Coherent electronic Raman excitation of valley-orbit split states of phosphorus dopants in silicon

TL;DR

The paper investigates coherent electronic Raman transitions between valley-orbit split donor states in silicon by exciting a bound-electron wavepacket with an ultrafast mid-infrared pump and tracking its time evolution with a delayed probe. The authors formulate a multivalley effective mass framework to describe the valley-orbit split $1s$ manifold ($A_1$, $E$, $T_1$) and derive the two-band Raman cross-section, identifying the dominant $1s(A_1)\rightarrow1s(E)$ channel and the Raman-forbidden $1s(A_1)\rightarrow1s(T_1)$ pathway under specific conditions. Experimentally, they observe coherent electronic oscillations whose amplitude and coherence time depend on temperature, dopant density, pump polarization, and carrier pre-excitation, with a displacive excitation mechanism enabling access to the Raman-forbidden transition at higher temperatures. The work provides time-domain control of valley-orbit dynamics in phosphorus-doped silicon, offering insights for valleytronics and suggesting extensions to other multivalley materials.

Abstract

In this study, we demonstrate coherent optical excitation of the electronic Raman transition between the $1s\left(A_1\right)$ and $1s\left(E\right)$ split states of phosphorus donor in crystalline silicon. The dynamics of the generated wavepacket is characterized in the time domain using a degenerate pump-probe technique with mid-infrared femtosecond pulses via transient polarization anisotropy of the probe pulse. In addition, we study the role of resonantly excited carriers, and we show that the amplitude and coherence time of the electronic wavepacket depend on the pre-excited carrier density. Further, we demonstrate that under certain conditions, the Raman-type excitation changes to displacive impulsive excitation, which allows us to address the Raman-forbidden transition between $1s\left(A_1\right)$ and $1s\left(T_1\right)$.

Figures (4)

• Figure 1: Measured periodic coherent oscillations of probe pulse transient transmittance polarization anisotropy $\Delta T/T_0$ of phosphorus-doped silicon samples (left) and corresponding Fourier-transformed spectrum (right) at different temperatures. Data were measured for two samples with different dopant concentration (O92 - lower dopant concentration, Q8S - higher dopant concentration) and two orientations of crystal with respect to pump pulse linear polarization: (a) Q8S sample with pump pulse linearly polarized along $\left[100\right]$ direction, (b) Q8S sample with pump pulse linearly polarized along $\left[110\right]$ direction, (c) O92 sample with pump pulse linearly polarized along $\left[100\right]$ direction, and (d) O92 sample with pump pulse linearly polarized along $\left[110\right]$ direction. Pump pulse has peak intensity of $I_0 = 2,65e11W\per\square cm$. Pre-excitation pulse was not used. Fourier-transformed spectra are displayed on a logarithmic scale.
• Figure 2: Experimentally measured properties of coherent valley-orbit excitation in Q8S and O92 sample of phosphorus-doped silicon crystal as a function of crystal temperature. Data were measured for $\left[100\right]$ and $\left[110\right]$ orientation of pump pulse linear polarization in both samples. In Q8S measurements, pump pulse has peak intensity of $I_0 = 1,66e11W\per\square cm$ for its both polarizations. In O92 measurements, pump pulse has peak intensity of $I_0 = 1,66e11W\per\square cm$ for $\left[100\right]$ polarization and $I_0 = 8,32e10W\per\square cm$ for $\left[110\right]$ polarization. Measured parameters: (a) Amplitude of coherent oscillation in logarithmic scale, (b) coherence time, (c) central valley-orbit transition energy, and (d) initial phase of coherent oscillations. The shaded areas represent the standard deviation of parameters obtained by fitting experimental data of transient transmittance polarization anisotropy $\Delta T/T_0$ with the functions (\ref{['eq24:ExpDecayCosPhonon']}) and (\ref{['eq25:ExpDecayCosExpDecBack']}). Pre-excitation pulse was not used.
• Figure 3: Experimentally measured properties of coherent valley-orbit excitation in Q8S and O92 sample of phosphorus-doped silicon crystal at the temperature of 15 K as a function of peak intensity of pump pulse on the sample. Data were measured for both polarizations of the pump pulse in the Q8S sample, and for $\left[100\right]$ polarization in the O92 sample. Measured parameters: (a) Amplitude of coherent oscillation, (b) coherence time, (c) central valley-orbit transition energy, and (d) initial phase of coherent oscillations. The shaded areas represent the standard deviation of parameters obtained by fitting experimental data of transient transmittance polarization anisotropy $\Delta T/T_0$ with the functions (\ref{['eq24:ExpDecayCosPhonon']}) and (\ref{['eq25:ExpDecayCosExpDecBack']}). Pre-excitation pulse was not used.
• Figure 4: Experimentally measured properties of coherent valley-orbit excitation $1s\left(A_1\right)\rightarrow1s\left(E\right)$ in Q8S at the temperature of 12 K as a function of density of pre-excited carriers. Pump pulse has peak intensity of $I_0 = 1,66e11W\per\square cm$ and polarization oriented along $\left[100\right]$ crystallographic direction. Measured parameters: (a) Amplitude of coherent oscillation, (b) coherence time, (c) central valley-orbit transition energy, and (d) initial phase of coherent oscillations. The shaded areas represent the standard deviation of parameters obtained by fitting experimental data of transient transmittance polarization anisotropy $\Delta T/T_0$ with the function (\ref{['eq25:ExpDecayCosExpDecBack']}).