Optical Detection and Ionization of Donors in Specific Electronic and Nuclear Spin States

We resolve the remarkably sharp bound exciton transitions of highly enriched ${}^{28}\mathrm{Si}$ using a single-frequency laser and photoluminescence excitation spectroscopy, as well as photocurrent spectroscopy. Well-resolved doublets in the spectrum of the ${}^{31}\mathrm{P}$ donor reflect the hyperfine coupling of the electronic and nuclear donor spins. The optical detection of the nuclear spin state, and selective pumping and ionization of donors in specific electronic and nuclear spin states, suggests a number of new possibilities which could be useful for the realization of silicon-based quantum computers.

Figure 1

Zeeman spectrum of the phosphorus bound exciton no-phonon transitions in a sample enriched to 99.991% ${}^{28}\mathrm{Si}$. (a) The PLE spectrum at $T=1.4\mathrm{K}$ with a 490 G field parallel to the [100] axis. For comparison, the spectrum of natural Si is shown, shifted to compensate for the dependence of the band gap energy on the average isotopic mass [13, 22]. (b) Level scheme showing the origin of the transitions. $D^0$ is the ground state of the phosphorus neutral donor, which has a zero-field hyperfine splitting of 486 neV, and under an applied field splits into four hyperfine levels determined by the projections of the electron spin $m_e=\pm \frac{1}{2}$ and the nuclear spin $m_I=\pm \frac{1}{2}$. The donor bound exciton $D^{0}X$ has two electrons in a spin singlet, and under a magnetic field splits only according to the $j=3/2$ hole “spin” projection, $m_h$. The six doublet transitions are ordered in increasing energy from left to right, in correspondence with the transitions shown in (a). The two “forbidden” transitions with $\Delta m=\pm 2$ are not shown.

Figure 2

Dependence of the phosphorus bound exciton PLE line shapes on temperature and isotopic enrichment. At the bottom is a section of the spectrum shown in Fig. 1a, while above it is a spectrum of the same sample at a temperature of 4.2 K (shifted up in energy to compensate for the temperature dependence of the band gap energy [27]). The spectrum labeled b is for a sample enriched to 99.983% ${}^{28}\mathrm{Si}$, and the spectrum labeled c is for a sample enriched to 99.92% ${}^{28}\mathrm{Si}$, both at 1.4 K.

Figure 3

Photoluminescence excitation spectrum of the zero-field structure of the phosphorus bound exciton transition in the sample enriched to 99.991% ${}^{28}\mathrm{Si}$. The large bracket at the bottom indicates the 486 neV zero-field hyperfine splitting of the phosphorus donor, while the two smaller brackets label an additional splitting which varies with experimental conditions.

Figure 4

Photocurrent spectroscopy of the phosphorus bound exciton transitions in a sample enriched to 99.991% ${}^{28}\mathrm{Si}$ with a magnetic field of 490 G applied parallel to the [100] axis. Because of electron-hole recombination, the electrons from the bound exciton Auger recombination reduce the larger nonresonant hole photocurrent from the dominant impurity, boron.