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Negative photoconductivity due to coherent trapping of electrons in n-GaAs T.O.Klaassen1, E.E.Orlova2, J.N.Hovenier1 and F. Ghianni1* 1Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands for Physics of Semiconductors, Russian Academy of Sciences, GSP-105, 603950, N. Novgorod, Russia *Now at: CBS, P.O. Box 4000, 2270 JM Voorburg, The Netherlands e-mail: [email protected] 2 Institute Abstract Experimental set up A planar antenna on epitaxial n-GaAs, illuminated by an external THz source, has been used to create intense THz fields to study donor and cyclotron resonance transitions in a magnetic field at low temperature. When the THz field is resonant with such a transition, the resulting extremely strong coupling between the two levels leads to coherent population trapping by single frequency excitation. This effect is visible through the observed negative photoconductivity. Using standard lithography, a 220 nm thick gold selfcomplementary log-periodic antenna with a 3 3 m apex. has been fabricated on an epitaxial n-GaAs layer on SI substrate (ND= 4.1014cm-3, NA< 1.1014cm-3) The distance between the triangular AuGeNi electrodes, necessary to apply a bias current, is 15 µm. (see Fig.2) Introduction The shallow donor spectra in semiconductors have been studied extensively in the past. A complete assignment of the many experimentally observed transitions has been given for nGaAs, together with the results of accurate theoretical calculations of the transition energies, including those of the so-called auto-ionising states [1,2] Because of the relatively easy accessible THz frequency and magnet field range needed for the observation of the n-GaAs spectrum, this shallow donor has been used as a model system for the Hydrogen atom in large magnetic fields. These spectra are studied at liquid helium temperature by monitoring the magnetic field dependence of the photoconductive signal while sweeping the magnetic field at constant THz frequency radiation. Commonly, an optically pumped far-infrared laser is used as monochromatic, wavelength multi-line, source. Apart from this linear spectroscopy also work on coherent effects has been reported earlier [3,4]. Here we present experimental results on the THz photo-conductivity under very strong resonant optical fields, which that point to the occurrence of coherent trapping of electrons in dressed donor states and Landau levels. (3,1,0) (2,1,0) 3p +1 (1,-1,0) 2p +1 -1 Transition energy (cm ) 150 CR 100 Photo of the log-periodic antenna (light gray part) The rough area under the antenna indicates the presence of the electrode layer underneath, used for the application of a bias current. The FIR magneto-photoconductivity is measured using a constant current bias source and a pulsed THz laser at various wavelengths: here we discuss only the data collected at λ = 118.8 µm . The OPFIR laser delivers 300 μs long pulses with a peak intensity at of about 0.5 W. The radiation is directed to the sample in the bore of a superconducting magnet through oversized dielectric waveguides and focussed with an adjustable polythene Fresnel lens onto the antenna. The sample is placed on a translation stage in order to position the antenna apex in the beam focus. Assuming on overall coupling efficiency of only 5%, the maximum THz intensity in the apex region is estimated to be about 250 kW/cm2, which equals a THz electric field strength of about 5 kV/cm. Experimental results 2s 2p 50 0 2p -1 0 0 1 2 3 4 5 6 7 8 Magnetic field (T) Fig. 1 Fig.2 Magnet field dependence of transition energies from the 1s ground state to some of the donor states, and the cyclotron resonance transition (CR). The dashed line shows some of the observable transitions for a field sweep at λ = 118.8 µm. In fig. 3 two photoconductive spectra are shown: the upper spectrum, taken with low bias current and low THz intensity, shows the usual photo-conductive response, a decrease in electrical resistance of the sample at those field values where the applied THz field is resonant with a transition between the donor groundstate and an excited state. This conductivity increase arises from the electrons that, after excitation in an excited state, end up in the conduction band, for instance under excitation of an acoustic phonon. Also a much smaller probability for direct excitation into the band exists. The second trace is obtained with a large bias current and very strong THz radiation, and shows an increase in the sample resistance compared to that without THz radiation at the same magnetic field positions. This phenomenon is observed not only for the 1s→2p+1 transition which has a very large transition probability, but also for weaker transitions like the 1s→3p+1 transition and transitions to auto-ionising states like the (1,-1,0) and (2,1,0). The cyclotron resonance transition (CR) also exhibits this strong “negative” photo-conductive effect (NPC). The large increase in conductivity with increasing bias current is due to impact ionisation. _ 3p+ 10 + 2p max THz Ibias=30A no THz 1 30 nA 10 CR 1 0 2 3 4 5 6 7 Magnetic field (T) Fig. 3 Sample resistance as a function of magnetic field for two extreme experimental conditions at λ = 118.8 µm. In fig. 4 the shape of the 1s→2p+1 and the CR transition under low bias as a function of THz field intensity are shown. Very strong saturation effects occur, and for the maximum intensity even an increase of resistance is observed at the centre of both transitions. Also a considerable direct excitation into the conduction band occurs. (for 4< B< 6T range no allowed transitions occur) THz power Resistance (kOhm) 100 10 I bias = 30 nA +1 1 2p 3 4 temperatures the effective electron mobility depends on the intensity of the THz field. The mobility first decreases and for intensities ≥ 2 mW/cm2 increases again with THz intensities up to 200 mW/cm2, the maximum intensity reported. low THz 110 210 From THz photo-Hall experiments on donor and CR transitions in GaAs  it is known that at cryogenic 5 CR 6 Resistance (kOhm) Resistance (kOhm) no THz Ibias = 100 nA 100 Discussion 300 nA +1 2p CR 3 A 10 A 30 A 1 3 4 5 6 Magnetic field (T) Fig. 5 Sample resistance at maximum THz intensity as a function of bias current. The dashed curves show the zero THz intensity traces. This increase is due to heating of the conduction electrons by absorption of THz radiation, which results in a decrease of the ionised impurity scattering. As can be deduced from the data in fig’s.4 and 5, the negative photoconductivity (NPC) is not due to heating of the conduction electrons by the THz field, nor by its influence on the impact ionisation mechanism. Under strong impact ionisation conditions and zero THz intensity, clearly the conduction electron density is virtually independent of field, whereas the NPC only occurs at resonance. A preliminary explanation for this effect would be the formation of donor and Landau level states, “dressed” by THz photons, that “trap” part of the electrons. The reduction of the conduction electron density would then lead to the observed increase in sample resistance. The estimated 5 kV/cm maximum THz field represents 5 mV over the 10 nm radius of the donor Bohr orbit, with a binding energy of 5.7 meV. A THz field of that magnitude can easily induce coherent effects. Magnetic Field [T] Fig. 4. Sample resistance at low bias as a function of THz intensity: saturation of the 2p+1 and the CR transition. The influence of the bias current at constant maximum THz intensity is presented in fig. 5. With increasing bias current the sample resistance in the absence of THz radiation decreases strongly. (the increase with increasing B-field is due to the normal magneto-resistance effect) The resistance at resonance in the presence of THz radiation is independent of bias current and, for small bias currents, smaller with THz radiation than without. However, for Ibias ≥ 10 μA the resistance at resonance with high intensity THz radiation is larger than without THz radiation: under those conditions negative photoconductivity occurs. Experiments have also been performed at wavelengths of 70.5, 96.5 and 184.3 m on those transitions which are observable for those frequencies in magnetic fields up to 7T. Essentially the same effects as reported here for λ = 118.8 µm are observed for transitions between donor states as well as for the CR transition. Clearly the resistance at resonance under intense THz fields is determined by the optical field and not at all by the bias current. Acknowledgements. E.E. Orlova acknowledges support by NWO as visiting scientist. References  A. van Klarenbosch, T.O. Klaassen, W.Th. Wenckebach, C.T. Foxon, ”Identification and ionization energies of shallow donor metastable states in GaAs:Si” J. Appl. Phys. 67, 6323-8 (1990).  P.W. Barmby, J.L. Dunn, C.A. Bates, T.O. Klaassen, “High-field calculations for shallow-donor impurities in bulk GaAs: A finite difference approach”, Phys. Rev. B 57, 9682-9 (1998).  P.C.M. Planken., et.al., “Far-infrared time-resolved measurement of the coherence lifetime of shallow-donor transitions in GaAs”, Phys. Rev. B51, 9643-7 (1995) .  B.E.Cole, et.al “Coherent manipulation of semiconductor quantum bits with terahertz radiation”, Nature Lett. 410, . 60-63 (2001)  J. Burghoorn, et.al , “Far-infrared photo-Hall experiments on shallow donor transitions in n-GaAs, Proceed. 15th ÏRMMW Conference, Orlando, December 1990, SPIE 1514(1990)369-70.