Transition metal impurities are known to adversely affect the efficiency of electronic and optoelectronic devices by introducing midgap defect levels that can act as efficient Shockley-Read-Hall centers. Iron impurities in GaN do not follow this pattern: their defect level is close to the conduction band and hence far from midgap. Using hybrid functional first-principles calculations, we uncover the electronic properties of Fe and we demonstrate that its high efficiency as a nonradiative center is due to a recombination cycle involving excited states. Unintentional incorporation of iron impurities at modest concentrations (1015 cm–3) leads to nanosecond nonradiative recombination lifetimes, which can be detrimental for the efficiency of electronic and optoelectronic devices.

The Group-III nitride semiconductors and their alloys are being investigated for a wide variety of commercial applications. They are the active material in light-emitting diodes,1 in high electron mobility transistors (HEMTs),2 and in tunnel devices.3 Fabrication of electronic devices requires the use of semi-insulating substrates or buffer layers, and Fe is used as an acceptor that compensates the unintentional n-type GaN.4 Research on Fe in GaN has also been motivated by efforts to achieve room-temperature ferromagnetism in GaN.5 In addition, unintentional incorporation of iron during epitaxial growth of GaN can be due to memory effects, or result from the presence of silica or alumina components in the system, or from the reaction of amides and halides formed from gas sources with stainless steel components.6 

Transition-metal impurities in semiconductors tend to form defect levels deep in the bandgap; for instance, copper, iron, or gold in silicon lead to multiple levels within the gap.7 These levels enable efficient Shockley-Read-Hall (SRH) recombination, as evidenced by large capture cross sections (∼1015 cm2).7 The SRH recombination has been blamed for efficiency losses in optoelectronic8 and electronic devices.9 For a defect density N and electron (hole) capture coefficients Cn (Cp), the SRH recombination coefficient A is defined as10,11

A=NCnCpCn+Cp.
(1)

There are strong experimental indications that Fe in GaN acts as an efficient nonradiative center. Using time-resolved photoluminescence,12,13 electron and hole capture coefficients Cn = 5.5 ×108 cm3 s−1 and Cp = 1.8 ×108 cm3 s−1 have been obtained for GaN samples intentionally doped with Fe. Such large capture coefficients indicate that a low concentration of unintentional Fe impurities, N 1015 cm−3, would be sufficient to lead to an A value of 107 s−1, large enough to adversely impact the efficiency of light-emitting devices.8 The presence of iron can also affect the performance of electronic devices. For example, current collapse in AlGaN/GaN HEMTs has a strong correlation with Fe doping in the GaN buffer.4 

Efficient SRH recombination requires high capture rates for both electrons and holes [see Eq. (1)]. Since Cn and Cp decrease approximately exponentially with the energy of the transition,14 it is generally assumed that only midgap states can lead to an efficient SRH recombination. The behavior of iron as an efficient recombination center is therefore surprising, since it has a deep acceptor level ∼0.6 eV from the conduction-band minimum (CBM).15–17 The position of this level leads to a high electron capture rate, but is so far from the valence-band maximum (VBM) in GaN that the hole capture rate would be negligibly small.

In this Letter, we resolve the puzzle by pointing out the importance of excited states in the recombination cycle. We perform first-principles calculations based on hybrid density functional theory (DFT) that provide detailed information about both ground states and excited states of substitutional Fe in GaN. Such excited states have been experimentally observed in luminescence and absorption studies of GaN:Fe.16,18 We demonstrate how these excited states lead to efficient electron and hole capture in a cycle that does not even involve the ground state, rendering Fe as an efficient nonradiative recombination center.

Our calculations are based on DFT using the Vienna Ab initio Simulation Package VASP.19,20 A fraction of screened Fock exchange α = 0.31 in the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional21 leads to an accurate band structure for GaN with a bandgap of 3.48 eV and a reliable description of defect levels.22 We also performed calculations using the Random Phase Approximation.23,24 We used the projector augmented wave (PAW) approach25 with a plane-wave energy cutoff of 400 eV. Ga d states were treated as part of the core. Our tests indicate that including the Ga d states as valence states results in transition levels for FeGa that differ from d-in-the-core by less than 0.02 eV. Point-defect calculations were performed using a 96-atom supercell and the Brillouin zone was sampled at a special k-point k = (1/4, 1/4, 1/4). Spin polarization was included in all cases. Spin configurations were calculated by enforcing the spin multiplicity. Tests using a 192-atom supercell showed transition levels changed by less than 0.09 eV. We consider nonradiative capture that occurs via multi-phonon emission.14 Electron and hole capture coefficients are computed from first-principles following the methodology described in Ref. 26. Calculations of the electron-phonon coupling matrix elements utilized the PAW wave functions within VASP for the valence-band, conduction-band, and defect states.

The formation energy of substitutional Fe on the Ga site in GaN is given by22 

Ef(FeGaq)=Etot(FeGaq)Etot(GaN)+μGaμFe+qEF+Δq,
(2)

where Etot(GaN) is the total energy of the pristine GaN supercell, Etot(Fe Gaq) is the total energy of the structure containing the impurity in charge state q, and μGa and μFe are the chemical potentials of Ga and Fe. μGa can vary between Ga-rich (equilibrium with bulk Ga) and Ga-poor conditions (equilibrium with N2 molecules). For μFe, the upper limit is set by the solubility-limiting phase, Fe3N. EF is the Fermi level, which is referenced to the VBM of GaN, and Δq is the finite-size correction for charged defects.27 

Formation energies for various configurations of iron in GaN are shown in Fig. 1. Iron on the nitrogen site (FeN) and in an interstitial configuration (Fei) have very high formation energies, larger than the formation energy of Fe Ga regardless of the position of EF or the choice of chemical potential. Hence, they are unlikely to occur. Indeed, electron paramagnetic resonance (EPR) measurements on the Fe-doped GaN have observed Fe substituting on the Ga site,28 consistent with our finding that FeGa has the lowest formation energy.

FIG. 1.

Formation energy versus Fermi level for FeGa, FeN and Fei in GaN in different charge states, under Ga-rich conditions. The wave function of the defect state of FeGa in the negative charge state is illustrated as an inset.

FIG. 1.

Formation energy versus Fermi level for FeGa, FeN and Fei in GaN in different charge states, under Ga-rich conditions. The wave function of the defect state of FeGa in the negative charge state is illustrated as an inset.

Close modal

FeGa occurs in high-spin configurations. The crystal field splits the 3d states into eg and t2g states (deviations from tetrahedral symmetry in the wurtzite phase are minor), and exchange splits the states into spin-up and spin-down states. The neutral charge state, FeGa0, is a spin sextuplet (S = 5/2). This state is commonly referred to as Fe3+, where the “3+” indicates the oxidation state, and we will follow this notation in this Letter. We find the occupied Fe d spin-up states to be located just below the GaN valence band, ∼7.3 eV below the VBM. The corresponding unoccupied spin-down states are located 0.57 eV above the CBM at Γ. The lattice distortion of the Fe3+ state is small, with the four nearest-neighbor N atoms moving outwards by 0.5% of the Ga-N bond length.

The negative charge state, FeGa (or 2+ oxidation state, Fe2+), is a spin quintuplet (S = 2). The four nearest-neighbor N atoms move outwards by 4%. One spin-down d state is now occupied, and has moved into the gap; the corresponding wave function is shown in the inset of Fig. 1. Figure 1 shows that the (0/–) (or Fe3+/Fe2+) thermodynamic transition level (acceptor level) is located 0.50 eV below the CBM. This result agrees with previous theoretical calculations17 and is consistent with transient capacitance measurements15 and with UV-VIS transmission spectra showing an absorption peak at ∼3 eV in Fe-doped GaN.16 

In the positive charge state, FeGa+ (4+ oxidation state), the Fe-N bonds relax inwards by 1.1% of the Ga-N bond length. The (+/0) (or Fe4+/Fe3+) thermodynamic transition level occurs at 0.26 eV above the VBM.

We now calculate the capture coefficients for electron and hole capture for the FeGa defect. The location of the (0/–) (Fe3+/Fe2+) level, at 0.5 eV below the CBM, enables fast electron capture by defects in the neutral charge state. However, capturing a hole from the VBM into the negative charge state of FeGa (Fe2+) would be a very slow process, since the energy of this transition is 3.0 eV. Our calculated hole capture coefficient for this process is lower than 10−20 cm3 s−1, severely limiting the overall nonradiative recombination rate [Eq. (1)], which is dominated by the slower of the two processes. Invoking a radiative process for hole capture into the negative charge state of FeGa (Fe2+) does not help: capture coefficients associated with band-to-defect transitions in GaN are on the order of 10−14–10−13 cm3 s−1,29 many orders of magnitude smaller than the values required for efficient SRH recombination.

The consideration of excited states of Fe3+ and Fe2+ drastically changes the recombination process. Starting from the sextuplet (S = 5/2) ground state of Fe3+ (corresponding to A61), quadruplet (S = 3/2) excited states can be obtained by a spin flip. Malguth et al.16 argued that in a tetrahedral crystal field these quadruplet states arise in the order T41,4T2,4E, and A41 (the latter two being degenerate); although GaN has wurtzite rather than zinc-blende symmetry, we will also adopt this notation here, as is common practice in the literature. A luminescence peak observed at 1.299 eV was attributed to the T416A1 transition, and transitions at 2.01 eV and 2.73 eV to two higher-lying excited states were also observed in absorption.16,18 More recently, Neuschl et al.18 proposed a different ordering of the quadruplet states, namely, T41,4E,4T2, and A41, without any degeneracy.

In the case of Fe2+, optical spectroscopy also provided evidence for a quintuplet (S = 2) T52 excited state 0.39 eV above the E5 ground state.16 In addition, the existence of a triplet excited state is dictated by the C3v symmetry of Fe2+,30 though this state has not yet been experimentally observed in GaN. The T31 triplet state has been observed for neutral Fe in ZnSe in ZnSe:Fe,31 which shows luminescence at 1.26 eV corresponding to a transition from this excited state to the E5 ground state. The similarity between Fe2+ in ZnSe and GaN is supported by the observation of the T52 excited state in ZnSe at 0.40 eV above the E5 ground state,31 very similar to the 0.39 eV difference between the T52 and E5 states of Fe2+ in GaN.16 

In our calculations, we evaluate the excited-state energies of Fe3+ and Fe2+ from differences in total energy within the Delta-self-consistent-field (ΔSCF) formalism.32 For the excited state of each charge state we allow for a full relaxation of all internal coordinates. For Fe3+ HSE calculations produce E0q=0(S=3/2)E0q=0(S=5/2) = 1.55 eV, where E0 corresponds to the ground-state energy for a given spin multiplet. ΔSCF calculations using RPA produce a value of 1.40 eV. Both HSE and RPA, thus, slightly overestimate the energy separation between the T41 and A61 states, which was experimentally determined to be 1.299 eV.16,18 When applied to Fe2+, HSE calculations find the T31 excited state 1.46 eV above the E5 ground state, again a slight overestimate (by 200 meV) compared to the experimental energy for the corresponding transition (in ZnSe).

Our ΔSCF calculations thus produce very reasonable results for the lowest-energy configurations of a given spin multiplicity. In particular, they confirm that there is indeed a spin-triplet excited state for Fe2+. However, one has to be very cautious in interpreting calculated energies: in order to describe spin multiplet states, one often needs wavefunctions composed of more than one Slater determinant,33 and this goes beyond the Kohn-Sham picture. For these reasons, in order to describe the energies of the E4,4T2, and A41 states of Fe3+, and of the T52 state of Fe2+, we rely on the results by Neuschl et al.18 and O'Donnell et al.31 cited above. For consistency, we also take the energies of the T41 (for Fe3+) and T31 (for Fe2+) states from experiment. A formation energy diagram that includes the excited states is shown in Fig. 2.

FIG. 2.

Formation energy diagram for Fe Ga under Ga-rich conditions. The blue solid line corresponds to the ground state of the neutral (q = 0) charge state, Fe3+. The blue dashed lines correspond to the quadruplet excited states of Fe3+.18 The red solid line corresponds to the quintuplet ground state and the dashed-dotted line corresponds to the quintuplet excited state of the negative (q = −1) charge state, Fe2+. The red dashed line corresponds to the triplet excited state of Fe2+. The vertical bars indicate transition levels at which hole and electron capture can occur into the ground or excited-state levels. The term symbols for the ground state and excited states are shown along the vertical axis on the right. (0/–) is the thermodynamic transition level of the Fe3+/Fe2+ ground state, (0*/*) is the transition level between the T41 excited state of Fe3+ and the T31 excited state of Fe2+, and (0**/*) is the transition level between the A41 excited state of Fe3+ and the T31 excited state of Fe2+.

FIG. 2.

Formation energy diagram for Fe Ga under Ga-rich conditions. The blue solid line corresponds to the ground state of the neutral (q = 0) charge state, Fe3+. The blue dashed lines correspond to the quadruplet excited states of Fe3+.18 The red solid line corresponds to the quintuplet ground state and the dashed-dotted line corresponds to the quintuplet excited state of the negative (q = −1) charge state, Fe2+. The red dashed line corresponds to the triplet excited state of Fe2+. The vertical bars indicate transition levels at which hole and electron capture can occur into the ground or excited-state levels. The term symbols for the ground state and excited states are shown along the vertical axis on the right. (0/–) is the thermodynamic transition level of the Fe3+/Fe2+ ground state, (0*/*) is the transition level between the T41 excited state of Fe3+ and the T31 excited state of Fe2+, and (0**/*) is the transition level between the A41 excited state of Fe3+ and the T31 excited state of Fe2+.

Close modal

The excited states open up new channels for nonradiative capture of electrons and holes. Fig. 3 is an energy level diagram that illustrates the sequence of processes that leads to efficient nonradiative capture of carriers due to the excited states of Fe3+ and Fe2+. As noted above, electron capture is a fast process, leading to the E5 state of Fe2+ [Figs. 2 and 3(a)], but hole capture to go back to the A61 ground state of Fe3+ would be a very slow process. However, as seen in Figs. 2 and 3(b), a transition from the E5 state to an excited state of Fe3+ can easily occur; for example, the level for a transition to the T42 state is only 0.36 eV above the VBM. Once in the T42 state, the system will rapidly lose energy (through spin-conserving intra-defect multiphonon emission) to end up in the T41 state, which has the lowest energy among the quadruplet states of Fe3+.

FIG. 3.

Nonradiative recombination cycle due to Fe in GaN. (a) Electron capture into the (0/–) level 0.5 eV below the CBM (corresponding to the experimentally observed acceptor level) marked with the green vertical bar in Fig. 2. (b) Hole capture into the level marked with the purple vertical bar in Fig. 2. (c) Once the cycle is initiated, electron and hole capture proceeds between the excited-state transition levels marked by the black (0*/*) and yellow (0**/*) vertical bars in Fig. 2. Spin-conserving intra-defect relaxations are illustrated with blue wiggly arrows.

FIG. 3.

Nonradiative recombination cycle due to Fe in GaN. (a) Electron capture into the (0/–) level 0.5 eV below the CBM (corresponding to the experimentally observed acceptor level) marked with the green vertical bar in Fig. 2. (b) Hole capture into the level marked with the purple vertical bar in Fig. 2. (c) Once the cycle is initiated, electron and hole capture proceeds between the excited-state transition levels marked by the black (0*/*) and yellow (0**/*) vertical bars in Fig. 2. Spin-conserving intra-defect relaxations are illustrated with blue wiggly arrows.

Close modal

One might think that the next step would be a transition to the A61 ground state of Fe3+. However, that transition (which gives rise to the characteristic 1.299 eV emission) is spin-forbidden, and as a result, it is very slow, with an 8 ms lifetime.34 Instead, starting from T41, rapid nonradiative electron capture can occur resulting in the T31 excited state of Fe2+; this process is indicated with the vertical bar marked (0*/*) in Fig. 2 (at 0.64 eV below the CBM). Transitions from T31 to lower-lying states for Fe2+ are, again, spin-forbidden, and therefore, it is more likely that this state captures a hole and converts to the A41 state. This process is indicated with the vertical bar marked (0**/*) (at 0.58 eV above the VBM). From here on, the cycle can rapidly repeat, with the system making transitions between the excited states [Fig. 3(c)].

The conclusion is that nonradiative recombination involves the quadruplet manifold of Fe3+ and the triplet excited state of Fe2+. This results in a very efficient nonradiative recombination due to the fast capture of both electrons and holes and spin-conserving nonradiative intra-defect transitions. The calculated capture coefficients, at room temperature, are Cn = 1.1 × 10−8 cm3 s−1 for the (0*/*) transition and Cp = 7.1 × 10−8 cm3 s−1 for the (0**/*) transition. These values compare favorably with Cn = 5.5 ×108 cm3 s−1 and Cp = 1.8 ×108 cm3 s−1 obtained from time-resolved photoluminescence measurements.13 The agreement is particularly impressive given that these coefficients depend exponentially on transition energies. The calculated Cn value is a bit too small, while Cp is a bit too large. If the energy position of the T31 state would shift up by a mere 0.1 eV, both Cn and Cp would be in almost perfect agreement with experiment. The total nonradiative capture coefficient is approximately 10−8 cm 3s1. If we assume the defect density to be 1015 cm−3 (a very conservative value), the SRH coefficient A [Eq. (1)] is 107 s−1, a value that can impact the efficiency of optoelectronic devices.8 

In summary, based on the first-principles calculations and careful analysis of electron and hole capture coefficients, we have evaluated nonradiative recombination rates for Fe impurities in GaN. We have solved the puzzle as to how Fe, which is known to be an acceptor with a level far from midgap (∼0.5 eV below the CBM) can be an efficient SRH center. The critical role of excited states was elucidated.

We gratefully acknowledge the discussion with T. K. Uždavinys. This work was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award No. DE-SC0010689. The work by A.A. was supported by Marie Sklodowska-Curie Action of the European Union (Project Nitride-SRH, Grant No. 657054). Computational resources were provided by the National Energy Research Scientific Computing Center, which is supported by the DOE Office of Science under Contract No. DE-AC02-05CH11231.

1.
S.
Nakamura
and
M. R.
Krames
,
Proc. IEEE
101
,
2211
(
2013
).
2.
U. K.
Mishra
,
P.
Parikh
, and
Y.-F.
Wu
,
Proc. IEEE
90
,
1022
(
2002
).
3.
W.
Li
,
S.
Sharmin
,
H.
Ilatikhameneh
,
R.
Rahman
,
Y.
Lu
,
J.
Wang
,
X.
Yan
,
A.
Seabaugh
,
G.
Klimeck
,
D.
Jena
, and
P.
Fay
,
IEEE J. Explor. Solid-State Comput. Devices Circuits
1
,
28
(
2015
).
4.
D.
Cardwell
,
A.
Sasikumar
,
A.
Arehart
,
S.
Kaun
,
J.
Lu
,
S.
Keller
,
J.
Speck
,
U.
Mishra
,
S.
Ringel
, and
J.
Pelz
,
Appl. Phys. Lett.
102
,
193509
(
2013
).
5.
P.
Alippi
,
F.
Filippone
,
G.
Mattioli
,
A. A.
Bonapasta
, and
V.
Fiorentini
,
Phys. Rev. B
84
,
033201
(
2011
).
6.
J.
Baur
,
K.
Maier
,
M.
Kunzer
,
U.
Kaufmann
,
J.
Schneider
,
H.
Amano
,
I.
Akasaki
,
T.
Detchprohm
, and
K.
Hiramatsu
,
Appl. Phys. Lett.
64
,
857
(
1994
).
7.
A.
Istratov
and
E.
Weber
,
Appl. Phys. A
66
,
123
(
1998
).
8.
A.
David
and
M. J.
Grundmann
,
Appl. Phys. Lett.
96
,
103504
(
2010
).
9.
S.
Mookerjea
,
D.
Mohata
,
T.
Mayer
,
V.
Narayanan
, and
S.
Datta
,
IEEE Electron Device Lett.
31
,
564
(
2010
).
10.
W.
Shockley
and
W.
Read
, Jr.
,
Phys. Rev.
87
,
835
(
1952
).
11.
12.
T.
Aggerstam
,
A.
Pinos
,
S.
Marcinkevičius
,
M.
Linnarsson
, and
S.
Lourdudoss
,
J. Electron. Mater.
36
,
1621
(
2007
).
13.
T. K.
Uždavinys
,
S.
Marcinkevičius
,
J. H.
Leach
,
K. R.
Evans
, and
D. C.
Look
,
J. Appl. Phys.
119
,
215706
(
2016
).
14.
C. H.
Henry
and
D. V.
Lang
,
Phys. Rev. B
15
,
989
(
1977
).
15.
A.
Polyakov
,
N.
Smirnov
,
A.
Govorkov
,
N.
Pashkova
,
A.
Shlensky
,
S.
Pearton
,
M.
Overberg
,
C.
Abernathy
,
J.
Zavada
, and
R.
Wilson
,
J. Appl. Phys.
93
,
5388
(
2003
).
16.
E.
Malguth
,
A.
Hoffmann
, and
M. R.
Phillips
,
Phys. Status Solidi B
245
,
455
(
2008
).
17.
Y.
Puzyrev
,
R.
Schrimpf
,
D.
Fleetwood
, and
S.
Pantelides
,
Appl. Phys. Lett.
106
,
053505
(
2015
).
18.
B.
Neuschl
,
M.
Gödecke
,
K.
Thonke
,
F.
Lipski
,
M.
Klein
,
F.
Scholz
, and
M.
Feneberg
,
J. Appl. Phys.
118
,
215705
(
2015
).
19.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
47
,
558
(
1993
).
20.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
(
1996
).
21.
J.
Heyd
,
G. E.
Scuseria
, and
M.
Ernzerhof
,
J. Chem. Phys.
118
,
8207
(
2003
).
22.
C.
Freysoldt
,
B.
Grabowski
,
T.
Hickel
,
J.
Neugebauer
,
G.
Kresse
,
A.
Janotti
, and
C. G.
Van de Walle
,
Rev. Mod. Phys.
86
,
253
(
2014
).
23.
M.
Kaltak
,
J.
Klimeš
, and
G.
Kresse
,
J. Chem. Theory Comput.
10
,
2498
(
2014
).
24.
M.
Kaltak
,
J.
Klimeš
, and
G.
Kresse
,
Phys. Rev. B
90
,
054115
(
2014
).
25.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
(
1994
).
26.
A.
Alkauskas
,
Q.
Yan
, and
C. G.
Van de Walle
,
Phys. Rev. B
90
,
075202
(
2014
).
27.
C.
Freysoldt
,
J.
Neugebauer
, and
C. G.
Van de Walle
,
Phys. Status Solidi B
248
,
1067
(
2011
).
28.
J.
Dashdorj
,
M.
Zvanut
,
J.
Harrison
,
K.
Udwary
, and
T.
Paskova
,
J. Appl. Phys.
112
,
013712
(
2012
).
29.
M. A.
Reshchikov
,
AIP Conf. Proc.
1583
,
127
(
2014
).
30.
B.
Henderson
and
G. F.
Imbusch
,
Optical Spectroscopy of Inorganic Solids
(
Oxford University Press
,
2006
), Vol.
44
.
31.
K.
O'Donnell
,
K.
Lee
, and
G.
Watkins
,
J. Phys. C.: Solid State Phys.
16
,
L723
(
1983
).
32.
R. O.
Jones
and
O.
Gunnarsson
,
Rev. Mod. Phys.
61
,
689
(
1989
).
33.
U.
von Barth
,
Phys. Rev. A
20
,
1693
(
1979
).
34.
R.
Heitz
,
P.
Thurian
,
I.
Loa
,
L.
Eckey
,
A.
Hoffmann
,
I.
Broser
,
K.
Pressel
,
B.
Meyer
, and
E.
Mokhov
,
Appl. Phys. Lett.
67
,
2822
(
1995
).