Unusual properties of the RY3 center in GaN

The investigation and identification of point defects in GaN is crucial for improving the reliability of light-emitting and high-power electronic devices. The RY3 defect with a characteristic emission band at about 1.8 eV is often observed in photoluminescence (PL) spectra of $n$-type GaN grown by hydride vapor phase epitaxy, and it exhibits unusual properties. Its emission band consists of two components: a fast (10-ns lifetime) RL3 with a maximum at 1.8 eV and a slow (100–300 μs lifetime) YL3 with a maximum at 2.1 eV and zero-phonon line at 2.36 eV. In steady-state PL measurements, the YL3 component emerges with increasing temperature from 90 to 180 K, concurrently with a decrease in the RL3 intensity. The activation energy of both processes is about 0.06 eV. In time-resolved PL, the YL3 intensity abruptly rises when the RL3 intensity begins to saturate. These and other phenomena can be explained using a model of an acceptor with two excited states. A delocalized, effective-mass state at about 0.2 eV above the valence band captures photogenerated holes. These holes transition to the ground state, which produces the RL3 component with a lifetime of ∼10 ns. Alternatively, they may nonradiatively transition over a 0.06 eV-high barrier to a localized excited state with a level at 1.13 eV above the valence band. Recombination of free electrons or electrons at shallow donors with the holes at this localized excited state is responsible for the YL3 component. The relative intensities of the RL3 and YL3 components are dictated by the probabilities of holes at the shallow excited state to transition to the ground or to the localized excited states. Transition metals and complex defects are considered as the main candidates for the RY3 center.

Figure 1

Band diagram and transitions associated with the RY3 band in GaN. ${\mathrm{A}}_1$, ${\mathrm{A}}_2$, and ${\mathrm{A}}_3$ are three states of the RY3 center, where ${\mathrm{A}}_1$ is the ground state of the acceptor, and ${\mathrm{A}}_2$ and ${\mathrm{A}}_3$ are excited states with a localized and delocalized hole, respectively. The electron and hole transitions are shown with solid and dashed arrows, respectively. Transition 3 is responsible for the RL3 component with a maximum at 1.8 eV. Transitions 4 and 4′ cause the YL3 component with a maximum at 2.1 eV and the ZPL at 2.36–2.38 eV. Other transitions are explained in the text.

Figure 2

Low-temperature (18 K) PL spectra for selected GaN samples at $P_{\mathrm{exc}}\approx {10}^{-4}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 3

PL spectra at select temperatures for sample H106, at $P_{\mathrm{exc}}={10}^{-4}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 4

The RY3 band in sample H106 at (a) $T=18$ and (b) 180 K. The solid line is the normalized SSPL spectrum at $P_{\mathrm{exc}}={10}^{-3}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The filled circles and empty squares show the fast (at $\sim {10}^{-8}\mathrm{s}$) and slow (at $\sim {10}^{-4}\mathrm{s}$) components, respectively, of the RY3 band obtained from TRPL excited with a nitrogen pulse laser. They are shifted arbitrarily in the vertical direction in a logarithmic scale, so that their sum (shown with the × symbols) matches the SSPL spectrum.

Figure 5

Temperature dependence of the PL quantum efficiency for the RL3 and YL3 components of the RY3 band (sample H106, $P_{\mathrm{exc}}={10}^{-4}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$). The lines are calculated using Eq. (1) with the following parameters: ${\eta }_{0i}=0.3$ and $C_3=0$ for the RL3 component, ${\eta }_{0i}=0.0035$ and $C_3=1100$ for the YL3 component; $C_1=100$, $C_2=2\times {10}^5$, $E_1=0.06$ eV, $E_2=0.22$ eV for both components; ${\eta }_{0i}=0.004$, $C_1=60$, $C_2=600$, $C_3=0$, $E_1=8$ meV, and $E_2=35$ meV for the exciton band. The error bars for the YL3 component are large for temperatures between 50 and 100 K, because the YL3 component, with no visible ZPL, is covered by much stronger RL3 component. At $T<50$ K, the YL3 ZPL can be resolved, so that uncertainty decreases: ${\eta }_{0,YL3}=0.010\pm 0.003$ at $T=18$ K (not shown).

Figure 6

Temperature dependence of the FWHM of the combined RY3 band and its components in samples with strong RY3 band. Empty symbols show the FWHM of the broad RY3 band in SSPL. Filled symbols show the FWHM of the RL3 and YL3 components obtained from TRPL. The dashed lines are calculated using Eq. (2) with the following parameters: $W_i\left(0\right)=0.37$ eV and $\hslash {\mathrm{\Omega }}_{0i}^e=0.035\mathrm{eV}$ for the RL3 component and $W_i\left(0\right)=0.435$ eV and $\hslash {\mathrm{\Omega }}_{0i}^e=0.060\mathrm{eV}$ for the YL3 component.

Figure 7

Temperature dependences of the integrated SSPL intensity (RL3 + YL3) in samples with strong RY3 band. All dependences are normalized at $T=170$ K for convenience of comparison. The solid line is calculated using Eq. (A17) in the Appendix with the following parameters: $C_1=100$, $E_1=0.06$ eV, $C_2=0.75\times {10}^{-14}{N}_v$ (where $N_v=3.2\times {10}^{15}{T}^{3/2}$), and $E_2=0.2$ eV. The dashed line shows the calculated dependence $3.5\times {10}^{-8}\exp (-E_3/kT)$ with $E_3=0.5$ eV. The dotted line is calculated using Eqs. (3) and (4) with ${\eta }_{0i}=0.3$, $C_{pi}={10}^{-6}\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$, $E_i=1.13$ eV, and ${\tau }_{0i}^{\mathrm{PL}}=200\mu \mathrm{s}$.

Figure 8

Temperature dependence of PL lifetime of the YL3 component in samples with strong RY3 band. $P_0=5\times {10}^{21}\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$. The dependence for the UVL band in sample H106 is shown for comparison. The dashed lines for ${\tau }_{0i}^{\mathrm{PL}}$ in sample H106 are calculated using Eq. (6) with $C_{ni}=2.5\times {10}^{-13}\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$ for the YL3 component and $C_{ni}=3.2\times {10}^{-12}\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$ for the UVL band, where the $n$(T) dependence is calculated using Eq. (8) with $N_D=7.0\times {10}^{16}\mathrm{c}{\mathrm{m}}^{-3}$, $N_A=4.3\times {10}^{16}\mathrm{c}{\mathrm{m}}^{-3}$, and $E_D=15$ meV. The solid lines are calculated using Eqs. (9) and (4) with the following parameters: $(1-{\eta }_{0i})C_{pi}{\tau }_{0i}^{\mathrm{PL}}=1\times {10}^{-15}\mathrm{c}{\mathrm{m}}^3$ and $E_i=0.18$ eV for the YL3 component; $C_{pi}=1\times {10}^{-6}\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$ and $E_i=0.182$ eV for the UVL band. The dotted line for the YL3 component is calculated using the same equations with $C_{pi}={10}^{-6}\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$, $E_i=1.13$ eV, and ${\tau }_{0i}^{\mathrm{PL}}=200\mu \mathrm{s}$.

Figure 9

Transients of the RL3 emission (between 1.78 and 1.86 eV) for sample H102 at selected temperatures obtained by using a frequency-tripled femtosecond pulsed Ti-sapphire laser (266 nm, $25\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, 80 MHz). Every fifth point is shown. The dependences are fitted using the following expression: $I^{\mathrm{PL}}\left(t\right)=\exp \left(-t/{\tau }^{\mathrm{PL}}\right)$, with ${\tau }^{\mathrm{PL}}=10.1$ ns (40 K), 8.3 ns (200 K), and 1.1 ns (300 K).

Figure 10

Temperature dependences of the RL3 emission lifetime in samples H102 and RS280 obtained from TRPL excited with a frequency-tripled femtosecond pulsed Ti-sapphire laser. The solid line is calculated using Eqs. (9) and (4) with the following parameters: ${\tau }_{0i}^{\mathrm{PL}}\equiv {\tau }_{0,\mathrm{RL}3}=10$ ns, ${\eta }_{0i}=0.3$, $C_{pi}=1\times {10}^{-7}\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$, and $E_i=0.17$ eV. The dashed curve accounts for the temperature dependence of ${\tau }_{0,\mathrm{RL}3}$ (see the Appendix) and is calculated with the following parameters: ${\eta }_{0i}=0.3$, $C_{pi}=2\times {10}^{-7}\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$, $E_i=0.22$ eV, ${\tau }_{31}=10$ ns, ${\tau }_{32}={[2\times {10}^6+3\times {10}^9\exp (-\mathrm{\Delta }E/kT)]}^{-1}$, where $\mathrm{\Delta }E=0.07$ eV.

Figure 11

Dependence of the PL quantum efficiency of the RL3, YL3 and UVL bands in sample H106. (a) $T=80$ K. The lines are calculated using Eqs. (10) and (11) with the following parameters: $N_i=3\times {10}^{16}\mathrm{c}{\mathrm{m}}^{-3}$, ${{\tau }_i}^{\lim }=5\times {10}^{-4}\mathrm{s}$, and ${\eta }_0=0.00008{\left(P_0\right)}^{0.11}$ (YL3); $N_i/{{\tau }_i}^{\lim }=5\times {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$, and ${\eta }_{0i}=0.3$ (RL3); $N_i=2.8\times {10}^{14}\mathrm{c}{\mathrm{m}}^{-3}$, ${{\tau }_i}^{\lim }=4\times {10}^{-5}\mathrm{s}$, and ${\eta }_{0i}=0.00013{\left(P_0\right)}^{0.065}$ (UVL). The dashed lines for the YL3 and UVL bands show simulated ${\eta }_{0i}$ values that account for a weak dependence on excitation intensity not related to PL saturation. (b) $T=180$ K. The lines are calculated using Eqs. (10) and (11) with the following parameters: $N_i=1.0\times {10}^{16}\mathrm{c}{\mathrm{m}}^{-3}$, ${{\tau }_i}^{\lim }=2\times {10}^{-4}\mathrm{s}$, and ${\eta }_{0i}=0.026$ (YL3); $N_i/{{\tau }_i}^{\lim }=3\times {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$, and ${\eta }_{0i}=0.09$ (RL3); $\alpha =1.2\times {10}^5\mathrm{c}{\mathrm{m}}^{-1}$.

Figure 12

Dependence of the PL quantum efficiency for the RL3, BL1, and UVL bands in sample RS280 at $T=100$ K. The lines are calculated using Eq. (10) with the following parameters: $N_i/{{\tau }_i}^{\lim }=3.2\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$, and ${\eta }_{0i}=0.075$ (RL3); $N_i=2.8\times {10}^{15}\mathrm{c}{\mathrm{m}}^{-3}$, ${{\tau }_i}^{\lim }={t_i}^{\mathrm{PL}}=5.3\times {10}^{-3}\mathrm{s}$, and ${\eta }_{0i}=0.095$ (BL1); $N_i=3\times {10}^{14}\mathrm{c}{\mathrm{m}}^{-3}$, ${{\tau }_i}^{\lim }={t_i}^{\mathrm{PL}}=1\times {10}^{-4}\mathrm{s}$, and ${\eta }_{0i}=0.013$ (UVL); and $\alpha =1.2\times {10}^5\mathrm{c}{\mathrm{m}}^{-1}$.

Figure 13

Time-integrated PL intensity as a function of the excitation photon flux for the RL3 and YL3 components in three GaN samples at $T=100$ K. A linear dependence (solid line) is shown as a guide to eye.

Figure 14

Time-integrated PL intensity as a function of the excitation intensity for the RL3 and YL3 components and their sum in sample H106 at $T=100$ K. The solid line is calculated numerically with $N_i=1.5\times {10}^{16}\mathrm{c}{\mathrm{m}}^{-3}$.

Figure 15

Time-integrated PL intensity as a function of the excitation photon flux for the RL3, RL1, and YL1 bands in sample H201 at $T=100$ K.

Figure 16

Schematics of transitions associated with the RY3 band in GaN. (a) Band diagram. (b) Configuration coordinate diagram. $A^{-}$ is the ground state of the RY3 center in $n$-type GaN (negatively charged acceptor); $A_1^0$ is the ground state of the neutral acceptor with a strongly localized hole, $A_2^0$ is the deep excited state with a localized hole, and $A_3^0$ is the shallow excited state with a weakly localized hole. The transitions 3 and 4 are responsible for the RL3 and YL3 components of the RY3 band.

Figure 17

Temperature dependence of PL quantum efficiency for the RL3 and YL3 components of the RY3 band (sample H106,$P_{\mathrm{exc}}={10}^{-4}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$). The dashed and solid lines are calculated using Eqs. (A10) and (A11), respectively, with the following parameters: $\mathrm{\Delta }E=0.07$ eV, $E_{\mathrm{A}3}=0.2$ eV, ${\tau }_{31}=10$ ns, ${\tau }_{p3}/{\tau }_{pS}=1.6(T/T^{*})$, $C_{p3}=6\times {10}^6(T^{*}/T)\mathrm{c}{\mathrm{m}}^3/\mathrm{s}$, $T^{*}=50$ K, ${\nu }_0=2\times {10}^6{\mathrm{s}}^{-1}$, ${\nu }_1=3\times {10}^9{\mathrm{s}}^{-1}$, $N_v=3.2\times {10}^{15}{T}^{3/2}\mathrm{c}{\mathrm{m}}^{-3}$, and $g=2$.