Mater. Res. Soc. Symp. Proc. Vol. 831 © 2005 Materials Research Society
E3.38.1
Discrete Steps in the Capacitance-Voltage Characteristics of GaInN/GaN Light Emitting
Diode Structures
Y. Xia1,2, E. Williams1,2, Y. Park2,3, I. Yilmaz1,2, J.M. Shah2,3, E.F. Schubert1,2,3, C. Wetzel1,2
1
Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy,
NY 12180, U.S.A.
2
Future Chips Constellation, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A.
3
Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute,
Troy, NY 12180, U.S.A.
ABSTRACT
A detailed modeling of the electronic bandstructure of GaInN alloys and GaInN/GaN
heterostructures typically used for high efficiency light emitting diodes is of high relevance for
future improvements. Here we are exploring opportunities to accurately quantify the carrier
dynamics under forward and reverse voltage bias. In GaInN/GaN LED-type heterostructures we
observe distinct steps in the junction capacitance as a function of bias voltage within the
depletion regime. Up to three individual steps can be identified that correspond to alternating
ranges of capacitive and resistive impedances. Our analysis suggests that we are quantitatively
monitoring the electron concentration in each individual quantum well. The pronounced clarity
of the data reveals a high level of epitaxial perfection and spatial homogeneity across the entire
area of the junction.
INTRODUCTION
III-nitride Quantum Well (QW) structure semiconductors have attracted much interest in
recent years because they are known as promising materials for green, blue, and UV light
emitting diodes (LED) [1-2]. It is known that huge piezoelectric fields exist in GaN-based
heterostructures with wurtzite crystal structure [3-5]. In GaInN layers biaxially compressed to
GaN in typical Ga-face growth along the c-axis, the piezoelectric field is opposite to the growth
direction [3, 4]. As a result the electron and hole wavefunctions in the QW are subjected to the
quantum confined Stark effect (QCSE) even without an external electric field. When we apply an
additional reverse bias voltage, the transition energy shows a blue-shift since piezoelectric field
is compensated [3]. Thus the application of an external electric field perpendicular to the layers
of QWs significantly changes the photoluminescence (PL) properties [6, 7]. On the other hand,
capacitance-voltage (C-V) measurements are widely used to determine the carrier concentration
in a p-n diode. Here we combine both methods in an attempt to quantify the net charges present
at the individual heterointerfaces and to analyze the carrier depletion dynamics.
This report presents C-V measurements of the GaInN/GaN QWs embedded in the
depletion region of a specially designed p+-n junction LED. We correlate this data with both PL
and photocurrent (PC) data as a function of the bias voltage from deep depletion up to forward
injection.
E3.38.2
EXPERIMENTAL
For the experiments, we used GaInN/GaN multiple quantum well (MQW) structure
consisting of five wells embedded in a p-n diode. The acceptor dopant concentration is about
1019 cm-3 Mg in the p+ layer. The donor concentration is about 1018 cm-3 Si in the n-layer. The
active region is nominally undoped. Similar to 525 nm green LEDs [8] the thickness of each well
layer amounts to 3 nm. For enhanced clarity, wells have been separated by barriers of the order
of 30 nm thickness. The C-V data was measured at room temperature by using an HP4191A
impedance/gain-phase analyzer. PL was performed at room temperature using the 457-nm-line of
an Argon ion laser for excitation. At this wavelength, photocarriers can only be excited in the
wells. The photons are not absorbed by the GaN barriers. The PL signal was analyzed by a Spex
1 m spectrometer and detected by a photo multiplier tube (PMT). The photocurrent was
measured by an HP34401a multimeter.
RESULTS AND DISCUSSION
Fig. 1 shows the PL intensity and photocurrent as a function of the applied bias voltage of
the GaInN/GaN MQW green LED-type structure. The spectrally integrated PL intensity was
measured at wavelength intervals of 10 nm from 510 to 550 nm and then averaged. In this way,
the signal is not affected by a shift of the emission peak. Electroluminescence (EL) intensity was
suppressed by a chopper and lock-in amplifier system. In both experiments photocarriers were
generated directly in the QWs by 457 nm (2.71 eV) blue laser light. As the voltage decreases
from 1.3 to -4 V, a stepwise decrease of the PL intensity is observed. This is not a result of a
0.4
2
Bias illumination
λ = 457 nm
P ~ 60 mW
T = 300 K
0.0
-4
-2
0
2
0
2
0.8
d IPC / dV (arb. units)
PL
PC
PL Intensity (arb. units)
Photocurrent IPC (µA)
4
2
Voltage (V)
Figure 1 PL intensity (averaged from 510 nm to 550 nm) and photocurrent as a
function of an external voltage in a green LED-type structure with laser
excitation energy of 2.71 eV. As a dashed line the second derivative of the
photocurrent is shown to identify characteristic points of the data (indicated by
vertical ticks).
E3.38.3
60
Step ΙΙΙ
PL intensity (arb. unit)
Avg from 510nm to 550nm
Capacitance (pF)
4
3
45
Step ΙΙ
30
2
Step Ι
-4
-2
0
2
Voltage(V)
Figure 2 Room temperature capacitance-voltage characteristics in a green
LED-type structure (left hand axis). Three distinct steps I, II, and III are
labeled. The associated PL spectrum as a function of external voltage is also
shown (right hand axis).
wavelength shift of the emission peak. In parallel we observe an increase in the simultaneously
measured photocurrent. The photocurrent shows changes in slopes near the steps in the PL. As a
dashed line we include the smoothened second derivative of the photocurrent as a function of
voltage. Overall we get three inflexions (indicated with vertical lines, which divide the voltage
range into four regions. Each region shows a different slope of the photocurrent and a
corresponding step in the PL signal. These results show that there is a strong correlation between
PC and PL. We suspect that an increase in photocurrent induces a decrease of the PL intensity.
Fig. 2 shows the capacitance-voltage measurement of the same structure together with the
PL intensity from Fig. 1. Over the bias range from -4 to +2.3 V under a modulation frequency of
1 MHz, we obtained a C-V curve which shows three distinct Steps I, II, and III. When applying
this voltage range to the LED-type structure, we sweep from deep depletion at -4 V to forward
injection at +2.3 V. The turn-on voltage for electroluminescence was determined to be +2.6 V.
Using the full-depletion approximation, we know the capacitance of a p+-n junction is inversely
proportional to the total depletion layer width x d . Because the sample is a p+-n structure diode,
we neglect depletion on the p+-side and x d is approximately equal to x n , which is the depletion
layer width across the nominally intrinsic MQW region and the n-type region. So the capacitance
C can be formulated by
A
,
(1)
C = ε 0ε r
xn
where the junction area is A ≈ 55,000µm 2 , ε r is the relative static dielectric constant, and ε 0 is
the vacuum dielectric constant. From Fig. 2 we can see that the capacitance increases slowly
from -4 to -1.6 V (Step I) due to a slowly decreasing depletion region width. Then it changes
18
Photocurrent
18
1.5x10
Photoluminescence
18
1.0x10
2
17
5.0x10
Charge
Conc.
2
0
PC intensity (arb. units)
4
2.0x10
PL intensity (arb. units)
-3
Net fixed charge concentration (cm )
E3.38.4
0.0
60
80
100
120
140
160
Depletion width(nm)
Figure 3 Net fixed charge concentration versus depletion width (left axis), PL
spectrum (right axis), and PC as a function of depletion width deduced from the
measured capacitance.
rapidly from -1.6 to -0.7 V indicating a strong variation in xn. The second step (Step II) follows
from -0.7 to +0.6 V again with weak variation of C and xn. Then another strong variation occurs
from +0.6 to +1.5 V. In all we can see three steps, while the capacitance changes from 27 to 66
pF. The PL intensity follows these steps very closely: First PL increases from -4 to -1.6 V. Then
it increases more rapidly from -1.6 to -0.7 V, which roughly corresponds to the behavior in the
C-V curve. Another step up occurs near +1 V, both, for the PL and the capacitance.
The overall decrease of the PL for increasing reverse bias must be attributed to carrier drift in the
electric field across the depleted part of the active layer after thermal excitation of the carriers
from the wells. When the external voltage drops from +1.3 to -4 V, the PL intensity decreases to
about 50%.
We now shall find an interpretation for the steps in the C-V curve. The variable slope
means that the net fixed charge concentration in the depletion region is not uniform. In some
parts the net fixed charge concentration is high leading to a weak variation of C with V, while in
other parts it is low. The higher the net fixed charge concentration is, the more DC bias voltage
increment we need to apply to get the same increment of depletion layer width. Therefore, the
capacitance changes slowly in the highly charged areas of the n-type region, while in the lowly
charged areas it changes quickly. For an interpretation we can use the model of donor and
acceptor doping with concentrations ND on the n-side and NA on the p+-side, respectively.
Considering
−1
⎡ ⎛ 1 ⎞
⎤
2
(2)
ND = −
d 2 ⎟ dV ⎥ , if N A ⟩⟩ N D ,
2 ⎢ ⎜
ε 0 ε r eA ⎣ ⎝ C ⎠
⎦
we can calculate the fixed charge concentration. Using Eq. 1 we can interpret the voltage axis in
terms of the depletion width. The results are shown in Fig. 3 together with the PL intensity and
E3.38.5
the photocurrent on the same depletion width axis. Here we can see three well pronounced peaks
which show clearly that the fixed charge concentration is not uniform. The maximum fixed
charge concentration we derive is about ND = 8 × 1017 cm-3, while the minimum value is about
7 × 1016 cm-3. From the relative width of both regions we assign the high concentration areas to
the wells and the low concentration areas to the barriers in between. The weak modulation of PC
and PL now reveals clear step-like functions. It is important to recognize that any featureless
curve will convert into a step-like function, when its voltage-axis is reinterpreted in terms of
depletion width based on our C-V measurement. We therefore emphasize that while such an
interpretation of the voltage axis is perfectly legitimate, we have good correspondence of steps in
PL, PC, and capacitance already when plotted on the voltage axis in Figs. 1 and 2. Following
our interpretation, PC and PL signals clearly correspond to the multitude of wells within the
depletion zone. Per our assumption to neglect depletion of the p+ layer, the depletion width
should be zero at the physical interface of the last barrier and the p+ layer. For increasing
depletion width we eventually deplete the QW that lies closest to the p-side. In our case of a
stretched QW sample this is most likely the well at 70 nm depletion width that closely
corresponds to Step III in the PL, PC and capacitance data. Depletion of every additional well
again strongly affects the other data. When the depletion region, starting from the p+ side,
reaches the position of the QWs, the PL intensity changes abruptly, while at the positions of the
barriers, the PL intensity changes slowly. PC has the same behavior. These results show that PL
and PC complement each other to a high degree.
This indicates that both processes are not controlled by a voltage dependence of the
absorption itself. In such a situation, PL and PC should vary in parallel. The results rather
suggest that the excited state and/or the recombination path are voltage controlled by the field
across the depleted region. A most likely process for this is thermoelectric field ionization and
carrier drift of photo excited carriers within the depletion zone. Such an ionization would
increase the current with increasing field strength and decrease the luminescence at the same
time. Another interpretation has been given in AlGaAs/GaAs QW heterostructures with 20 nm
barriers [9]. In this case carrier tunneling was suggested as the controlling mechanism.
Steps in the capacitance-voltage behavior of MQW samples have previously studied in
theory in Ref [10]. The resulting carrier concentrations have been attributed to the accumulated
localized but otherwise mobile carriers within each QW. The value of ND therefore refers to the
density of electrons that are trapped within the individual QW until they are ionized from the
well due to field depletion. In GaAs/AlGaAs heterostructures the method has been used to
characterize the homogeneity of such superlattices [11]. In that case, carrier density peaks of 5.2
nm FWHM have been identified. In our case, peak widths as narrow as 6 nm FWHM have been
found at a total depletion width of 110 nm. This implies a very high uniformity of barrier and
well widths across the entire are of the junction mesa. Lateral variations of the growth rate and
layer thickness variations beyond a fraction of 6 nm / 110 nm = 5 % would have been expected
to result in additional broadening of the charge concentration peak. The consistently pronounced
clarity of three well-resolved well layers suggests a very high quality of the QW layer
thicknesses and interfaces.
E3.38.6
CONCLUSIONS
In summary, we find very distinct steps in the capacitance for voltages that deplete the
active light emitting region. We associate those to the stepwise depletion of electrons from the
three QWs nearest to the p-side. We find that photocurrent and photoluminescence complement
each other as they switch in parallel with the number of the depleted QWs. To the best of our
knowledge this is the first time individual QWs can be identified by capacitance-voltage in
group-III nitride LED-type structures. The small line width of the observed features in relation to
the large total depletion width indicates a very high uniformity of well and barrier thicknesses
across the entire mesa junction area.
ACKNOWLEDGMENTS
The authors wish to thank Steven Kurtz for initial experiments on the subject and
Lumionics Corporation for providing suitable epi material.
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