A new technique for determining carrier diffusion lengths

in direct gap semiconductors by cathodoluminescence measurement

is presented. Ambipolar diffusion lengths are

determined for GaAs quantum well material, bulk GaAs,

and Al_xGa_(1-x)As with x up to 0.38. A large increase in

the diffusion length is found as x approaches 0.38 and is

attributed to an order of magnitude increase in lifetime

Eng, L. E.

Lebens, J. A.

Sercel, P. C.

Vahala, K. J.

Yariv, A.

Zarem, H. A.

English

Caltech Authors - Main

A NOVEL TECHNIQUE FOR THE DIRECT DETERMINATION OF 
CARRIER DIFFUSION LENGTHS IN GaAs/ AlGaAs HETEROSTRUCTURES 
USING CATHODOLUMINESCENCE 
P. C. Sercel, H. A. Zarem, J. A. Lebens, L. E. Eng, A. Yariv, and K. J. Vahala 
Department of Applied Physics, 128-95 
California Institute of Technology 
Pasadena, California 91125 
818/356-2194 
Abstract 
A new technique for determining carrier diffusion lengths 
in direct gap semiconductors by cathodoluminescence mea-
surement is presented. Ambipolar diffusion lengths are 
determined for GaAs quantum well material, bulk GaAs, 
and AlzGa1-zAs with x up to 0.38. A large increase in 
the diffusion length is found as x approaches 0.38 and is 
attributed to an order of magnitude increase in lifetime. 
1 INTRODUCTION 
Measurement of material parameters such as carrier diffusion 
length in GaAs/ AlGaAs heterostructures is of great interest 
due to the importance of these structures for optoelectronic 
devices, high electron mobility transistors (HEMT), resonant 
tunneling diodes, etc. Minority and ambipolar carrier dif-
fusion lengths are important both as transport parameters 
and as quantities which can be used to obtain information 
on carrier lifetime or mobility. Many methods have been 
used to measure diffusion lengths, most notably, the Haynes-
Shockley experiment [1]. More recently, techniques such as 
short-circuit photocurrent measurements [2], electron beam 
induced currents [3], transient grating techniques [4], and 
time of flight studies [5] have been applied. Here, we present 
a simple new technique for determining the carrier diffu-
sion length using cathodoluminescence (CL). This method 
can be applied to direct gap semiconductors to determine ei-
ther minority carrier or ambipolar diffusion depending on the 
sample doping and excitation conditions. Due to the preci-
sion and ease with which one can control the position of the 
electron beam in a scanning electron microscope (SEM) the 
method is very straightforward and accurate. Furthermore, 
the ability to examine the sample under the high magnifi-
cations available with an SEM allows this technique to be 
applied to submicron devices and arrays of microstructures 
such as quantum wires. In this paper we apply the tech-
nique to ambipolar diffusion in GaAs quantum well material, 
bulk GaAs, and AlxGa1_xAs with aluminum mole fraction 
x up to 0.38. Transport in the X and L valleys is found to 
significantly affect the diffusion length in higher aluminum 
material. 
2 DESCRIPTION OF THE TECHNIQUE 
The experiment is performed in a modified SEM with a fiber 
optic CL collection system [6]. In the SEM, an energetic elec-
tron beam is incident upon the sample, generating electron 
hole pairs within the interaction region of the beam with the 
sample. One end of the fiber is placed approximately 0.5mm 
from the sample, collecting luminescence from a region ap-
proximately lOOJ.Im in radius while the other end is coupled 
into a monochrometer allowing spectral resolution of the CL 
signal. A thin aluminum mask covers half of the sample and 
prevents detection of the luminescence emanating from the 
region under it. All detected luminescence is from radiative 
recombination which occurred in the unmasked region. This 
is shown schematically in Fig.l. By generating the carri-
ers in the masked region of the sample and measuring the 
luminescence intensity as a function of the distance of the 
beam from the mask edge, l(x), we are able to determine 
the diffusion length, Ln. To allow different material compo-
sitions to be investigated on a single sample, carriers were 
confined to narrow channels of the material being studied by 
high bandgap barriers on either side. It is important that 
the barriers be thin compared to x so that only those carri-
ers which were generated in the channel contribute to its CL 
signal. Signals from different channels were separated with 
the monochrometer. 
The simplicity of the technique results from the fact that 
the luminescence signal depends exponentially on x/Ln. Be-
cause of the large collection area of the optical fiber, the 
CL signal is proportional to the net flux of carriers into the 
unmasked region. Equation 1 governs the concentration of 
carriers outside of the generation region 
c 2c 0 = -- + D \J 
T 
(1) 
where C, r and D are the carrier concentration, lifetime, and 
diffusivity. In the one dimensional problem, the solution to 
Eq. 1 is simply C(x)=C0exp(-x/Ln), where Ln = $T. The 
corresponding flux is also proportional to exp( -x/Ln ). In 
addition, this solution would apply if we generated a line 
of constant carrier density, parallel to the mask edge. By 
breaking the line into infinitesimal elements, and examining 
the flux due to an individual element, it can be shown that 
the net flux caused by a single point source is also propor-
tional to exp(-x/Ln) [7]. This argument is easily extended to 
an arbitrary generation region. The exponential dependence 
11.3.1 
CH2637-7/89/0000-0285 $1.00 © 1989 IEEE IEDM 89-285 
on x is significant not only because of the ease with which 
it is handled numerically, but also because it allows us to 
ignore the size and shape of the interaction region so long as 
it remains completely under the aluminum mask. 
signal through it. All data presented here were taken at room 
temperature. 
The sample was excited by a lOkV electron beam with a 
current of approximately 20nA. This yields a carrier density 
on the order of 1018cm-3 in the generation volume. With a 
3 
10 kV beam, the generation volume has a radius of approx-
DESCRIPTION OF THE EXPERIMENT imately 0.1~£ in the channels [11]. To ensure that the entire 
The samples used in this experiment were grown by molec-
ular beam epitaxy in a Riber 2300 R & D system. Layers 
with AI mole fractions of 0.09, 0.19, 0.25, 0.35, and 0.38 
were grown as well as a GaAs layer and a 100A GaAs quan-
tum well. There was no intentional doping in any of the 
samples. The determination of the AI mole fraction was 
accomplished by room temperature photoluminescence (PL) 
measurements. The PL spectra were taken using a relatively 
low intensity(:::::: 1W/cm2 ) excitation by the 5145A line of 
an Argon ion laser, and Al mole fractions, x, were deter-
mined from the PL spectra peak energy, EP, using the rela-
tion Ep(eV) = 1.42+1.45x -0.25x2 which has been shown to 
hold for 0 < x $ 0.45 and similar excitation conditions [8]. 
There is some disagreement as to the relationship between 
bandgap energy and AI mole fraction [9,10], particularly in 
the range 0.35 < x < 0.45. We have used the relationship of 
Ref. [9] since it is more recent. 
To form the mask, stripes of aluminum, 750A thick and 
100~tm wide were evaporated onto the surface of the samples. 
While thin enough to allow the electron beam to penetrate 
into the sample with minimal scattering, this mask was found 
to be sufficiently thick to prevent detection of a luminescence 
e Beam~ 
A 1 Mask 750A ~ 
Barrier .. 
Channel ., 
Barrier .. 
AlGaAs ~ 
interaction region remained under the mask scans were per-
formed over distances greater than 0.91£ from the mask edge. 
As an additional precaution the beam was scanned toward 
the mask edge to ensure that material between the beam and 
the mask edge had not been altered by the beam. Figure 2 
shows typical data runs for three different channels. 
4 INTERPRETATION OF THE DATA 
Figure 3 shows the results of the diffusion length measure-
ments. The diffusion lengths given represent an average over 
four measurements in different regions of the sample. The 
error bars represent the standard deviations. For the quan-
tum well material, Lo is approximately the same as in the 
GaAs channel. The reduction in the diffusion length for the 
Al_1gGa.81 As channel can be attributed to a reduced mobility 
due to alloy scattering and increased effective mass [12]. A 
surprising result is the trend towards extremely large diffu-
sion lengths for the Al.,Ga1_.,As material for x beyond 0.2. 
Increased alloy scattering, intervalley scattering, and effec-
tive mass, cause further reductions in the mobility leading us 
to conclude that it is an increased lifetime which is respon-
X 
Figure 1: Schematic diagram of the experiment. An elec-
tron beam is incident on the sample, generating electron hole 
pairs. Luminescence is collected with the optical fiber. The 
AI mask blocks detection of luminescence from the region 
under it. 
11.3.2 
286-IEDM 89 
sible for the large values of Lo. Using the electron mobility 
data of Ref. [12], and a. heavy hole mobility calculated from 
Ref. [13], our Lo measurements imply a.n order of magnitude 
increase in lifetime for the 0.35 and 0.38 Al mole fraction 
samples as compared to Ga.As. 
We believe the increase in lifetime to be due to a.n in-
crease in the occupancy of the indirect X and L valleys a.s 
the aluminum mole fraction is increased towards 0.4, at which 
point AlGa.As becomes an indirect gap semiconductor. As 
the AI mole fraction is increased from zero to 0.35, the en-
ergy separation between the r, X, and L valleys decreases 
to less than 0.05eV [10,9]. This situation persists over the 
range 0.35 < x < 0.45. In this region, all three valleys will 
be significantly populated under room temperature excita-
tion. Since intervalley scattering and intra.band relaxation 
processes all occur on a time scale which is much shorter 
than the carrier lifetime [14,15], the carriers in the conduc-
tion band may be assumed to be in thermal equilibrium, 
and Fermi-Dirac statistics may be applied. We have calcu-
lated the populations of the three valleys of the conduction 
band using Fermi-Dirac statistics and the parabolic band 
approximation. The bandgaps for these valleys were taken 
from Ref. [9] and the density-of-states effective masses from 
Ref. [13]. We define the parameter R(n) = nfnr where n is 
the carrier concentration and nr is the population of the r 
valley. On average, each electron will spend 1/ R of its life 
8 
D 100Aaw 
+ X = 0.38 7 0.19 0 X = 
->- 0 
- ~ 6 ., \, c CD 
-
(A,8 c 
-
5 
'\, 
' 
0) \ 0 ...I 
' 
4 'b ~0 IIJ 
3 
0 2 3 4 
Beam Posltlon(~m) 
Figure 2: Log of the cathodoluminescence intensity as a 
function of beam position for quantum well, Al.38Ga.62 As 
and Al.19Ga.81 As channel. The ambipolar diffusion length is 
given by the reciprical of the slope. 
in the r valley. Taking the lifetime in the indirect valleys 
as infinite compared to the lifetime in the r valley, R can 
be viewed as a lifetime enhancement factor, that is, the car-
rier lifetime is given by r = Rrr, where rr is the lifetime 
in the r valley. Using an approximate value for the carrier 
concentration of 1018cm-3 we find for Al.38Ga.s2As R ~ 10 
in agreement with our expectation. To obtain a quantitative 
confirmation of our hypothesis would require precise knowl-
edge of the carrier concentrations, or a direct measurement 
of carrier lifetime as a function of aluminum mole fraction. 
Further work to measure these lifetimes is in progress. 
In conclusion, we have presented a new method for mea-
suring either minority carrier or ambipolar diffusion lengths 
by cathodoluminescence. The technique is extremely accu-
rate due to the precision with which one can position an 
electron beam in an SEM. A simple exponential dependence 
of the CL intensity with beam position facilitates extraction 
of Lo from the data. A trend towards large Lo was observed 
for Al.,Ga1_.,As with x approaching 0.38 and was explained 
to result from intervalley scattering. Further investigations 
of this effect are in progress. 
The authors would like to acknowledge the support of 
the Office of Naval research and the SDIO-ISTC. One of us 
(P.S.) would like to acknowledge the support of a graduate 
NSF fellowship. 
3 
"E 
IT :300K I + ~ 
:::t 2 
... 
(.!) + 
z 
w 
-l 
z 
0 (ij 
::> 
u. 
u. 
.i5 
-
0 
0.0 0.1 0.2 0.3 0.4 0.5 
AL MOLE FP.ACTION 
Figure 3: Ambipolar diffusion length at a carrier density of 
1017-1018cm-3 • The samples with AI mole fraction greater 
than 0.3 have high values due to the increased lifetime. A 
100A GaAs quantum well showed the same value as the 
thicker GaAs (x = 0.0) layer. 
11.3.3 
IEDM 89-287 
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11.3.4 
288-IEDM 89 


A novel technique for the direct determination of carrier diffusion lengths in GaAs/AlGaAs heterostructures using cathodoluminescence

Heterostructure Lasers

http://authors.library.caltech.edu/31634/1/SERiedm89.pdf

A novel technique for the direct determination of carrier diffusion lengths in GaAs/AlGaAs heterostructures using cathodoluminescence

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