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Transport in split-gate silicon quantum dots
Superlattices and Microstructures, Vol. 27, No. 5/6, 2000 doi:10.1006/spmi.2000.0844 Available online at http://www.idealibrary.com on
Transport in split-gate silicon quantum dots ˇ C ´ , D. VASILESKA , T. T HORNTON , S. M. A. G UNTHER , M. K HOURY , S. M ILI CI G OODNICK
Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287-5706, U.S.A. (Received 9 February 2000) We report on the transport properties of novel Si quantum dot structures with controllable electron number through both top and side gates. Quantum dots were fabricated by a split-gate technique within a standard MOSFET process. Four-terminal dc electrical measurements were performed at 4.2 K in a liquid helium cryostat. Strong oscillations in the conductance through the dot are observed as a function of both the top gate bias and of the plunger bias. An overall monotonic and quasi-periodic movement of the peak conductance is observed which is believed to be associated with the bare level structure of the electronic states in the dot coupled with the Coulomb charging energy. Crossing behavior is observed as well, suggestive of either many-body effects or symmetry breaking of the dot states by the applied bias. c 2000 Academic Press
Key words: silicon quantum dots, transport, split-gate.
1. Introduction There is considerable interest in quantum dots, as they represent the ultimate reduction in the dimensionality of a semiconductor device. In addition, it is hoped that these devices can extend the observations of single-electron tunneling [1] into the semiconductor device realm where they can be coupled to normal transistors. While there have been several observations of single-electron behavior in GaAs heterostructures, efforts in Si-based devices have been limited to either lithographically defined dots [2, 3], or devices which have relied upon accidental definition of dots [4, 5]. Here, we describe the fabrication and measurements of a dual gate-defined quantum dot, which is embedded within a Si metal-oxide-semiconductor (MOS) fieldeffect transistor. The dot is formed in the inversion layer created by the top gate, with its lateral definition being provided by two side gates embedded within the gate oxide, thus allowing independent control of both the two-dimensional electron gas density (2DEG) adjacent to the dot, as well as the shape of the dot itself.
2. Fabrication Quantum dots of differing geometry were fabricated by a split-gate technique within a MOSFET structure using the process described by Khoury et al. [6] as shown in Fig. 1. Basically, a channel-stop region is formed by implanting a p− (100) Si wafer with boron. A thin gate oxide is grown over which narrow chromium gates are defined using e-beam lithography. A field oxide and top inversion gate are deposited for independent control of the dot occupancy. 0749–6036/00/050373 + 04 $35.00/0
c 2000 Academic Press
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Fig. 1. Schematic diagram of the multilayer Si quantum dot structure. The inset shows the electron micrograph of the depletion gate structure for a 200 × 200 nm2 dot.
In the inset of Fig. 1, we show the electron micrograph of a typical device studied here. The dot itself is defined by the side gate pattern, which depletes electrons under the side gates when they are negatively biased, leaving an island of electrons. The input and output quantum point contacts, as well as the plunger gates, are independently biased.
3. Experimental results Four-terminal dc electrical measurements were performed at 4.2 K in a liquid helium cryostat. Equilibrium measurements were performed by applying a small source–drain excitation. Strong oscillations in the conductance are observed in structures with both normal and with overlapping constrictions. Typical oscillations are shown in the plot in Fig. 2, which are suggestive of Coulomb oscillations due to the filling of the dot one electron at a time. In the figure, the top gate bias was swept for fixed depletion gate. In all measurements, the device is operating within the tunneling regime, where the resistance of the input and output constrictions is much greater than 25 k (the inverse of G 0 = e2 / h, the fundamental conductance). Splitting of conductance peaks is observed, which could be due to breaking of the valley degeneracy in Si, as well as the normal spin degeneracy of the states due to the Coulomb charging energy. Figure 3 shows the position of the conductance peaks observed as a function of both inversion gate and side gate bias for the 200 × 200 nm2 symmetric structure shown in the micrograph of Fig. 1. These results correspond to a different device than that of Fig. 2, hence the voltage scales are different. Here all the side gates are tied together to a single voltage source. A monotonic decrease in peak position in terms of depletion (side) gate bias with top gate (inversion) gate bias is evident, which follows from the effect of the top gate in increasing the Fermi energy of the 2DEG surrounding the dot, hence lowering the threshold for conduction in terms of depletion gate bias. In Fig. 3, we have plotted both the major peaks (solid circles) as well as shoulders or minor peaks indicated by open squares. Overall, the peaks lie on a background of increasing conductance starting with the minimum in the lower left-hand corner, and increasing to a maximum at the upper right-hand side, as indicated by the background shading (darker regions correspond to regions of lower conductance). This trend in conductance reflects
Superlattices and Microstructures, Vol. 27, No. 5/6, 2000
375
7× 10–6 6× 10–6
Conductance (ohm–1)
5× 10–6 4× 10–6 3× 10–6 2× 10–6 1× 10–6 0 –1×10–6 9.5
10
10.5
11
11.5
12
Inversion gate bias (V) Fig. 2. Single electron oscillations in the quantum dot structure of Fig. 1.
× 10–10 12 0.2 0.15
10
Depletion gate bias (V)
0.1
8
0.05 6
0 –0.05
4
–0.1 2 –0.15 0
–0.2 –0.25 1.6
1.8
2
2.2
2.4
2.6
Inversion gate bias (V) Fig. 3. The peak (solid points) and shoulder (open squares) positions of conductance peaks for various top (inversion) and side (depletion) gate biases for a 200 × 200 nm2 dot structure.
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Superlattices and Microstructures, Vol. 27, No. 5/6, 2000
the decreased resistance of the quantum point contacts forming the entrance and exit barriers as the 2DEG density is increased, and the side gates open up the dot. In addition to the monotonic behavior observed in the evolution of the peak positions with Vtg and Vsg , there is strong evidence for crossing behavior, as one ‘row’ of peaks appears to crossover to an adjacent row at several points in the diagram (for example at Vtg = 2.2, Vsg = 0.075 and 0.15 V). Such behavior is even more evident in data in which only one of the gates is swept (for example, the plunger gate).
4. Discussion of results The crossing behavior shown in Fig. 3 is reminiscent of similar crossover behavior observed in the capacitance spectroscopy of GaAs/AlGaAs quantum dots reported by Zhitenev et al. [7]. There, such crossing behavior was attributed to a localization–delocalization transition of the states in the dot as increasing electrons filled it, which is essentially a many-body effect due to the other electrons in the system. An alternative explanation of the crossing behavior observed in the present system is related to the electronic states of a square symmetry dot, if it is deformed asymmetrically from one side. In a square dot, assuming that the depletion potential results in a quasi-harmonic potential, the allowed states may be approximated by 1 1 E n,m = ~ωx (Vtg , Vsg ) n + + ~ω y (Vtg , Vsg ) m + + E 0 (Vtg , Vsg ), 2 2 where ωx and ω y represent the confinement potentials in the x and y directions, and E 0 is the background potential which changes monotonically with top and plunger bias. Obviously, ωx and ω y are also both functions top and side gate bias. If ωx = ω y , degeneracies occur in the energy spectrum as one would expect for a two-dimensional harmonic oscillator, i.e. the levels are N -fold degenerate corresponding to the N th ‘shell’ of states. If the side gate bias changes for example ω y much more than ωx , different slopes are expected as a function of top and plunger gate bias for the states arising from confinement in different directions, giving rise to a crossing of states associated with confinement in different directions. The determination of the exact behavior of the dot states with bias requires fully self-consistent analysis of the eigenstates in this three-dimensional structure. Such studies are presently underway, and indicate that such symmetry breaking by the applied bias may account for crossing behavior when asymmetric bias is applied [8], although less so for the present case in which all the gates are tied together, suggestive that multi-particle effects still play an important role in determining the exact spectrum of states in the dot. Acknowledgement—This work has been supported by the Office of Naval Research MURI Program.
References [1] See e.g., D. K. Ferry and S. M. Goodnick, Transport in Nanostructures (Cambridge University Press, Cambridge, U.K., 1997). [2] L. Guo, E. Leobandung, L. Zhuang, and S. Y. Chou, J. Vac. Sci. Technol. B15, 2840 (1997). [3] L. Zhuang, L. Guo, and S. Y. Chou, Appl. Phys. Lett. 72, 1205 (1998). [4] H. Ishikuro and T. Hiramoto, Appl. Phys. Lett. 71, 3691 (1997). [5] A. C. Irvine, Z. A. K. Durani, H. Ahmed, and S. Biesemans, Appl. Phys. Lett. 73, 1113 (1998). [6] M. Khoury, M. J. Rack, A. Gunther, and D. K. Ferry, Appl. Phys. Lett. 74, 1576 (1999). [7] N. B. Zhitenev, M. Brodsky, R. C. Ashoori, L. N. Pfeiffer, and K. W. West, Science 285, 715 (1999). [8] S. Miliˇci´c, F. Badrieh, D. Vasileska, A. Gunther, and S. M. Goodnick, Superlattices and Microstructures 27, 377 (2000).
Transport in split-gate silicon quantum dots ˇ C ´ , D. VASILESKA , T. T HORNTON , S. M. A. G UNTHER , M. K HOURY , S. M ILI CI G OODNICK
Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287-5706, U.S.A. (Received 9 February 2000) We report on the transport properties of novel Si quantum dot structures with controllable electron number through both top and side gates. Quantum dots were fabricated by a split-gate technique within a standard MOSFET process. Four-terminal dc electrical measurements were performed at 4.2 K in a liquid helium cryostat. Strong oscillations in the conductance through the dot are observed as a function of both the top gate bias and of the plunger bias. An overall monotonic and quasi-periodic movement of the peak conductance is observed which is believed to be associated with the bare level structure of the electronic states in the dot coupled with the Coulomb charging energy. Crossing behavior is observed as well, suggestive of either many-body effects or symmetry breaking of the dot states by the applied bias. c 2000 Academic Press
Key words: silicon quantum dots, transport, split-gate.
1. Introduction There is considerable interest in quantum dots, as they represent the ultimate reduction in the dimensionality of a semiconductor device. In addition, it is hoped that these devices can extend the observations of single-electron tunneling [1] into the semiconductor device realm where they can be coupled to normal transistors. While there have been several observations of single-electron behavior in GaAs heterostructures, efforts in Si-based devices have been limited to either lithographically defined dots [2, 3], or devices which have relied upon accidental definition of dots [4, 5]. Here, we describe the fabrication and measurements of a dual gate-defined quantum dot, which is embedded within a Si metal-oxide-semiconductor (MOS) fieldeffect transistor. The dot is formed in the inversion layer created by the top gate, with its lateral definition being provided by two side gates embedded within the gate oxide, thus allowing independent control of both the two-dimensional electron gas density (2DEG) adjacent to the dot, as well as the shape of the dot itself.
2. Fabrication Quantum dots of differing geometry were fabricated by a split-gate technique within a MOSFET structure using the process described by Khoury et al. [6] as shown in Fig. 1. Basically, a channel-stop region is formed by implanting a p− (100) Si wafer with boron. A thin gate oxide is grown over which narrow chromium gates are defined using e-beam lithography. A field oxide and top inversion gate are deposited for independent control of the dot occupancy. 0749–6036/00/050373 + 04 $35.00/0
c 2000 Academic Press
374
Superlattices and Microstructures, Vol. 27, No. 5/6, 2000
Fig. 1. Schematic diagram of the multilayer Si quantum dot structure. The inset shows the electron micrograph of the depletion gate structure for a 200 × 200 nm2 dot.
In the inset of Fig. 1, we show the electron micrograph of a typical device studied here. The dot itself is defined by the side gate pattern, which depletes electrons under the side gates when they are negatively biased, leaving an island of electrons. The input and output quantum point contacts, as well as the plunger gates, are independently biased.
3. Experimental results Four-terminal dc electrical measurements were performed at 4.2 K in a liquid helium cryostat. Equilibrium measurements were performed by applying a small source–drain excitation. Strong oscillations in the conductance are observed in structures with both normal and with overlapping constrictions. Typical oscillations are shown in the plot in Fig. 2, which are suggestive of Coulomb oscillations due to the filling of the dot one electron at a time. In the figure, the top gate bias was swept for fixed depletion gate. In all measurements, the device is operating within the tunneling regime, where the resistance of the input and output constrictions is much greater than 25 k (the inverse of G 0 = e2 / h, the fundamental conductance). Splitting of conductance peaks is observed, which could be due to breaking of the valley degeneracy in Si, as well as the normal spin degeneracy of the states due to the Coulomb charging energy. Figure 3 shows the position of the conductance peaks observed as a function of both inversion gate and side gate bias for the 200 × 200 nm2 symmetric structure shown in the micrograph of Fig. 1. These results correspond to a different device than that of Fig. 2, hence the voltage scales are different. Here all the side gates are tied together to a single voltage source. A monotonic decrease in peak position in terms of depletion (side) gate bias with top gate (inversion) gate bias is evident, which follows from the effect of the top gate in increasing the Fermi energy of the 2DEG surrounding the dot, hence lowering the threshold for conduction in terms of depletion gate bias. In Fig. 3, we have plotted both the major peaks (solid circles) as well as shoulders or minor peaks indicated by open squares. Overall, the peaks lie on a background of increasing conductance starting with the minimum in the lower left-hand corner, and increasing to a maximum at the upper right-hand side, as indicated by the background shading (darker regions correspond to regions of lower conductance). This trend in conductance reflects
Superlattices and Microstructures, Vol. 27, No. 5/6, 2000
375
7× 10–6 6× 10–6
Conductance (ohm–1)
5× 10–6 4× 10–6 3× 10–6 2× 10–6 1× 10–6 0 –1×10–6 9.5
10
10.5
11
11.5
12
Inversion gate bias (V) Fig. 2. Single electron oscillations in the quantum dot structure of Fig. 1.
× 10–10 12 0.2 0.15
10
Depletion gate bias (V)
0.1
8
0.05 6
0 –0.05
4
–0.1 2 –0.15 0
–0.2 –0.25 1.6
1.8
2
2.2
2.4
2.6
Inversion gate bias (V) Fig. 3. The peak (solid points) and shoulder (open squares) positions of conductance peaks for various top (inversion) and side (depletion) gate biases for a 200 × 200 nm2 dot structure.
376
Superlattices and Microstructures, Vol. 27, No. 5/6, 2000
the decreased resistance of the quantum point contacts forming the entrance and exit barriers as the 2DEG density is increased, and the side gates open up the dot. In addition to the monotonic behavior observed in the evolution of the peak positions with Vtg and Vsg , there is strong evidence for crossing behavior, as one ‘row’ of peaks appears to crossover to an adjacent row at several points in the diagram (for example at Vtg = 2.2, Vsg = 0.075 and 0.15 V). Such behavior is even more evident in data in which only one of the gates is swept (for example, the plunger gate).
4. Discussion of results The crossing behavior shown in Fig. 3 is reminiscent of similar crossover behavior observed in the capacitance spectroscopy of GaAs/AlGaAs quantum dots reported by Zhitenev et al. [7]. There, such crossing behavior was attributed to a localization–delocalization transition of the states in the dot as increasing electrons filled it, which is essentially a many-body effect due to the other electrons in the system. An alternative explanation of the crossing behavior observed in the present system is related to the electronic states of a square symmetry dot, if it is deformed asymmetrically from one side. In a square dot, assuming that the depletion potential results in a quasi-harmonic potential, the allowed states may be approximated by 1 1 E n,m = ~ωx (Vtg , Vsg ) n + + ~ω y (Vtg , Vsg ) m + + E 0 (Vtg , Vsg ), 2 2 where ωx and ω y represent the confinement potentials in the x and y directions, and E 0 is the background potential which changes monotonically with top and plunger bias. Obviously, ωx and ω y are also both functions top and side gate bias. If ωx = ω y , degeneracies occur in the energy spectrum as one would expect for a two-dimensional harmonic oscillator, i.e. the levels are N -fold degenerate corresponding to the N th ‘shell’ of states. If the side gate bias changes for example ω y much more than ωx , different slopes are expected as a function of top and plunger gate bias for the states arising from confinement in different directions, giving rise to a crossing of states associated with confinement in different directions. The determination of the exact behavior of the dot states with bias requires fully self-consistent analysis of the eigenstates in this three-dimensional structure. Such studies are presently underway, and indicate that such symmetry breaking by the applied bias may account for crossing behavior when asymmetric bias is applied [8], although less so for the present case in which all the gates are tied together, suggestive that multi-particle effects still play an important role in determining the exact spectrum of states in the dot. Acknowledgement—This work has been supported by the Office of Naval Research MURI Program.
References [1] See e.g., D. K. Ferry and S. M. Goodnick, Transport in Nanostructures (Cambridge University Press, Cambridge, U.K., 1997). [2] L. Guo, E. Leobandung, L. Zhuang, and S. Y. Chou, J. Vac. Sci. Technol. B15, 2840 (1997). [3] L. Zhuang, L. Guo, and S. Y. Chou, Appl. Phys. Lett. 72, 1205 (1998). [4] H. Ishikuro and T. Hiramoto, Appl. Phys. Lett. 71, 3691 (1997). [5] A. C. Irvine, Z. A. K. Durani, H. Ahmed, and S. Biesemans, Appl. Phys. Lett. 73, 1113 (1998). [6] M. Khoury, M. J. Rack, A. Gunther, and D. K. Ferry, Appl. Phys. Lett. 74, 1576 (1999). [7] N. B. Zhitenev, M. Brodsky, R. C. Ashoori, L. N. Pfeiffer, and K. W. West, Science 285, 715 (1999). [8] S. Miliˇci´c, F. Badrieh, D. Vasileska, A. Gunther, and S. M. Goodnick, Superlattices and Microstructures 27, 377 (2000).