Direct measurement via cyclotron resonance of the carrier effective masses in pristine diamond

We have determined effective mass parameters for ultrapure diamond by time-resolved cyclotron resonance of optically excited carriers. The transverse and longitudinal electron masses are found to be $m_t/m_0=0.280\left(2\right)$ and $m_l/m_0=1.56\left(2\right)$, where $m_0$ is the free-electron mass. The Luttinger parameters are extracted as ${\gamma }_1=2.67\left(2\right),{\gamma }_2=-0.40\left(2\right)$, and ${\gamma }_3=0.68\left(2\right)$, which give the light- and heavy-hole bands with considerable anisotropy and the split-off hole mass. The resonance widths indicate scattering times longer than 100 ps and carrier mobilities as high as ${10}^6{{\mathrm{cm}}^2{\mathrm{V}}^{-1}\mathrm{s}}^{-1}$ at 10 K.

Figure 1

Concept of the time-resolved cyclotron resonance of optically excited carriers. We first generate excitons with optical pump below the band gap [panel (a)]. The excitons collide with each other and ionize into free carriers. The free carriers exhibit absorption of the microwave with the electric field $\mathbf{E}$ due to the CR motion in the plane perpendicular to the external magnetic field ${\mathbf{B}}_{\mathbf{ex}}$ [panel (b)].

Figure 2

Cyclotron resonance curves in diamond at 10 K with the magnetic field applied along the direction of ${40}^{\circ }$ to the [001] axis in the $\left(1\overline{1}0\right)$ plane. (a) Real and (b) imaginary parts of the microwave electric field are shown. Inset: The effective mass $m_{\mathrm{eff}}=e{B}_i/\left(2\pi \nu \right)$ and the inverse scattering time $1/\tau =2\pi \nu {\Gamma }_i/B_i$ for the light hole as a function of delay time following the optical excitation. The hatched area indicates the timing window for the profiles in (a) and (b).

Figure 3

(a) Real and (b) imaginary parts of the cyclotron resonance curves at different field directions measured from the [001] axis. (c) Angular dependence of the effective masses of e1, e2, e3, lh, and hh. The circles are data points, and the solid lines are fits as explained in the text. The dashed horizontal line labeled “so” indicates the calculated split-off hole mass. The thin black lines represent deviations in the calculated hole masses due to errors in $A,B^{\prime }$, and $C$. The negative angles mean the magnetic field in the (100) plane and the positive angles in the $\left(1\overline{1}0\right)$ plane.

Figure 4

Comparison of the energy dispersions around the $\Gamma$ point within the $\pm 2\%$ of the Brillouin zone of diamond for the light hole (upper panels) and the heavy hole (lower panels) in the $k_x-k_y$ plane. (a) Present study for diamond, (b) theory with spin-orbit coupling for diamond,[7] (c) previous experiment for diamond,[25] (d) silicon,[21] and (e) germanium.[21] The contours represent light-hole energies from $-0.6$ to $-6\mathrm{meV}$ in steps of $-0.6\mathrm{meV}$ and heavy-hole energies from $-0.3$ to $-3\mathrm{meV}$ in steps of $-0.3\mathrm{meV}$.