Physica B 227 (1996) 98-101
Microwave modulation of Coulomb-blockade oscillations in a quantum dot K. Fujii a'b'*, W. G 6 d e l b, D . A . W h a r a m b, S. M a n u s b, J.P. K o t t h a u s h, G. B 6 h m c, W . K l e i n c, G. Tr/inkle c, G. W e i m a n n c a Faculty of Science, Osaka University, Toyonaka 565, Japan b Sektion Physik der LMU, Geschwister Scholl Platz 1, 80539 Miinchen, Germany c Walter Schottky Institute, TU Miinchen, Am Coulombwall, 85748 Garching, Germany
Abstract The effects of microwave radiation on the Coulomb-blockade oscillations in a quantum dot are investigated. The application of microwaves leads to a pronounced splitting of the Coulomb-blockade oscillations, whose magnitude is proportional to the microwave amplitude. From the observed amplitude dependence of the peak splitting, the electron temperature in the quantum dot can be estimated to be 100 mK. Interestingly, this is different from that estimated by the minimum conductance between adjacent Coulomb oscillation peaks. Keywords: Quantum dot; Microwaves; Coulomb-blockade
1. Introduction Recently, high-frequency effects on the transport properties of small quantum dots have been investigated both theoretically and experimentally [1-3]. Kouwenhoven et al. [2, 3] have investigated the effect of microwaves on the Coulomb blockade oscillations (CBOs). They observed the emergence of pronounced sidebands under the application of microwave radiation and interpreted their results in terms of photon assisted tunneling through the quantum dot. They employed an asymmetric configuration, in which microwaves were applied to one of the metallic electrodes used to define the tunnel barriers to the quantum dot. In all experiments to date, the wavelength of the microwave radiation is much larger than the dot size, and hence it is difficult to focus the radiation on the * Corresponding author.
mesoscopic device without causing significant heating of the device. In this work we investigate the effects of high-frequency radiation on the CBOs of a quantum dot structure where the microwaves are applied to a center electrode in a symmetric configuration. Microwave radiation of frequencies up to 5.40 GHz was applied to the dot via this center gate electrode, which was optimised for microwave propagation to enhance the coupling between the quantum dot and the electric field. In our measurements, however, the frequencies employed are lower, but comparable, to those of the measurements of Kouwenhoven et al. .
2. Experimental procedure Using electron beam lithography, the metallic electrode structure used to define the quantum dot was fabricated on the surface of a GaAs/A1GaAs
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K. Fujii et al. / Physica B 227 (1996) 98-101
heterostructure, whose mobility and sheet electron density are 1.15 x 106 cm2/(V s) and 3.52 x 1015 m -2 at 4.2 K, respectively. The two dimensional electron gas (2DEG) is situated 60 nm beneath the surface. The application of appropriate negative biases to the lithographic electrodes confines the electrons within a region of dimensions 300 nm x 350 nm and hence defines the quantum dot. The number of electrons in the dot is estimated to be less than 400. The applied microwave signal propagates along a wedge shaped center gate which, in conjunction with a metallic ground plane located at the base of the sample, acts as a microstrip line for the high-frequency radiation. The applied microwave frequency varied between 1.0 GHz and 5.4 GHz, and the measurements were performed at 20 mK in the mixing chamber of a dilution refrigerator.
v=3.05 GHz T=20 mK
~ ~,~-48.9 dB-
3. High-frequency measurements In Fig. 1, CBOs of the conductance are shown under the application of microwave radiation with a frequency of 3.05 GHz as a function of the applied microwave amplitude. A power of -67.0 dBm in a 50 ~2 transmission line corresponds to a voltage amplitude of 100 pV. The CBO conductance peaks are observed to broaden with increasing microwave amplitude and a splitting of each peak is clearly observed when the microwave amplitude exceeds 300 ktV. As illustrated in Fig. 2 this peak splitting increases linearly with microwave amplitude below 500 pV, while, above this value, the splitting saturates with A V = 1.7 mV which is almost twice the amplitude of the microwaves. We observe a significant frequency dependence of the lineshape of the CBOs which can be explained by the frequency response of the transmission line. The observed peak splitting, however, does not depend on the microwave frequency, in contrast with what is expected from photon assisted tunneling through a Coulomb blockade system. The microwave loss in the transmission line is minimal at a frequency of 3.05 GHz, where it is estimated to attain a value o f - 6 0 dB. The observed peak separation can be interpreted as the modulation of the center gate voltage due to the electric field of the microwaves.
dB -50.1 dB
i1) o c-
'o E o
W"---: 0.0 -0.444
~'----"~"-~'I ' ' ' ~ -0.446
C e n t e r G a t e V o l t a g e (V)
Microwave amplitude (mY) Fig. 1. Conductance oscillation under microwave radiation of 3.05 GHz for various microwave amplitudes. Each peak broadens and then splits with increasing microwave amplitude.
Fig. 2. Microwave amplitude dependence of the peak splitting of a CBO peak deduced from the data shown in Fig. 1.
K. Fujii et al./ Physica B 227 (1996) 98-101
However, considering the low applied power and the poor impedance matching, it is suprising that the very small effective power that is transmitted to the dot (~ fW) can lead to measureable effects. 4. Discussion In the limit where the quantum states of the dot are well separated, the lineshape of a CBO conductance peak is described by the following function :
Gmaxc°sh-2 .I E2kB_~eEres ]
Here Eres is the energy at the peak conductance and Te is the electron temperature of the quantum dot. This energy can be correlated with the gate voltage via ~eV = E, and it is reasonable to use a conversion factor ~ = ~ = 0.1 for our structure . The modulation amplitude v and electron temperature Te are treated as fitting parameters, and we can readily fit the lineshape of a typical CBO under the influence of microwave radiation using Eq. (1) averaged over one period 3. The lineshape of a CBO has been calculated for various Te between 58 and 233 mK, and in Fig. 3, the full width at half maximum (FWHM) obtained from the calculated lineshape is shown as a function of the microwave amplitude, as well as that deduced from experimental data. The experimental data are normalized using the FWHM without microwaves. The microwave amplitude is derived from the energy conversion factor c~. The amplitude dependence of the FWHM obtained experimentally shows good agreement with that at T~ = 116 inK. It is difficult to estimate the electron temperature solely from the FWHM of CBO peak without microwave radiation and, in our experiments, the FWHM seems to be wider than that expected at 20 mK. The amplitude dependence of the lineshape, however, gives us more reliable information about Te. The amplitude dependence of the calculated peak conductance at 100 mK also shows good agreement with that of our experimental data. The comparison between the experimental and calculated lineshape clearly demonstrates that the microwave modulates the center gate voltage in a sinusoidal fashion and indicates that T~ does not increase
until the microwave amplitude exceeds 500 ~tV. The estimated electron temperature, 100 mK, agrees with that in the experiments of Kowenhoven . Above this critical amplitude, the electron temperature rises rapidly, as indicated by the analysis of the CBO amplitude. The temperature dependence of CBOs has been investigated by several authors [6-8]. Significantly, the temperature variation of the minimum conductance amin between adjacent CBOs shows activated behavior and thus yields an independent estimation of the electron temperature. The electron temperature thus derived does not coincide with that estimated one from the lineshape analysis, and this may indicate that the electron system is not in equilibrium under microwave radiation. The thermalization within the dot is certainly different from that in the whole 2DEG system including both the reservoirs and the quantum dot, and the latter effective temperature is primarily the result of heating due to the electric field of the applied microwave radiation.
. . . .
I . . . .
I . . . .
. . . . 0,050
I . . . . 0.100
4.00 0 Z 2.00
000 ''~'', 0.000
I . . . . 0.150
I .... 0.200
Fig. 3. Calculated FWHM of the CBO peak is shown as a function of microwave amplitude, as well as that obtained in our experiment. The calculation is performed for several Te between 58 mK and 232 mK.
K. Fujii et al. / Physica B 227 (1996) 98-101
Acknowledgements One of the authors (K.F.) acknowledges support from the Grant-in-Aid for Scientific Researching Priority Area from the Ministry of Education, Science and Culture of Japan, as well as from the Sonderforschungsbereich SFB 348 of the German Research Association (DFG).
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