Interband nonradiative Auger recombination in quantum-well InGaAsP/InP heterostructure lasers has been calculated. It is found that the Auger rate is much reduced in the quasi two-dimensional quantum-well lasers. This suggests that the temperature sensitivity of quantum-well InGaAsP lasers is much less than ordinary structures with much higher values of T0at around room temperatures

Chiu, L. C.

Yariv, Amnon

English

Caltech Authors - Main

1406 IEEE JOURNAL O F  QUANTUM ELECTRONICS, VOL. QE-18, NO. 10, OCTOBER 1982 
Auger  Recombination in Quantum-Well InGaAsP 
Heterostructure Lasers 
Abstract-Interband nonradiative Auger recombination in quantum- 
well InGaAsP/InP heterostructure lasers has  been calculated. It is found 
that the Auger rate is much reduced in the quasi  two-dimensional 
quantum-well lasers. This suggests that the temperature sensitivity of 
quantum-well  InGaAsP  lasers is much less than ordinary  structures with 
much higher values of To at around  room temperatures. 
A CONTINUING problem with lasers and light emitting diodes (LED) based on the  quaternary  compound 
In,-,Ca,AsyP1-y lattice  matched  to  InP is their  temperature 
sensitivity. In LED’s, the optical output power saturates at 
high current densities and, in lasers, the threshold current in- 
creases  rapidly with  temperatures above 220-250 K. 
In the case of lasers, the threshold current has been found 
empirically to vary with temperature T as Ith - exp (T/To).  
The quantity To determines  the  temperature sensitivity of the 
device. In InGaAsP lasers, the log (Ith) versus T plot  exhibits 
a break-pomt temperature below which the To is typically 
about  110 K, whereas above the  break-point  temperature, To 
has a low value of -50-60 K [I]-[3]. The break-point typi- 
cally occurs at around 220-250 K. The To in GaAlAs/GaAs 
lasers, on the other hand, remains at about 120-170 K over 
the same temperature range [4]. Many mechanisms have been 
proposed to account for the low To of the quaternary lasers. 
Among the various  mechanisms considered,  the  interband 
Auger recombination  has  been  found  to be a  dominant  factor 
Although  itas been demonstrated  that GaAlAs/GaAs 
quantum-well lasers exhibit higher To’s [8], it is unclear 
whether InGaAsP quantum-well lasers would be free from a 
break-point  in  the  threshold  current versus temperature charac- 
teristics. In this paper, we present an analysis of the non- 
radiative Auger recombination in the  quantum-well lasers. I t  is 
found  that  the rate of Auger recombination is greatly reduced 
in  such quasi two-dimensional structures. It is thus suggested 
that  the log (Ith) versus T plot  for  such lasers would  be free 
from a low temperature break-point and the To for tempera- 
tures above 220-250 K should  remain above - 120 IC. Experi- 
mental confirmation of this prediction will also serve as a 
check on the  importance  of Auger recombination in ordinary 
InGaAsP lasers. The data in [9] for multiple quantum-well 
lasers do indicate that the breakpoint is -300 K, which is 
considerably higher than  ordinary  quaternary lasers. 
PI - v i .  
Manuscript received April 5, 1982;revised  June 11, 1982. This work 
was supported by the Office of Naval Research and  the Air Force Office 
of  Scientific  Research. 
The  authors are  with the California Institute of Technology, Pasadena, 
CA 91125. 
AMNON YARIV 
il L 
Fig. 1. The CHCC Auger recombination processes. 1 ,  2 and l’, 2‘ are 
the initial and final states, respectively. 
In this paper, only the CHCC (see Fig. 1) process will be 
considered.  The rate of Auger transition can be written 
as [lo] 
x [ f l f i  (1 - f l l > ( l  - f 2 0  - ( 1  - f 1 ) Q  - f 2  )fi8f2t1 
. 6 (Ef - Ei) dkl dkljdk2. ( 1 )  
In the above, the f ’ s  are the Fermi factors, Ef,i  are the final 
and  initial energies of  the particles,  respectively, e is the elec- 
tronic charge, V is the  volume, LD is the screening length, and 
2 < 2p < 3 due to spin symmetry.  The overlap  integrals 
lFlF2 l 2  are given by [ 1 I ]  
where me is the  electron mass, Eg is the bandgap energy,  and 
f c u  is the oscillator strength.  The screening length is calculated 
from [12] 
where e, is the relative dielectric constant, E ,  is the permit- 
tivity of free space, kB is the  Boltzmann  constant,  and Tis  the 
temperature. 
Equation ( 1 )  has been modified [see (5)) to calculate the 
rate of Auger recombination in a  quantum-well  structure.  It is 
well known  that  when  the active layer thickness L ,  of a semi- 
conductor laser is of  the  order  of  the carrier de Broglie wave- 
length,  quantum size effects arise [ 131. The  nonradiative 
band-to-band Auger process then changes in a fundamental 
0018-9197/82/1000-1406$00.75 0 1982 IEEE 
IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-18, NO. 10, OCTOBER 1982 1407 
way. For a quasi two-dimensional  layer,  it is usually assumed 
that the single-particle Hamiltonian can be separated into a 
quantized  component  normal  to  the  layer  and  continuous 
components  in  the plane of the layer [14]. In  such a  case, the 
energy spectrum is given by [ 151 
where n denotes  the  nth  quantized  state  of k,, m" is the  effec- 
tive mass of  electrons  or  holes,  and kx ,  k,, are the  continuous 
components  of  the  crystal  momentum. We recognize that  the 
actual  band  structure  of  quantum-well  structures  has  not  been 
established and  the  parabolic  band  approximation is employed 
here. However, in  the case of  the CHCC process, taking non- 
parabolicity into account would  lead to slower Auger rate 
[I61 and  thus, even longer lifetime. Also, possible anisotropy 
in the effective masses has been neglected, and the effective 
masses of  the  electrons  and  holes  in  the  direction  perpendicular 
and parallel to  the plane of the  layer have been  taken  to be the 
same. This would not affect the transition rate significantly 
unless the anisotropy factor is bigger than - 1.5. The Auger 
rate  for  such  quasi two-dimensional systems  becomes 
x [flfi(l -fv)(l - f i t ) -  (1 -f1)(1 - f 2 > f 1 f z 1 1  
. 6 (Ef - Ei)dkldklfdk2' (5 1 
where S denotes  summing over discrete  states  and  integrat- 
ing over continuous  states. 
In this work, all the calculations have been performed for 
Ino.72Ga,,28Aso.60Po.~o  for  which  the emission wavelength is 
about 1.3 pm.  To  find  the  confined  quantized  states,  the dis- 
continuities are taken  to  be -0.31 and -0.15 eV in the con- 
duction and valence bands, respectively [ 171. The quantum- 
well is assumed to be a finite  square well and  the  summation 
is extended only over the confined states in (5). The small 
Fermi  factors  at  the  top  of  the well (-10-5-10-6) justify  this 
approximation. The rate is then calculated numerically and 
the Auger lifetime is obtained  from  the  expression 
where An is the injected carrier density at threshold. It is 
assumed here  that  the  injection level is  high, so that An G nth ,  
an assumption  which is excellent in the case of  injection lasers. 
The  results  of  the  calculation  are  presented  in Figs. 2-4. In 
Fig. 2, l/rA is plotted against the  electron  density  at a tempera- 
ture  of 300 K and  for a quantum-well  with  width  100 8. The 
slope of 2.45 (?2) is typical of the nonradiative process in 
degenerate materials [ 6 ] .  In Fig. 3, the nonradiative Auger 
lifetimes  of  the  quantum-well  and  ordinary laser structures are 
compared under the same injection conditions and tempera- 
tures. A well with width 100 has also been assumed for the 
quantum-well laser. It  shows  that  the Auger lifetime is about 
two  orders  of magnitui-le longer in the  quasi two-dimensional 
I 3  MICRONS 
T = 300°K 
SLOPE = 2.47 
WIDTH = 1008 
'1. 
0.5 
I I '  
5 ~ 1 0 ' ~  1OI8 5 X 10'' 
CONCENTRATION ( ~ r n - ~ )  
Fig. 2. The inverse of Auger lifetime as a function of carrier 
concentration for a 1.3 pm quantum-well (width = 100 A) InGaAsP 
laser at 300 K. 
1 0 - 5 7 7  
1.3 MICRONS 
\N13TH = IOOX --- W A S 1  2 - 0  i 
I 
275 325 375 425 
TEMPERATURE ( O K )  
Fig.  3. Comparison  of calculated Auger lifetimes for a 1.3  pm 
quantum-well (width = 100 A) and  ordinary InGaAsP lasers under  the 
exact same injection conditions. 
system. In Fig. 4 the lifetime versus width of well at a tem- 
perature of 300 K is plotted.  It can be seen that  the  lifetime 
decreases rapidly  with increasing well width.  This  is  expected 
since the  number of confined states increases and  the energy 
separation between states decreases when the width of the 
well increases. Moreover, the  quantum size effect  would have 
to disappear  gradually as the  width increases. 
The  dramatic increase in  lifetime in  a quasi  two-dimensional 
system as compared  to  the  three-dimensional  system is due  to 
the  nature  of  the  difference  in  the  density  of  states,  and,  more 
importantly,  the decrease  in the  number of configurations 
that can  satisfy the  requirement  of  both  momentum  and 
energy conservation simultaneously. Although the calculation 
is carried out  for a single quantum-well  only,  the energy band 
within  the well for a multiple  quantum-well as well as super- 
lattice structure can be shown to be very narrow [18], [19] 
1408 IEPX JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-18, NO. 10, OCTOBER 1982 
Fig. 4. Calculated Auger lifetime for a 1.3 p m  quantum-well laser as a 
function of well width at 300 K. 
and the results given here will approximately be valid in these 
cases too. 
The  threshold  current  density can  be written as 
for  ordinary lasers and single quantum-well lasers, and 
n th  eNd 
J th  = ___ 
7 
for  multiple  quantum-well lasers [ 151. In the above equations, 
e is the  electronic charge, d is the active layer thickness, nth is 
the injected carrier density at threshold, N is the number of 
quantum wells,  and T is the carrier lifetime. In lasers, it  is  the 
existence  of  competitive  nonradiative processes which  shorten 
the carrier lifetime [5]-[7]. From ( 7 )  and (8), it is obvious 
that a decrease in T causes a corresponding increase in the 
threshold at the same n th .  Although the nonradiative Auger 
lifetime is longer in the quantum-we11 lasers, it is the relative 
magnitude  between  the radiative  and  nonradiative lifetimes 
that is important. 
In  quantum-well lasers, it can  be shown  that  the  ratio of the 
radiative lifetime  in  a  three-dimensional  structure  and  a quasi 
two-dimensional system under the constant matrix element 
assumption can be written as (neglecting light and split-off 
hole bands) 
where m, is the  reduced mass of  the  electron  and  hole, L,  is 
the width of the well, w is the frequency of light, E, is the 
bandgap energy,  and n is the  number  of pairs of levels where 
optical transition can take place. Taking n = 1, it can easily 
be verified that the ratio is less than one for (4w - E,)‘/2 < 
0.275. Since under  ordinary laser operation (Am - E,)’/’ << 
0.275, the radiative lifetime in a quantum-we11 laser is even 
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shorter  than in a  conventional laser. This can be verified in the 
GaAs-GaAlAs system from  the  data in 181. Thus,  the radiative 
lifetime at threshold for quantum-well lasers remains in the 
nano  or  subnanosecond regime. For  a single quantum-well 
laser, despite the higher gain [see (9)], the carrier density at 
threshold is about  1.3  times  that  of  a  conventional laser due to 
the small optical  confinement  factor. However, it  can be seen 
from Fig. 2 that even at densities of several times that of 
ordinary lasers, the Auger lifetime  is still much longer than  the 
radiative lifetime. Thus, in the quantum-well lasers, the non- 
radiative Auger processes are no longer competitive with the 
radiative  process. Therefore,  it is predicted  that  such lasers will 
not have a low temperature break-point above which the To 
decreases considerably. If such behavior can be confirmed by 
experimental  observation,  the case for  the  importance  of Auger 
recombination in ordinary  InCaAsP lasers will also be 
strengthened. 
In conclusion,  the  nonradiative Auger lifetimes  in a quantum- 
well InGaAsP laser have been calculated  and  found  to be much 
longer than  the radiative lifetime. It is thus  predicted  that  the 
quantum-well laser will not be  characterized  by a  low To and, 
as a  result, will not be as temperature sensitive as the  ordinary 
lasers. In ordinary lasers, the rate constant for Auger recom- 
bination is material  dependent  and, a t  a given temperature, is 
fixed 1201. Thus,  it is difficult  to  obtain lasers with high 
To’s. However, the results of this work suggest that InGaAsP 
lasers with high To’s could be obtained  by employing the 
single or  multiple  quantum-well  structures. 
IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-18, NO. 10, OCTOBER 1982 1409 
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CW Laser Action in Ethyl  Chloride 
N. G. DOUGLAS AND PETER A. KRUG 
Abstract-We have observed far infrared output at 447, 698, 1306, 
and  1669  pm in ethyl  chloride using a metallic-waveguide laser and a 
COz pump laser. The measurements were made with a metal-mesh 
I 
Fabry-Perot  interferometer and, together with the  pump assignments, 
they  are in disagreement with previously  published values. I 1 I 
I 
E THYL chloride, C2H5C1, is a particularly useful active medium in optically pumped far infrared (FIR) lasers 
since it provides radiation  at several wavelengths in  the sparse 
region around 1 mm [l] . We report here new measurements 
of the  FIR wavelengths and C 0 2  pump line assignments for PLATE  DISPLACEMENT  (mm) 
the  literature [2]. Measurement  of the  full 34  transmission  maxima  yields a wavelength 
this molecule which are at variance with those appearing in Fig, 1. Segment of a Fabry-Perot interferogram for the 1306 Mm line, 
Our FIR laser consisted of a 2.0 m long cylindrical copper accuracy of about 0.1 percent. 
waveguide of  19  mm inside diameter and  plane  polished alumi- 
num  end mirrors. Input and output  coupling was through 
circular holes of diameter 1.5 and 2.0 mm, respectively. The 
output mirror could be translated 4 mm with 51 pm resolu- 
tion. The C 0 2  pump laser was grating tuned and delivered 
about 20 W on each line concerned. FIR radiation was de- 
tected  with a Golay cell and  a lock-in amplifier. 
Using a  plane  parallel inductive  metal-mesh  free space Fabry- 
Perot interferometer whose plate separation could be varied 
by  12  mm, we measured  FIR  output wavelengths of 447 k 1 
pm,  698 f 1 pm,  1306 k 2 pm,  and  1669 1: 2 p m .  Wavelength 
uncertainties  are  determined  by  the finesse of  the  interferom- 
eter  for  the  shorter lines and  by  the available scanning range 
at longer wavelengths. Fig. 1  shows  a typical  Fabry-Perot 
interferogram for the 1306 pm line. The performance of the 
interferometer was checked by measuring the wavelength of 
the well-known 570.57 pm methanol line. 
Previous  wavelength measurements  on  ethyl  chloride [ 2 ]  
were apparently made by translating the end mirror of the 
waveguide laser cavity. When we did this for the lOR(28) 
pumped lines we found, in addition to wavelengths of 447 
and 1306 pm, a periodicity corresponding to a wavelength 
of 1346 f 5 pm (see Fig. 2). However, measurement of the 
free space wavelength of  this  feature yielded a value of 1306 
pm. We believe this line to be the  same as that  reported earlier 
as having a wavelength of 1350 pm 121. 
Calculations indicate that a TE,, circular waveguide mode 
Manuscript  received  April 27, 1982. This  work was supportcd in part would account for this longer guide wavelength in a laser 
by the Australian  Research Grants Committee and the Australian  Insti- whose end mirror is to the end of the waveguide. ln our 
tute of  Nuclear  Science and Engineering. 
The authors are  with the  School of  Physics, Sydney University,  Syd- laser the Output mirror was kept between and mm from 
ney,  Australia. the  end  of  the guide in  order  to  reduce losses. While losses 
. .  
0018-9197/82/1000-1409$00.75 0 1982 IEEE 


Auger recombination in quantum-well InGaAsP heterostructure lasers

1409 “Quantum size effect and perspectives of its practical application,”

Auger recombination in germanium,” Phys.

Auger recombination in InAs,

Band-to-band Auger effect in long wavelength multinary 111-V alloy semiconductor lasers,”

Electronic properties of a semiconductor superlattice. I. Self-consistent calculation of subband structure and optical spectra,”J.

Heterostructure Lasers.

Interband Auger recombination in InGaAsP,”

Lowtemperature behavior of the threshold current and carrier lifetime

New transport phenomenon in a semiconductor ’superlattice,’

Nonradiative carrier loss and temperature sensitivity of threshold in 1.27 um (GaIn)(AsP)/ InP D.H. lasers,’’

of InP-Inl-,Ga,P1-,As, (x - 0.13, z - 0.29) by quantum-well luminescence,”

Temperature dependence of threshold current for quantum-well A1,Gal-,AsGaAs heterostructure laser diodes,”

The authors are with the School of Physics, Sydney University, Syd- laser the Output mirror was kept between and mm from ney, Australia. the end of the guide in order to reduce losses. While losses .

The case for Auger recombination in InI-,Ga,AsyP1-y,”

Theory of layer structures,”

http://authors.library.caltech.edu/10738/1/CHIieeejqe82a.pdf

Auger recombination in quantum-well InGaAsP heterostructure lasers

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