A search for unconfined fractional charges in Si based on fractional-charge impurity energy-level predictions of Derkits [Phys. Rev. Lett. 45, 1374 (1980)] is described. An upper limit (95% C.L.) of 2.3xlO~~2 0 fractional charges per atom is obtained using a combination of an infrared photoionization and a field ionization technique. This optoelectronic approach has the advantage of giving an estimate for the concentration of fractional charges, being repeatable and without mechanical techniques. By comparison, drop type experiments detect the presence of fractional charge modulo one unit of fractional charge. PACS numbers: 14.80.Dq, 29.40.Wk, 78.30.Hv Although pointlike fractionally charged constituents within hadronic particles have been clearly demonstrated experimentally, searches for free fractional charge in natural materials have not yielded any substantiated positive results [1,2]. The commonly accepted theoretical view is that at least one class of fractional-charge particles (FCP) is absolutely confined in integer-charge bound states. This view has made it appear doubtful that searches for fractional charge will be successful. On the other hand, newly developed theories must be tested and some past searches may have suffered from the elimination of FCP's from samples prior to or during experiments.This new FCP detection method is based on Chaudhuri, Coon, and Derkits' prediction [3] of the existence of localized states in semiconductors associated with electrons or holes weakly bound to fractional-charge impurities (FCI's), and the integer-charge experimental results [4]. In principle, the spectrum of states of electrons or holes weakly bound to FCLs could provide an experimental signature for fractional charge which is nearly as detailed as the H2 spectrum. Fractional-charge elements [5], if they exist, would consist of quarks or quarks bound to nuclei [6] surrounded by electrons and would not be neutral.In analogy with the well-known shallow "donor" impurities in semiconductors in which an electron is weakly bound to a positive ion D=D + +e~ the existence of shallow fractional-charge donors has been predicted [3], Z)~1 /3 =Z) +2/3 -r-^-,Z)-2/3 =Z) +1/3 + ^-. For a hydrogenic system, the binding energy is (m*/ m 0 )[Z//c-] 2 x 13.6(eV). Phosphorus in Si:P is similar to a proton bound to a Si atom giving rise to shallow levels, which can be observed by infrared (IR) spectroscopy [7]. The Z 2 scaling of hydrogenic energy levels has been found to hold true in the effective mass approximation [8], suggesting that impurity levels also scale as the square of the ionic charge, including fractional ionic charge. For Z < 1 valley-orbit splitting and central cell correction are less important relative to the effective mass approximation as they scale as Z 4 [3].
Shallow levels for integer ions have been observed [4] via a \s(A\)to 2p ~ transition peak [in the photoresponse at 32 pm (38.7 meV)] using this technique. This corresponds to the experimentally observed transition energy (39.2 meV) [7] and the effec...