Asymmetry in the Hot Carrier Dynamics in GaN
and its Impact on the Efficiency Droop
Vatsal A. Jhalani
†
,
1
Jin-Jian Zhou
†
,
1
and Marco Bernardi*
1
1
Department of Applied Physics and Materials Science, Steele Laboratory,
California Institute of Technology, Pasadena, California 91125, USA.
(Dated: March 24, 2017)
* Corresponding author. Email: bmarco@caltech.edu
†
These authors contributed equally to this work.
GaN is a key material for lighting and power electronics. Yet, the carrier transport and ultrafast
dynamics that are central in GaN devices are not completely understood. We present first-principles
calculations of carrier dynamics in GaN, focusing on electron-phonon (e-ph) scattering and the
cooling of hot carriers. We find that e-ph scattering is significantly faster for holes compared to
electrons, and that for hot carriers with an initial 0.5
−
1 eV excess energy, holes take a significantly
shorter time (
∼
0.1 ps) to relax to the band edge compared to electrons, which take
∼
1 ps. The
asymmetry in the hot carrier dynamics is shown to originate from the valence band degeneracy, the
heavier effective mass of holes compared to electrons, and the details of the coupling to different
phonon modes in the valence and conduction bands. The ballistic mean free paths (MFPs) of
electrons and holes also differ significantly. The slow cooling of hot electrons and their long MFPs
(over 3 nm) are investigated as a possible cause of efficiency droop in GaN light emitting diodes.
Taken together, our work provides microscopic insight into the carrier dynamics of GaN, and shows
a computational approach to design novel lighting materials.
INTRODUCTION
Wurtzite GaN has emerged as a promising material for
solid state lighting [1] and power electronics [2, 3], with
potential technological benefits that are driving intense
research in industry and academia. However, material
properties essential for device performance and energy
efficiency, such as carrier transport and recombination,
are not completely understood in GaN and remain the
subject of debate. Carrier transport and ultrafast dy-
namics are regulated by scattering with phonons, carri-
ers and impurities [4]. In particular, the electron-phonon
(e-ph) interaction [5, 6] plays a dominant role on trans-
port at room temperature in relatively pure materials.
It further regulates the energy loss (or “cooling”) of ex-
cited carriers injected at heterojunctions, a scenario of
relevance in GaN light emitting diodes. The excited (so-
called “hot”) carriers rapidly lose their excess energy with
respect to the band edges, dissipating heat by phonon
emission through e-ph coupling. Hot carriers (HCs) are
also central in degradation and current leakage in GaN
transistors for power electronics [7, 8], and set the oper-
ational basis for hot electron transistors [9].
Microscopic understanding of carrier dynamics is chal-
lenging in GaN since experimental results are modulated
by defects and interfaces, and are typically interpreted
with empirical models [10–16]. For example, the hot elec-
tron cooling times measured by different groups range
over two orders of magnitude [10, 12–17], and reports
of hot hole dynamics are scarce [11]. In addition, the
efficiency decline in GaN light emitting diodes (LEDs)
at high current, a process known as efficiency droop
[18], has been intensely investigated but its carrier dy-
namics origin remains unclear. First-principles calcula-
tions focused on Auger recombination [19, 20] as a possi-
ble cause, though other mechanisms have been proposed
[18], including HC effects and electron leakage. These
processes have seen less extensive theoretical treatment
compared to Auger, leaving simplified models to guide
device design.
We recently developed first-principles calculations of
carrier dynamics [6] that can obtain carrier mobility
[21, 22], ultrafast dynamics [23–26], HC relaxation times
[23, 24] and ballistic mean free paths [23, 25] in excel-
lent agreement with experiment. These approaches are
free of empirical parameters and use the structure of the
material as the only input. In particular, we recently
developed a method [22] to accurately compute the e-ph
relaxation times (RTs), namely the average time between
e-ph collisions, in polar materials, as is needed for GaN.
These approaches are extended in this work to investi-
gate HC dynamics in GaN from first principles.
Here, we compute the e-ph RTs over a wide energy
range, and study the cooling of HCs by numerically solv-
ing the electron Boltzmann transport equation (BTE).
Both the RTs and the simulated ultrafast dynamics re-
veal a large asymmetry between the hot electron and hole
dynamics, with hot holes relaxing to the band edges sig-
nificantly faster than hot electrons. The origin of this
asymmetry, the role of different phonon modes and the
limitations and failure of phenomenological models are
analyzed in detail. We additionally find significantly
longer mean free paths (MFPs) for electrons compared
to holes, with implications for GaN devices. We show
that the slow cooling rate of hot electrons can lead to in-
efficient light emission at high current, and conclude that
HC cooling may play a key role in LED efficiency droop.
arXiv:1703.07880v1 [cond-mat.mtrl-sci] 22 Mar 2017