Excitonic mobility edge and ultra-short photoluminescence decay time in n-type

We use time-resolved photoluminescence (PL) spectroscopy to study the recombination dynamics in Si-doped GaAsN semiconductor alloys with a nitrogen content up to 0.2%. The PL decay is predominantly monoexponential and exhibits a strong energy dispersion. We nd ultra-short decay times on the high-energy side and long decay times on the low-energy side of the photoluminescence spectrum. This asymmetry can be explained by the existence of an additional non-radiative energy transfer channel and is consistent with previous studies on intrinsic GaAsN epilayers. However, the determined maximum decay times of GaAsN:Si are signi cantly reduced in comparison to undoped GaAsN. The determined excitonic mobility edge energy constantly decreases with increasing N content, in agreement with the two-level band anticrossing model.

Dilute nitrides like (In)GaAs 1−x N x have attracted considerable attention in the last decades because of their band gap tunability 1,2 in the telecommunication region and beyond 3 .
The rst In y Ga 1−y As 1−x N x -based laser with an emission wavelength of 1.3 µm was demonstrated in 2000 by Livshits et al. 4 . Vertical cavity surface emitting lasers 5,6 and edge-emitting devices 7 for 1.5 µm have been presented in subsequent years. Besides their technological potential, dilute nitrides feature unusual fundamental properties like e.g. a giant band gap reduction 1 with N content, an unusual pressure and temperature dependence of the electronic properties 810 , highly non-parabolic conduction bands 11 , and the diculty in doping GaAsN with Si-dopants due to the formation of Si-N complexes 12 . Dierent methods have been applied on the system GaAsN in order to determine the electron eective mass. A decrease 13 , an increase 1416 and a non-monotonic dependence 17 of the electron eective mass with increasing N content were observed. Using cyclotron resonance absorption spectroscopy, we found a moderate increase of the electron eective mass with increasing N content 18 . Our result is in excellent agreement with calculations based on the two-level band anticrossing (BAC) model 9 . Thus we conclude that the dierent sensitivity of the used methods to carrier localization eects is responsible for contradicting results.
A signicant size and electronegativity dierence between nitrogen and arsenic atoms causes a non-uniform N distribution, which creates localization potentials and increases the disorder of the system. Photoluminescence (PL) is particularly sensitive to disorder eects like N-induced localization centers. Compositional uctuations 1921 create regions with a locally reduced band gap and lead to PL emission at lower energies, similarly to quantum dots 20,22 . Localized excitons dominate the low-temperature PL 19,22,23 and exhibit strongly energy-dependent PL decay times 19,24 . Since most telecommunication applications require n(or p)-type doping, it is highly desirable to understand the impact of a typical dopant like silicon on the recombination dynamics of GaAsN.
We apply a systematic and temperature dependent time-resolved PL study on Si-doped GaAs 1−x N x epilayers with x = 0% − 0.2%. The GaAsN:Si layers were grown by molecular beam epitaxy at a reduced temperature of 500 • C with a thickness of 1 µm. The N content was monitored by x-ray diraction and the n-doping is nominally 1×10 17 cm −3 . More details on the sample series can be found in Refs. 18,25 . For the time-resolved PL study, the samples were illuminated by a picosecond titanium-sapphire laser (Spectra Physics: Tsunami 3960) with a photon energy of 1.61 eV. The detection unit consists of a Bruker Chromex 250is/is  and x = 0.1%. The PL decay of the N containing sample in Fig. 1 (b) exhibits a strong energy dispersion in comparison to the reference sample in Fig. 1 (a). We obtain ultrashort decay times on the high energy side and long decay times on the low-energy side of the spectrum. Similar observations were made in intrinsic (In)GaAsN epilayers 2628 and quantum-wells 24,29 .
In order to study the origin of this energy dispersion, we investigate line proles of the PL decay at given photon energies. Three neighboring low-temperature decay line proles are shown in Fig. 2 (a) -(c). The underlying time-resolved PL measurement is taken at 5 K and 9.5 W/cm 2 . The decay dynamics is characterized by a t function which is a sum of a monoexponential decay and a constant oset, as shown with pink curves. The oset accounts for recombination processes with ultra-long decay times, which originate from eciently trapped carriers, as observed e.g. in n-type InGaAs/GaAs quantum dots 30  100 ps in Fig. 2 (a) shortly after laser excitation. This ultrafast PL decay, which is typical for the high energy side of the spectrum is related to carrier cooling 31 . Note that intraband scattering of photoexcited electrons occurs on an even shorter timescale, namely on a sub-ps scale 32 . These fast parts of the dynamics are not within the scope of this study. A schematic representation of all radiative and non-radiative recombination and decay channels is given in Fig. 3. We use the monoexponential decay function after a certain thermalization time of 50 ps for our data analysis. The PL decay time of localized excitons decreases by a factor of 3.1 in a small energy interval of 14 meV. The energy dependent PL decay of localized excitons can be tted by 26,33 τ with a maximum decay time τ R , an energy E m corresponding to the so-called mobility edge (see below) and an energy scaling factor α with 1/α in the order of 2.59 meV − 9.55 meV.
According to Eq. (1), excitons with an energy E can recombine radiatively or be transferred non-radiatively towards lower energy states. The non-radiative transfer can be regarded as an exciton hopping process. After optical excitation, excitons preferentially hop several times to lower energies before they recombine radiatively 34   The temperature dependent PL decay times are presented in Fig. 4  A similar decay time asymmetry has previously been observed in intrinsic GaAsN epilayers 24,27 . However, our determined maximum decay time values are signicantly shorter (up to τ R ≈ 0.8 ns) than the reported values of τ R ≈ 5 − 8 ns 27 in the intrinsic material. It is well-known that n-type doping reduces the band-band recombination time, since it increases the product of the electron and hole densities np = (n opt + n dop )p opt (2) where n opt and p = p opt are the concentrations of optically injected electrons and holes, respectively, and n dop is the (electrically active) doping concentration. Nevertheless, in case of n-doped GaAs 38,39 the impact of the doping is insignicant below 10 18 cm −3 . Furthermore, Si-doping leads to a higher contribution by non-radiative Shockley-Read-Hall and Auger recombination rates, as was observed in n-type GaAs 40 . Especially Shockley-Read-Hall recombinations signicantly increase with the defect density. This behavior has a substantial impact on possible applications.
In summary, we performed temperature dependent time-resolved photoluminescence investigations on Si-doped GaAsN alloys with dierent nitrogen contents. Because of an additional non-radiative interexcitonic transfer channel, we found a strong energy dispersion of the photoluminescence decay times. The photoluminescence decay is predominantly non-radiative on the high-energy side of the spectrum. The radiative transitions are mainly delocalized and have ultra-short decay times in comparison to the low-energy part of the spectrum, which is characterized by radiative transitions of localized excitons and trions.
An increase of the bath temperature reduces the decay times and thus the energy dispersion, in agreement with previous observations in intrinsic (In)GaAsN 26,28,29 . However, the determined maximum decay times of GaAsN:Si are signicantly reduced in comparison to undoped GaAsN 27 . This can be explained by a higher contribution of Shockley-Read-Hall and possibly Auger recombinations in GaAsN:Si in comparison to undoped GaAsN. We determined the excitonic mobility edge energy as a function of the N content. The edge energy decreases with increasing N content, which is in excellent agreement with the two-level BAC model 9 .