Ultrafast room-temperature valley manipulation in silicon and diamond

Abstract

Some semiconductors have more than one degenerate minimum of the conduction band in their band structure. These minima-known as valleys-can be used for storing and processing information, if it is possible to generate a difference in their electron populations. However, to compete with conventional electronics, it is necessary to develop universal and fast methods for controlling and reading the valley quantum number of the electrons. Even though selective optical manipulation of electron populations in inequivalent valleys has been demonstrated in two-dimensional crystals with broken time-reversal symmetry, such control is highly desired in many technologically important semiconductor materials, including silicon and diamond. We demonstrate an ultrafast technique for the generation and read-out of a valley-polarized population of electrons in bulk semiconductors on subpicosecond timescales. The principle is based on the unidirectional intervalley scattering of electrons accelerated by an oscillating electric field of linearly polarized infrared femtosecond pulses. Our results are an advance in the development of potential room-temperature valleytronic devices operating at terahertz frequencies and compatible with contemporary silicon-based technology.

Keywords: Electronic properties and materials; Ultrafast photonics.

Fig. 1. Generation and detection of the valley-polarized electron population in silicon and diamond.

a, Electrons are excited by a resonant pre-excitation pulse and equally distributed to all conduction band valleys. Blue ellipsoids represent constant energy surfaces. b, After 100 ps, the linearly polarized infrared pump pulse with the electric field amplitude F_pump generates the valley-polarized electron distribution with a higher population in valleys with their principal axes parallel to the pump polarization (blue ellipsoids) than in the other valleys (red ellipsoids). The valley polarization is measured from the polarization anisotropy of free-carrier absorption of a linearly polarized probe pulse with polarization rotated by 45° (electric field F_probe) incident on the sample in time delay Δt with respect to the pump pulse. c,d, Time evolution of electron populations in the three inequivalent groups of valleys in silicon (c) and diamond (d) at room temperature calculated by Monte Carlo simulations. e,f, Measured polarization anisotropy of free-carrier absorption and the corresponding degree of valley polarization V (in relative units (rel.u.)) in silicon (e) with a pre-excited electron density N = 1.8 × 10¹⁷ cm⁻³ and diamond (f) with N = 6.4 × 10¹⁶ cm⁻³ at room temperature for two orientations of the pump polarization along the [100] direction (black curves) and [010] direction (red curves). The electric field amplitude of the pump pulse was 0.7 V nm⁻¹ in silicon and 1.3 V nm⁻¹ in diamond, in both the experiment and simulation. Source data

Fig. 2. Relaxation time of valley polarization in silicon and diamond crystals as a function of lattice temperature.

a,b, Measured relaxation time of valley polarization τ_rel in silicon (a) and diamond (b) compared with the intervalley scattering time obtained from the numerical solution of the Boltzmann transport equation using a Monte Carlo approach (solid curve). The experimental points represent the decay time obtained by fitting the experimental data for Δα averaged over 20 temporal scans per point by a single-exponential decay function. The shaded regions represent the standard deviation of the exponential decay time obtained by fitting the measured dynamics of Δα. The pre-excited electron density is N = 1.8 × 10¹⁷ cm⁻³ (black squares) and N = 1.5 × 10¹⁸ cm⁻³ (green circles) for the data in a and N = 4.4 × 10¹⁵ cm⁻³ (black squares) and N = 6.4 × 10¹⁶ cm⁻³ (green circles) for the data in b. Source data

Fig. 3. Switching the valley polarization of electrons in silicon and diamond at terahertz frequencies.

a,b, Valley-polarized electron population is generated in silicon at temperature 7 K (a) and in diamond at room temperature (295 K) (b) using a pump pulse with linear polarization along the [100] direction (insets (i) in a and b). After 1.4 ps, a second pump pulse with linear polarization along the [010] direction (insets (ii) in a and b) switches the direction of valley polarization, which manifests itself as a change of sign of the measured Δα of the probe pulse, which is directly proportional to the degree of valley polarization V. Source data

Extended Data Fig. 1. Polarization anisotropy of free-carrier absorption in silicon and diamond.

Measured difference between the polarization components of free-carrier absorption parallel and perpendicular to the pump field Δα in a silicon and b diamond for sample orientation with pump field along [100] direction (black curves) and Δα_[110] for [110] direction (red curves). The oscillations observed in the signal with pump polarization along [110] in silicon are due to impulsive excitation of coherent optical phonons with energy of 65 meV, which is smaller than the spectral width of the pump pulse, via stimulated Raman scattering. This process is not allowed with pump polarization along [100] due to symmetry reasons. Phonon oscillations are not present in diamond because the optical phonon energy of 160 meV is larger than the bandwidth of the pump pulse. Insets: Brillouin zone of silicon and diamond with the six conduction band valleys for the configuration with pump along [100] direction (lower insets) and [110] direction (upper insets). Blue ellipsoids correspond to the valleys with higher electron population after interacting with the pump pulse while red ellipsoids show valleys with lower electron population. Source data

Extended Data Fig. 2. Dependence of polarization anisotropy of free-carrier absorption in silicon and diamond on the electric field amplitude of the pump pulse.

Measured difference between the polarization components of free-carrier absorption parallel and perpendicular to the pump field Δα and the associated degree of valley polarization V in a silicon and b diamond (black squares) at room temperature as a function of the electric field amplitude of the pump pulse F₀. The data represent the amplitude of the single-exponential decay fit of the measured dynamics of Δα. The experimental data are compared to the calculated Δα (black curve) obtained from Monte Carlo simulations. Δα is calculated from the simulated electron populations in individual valleys in the time delay of Δt=100 fs using Drude model with the electron density of N_Si = 7.5 × 10¹⁷ cm⁻³ in silicon and N_C = 2.6 × 10¹⁶ cm⁻³ in diamond. The values of the average electron scattering time in the two materials used in the Drude model are τ_Si = 90 fs and τ_C = 30 fs, respectively. The error bars represent the estimated total measurement uncertainty. The main source of the uncertainty is the long term fluctuations of experimental conditions (power and pointing stability of the laser system). Source data

Extended Data Fig. 3. Numerical simulations of the degree of valley polarization induced in silicon and diamond at temperature of 77 K using pump pulses with different parameters.

The data show the calculated degree of valley polarization V as a function of the peak electric field amplitude of the pump pulse in a silicon and b diamond for three different sets of pulse parameters, namely central photon energy of 0.62 eV (carrier frequency f=150 THz) and pulse duration 40 fs (black curves, pulse parameters applied in the experiments presented in this work), central photon energy of 62 meV (f=15 THz) and pulse duration of 400 fs (red curves) and central photon energy of 6.2 meV (f=1.5 THz) and pulse duration of 4 ps (blue curves). Source data