Supporting Information. Vertical Graphene-Base Hot-Electron Transistor

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1 Supporting Information Vertical Graphene-Base Hot-Electron Transistor Caifu Zeng, Emil B. Song, Minsheng Wang, Sejoon Lee, Carlos M. Torres Jr., Jianshi Tang, Bruce H. Weiller, and Kang L. Wang Department of Electrical Engineering, University of California, Los Angeles, California 90095, United States, The Aerospace Corporation, Los Angeles, California 90009, United States, and Quantum-functional Semiconductor Research Center, Dongguk University-Seoul, Seoul , Korea 1. The common-base emitter current In hot-electron transistors, the emitter/base junction should allow the injection of electrons into the graphene base. The emitter current is the source of all the electrons injected into the graphene base and it consists of two components: one component is due to Fowler-Nordheim tunneling, and the other component is due to thermionic emission (e.g. the current over the tunneling barrier and the leakage current through pin-holes). Although both of these components contribute to the total emitter current, the current through pin-holes does not contribute to the collector current. 1

2 Figure S1. The I E vs V BE characteristics at V CB = 0 V for (a) D1, (b) D2, and (c) D3 in the common-base configuration. 2. The collector/base leakage current To separate the thermionic and hot-electron contributions in the calculation of α, we have investigated the base/collector leakage current, given by the I-V characteristic corresponding to I E = 0 A. 1 As show in Figure S2, the leakage currents are much smaller than the on-state collector current for our devices, which means that the collector current is mainly due to the injected hot electrons rather than the leakage current through the filtering barrier. 2

3 Figure S2. The base/collector leakage current as a function of the collector bias, V CB, for (a) D1, (b) D2 and (c) D3. 3. The common-emitter output characteristics The common-emitter output characteristics are specified by the dependence of I C on the V CE at various V BE with the emitter electrode grounded. The common-emitter output characteristics for D1 is shown in Figure S3. The common-emitter current gain, β, is defined as I C /I B. β extracted from D1 is ~ at V CE = 5.0V and V BE = 5.0 V. α = β / (β + 1) = , which is very close to the value of α (~ ) directly obtained from the common-base measurement. Figure S3. The common-emitter output I-V characteristics for D1 at various V BE bias. The red arrow indicates the direction of increasing V BE from 4.0 V to 5.0 V with 0.2 V a step. 3

4 4. I-V characteristics for devices with broken dielectrics We fabricated more than 20 devices for each D1, D2 and D3 type of GB-HETs. A significant fraction of the devices were found to have leaky or broken dielectrics. Some devices have leaky emitter/base junction (i.e. the tunneling barrier), some devices have leaky base/collector junction (i.e. the filtering barrier), and some devices have both emitter/base junction and base/collector junction leaky. The typical I-V characteristics for devices with leaky dielectrics are shown in Figure S4 and they are significantly different from those characteristics for functioning devices in Figure 3b, 4a, and 4b. As shown in Figure S4(a), a device with a leaky emitter/base junction shows very large I E and I B at very low V BE bias. I E reaches ~ 400 na when V BE is only 3 V, but I C is still less than 1 pa and is not controlled by V BE. The leaky tunneling barrier allows a significant amount of low-energy electrons to enter the graphene base, but those electrons will not contribute to the collector current. Therefore, the device cannot be turned on and I C is always very small. Figure S4(b) illustrates the I-V characteristics for a device with a leaky base/collector junction. I C and I B reach and stay at the compliance level (1 µa) of the instrument setup once the measurement starts. This is because I C in this device is dominated by the leakage current from the base rather than the hot-electron current from the emitter. Figure S4(c) shows the I-V characteristics for a device with leaky base/collector junction and emitter/base junction. In this case, the base is permeable with the emitter and collector directly communicating with each other. I C and I E are almost identical with very small I B. Even though the current gain is large (i.e. ~1), the device loses the isolation 4

5 between the output and input, and becomes a two-terminal device rather than a threeterminal transistor. Figure S4. The transfer and input I-V characteristics for (a) a device with a leaky emitter/base junction, (b) a device with a leaky base/collector junction, and (c) a device with both junctions leaky. The V CB bias is set to 0.1 V. 5. The structure and fabrication of the emitter-up GB-HET A schematic diagram of the structure of the emitter-up GB-HET (D4) is shown in Figure S5. The Ti/Au, graphene, and silicon are used as the emitter, base and collector, respectively. The Al 2 O 3 layer serves as the tunneling barrier and the graphene/silicon 5

6 Schottky barrier (SB) serves as the filtering barrier. The fabrication starts with patterning and depositing the collector contact on top of a silicon-on-insulator (SOI) substrate. Graphene flakes are prepared by mechanical exfoliation on the surface of a hydrogenfluoride treated SOI substrate. The thicknesses of the buried oxide layer (140 nm) and the surface silicon layer (70 nm) of the SOI substrate are optimized so that the thin graphene flakes are easily visible under the optical microscope 2. The thickness of the graphene flake is identified according to the optical contrast between the graphene and the substrate and further confirmed by Raman spectroscopy. Subsequently, the base contact (10-nm-thick Ti/100-nm-thick Au) is patterned by e-beam lithography and deposited on graphene. Then, to create a tunneling barrier, a 1.2-nm-thick Al layer is evaporated on top of graphene and naturally oxidized (Al 2 O 3 ) in air. 3-5 The emitter contact is then patterned and deposited on top of the Al 2 O 3 layer. Next, the insulating isolation layers are provided by atomic-layer-deposition (ALD) of 30-nm-thick Al 2 O 3 followed by plasma-enhancedchemical-vapor-deposition (PECVD) of 150-nm-thick SiO 2. Via-holes are etched through the isolation layers by reactive-ion-etching to reach the contact metals. Finally, the electrodes and pads are patterned and deposited onto the contacts through the via-holes. 6

7 Figure S5. (a) A schematic diagram to show the emitter-up GB-HET. (b) Detailed material parameters for the emitter-up GB-HET. (c) Top view optical microscopy image for D4. The scale bar is 10 µm. The boundaries of the graphene film are labeled by blue lines for clarity. 6. The Schottky contact between graphene and silicon The emitter-up GB-HET can be treated as two coupled diodes. One is the metal-oxidegraphene (emitter-base) tunneling diode, which has been studied extensively in previous works 3, 5 and the other is the graphene-silicon (base-collector) Schottky diode. To assure the formation of a Schottky contact, we measured the I-V characteristics of the graphenesilicon contact at various temperatures (Figure S6) and quantitatively analyzed the Schottky barrier (SB) height. The Schottky diode equation 6 is given by: 7

8 qϕ qv bias = 1 kbt ηkbt * 2 b I AA T exp exp where A is the area of the Schottky junction, A* is the effective Richardson constant, is the elementary charge, k B is the Boltzmann constant, ϕ b is the SB height, and T is the temperature. According to the above equation, the diode current becomes insensitive to in the reverse bias saturation regime as exp( qv η k T) ( ϕ / ) bias / << 1 so that 2 Isat T exp q b kbt. Hence, the graphene-silicon SB height ϕ b can be extracted B from the plot of 2 ln( sat / ) I T versus 1/ T (inset of Figure S6). The extracted graphenesilicon SB height is ~0.19 ev, which is in good agreement with other experimental results 6 and thus confirms the formation of SB between graphene and silicon. Figure S6. I-V characteristics of the base-collector (graphene-silicon) Schottky diode at various temperatures (from 300 to 335K in a 5 K step). The red arrow indicates the 8

9 direction of increasing temperature (T). The inset shows the plot of l 2 n( sat / ) I T versus 1 / T at V BC = 1.5 V, which is used to extract the Schottky barrier height of ~0.19 ev. 7. The common-base output characteristics of D4 The output characteristics of D4 are measured by using the same setup as shown in Figure 1 for D1 D3. The device also displays a noticeable saturation regime, which persists up to V CB ~ 3 V. When V CB is increased in the saturation regime, the graphenesilicon SB height is insensitive to V CB, while the depletion width in the silicon region slightly decreases. Although the decrease of the depletion width causes a slight increase of I C, I C is mainly controlled by V BE but not significantly affected by V CB within the saturation regime. Figure S7. Output I-V characteristics of D4 at various V BE. 9

10 References: S1. Moise, T. S.; Kao, Y. C.; Seabaugh, A. C. Applied Physics Letters 1994, 64, (9), S2. Song, E. B.; Lian, B.; Xu, G.; Yuan, B.; Zeng, C.; Chen, A.; Wang, M.; Kim, S.; Lang, M.; Zhou, Y.; Wang, K. L. Applied Physics Letters 2010, 96, (8), S3. Zeng, C.; Wang, M.; Zhou, Y.; Lang, M.; Lian, B.; Song, E.; Xu, G.; Tang, J.; Torres, C.; Wang, K. L. Applied Physics Letters 2010, 97, (3), S4. Tombros, N.; Jozsa, C.; Popinciuc, M.; Jonkman, H. T.; van Wees, B. J. Nature 2007, 448, (7153), S5. Staley, N.; Wang, H.; Puls, C.; Forster, J.; Jackson, T. N.; McCarthy, K.; Clouser, B.; Liu, Y. Applied Physics Letters 2007, 90, (14), -. S6. Yang, H.; Heo, J.; Park, S.; Song, H. J.; Seo, D. H.; Byun, K.-E.; Kim, P.; Yoo, I.; Chung, H.-J.; Kim, K. Science