Electronic band structure of phosphorus-doped single crystal diamond: Dynamic Jahn-Teller distortion of the tetrahedral donor ground state

The electronic band structure of the phosphorus-doped high-quality high-pressure and high-temperature–grown single crystal diamond was studied by infrared absorption, magneto- and electron paramagnetic resonance spectroscopy, and first-principles calculations. The complete picture of the $1s\to n{p}_{\pm }$ and $1s\to n{p}_0$ ($n=2$, 3, 4) donor transitions with new $1s\to 3p{}_0,4p{}_0$ and $1s\to 4p{}_{\pm }$ transitions allowed us to refine the energy levels of ground and exited states with those obtained from effective mass approximation calculation. For the first time, as far as we know, we have observed the fine doublet structures of the $1s$(${\mathrm{B}}_2,\mathrm{E})\to 2p_{\pm }, 1s$(${\mathrm{B}}_2,\mathrm{E})\to 4p{}_0, 1s$(${\mathrm{B}}_2,\mathrm{E})\to 3p{}_{\pm }$, and $1s$(${\mathrm{B}}_2,\mathrm{E})\to 4p{}_{\pm }$ donor transitions with the splitting value of 1.05 meV. These doublet structures arise from the dynamic Jahn-Teller (JT) distortion which splits the energy level of the $1s$(${\mathrm{T}}_2$) state in the ${\mathrm{T}}_d$ configuration into those of the $1s$(${\mathrm{B}}_2$) ground state and the $1s$(E) state in the ${\mathrm{D}}_{2d}$ configuration. The dynamic JT distortion of the tetrahedral donor ground state has been proved by following facts: the observation of vibronic energy levels and temperature behavior of doublet bands in the IR spectrum, the absence of P-donor-related electron paramagnetic resonance signals, and first-principles calculations. We believe that the dramatic broadening of the $2p{}_0$ band attributed to the $1s$(${\mathrm{B}}_2,\mathrm{E})\to 2p_0$ donor transition at 524 meV is caused by the resonant interaction of this 524 meV energy level with that of ∼517 meV formed due to the dynamic JT coupling of the $1s$(E) energy level equal to 387 meV with the longitudinal acoustic phonon of $\sim 130$ meV.

Figure 1

(a) Dispersion of electronic bands along symmetric directions of the hexagonal Brillouin zone of a P-doped diamond. Insert: Points of the Brillouin zone and the P1-P2 line corresponding to the ${\mathrm{\Delta }}_{\mathrm{FCC}}$ line in the Brillouin zone. (b) The partial density of the electronic states of phosphorus and carbon atoms in a P-doped diamond. (c) Insert shows the crystal structure of the P center in diamond with Jahn-Teller distortion in the ${\mathrm{D}}_{2d}$ configuration according to Ref. [27].

Figure 2

Infrared absorption spectra of the (111) P-doped single crystal diamond plate at 90 K and room temperatures. Phosphorus concentration measured by SIMS is $\sim 1.1\pm 0.1\times {10}^{17}{\mathrm{cm}}^{-3}$. The spectral resolution is 1 ${\mathrm{cm}}^{-1}$. Insert shows the photo of investigated diamond plate.

Figure 3

Absorption coefficient of the (111) P-doped single crystal diamond plate at 15 K. The phosphorus donor concentration is $\sim 1.0\pm 0.1\times {10}^{17}{\mathrm{cm}}^{-3}$. The spectral resolution is 0.2 ${\mathrm{cm}}^{-1}$. The photoionization continuum is subtracted. The insert shows the energy diagram of excited donor phosphorus levels in accordance with experiment and EMA [37]. In this insert, the ground state of $1s$ was assumed to be 600 meV.

Figure 4

(a) The evolution of infrared absorption spectra of the (111) P-doped single crystal diamond plate with temperature decreasing from 300 to 15 K. The spectral resolution is 0.2 ${\mathrm{cm}}^{-1}$. Phosphorus donor concentration, $N_D$, is $\sim 1.1\times {10}^{17}{\mathrm{cm}}^{-3}$. (b) The thermal population decrease of the $n_2$ energy level lying at 8.5 ${\mathrm{cm}}^{-1}$ above the lowest $n_1$ energy level of the doublet is in accordance to the Boltzmann law.

Figure 5

(a) Infrared absorption spectra of the $1s$(${\mathrm{B}}_2,\mathrm{E})\to n{p}_0,\mathrm{n}p{}_{\pm }$ transitions in P-doped diamond at temperatures of 2 and 20 K, and magnetic fields of 0 and 9 T. The insert shows the reconstructed optical transition scheme obtained by dividing bands into Gaussian contours. (b) Contour separation of the $1s$(${\mathrm{B}}_2,\mathrm{E})\to 2p_{\pm }$ transition in magnetic field 9 T, $T=20$ K. Left insert: scheme of the observed optical transitions. Right insert: Table with the parameters (position and width in ${\mathrm{cm}}^{-1}$) of the separated contours.

Figure 6

The evolution of the IR absorption spectra with increasing the magnetic field from 0 to 9 T at the temperature of 2 K.

Figure 7

Echo-detected EPR spectrum at room temperature. The Han pulse sequence was $\pi /2_x$ (16 ns)-$\tau$ (300 ns)-${\pi }_x$ (32 ns)-$\tau$-echo.