A Study on Synthesis of Graphene Films by CVD and Analytical Drain Current Modeling for GFETs
- A Study on Synthesis of Graphene Films by CVD and Analytical Drain Current Modeling for GFETs
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- Graphene has been attracting great world-wide attention due to its fascinating properties and proposed as a substitute for silicon in field-effect transistors. To fabricate a lot of arrays of graphene field-effect transistors (GFETs) on Si wafers, large-area synthesis of graphene films is a fundamental work. In addition, to simulate the characteristics of GFETs and interpret the behavior, an analytical drain current model for GFETs is needed. In this dissertation, large-area synthesis of graphene films by chemical vapor deposition (CVD) was investigated, and a new analytical drain current model for GFETs was derived.
For the large-scale synthesis of graphene films, CH4 was used as a precursor gas for supply of C atoms, and 300-nm-thick Ni films cut into 4 cm2 pieces or 25-m-thick Cu foils cut into 1 cm2 pieces were used as catalytic metals to lower the height of the energy barrier for pyrolysis reaction and provide a base for the formation of graphene structure. In an optical image of graphene films grown on Ni films, many different contrasts were observed. This indicated that non-uniform graphene films were synthesized on Ni films. In a Raman spectrum from the graphene films transferred onto SiO2/Si wafers, G peak and 2D peak were located at 1583 cm-1 and 2691 cm-1, respectively. A 2D-to-G ratio was about 0.53, and the full width at half maximum (FWHM) of 2D band was 63.5 cm-1. These results indicated that few- or multi-layer graphene films were typically grown on Ni films. When a flow rate of methane and a reaction time were decreased to reduce a supply of C atoms, graphene coverage was decreased. As the reaction time was decreased to 1 min, graphene films could not be grown on Ni films even under 35 sccm of CH4. In addition, even for a sufficient reaction time (5 min), Ni films could partially be covered with graphene films under 5 sccm of CH4. For the synthesis of uniform single-layer graphene films on Cu foils, low-pressure CVD (LPCVD) process conditions were optimized in each step. In heating and annealing steps, 20 sccm of H2 was used to make the Cu surface smooth. In a growth step, uniform single-layer graphene films could be grown on Cu foils under 20 sccm of H2 and 40 sccm of CH4 for 20 min at total pressure of 1.7 Torr. In a cooling step, a fast cooling rate (>10 oC/s) was a key factor to avoid additional or unwanted reactions after the growth step. In an optical image of graphene films grown on Cu foils, contrast was uniform. This indicated that uniform graphene films were synthesized on Cu foils. In a Raman spectrum from the graphene films grown under the optimum conditions, G peak was located at 1581.5 cm-1, and a single-Lorentzian 2D peak was located at 2675.5 cm-1, respectively. A 2D-to-G intensity ratio was 2.1, and FWHM of 2D band was 40.5 cm-1. In addition, D peak was not detected. These results indicated that high-quality single-layer graphene films were typically synthesized on Cu foils. The height of single-layer graphene from the flat substrate measured by atomic force microscopy (AFM) was 2.475 nm. After the growth of graphene films, few- or multi-layer graphene films could directly be transferred on a desired substrate without a supporting layer. On the other hand, fragile uniform single-layer graphene films could fully be transferred using polydimethylsiloxane (PDMS) or AZ5214E as a supporting layer.
The new analytical drain current model for the quantitative description of the output characteristics of GFETs in the sub-linear region was derived from a previously-developed diffusion-drift theory for GFETs. The output characteristics of GFETs could properly be reproduced by the new model, and their peculiar behavior could correctly be interpreted in the low carrier density limit. In this limit, carrier velocity at the source end was lower than the saturation velocity caused by optical phonon emission. Therefore, the saturation velocity could be neglected. In addition, in this limit, an inflection point in the output characteristics corresponded with VDS at which charge carriers at the drain end were fully depleted. This indicated that the peculiar behavior was attributed to an ambipolar property of graphene. For a simple calculation, a diffusion-to-drift current ratio was assumed to be constant along the graphene channel, and a representative value of the ratio was used instead. The ratio was defined as the product of the ratio at the source end and a weighting parameter, and the weighting parameter could reasonably be deduced. For realistic simulations for GFETs, extrinsic series resistances, the sum of contact resistances and access resistances, were considered to accurately calculate extrinsic drain-source voltages, and carrier mobility that could be degraded by high gate voltages was calculated using a modified classical formula. The simulation results in the sub-linear region showed good agreement with several sets of experimental data in previous literatures even though a diffusion-to-drift current ratio was a constant value.
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