminescence at 77°K without Nitrogen Doping The luminescent properties of GaAsl_xPx at 300°K are of most interest from a practical point of view. However, in order to understand the nature of the radiative recombination mechanisms which give rise to the 300°K luminescence, it is necessary to study the EL at 77°K where the emission peaks are more clearly defined and the radiative processes can be better understood. We will first discuss the 77°K EL without nitrogen doping. The EL as a function of alloy composition can be divided into two portions, corresponding to the direct and indirect energy gap regions. In the direct bandgap region, with x < 0.46 at 77°K, the EL is similar to that of GaAs, and in the indirect bandgap region, x > 0.46, the EL can be correlated with the EL observed in GaP. Typical EL spectra in the direct and indirect regions are shown in Figs. 11 and 12 respectively. In the direct bandgap region two emission peaks are visible. The separation between the peaks is approximately 15 meV for alloy compositions near GaAs and increases to approximately 33 meV for x ~ 0.4. The higher energy peak, P1, is due to near-band=edge transitions which may be the recombination of either free electrons and holes, free excitons, or transitions involving shallow donor impurities.(64) Since the binding energies of these donors is only ~ 6 meV these transitions cannot be distinguished here and will be grouped together and referred to as near=band-edge transitions. The second peak, P2, located approximately 12-33 meV lower in energy, depending on the alloy composition, is due to transitions involving the zinc acceptor impurities. The fact that the peak separation increases with increasing alloy composition is consistent with the fact that the Zn binding energy increases from 31 me¥ in GaAs (6s) to 64 meV in GaP (66) and would be approximately 43 meV for x = 0.4 assuming a linear variation with alloy composition. This suggests that the emission peak separation is approximately 16 meV less than the zinc binding energy for GaAs and decreases to approximately 10 meV less than the binding energy for GaAs~_xP~ with x - - 0 . 4 . One explanation for the fact that the peak separation is significantly less than the binding energy is that the electrons may be injected into a region which is so heavily doped with zinc that band tailing effects reduce the energy of the near band-edge recombination.(~ 5) This effect would be expected to be more pronounced in GaAs than in GaAsl _xP~ since the mobility is higher and hence the diffusion length is longer, resulting in electron penetration further into

148

M . G . CRAFORO

the increasingly p+ region. This explanation is consistent with the position of Pt which is 10 meV1 below the band edge for alloy compositions close to GaAs. ° 5) In the indirect bandgap region the emission spectra are much more complicated, as can be seen in Fig. 12, which shows the near band-edge emission for a series of diodes with alloy compositions near GaP. A broad donor-acceptor pair band which occurs at approximately 200 A longer wave length than the peaks shown in Fig. 12, has been omitted. The EL for the diode with x = 0.98 is very similar to that observed in GaP which is shown by the dashed lines, and exhibits a variety of intrinsic phonon-assisted free exciton transitions in addition to an extrinsic line labeled Te which is due to the recombination of an exciton bound at a neutral donorJ 67) In addition, the no-phonon free exciton line, which is not observed in GaP, can be clearly resolved in the x = 0.98 sample. This emission which is

1.555 eV 2.017 eV 77-K

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forbidden in GaP due to momentum conservation requirements is allowed when As is added to the crystal since momentum can be conserved by scattering from the arsenic impurity sitesJ 6s~ As x decreases, and increasing concentrations of As are added to the crystal, the structure of the emission spectra becomes less well defined. This is expected due to the statistically random nature of the As-P distribution in the ternary lattice. In addition to this smearing of the emission band structure, it can be seen that two emission lines, namely E~x and E~-LA, dominate the near-band-edge emission of x < 0.9. The domination of the Egx-LA emission, as compared to the other phonon-assisted transitions, is expected from group theory considerations, t69) The Eg~ and Eux-LA peaks continue to dominate the nearband-edge recombination for alloy composition throughout the indirect bandgap regions.

Properties a n d electroluminescence o f the G a A s l - ~ P x ternary system

T-T~K

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WAVELEt,~'TH 111 FIG. 12. Electroluminescenc¢ of GaAsl_=P= diodes without nitrogen at 77°K. (2°) The spectra have been shifted so that Eo~ is aligned vertically for the different alloy compositions. The electroluminescence of a nitrogen-free GaP diode, taken from ref. 67, is shown for comparison by the dashed line. The diode current is 5 mA (5 A/cm2).

149

150

M . G . CRAFORD

2.alt~v I~

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Properties and electroluminescence of the GaAsi _xPx ternary system

151

This can be seen for x = 0.54 crystal in Fig. 13 which shows Egx and Eg~LA, here labeled P1 and P2 respectively. In addition, Fig, 13 shows the shallow donor-acceptor pair band. It can be seen that as the current is increased, the peak position of the pair band is shifted to higher energies but the positions of Pt and P2 do not shift. In addition, it can be seen that the intensity of the pair band saturates with increasing current densities while the intensities of P~ and P2 continue to increase and totally dominate the emission at high currents. These results are expected and are consistent with the behavior of similar emission lines found in GaP where it is well known that the pair band shifts to higher energies and saturates at high current densities whereas the near-band-edge emission lines do not. (7°) --

I

!

I

!

/

I

I

I

/ PEAK EMISSION ENERGY VS ALLOY COMPOSITION FOR GoAIII.X Px WITHGJT NITROGEN T=77"K

2,3

/

/

,

~

r

/ /

EC / ,.,

/

,

,

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1.0

x FIG. 14. Peak emission energy vs. alloy compositionfor GaAsl_xP~ diodes without nitrogen at 77OK. (2o)The diode current is 5 mA (5 A/cm2). The peak emission energies of the lines described above are plotted as a function of alloy composition in Fig. 14. The dashed lines represent the positions of the conduction bandedges for the direct, Er, and indirect Ex, conduction band minima. The direct band-edge, which can be represented by the equation Er(x) = 1.51 + 1.153x+0.210x ~,

(10)

was determined by electroreflectance measurements at 300°K (17) which were adjusted to

152

M . G . CXAFORD

T, $.W.Y.•'fffKl - ~

/ ~ ' i 'i ~ i A'~olettt ~

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WAVELFN .G (~TH FIG. 15. Electroluminescence of GaAsl_~Px diodes with nitrogen at 77°K. (2°) The spectra have been shifted so that Egx is aligned vertically for the different alloy compositions. The electroluminescence of a nitrogen-doped GaP diode is shown for comparison by the dashed line. The diode current is 5 mA (5 A/cm2).

Properties and electroluminescence of the GaAst_xPx ternary system

153

77OK.(15) The indirect band edge was determined from the position of the no-phonon free exciton line, assuming that the exciton binding energy is 10 meV independent of alloy composition, and has the form(2°) Ex = 1.993+0.099x+0.241x 2.

(11)

The alloy composition, x, at which the transition from a direct to an indirect semiconductor occurs, has been found to be 0.46 at 77°K. (2°) 5.2.

Electroluminescence at

77°K

with Nitrogen Doping

The emission spectra for a series of nitrogen-doped diodes are shown in Fig. 15. In these diodes, at 77°K, the nitrogen completely dominates the emission and none of the emission lines described above for nitrogen-free diodes are resolved. It can be seen that for x = 0.98 the spectrum is again very similar to GaP with the A-line, the NN3 line and the NN1 pair lines clearly resolved in addition to a variety of phonon replicas. The A-line is due to recombination at isolated nitrogen atoms, while the NN1 and NN a lines are associated with recomI

I

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|

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PEAK EMISSION ENERGY VS ALLOY COMPOSITION FOR GoASI_xP x WITH NITROGEN

2.30

I

/ /

//

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/ /

,

/

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T=77"K

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Peak

tst

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FIG. 16. Peak emission energy vs. alloy composition for GaAsl_=Px diodes with nitrogen at 77°K. (2°) The curves for Er and Ex are taken from cqns. (10) and (I1). The peak position and width at half maximum for the optical absorption data are shown. The dashed lines indicate the half power points for the N N pair band luminescence. The diode current is 5 mA (5 A]cm2).

154

M . G . CRAFORD

bination centers consisting of nitrogen atoms on nearest-and third nearest-neighbor group V element sites, respectively.(24) The NNa line occurs at nearly the same energy as an optical phonon replica of the A-line/24) As a consequence this line is often designated A-O/24,4~) Although both processes may contribute to this recombination, it is likely that in the heavily nitrogen-doped GaAsl-~Px samples discussed here, NN3 recombination is dominant. (2°) As the arsenic concentration in the crystal is increased, the fine structure of the emission spectra disappears and for x < 0.85, in heavily nitrogen-doped diodes, the emission becomes a single broad band. For alloy composition near x = 0.8 this band exhibits a shoulder or secondary peak on the low energy side as shown in Fig. 15. However, for alloy composition x < 0.6 the low energy shoulder is generally not visible. The broad emission band is apparently a combination of the NN 1 and NN3 pair bands.

I

1,4

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OPTICAL ABSORPTION AND ELECTROLUMINESCENCE FOR GoAso.44Po,so:N T==77*K

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(~)

FIG. 17. Relative a b s o r p t i o n coefficient a n d electroluminescence vs. wavelength for nitrogen-doped

GaAso.4,tPo.s6 at 77°K. The diode current is 5 mA (5 A/cm2). The peak emission energies for the nitrogen-doped diodes are plotted as a function of alloy composition in Fig. 16. Optical absorption data for a series of nitrogen-doped GaASl_xPx samples are also shown in Fig. 16. The peak energy of the optical absorption band is believed to correspond to the A-line. As can be seen in Fig. 16, in the region where the A-line can be resolved in the EL spectra, the agreement between the optical absorption and EL A-line is good. It is not unreasonable that the A-line should dominate the absorption even though the pair band emission dominates the luminescence. There is a high concentration of isolated nitrogen atoms with large oscillator strengths, and as a result the A-line is expected to be very strong in absorption. However, rapid thermalization of electrons can occur from the A-line states to the less populous but energetically favorable NN pair band states and thus give rise to strong luminescence from this band at the expense of the

Properties and electroluminescence of the GaAsl_xP x ternary system

T-3OO* K ELECTROLUMINESCENCE FOR GaA%.,. Po.u IEgI_LA

WITHOUT

NITROIEN S.W, ti"

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FIG. 18. Electroluminescence of a nitrogen-free GaAso.,1Po.s9 diode as a function of temperature. (2°) The spectra have been shifted so that Eg~ is aligned vertically. The diode current is 5 mA (5 A/cm2).

155

156

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FIG. 19. Electroluminescenee of a nitrogen-doped GaAso.lPo.9 diode as a function of temperature. (2°) The spectra have been shifted so that the A-line is aligned vertically. The diode current is 5 m A (5 A/cm2).

Properties and electroluminescence of the GaAsl_xPx ternary system

157

A-line. (2°) The relationship between optical absorption and electroluminescence is illustrated in Fig. 17 where it can be seen that the high-energy portion of the EL spectra corresponds to the low energy portion of the optical absorption band. 5 . 3 . Electroluminescence at 3 0 0 ° K

As the temperature is increased from 77°K to 300°K the electroluminescence of nitrogenfree and nitrogen-doped diodes changes markedly as seen in Figs. 18 and 19. In the case of nitrogen-free diodes the near-band-edge free exciton line, Egx, and the Eox-LA line increase relative to the shallow donor-acceptor pair emission band. At 300°K the radiation is completely dominated by exciton, and phonon-assisted exciton, recombination. The presence of free-electron-hole recombination cannot be excluded because the 10meV separation between the exciton recombination would be impossible to resolve at 300°K due to broadness of the emission bands. The observation that the relative intensity of the donoracceptor pair band decreases rapidly with increasing temperature correlates with the results observed in GaP. (¢7'67) The radiative decay time for these pair states is much longer than for the emission band closer to the band edge, and as a consequence electrons and holes

PEAK EMISSION ENERGY VS ALLOY COMPOSITION FOR GaASt_xPT'3OOSK ~

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FIG. 20. Peak emission energy vs. alloy composition for GaAsl_~Px diodes with and without nitrogen doping at 300°K. (2°) The position of Er was taken from ref. 17. The positions o f Ex and the A-line have been adjusted from the 77°K data shown in Figs. 14 and 16. The diode current is

5 m A (5 A/cm2). iF'*

158

M.G. Qo~oRo

trapped in the donor and acceptor states have sufficient time to thermalize into the conduction and valence bands, respectively, and hence have the opportunity to recombine by means of an alternate radiative or nonradiative recombination path/7 o) The behavior for the nitrogen-doped diode shown in Fig. 19 is similar, in that the nearband-edge transitions dominate the recombination at high temperatures, and for the diode shown, the N N pair band recombination becomes insignificant at room temperature. However, this behavior is not characteristic of all alloy compositions. For alloy compositions x < 0.8, the N N pair band dominates the room-temperature recombination. This may be a result of either an increased nitrogen concentration for alloy compositions x < 0.8, or may be related to an increase in the oscillator strength for the N N pair band transition. The N N pair band is apparently a combination of the NN1 and N N a bands. The peak emission energy plotted as a function of alloy composition for diodes with and without nitrogen doping is shown in Fig. 20. The position of the direct energy gap E r has been determined by Thompson e t al. (1~) The position of Ex has been adjusted from the 77°K EL data. (2°) The direct-indirect transition occurs at x = 0.49 at 300°K. (2°) It can be seen that for diodes without nitrogen doping the peak emission energy follows the band edge rather closely for all alloy compositions, particularly in the direct bandgap region. For these devices the room temperature recombination, which corresponds to P1 at 77°K, is extremely near the band edge and may in fact be free-electron-hole recombination. The

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WITHOUT

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Properties and electroluminescence of the GaAst_xPx ternary system

159

acceptor associated recombination, responsible for P2 at 77°K in Fig. 11, has been shown to be insignificant at room temperature due to the fact that a large fraction of the acceptor states are ionized. ¢71) In the case of nitrogen-doped diodes the N N pair band dominates the recombination for alloy compositions from x = 0.3 to x = 0.8. For x > 0.8 the emission gradually becomes dominated by recombination nearer the band edge. For nitrogen samples with alloy compositions in the direct energy bandgap region, x < 0.49, E r emission is present in addition to the N N pair line; this is illustrated in Figs. 21 and 22. In Fig. 21, a sample with x = 0.4, the nitrogen emission curve exhibits a high energy shoulder which corresponds to the emission of the nitrogen-free sample. The emission of the nitrogen-free sample is equivalent to that observed in the red emitting GaAsl-~Px diodes available commercially. The sample shown in Fig. 22 was grown with a 5 times lower nitrogen concentration than the other samples

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FIo. 22, Electroluminescence for a nitrogen-doped GaAso.szPo.4a sample at 300°K,(2°) This sample has ~ 5 x less nitrogen than the other diodes studied and as a result the A-line is visible in addition to the Er and NN emission. The diode current is 5 mA (5 A/cm2). discussed here. As a consequence, the A-line, as well as the E r and N N line emission are observed. The position of the peak A-line emission from this diode is plotted in Fig. 20 and can be seen to be in good agreement with the position of the A-line as determined by optical absorption which is shown by the dashed line in Fig. 20. The efficiency vs. alloy composition for GaAsl _xPx diodes with and without nitrogen is shown in Fig. 23. (z°) For nitrogen-free diodes the quantum efficiency falls off sharply with increasing alloy composition in the vicinity o f x = 0.4-0.5 due to the transition from a direct to an indirect energy gap. The efficiencies of the samples with x > 0.5 shown in Fig. 23 are somewhat different than the efficiencies for corresponding alloy compositions shown in Fig. 8. This is believed to be due to the fact that the samples shown in Fig. 23 were grown on GaP substrates whereas those shown in Fig. 8 were grown on GaAs substrates.

160

M.G.

'°+1

CRA~RO

1

. . . . . .

l

e~e~

EFFICIENCYvs. ALLOYCOMPOSITIONl ~ FORGaASl.xPx

o

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K

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o

O

°

.

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0.I

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0.4

0.3

0.6

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0.II

0.9

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FIG. 23. Efficiency vs. alloy composition for GaAsI_+P+ at T = 300°K. <1+) The diode current density is 20 mA (20 A/cra2).

i

i

i

i

i

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ALLOYCOMPOSITION T-=500" K 2= 2¢ _o

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I 0.6

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,.0

FIG. 24. Efficiency enhancement ratio for nitrogen doping as a function of alloy composition at 300°K, taken from the data of reL 16.

Properties and elcctroluminescence of the GaAsl_~Px ternary system

161

In the case of the nitrogen-doped diodes shown in Fig. 23 the effect of the direct-indirect transition is much less sharply defined than for nitrogen-free samples, and the efficiency falls off gradually from x = 0.5 to x = 1.0. The decrease in efficiency with increasing phosphorus concentrations can be attributed to two factors. First, the separation between the direct and indirect minima is increasing with increasing phosphorus concentrations. Faulkner ~2S) has shown that the probability for radiative recombination involving the nitrogen center should be a m a x i m u m in the vicinity of the direct-indirect transition, where x ~ 0.49 and AE ~ 0, since this energy separation AE appears in the denominator of the matrix element for the radiative transition. As a result, the radiative recombination due to this transition is expected to become less efficient with increasing x for alloy compositions x > 0.49. ~16) Second, the binding energies of the nitrogen and NN pair band increase with decreasing phosphorus concentration. This increased binding energy reduces the probability of thermal deionization, and as a consequence the efficiency of these transitions is expected to increase with decreasing x. <16) As expected, the efficiency enhancement due to nitrogen doping is most pronounced in the region from x = 0.45 to x = 0.7. This is illustrated in Fig. 24 where the ratio of the efficiency of nitrogen-doped to nitrogen-free diodes is shown as a function of alloy composition. It can be seen that greater than a 20 x increase in efficiency is observed for alloy compositions between x = 0.5 and x = 0.6. This enhancement decreases with increasing alloy composition with the result that for GaP green-emitting diodes the efficiency of nitrogen-doped devices is approximately 3 times greater than that for the nitrogen-free diodes. For liquid phase epitaxial (LPE), grown-junction, green-emitting diodes fabricated by Logan et al., the nitrogen doping was observed to produce a 10 times improvement in efficiency.<47) It is not clear at the present time why the efficiency enhancement due to nitrogen doping is less for Zn diffused vapor phase epitaxial (VPE) diodes than for LPE grown junction devices. However, the techniques used in the incorporation of nitrogen in VPE GaP are still at a relatively early stage of development, and it is likely that future improvements will result in a greater enhancement due to nitrogen doping. In the case of nitrogen-free GaP diodes the efficiency and brightnesses obtained for Zn diffused and LPE grown junction devices are nearly equivalent. <67) Furthermore, the quality of the VPE GaP crystals appears to be excellent as evidenced by electrical transport and radiative decay time measurements. ~67) Electron mobilities as high as 3000 cm2/V-sec have been observed in vapor phase epitaxial GaP wafers at 77°K. ~31) Radiative decay time constants of nitrogen-free diodes are routinely in excess of 200 nsec and have been observed to be as long as 400 nsec. t59) These radiative decay time results are equivalent to the best reported results for liquid phase epitaxial layers,t 72) and suggest that the concentration of nonradiative centers which would reduce the radiative decay time is relatively low in the VPE crystals. When these factors are taken into account it seems probable that, when improved growth techniques are developed for the nitrogen-doped crystals, the quantum efficiencies obtained for Zn diffused VPE diodes will become equivalent to those presently achieved only with LPE grown junction devices. For display applications the luminous efficiency and brightness of the devices and not the quantum efficiency are the important parameters. In Fig. 25 the brightness for nitrogendoped and nitrogen-free diodes is plotted as a function of alloy composition. ~73) It can be seen that for diodes without nitrogen doping the brightness peaks sharply in the vicinity of x = 0.4, as shown in Fig. 8, and thereafter decreases rapidly in the region of the directindirect transition and continues to fall steadily to brightness values of less than 50 ft-

162

M . G . CRAFORD

Lamberts for alloy compositions greater than x = 0.7, and then increases again at x = 1.0. This is apparently related to the fact that the crystalline perfection in GaP is superior to that of the ternary alloy. The brightness of nitrogen-doped diodes steadily increases from x = 0.3 and reaches a rather broad maximum for compositions between x = 0.6 and x = 0.8. For alloy compositions between x = 0.8 and x = 1.0 there is a reduction in the brightness, and, as in the case of nitrogen-free diodes, the brightness increases sharply for GaP. It can be seen by comparing Fig. 25 and Fig. 23 that the brightness for nitrogen-doped diodes remains

BRIGHTNESS VS ALLOY COMPOSITION FOR G a A s I . x P x

• I "

I

p

rlx

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Fx6.25. Brightness (at 10 A/cm 2) for GaAsI_=P~ diodes with and without nitrogen doping as a function of alloy composition.(73) relatively constant in the region 0.5 < X < 1.0, whereas the quantum efficiency has decreased by more than an order of magnitude. This is, of course, due to the fact that the sensitivity of the eye is increasing sharply in this region, and this increase in eye sensitivity compensates for the decrease in quantum efficiency. From the practical point of view it is important to determine the efficiency enhancement due to nitrogen doping as a function of emission wavelength, i.e. the color of the emission. Figure 26 shows the brightness plotted as a function of peak emission wavelength and peak emission energy rather than alloy composition. (73) Also shown, along the horizontal axis, are the colors which correspond to the different peak emission wavelengths. It can be seen

Properties and electroluminescence of the GaAsl -xPx ternary system

163

that for red emission the nitrogen-doped diodes are not yet equivalent to the best redemitting nitrogen-free diodes. However, in the case of orange, yellow, and green diodes the nitrogen doping has resulted in a marked improvement in device brightness. By way of comparison, it should be pointed out that the present commercially available red-emitting diodes typically have brightnesses of 400-800 ft-Lamberts at 10 A]cm ~ and not the 900 ftLamberts shown in Figs. 25 and 26. Thus the brightnesses obtained in the research laboratory for orange, yellow, and green diodes are already approximately equivalent to the commercially available red-emitting devices. PEAK EMISSION ENERGY (eV)

~

z;o

Le I

1~

"

z.I ,

2.z

i

_

I

BRIGHTNESS FOR GoASI_xPX T" ~LO0"K

"~

80¢

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0

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FJo, 26. Bdghmess (at 10 A/cm 2) for GaAs~-~Px diodes with and without nitrogen doping as a

function of peak emission wavelength.(~3) 6. SUMMARY In this paper the material and device properties of the GaAs l_xPx ternary alloys have been described. These alloys are "well-behaved" in the sense that the majority of the EL and electrical transport properties closely resemble those of GaAs for direct alloys and GaP for indirect alloys. Although the region of the direct-indirect transition has been extensively studied, the device physics in this alloy composition region are not yet fully understood. This is particularly true in the case of nitrogen-doped alloys, since the oscillator strength for the

164

M . G . CRAFORD

radiative transitions involving nitrogen should be greatly enhanced for alloy compositions near the direct-indirect transition. As a result of economic and technological considerations, GaAsl -~Px is currently preferred for commercial light-emitting diode applications. However, G a P red-emitting diodes, which have received considerably more attention in the research laboratories than have GaAsl_~P~ diodes, have also recently entered the commercial market place. Research results indicate that G a P diodes offer potentially a 3-5 times improvement in luminescence efficiency over the currently available GaAs~_~Px diodes.(7'° However, in the case of the G a P diodes the p-type region is grown by means of liquid phase epitaxy rather than by impurity diffusion. As a consequence the fabrication of these devices is not compatible with conventional planar techniques. Furthermore, it has not yet been demonstrated that liquid phase epitaxial-grown junction devices can compete with VPE devices on a cost-effectiveness basis. The unanswered questions at the present time are: 1. Can liquid phase epitaxial GaP devices be reliably and economically fabricated on the commercial scale ? 2. Can the luminescence efficiency of GaAs~_xP~ devices be improved to compete with the potential luminescence efficiency of G a P devices ?

ACKNOWLEDGEMENTS The author would like to thank A. H. Herzog, W. O. Groves, D. L. Keune, and A. Onton (IBM) for making portions of the data used in this paper available to him prior to publication, and Drs. D. E. Hill and R. E. Pellin for reviewing this manuscript. The author would also like to thank N. Holonyak, Jr. (University of Illinois) for m a n y helpful discussions. REFERENCES 1. N. HOLONYAK,Jr., D. C. JILL.SONand S. F. BEVACQUA;presented at the August 1951 A.I.M.E. meeting in Los Angeles and published in Metallurgy of Semiconductor Materials, p. 49, Interscience Publishers, Inc., New York, 1962. 2. N. HOLONYAK,Jr. and S. F. BEVACQUA,.4ppl. Phys. Lett. 1, 82 0962). 3. F. A. PtZZARELLO,J. Electrochem. Soc. 109, 226 0962). 4. S. Ku, J. Electrochem. Soc. 110, 991 (1963). 5. D.A. CUSANO,G.E. FENNERandR. O. CARLSON,Appl.Phys.Lett.5,144(1964). 6. G.E. GOTTLmB,J. Electrochem. Soc. 112, 192 (1965). 7. M. RUBENSTEIN,J. Electrochem. Soc. 112, 426 (1965). 8. M. PILKtmNand H. RUPPRECHT,J. ,4ppl. Phys. 36, 684 (1965). 9. J.J. TmTSENand J. A. AMICK,J. Electrochem. Soc. 113, 724 (1966). 10. H.P. MARUSKAand J. I. PANKOVE,Solid-State Electron. 10, 917 (1967), 11. J. W. BURD, Trans. Metall. Soc. ,,lIME 245, 571 0969) and R. A. RUFa-mWEIU,Technical Report AFML-TR-68-319, Contract AF33(615)-3618 (1968). 12. R.A. BURMEmTER,Jr., G. P. F t G ~ , and P. E. GREENE,Trans. Metall. Soc. ,41ME245, 587 (1969). 13. D.G. THOMAS,Brit.J. Appl.Phys. (J. Phys. D)2, 637 (1969). 14. A.A. BERGHand P. J. DEAN,Proc. IEEE60, 156 (1972). 15. A.H. HERZtm,W. O. GROVESand M. G. CRmORD,d. ,4ppl.Phys. 40, 1830 0969). 16. W.O. GROVES.A. H. HERZO~and M. G. CRAFORD,Appl. Phys. Lett. 19, 184 (1971). 17. A.G. THOMPSON,M. CARDONA,K. L. SHAKLEEand J. C. WOOLLEY,Phys. Rev. 146, 601 (1966). 18. R.J. STmN,in Semiconductors andSemimetals (R. K. WILLAROSONand A. C. BEER,eds.), vol. 8, p. 1, Academic Press, New York, 1972, 18a. J. M. CHAMBF~LAINand R. A. STRADLINO,SolidState Commun. 7, 1275 (1969). 19. H. EHRENREICH,Phys. Rev. 120, 1951 0960). 20. M. G. CRAFORD,R. W. SHAW,A. H. HERZO~and W. O. GROVES,d. ,4ppl. Phys. 43, 4075 (1972).

P r o p e r t i e s a n d e l e c t r o l u m i n e s c e n c e o f t h e G a A s x _ x P x t e r n a r y systems

165

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