3.5 nm; the properties of these diodes were
studied in references [6] [7] [8] [9] [10].
Various groups [1] [2] [3] [4] [5] have studied the problem of GaN-based light-emitting diode (LED) degradation in the last few years, but mechanisms of degradation are not yet understood. The goal of the present work was a research of aging processes in LED's for which luminescence and electrical properties were investigated in [6] [7] [8] [9] [10]. Preliminary results of this study were published in references [11] [12]. The experiments were done at moderately high currents, not far from the normal LED operating conditions. Changes of LED properties were observed over 102-103 hours. Models are proposed to explain these changes.
Blue
and green LED's based on
InxGa1-xN/AlyGa1-y/GaN
heterostructures were studied; Dr. S. Nakamura (Nichia Chemical Co) has sent
the samples to us. [1] [6] The heterostructures had an InGaN single quantum well
active layer with thickness d 3.5 nm; the properties of these diodes were
studied in references [6] [7] [8] [9] [10].
The choice of aging conditions was made as follows. Estimations of changes of the LED characteristics were carried out while increasing the constant current over the range J=10-100 mA. Remarkable changes of spectra, capacitance-voltage (C(V)) and current-voltage (J(V)) characteristics were detected at 60-100 mA for hundreds of hours. A constant current J=80 mA was chosen for further experiments. The temperature of the LED's active area was estimated from the spectra at 80 mA to be T = 360-370 K [12]. The tests were carried out over 2000 hours. An essential part of the work was a study of the distributions of charged center effective concentration (CCEC) in the space charge region during aging.
The measurement technique is described in reference [13]. If the DC voltage on
a p-n-junction is V and an AC voltage of small amplitude 
V induces a
small change of a charge Q, then we can use an equation:
| V = (dV/dQ) ·Q
+(1/2)(d2V/dQ2) ·Q2 = ( Q)(W/ 0S)+ (Q/S)2
/2·0·eN(W) = VW +VN . | (1) |
(W- width of the space charge region , S - a square of the
structure, - dielectric constant, e -electron charge, N -
concentration of the charged centers). Two voltages, VW and
VN , were measured separately using an AC
charge·Q of constant amplitude as a sum of two high frequency
signals of nearby frequencies 
1 and 2. The
signal VN was measured at the frequency 
=
(1 - 2); the signal VW
was measured at the frequency (1 + 2)/2.
Values of W and N, calculated from VW and
VN at different V, were plotted as curves N(W).
The
intensity of EL spectra at 15 mA increased by 10 + 40 % within the first 50-100
hours of operation (at 80 mA) for blue LED's and within 800 hours
for green LED's. The intensity fell slowly during the following period,
800-1000 hours for blue and > 1000 hours for green LED's (see [10] [11]). The
strong changes of the spectra were detected for blue LED's at low currents, J
< 0.15 mA, where the tunnel and the injection components of the current are
of the same order of magnitude. The intensity of luminescence decreased, but
the relative intensity of the tunnel band (studied in [6] [7] [8] [9] [10]) increased about
three times (see Figure 1).
The intensity of the breakdown luminescence spectra (studied in [10]) decreased in the process of aging. But the relative intensity of a yellow band (2.1-2.3 eV) increased (see Figure 2). It is known that the yellow band is caused by complexes with structural defects [9]; we conclude that defects are created on the borders of the space charge region, where the recombination take place.
The changes of J(V) during aging are shown in Figure 3. A tunnel component of the direct current at low V grew both for blue and green LED's. The series resistance Rs (sufficient at higher J) grew during the 2nd period of aging. Defect formation depended on Rs (see the discussion below).
The effective concentration of charged acceptors on the p-side of the blue
LED's junction grew by 10-15% during the 1st period of aging; during the
2nd period ( 1000 hours) it fell (see Figure 4). The width of the space
charge region grew by only 30%. The CCEC of green LED's slowly grew for
600-800 hours by 10 % and after that fell insignificantly. It is to be
noted that the change of CCEC takes place over a distance W 40-80 nm, of
the same order of magnitude as a mean free path 1fp (see an
estimation below).
A model of the 1st stage may be as follows. There are residual complexes Mg-H in the active layer; electrons at high injection currents can disrupt them so, that the hydrogen goes out of complexes and the charge of Mg-ions should be compensated by holes:
| Mg-H = > Mg - + (+) + H. | (2) |
We suppose that in the 2nd stage the formation of donor defects which compensate acceptors prevails. A possible defect may be the Nitrogen vacancy - VN; the probability of VN formation in p-type GaN is appreciably higher than that of Gallium vacancies [10] [11]:
| GaN => Ga + V+N + (-) + N. |
These defects increase the probability of nonradiative recombination. The sign of the charges in this equation are given conditionally, they are not confirmed. Such a model explains the second stage of the aging process. In addition, there takes place a migration of defects on the borders of growth columns: the defects accumulate in "weak points" of maximal electrical field. It is possible in such a way to explain the growth of the tunnel components of the current and spectra.
The formation of structural defects in GaN at a rather low temperature (about T=370 K) needs to be explained. This is possible by using a model of defect creation by hot electrons in p-n heterostructures. This model was developed for GaAs-based structures and has explained the aging processes in n-AlGaAs/p-GaAs heterojunctions rather well [14]. It is supposed that the electrons receive an additional kinetic energy crossing the heterojunction with a conduction band offset. These hot electrons transfer the energy to the atoms that are displaced. The assumption is based on the experimental fact that the defects are formed over a depth of about the mean free path lfp from the heterojunction boundary (not on the diffusion length, Ln >> 1fp).
Electrons injected from the n-side of a heterojunction into the p-layer have an
energy E relative the bottom of the conduction band in the quantum well:
E >> kT:
| E = E-Ec > Ec =
Ec2 - Ec1 >> kT. | (3) |
Electrons should give this energy back at the other side of a well (on the
p-side, see Figure 5a). The average energy of electrons remains the same as on
the n-boundary at a voltage of about a contact potential, V 
k
(see Figure 5b). There are compensated layers in the investigated
structures on both sides of the quantum well [7] [8] [9] [10]. At V >
k most of the forward voltage falls on the quantum wells in
the layers. Electrons get additional energy in the electrical field of the
compensated layers over a mean free path lfp (see Figure 5c).
Kinetic energy of electrons at a high current density can be transferred to a lattice during the relaxation time on a length of the order lfp not only by phonon scattering, but also by sub-threshold defect formation. It should occur either in the compensated layers near the active layer, or in the p- space charge layer.
If electrons transfer energy to the Mg-H complexes, the reaction of breaking
the complex and activating the Mg-acceptor (equation 1) will go with a high
probability. This mechanism will take place mainly on the border of the active
layer in p-AlGaN. The threshold energy Ed of breaking the complex
Mg-H is greater than the thermodynamic Frenkel energy; estimates have given a
value of Ed 4 eV.
It is known that at high temperatures nitrogen leaves the GaN lattice as a gas, N2, forming vacancies VN [15]. If hot electrons transfer an energy to the lattice breaking the Ga-N bond, the formation reaction for defects (equation 2) will occur at lower T. It is to be noted that the formation probability of equilibrium donor vacancies VN is higher in p-GaN [16].
The processes of Mg- activation and VN creation are simultaneous. At the 1st stage the Mg- activation prevails, but it is limited by a low Mg-H concentration. At the 2nd stage the VN creation prevails and it is not limited: N- atoms are intrinsic in the lattice. A dynamic equilibrium concentration of N- vacancies will be established at a long aging time.
The
theoretical analysis will be done for sub-threshold defect formation during hot
electron injection by an analogy with the theories of the high energy particle
interactions with atoms of a crystal [17]. The main difference consists of the
fact that the energy of hot electrons, E, is orders of magnitude less
than the threshold energy Ed of atom displacement. In this case the
process of interaction goes through the excitation of an electronic subsystem
[17] [18]. The displacement of atom in a lattice by electrons with kinetic
energy E has a probability:
| w (E) ~ exp(-Ed/E), | (4) |
where Ed is the displacement threshold energy. The effective
probability of displacement integrated over all energies E and
velocities vx, is equal to
 =  w(E) exp(- x) vx
dvx exp(-y)dvy
exp(-z)dvz / vx
f0dvxdvydvz , | (5) |
where i = mn*vi2/2kT,
f0 is the distribution function of electrons in the n-emitter, and
vi are components of the electron's thermal velocity.
Let's
assume that the diffusion of generated defects is low, and we may neglect the
electrical field in the considered area. Then the concentration of the
displaced intrinsic atoms N0 changes in time t and distance x
according to the equations:
N0 = G(x)  0(T) [1-exp(-t
/0(T))]; G(x)=N0  0(x);
0(x) = (3/2)(j/q) 0 a(x)
 0 ; a(x) = exp(-x/lfp) [1- exp(-x /lfp)] exp(-x/LD), | (6) |
where N0 is the concentration at the time t=0, a(x) is the
spatial distribution of the generation rate of point defects, G(x) is their
generation rate, j = J/S is the current density, q is the electron charge.
0 is the characteristic relaxation time of defect displacement,
LD is the diffusion length, 0 is the cross-section
of hot electron interaction with the atom. This dependence will saturate with
time with a time constant 0(T).
The change of concentration of Mg-H complexes, whose concentration is less than the concentration of intrinsic atoms, Nc << N0, is described by an equation:
| Nk (x,t) = Nk0 [k(x)
k(T)/ (k(x) k(T) +1)]
{1-exp(-t(k(x) k(T) +1)/
k(T))}; | (7) |
where k(x) and k(T) are analogous to the
parameters 0(x) and 0(T) in equation 6. The
dependence Nk (x, t) is described by the equation
| Nk (x,t) = Nk0 {1-exp(-
k(x) t )}. | (8) |
It is assumed in this equation that the concentration Nk0 is
rather low and that the hydrogen atoms have a high probability to exit the
lattice at high values of k(T).
The value of the mean free path lfp is of the order
lfp 3.10-6 cm; it is included in the expression for
a(x) assuming an electron mobility of 400-600 cm2/V·s which
is determined mainly by the lattice phonon scattering. The interaction
cross-section 0= (No lfp )-1
may be assumed to be 9-10-17 cm2. Let us take
values of t0102-103 hours from
our experiments at J = 80 mA (j = 80 A/cm2) for blue LED's.
It is then possible to estimate the threshold energy and effective probability
of displacement of atoms, 0 in equation 6: Ed
7-8 eV; 0 2·10-14. Estimates of the
effective probability of atoms displacement for Mg-H complexes give these
parameter values: Ed 3-4 eV; k
10-5, k 8·10-10 .
These values are used for an explanation of the changes of the concentration of
the charged impurity N0, Nk in the
described experiments.
A dependence N(t) was calculated using equation 7 and equation 8
with the parameters estimated above (see Figure 6). The points on the curves
correspond to the measurements given in Figure 4 for blue and green LED's; the
changes of effective charge concentration are close to the calculated curves.
Our estimates give only orders of magnitude of the parameters. They only show that sub-threshold creation of point defects by injected hot electrons in GaN heterostructures can explain LED aging effects.
Luminescence spectra and electrical properties of blue and green LED's based on InGaN/AlGaN/GaN heterostructures with single quantum wells change remarkably within 100 -2000 hours of operatingat a current 80 mA.
An increase of luminescence intensity at currents 15 mA and an increase of
charged acceptor concentration in the space charge region during the first
period of aging is explained by activation of Mg acceptors due to an exit of H
atoms from residual Mg-H complexes.
The slow fall of luminescence intensity and charged acceptor concentration during the second period can be explained by creation of donor defects by injection of hot electrons into quantum wells. The first period for blue diodes is shorter (70-100 hours.) than it is for green ones (800-1000 hours), which is caused by the greater compensation of acceptors and lower electric fields in the green diodes.
A model of injection stimulated sub-threshold formation of defects (breaking of bonds Mg-H or bonds Ga-N by hot electrons injected into quantum wells) can explain effects of aging.
© 1998 The Materials Research Society
