Quantitative analysis of electrically detected Ramsey fringes in P-doped Si

This work describes detection of the laser preparation and subsequent coherent manipulation of the quantum states of orbital levels of donors in doped Si, by measuring the voltage drop across an irradiated Si sample. This electrical signal, which arises from thermal ionization of excited orbital states, and which is detected on a millisecond time scale by a voltmeter, leads to much more sensitive detection than can be had using optical methods, but has not before been quantitatively described from first principles. We present here a unified theory which relates the voltage drop across the sample to the wave function of the excited donors, and compare its predictions to experiments in which pairs of picosecond pulses from the Dutch free-electron laser FELIX are used to resonantly and coherently excite P donors in Si. Although the voltage drop varies on a millisecond time scale we are able to measure Ramsey oscillation of the excitation on a picosecond time scale, thus confirming that the donor wave function, and not just its excited state population, is crucial in determining the electrical signal. We are also able to extract the recombination rate coefficient to the ground state of the donor as well as the photoionization cross section of the excited state and phonon induced thermal ionization rate from the excited state. These quantities, which were previously of limited interest, are here shown to be important in the description of electrical detection, which, in our unoptimized configuration, is sensitive enough to enable us to detect the excitation of ∼107 donors.