Graphene is a carbon monolayer which is a promising material due to its electrical, thermal and optical properties. The carrier mobility of graphene is larger than that of silicon approaching to 200,000 cm²V^-1s^-1. However, electrons and holes in graphene follow the linear relationship between energy and momentum, so that there is no bandgap in graphene material. This property makes graphene-based device unsuitable for digital logic which need high on-off current ratio. Bilayer graphene and graphene nanoribbon have been reported to have bandgap but at the cost lower mobility. Recently graphene diode has been studied to explore the alternative method of using graphene in circuit design [1]. The Schottky junction built by graphene and silicon has two unique features compared to traditional Schottky junction: 1) There is no dangling bond on the interface of graphene/silicon junction [2]; 2) The Fermi level of graphene can be adjusted electrostatically which makes it suitable for photonics.

In this work, we present theory of Schottky photodiode based on graphene/n-type silicon junction and propose a SPICE model for photo effects. Schottky diode is formed by depositing monolayer graphene over the n-silicon substrate. Graphene layer and n-silicon substrate are contacted by the metal electrodes. The bias voltage is applied between the metal and the silicon substrate. Unlike the traditional metal/semiconductor Schottky diode where Schottky barrier height is fixed, the Schottky barrier height between graphene and silicon varies due to graphene’s Fermi level which shifts with the bias voltage. When forward bias is applied, the Schottky barrier height increases. With reverse bias, the barrier height decreases. Taking the effect of carrier tunneling into consideration [3], I-V characteristics can be obtained. The variable potential between graphene/silicon diode can be used to convert incident light photons into electric signal. I-V characteristic of graphene/silicon Schottky diode under laser light exposure with 633nm wavelength and 10mW power at room temperature shows the maximum normalized photocurrent-to-dark current ratio (NPDR=(I_photo/I_dark)/P_in) close to 239W^-1.

SPICE based models are universally used in circuit design and can also be used for photonics based integrated circuits. The SPICE model can illustrate the electrical and optical properties of a device and thus can be utilized in design of photonics based integrated circuits [4]. We have used analog behavioral modeling, which is a functional library in SPICE, to model a Schottky photodiode based on graphene. The proposed device model in SPICE includes controlled source and parasite passive device. We initially obtain I-V characteristic which is controlled by the external bias voltage. Then we compute quantum capacitance (C_q), junction capacitance (C_j) and contact resistance (R_c), all of which are variables under bias voltage. Other associated components such as silicon oxide capacitance and junction resistance (R_j) can be determined from the structure of Schottky photodiode which have fixed values. Current versus bias voltage characteristics under the incident light source are in close agreement with theory and SPICE compatible proposed model.

Acknowledgment: Part of the work is supported under Contract Number LEQSF(2016-17)-R-C-04, and NSF CREST Center for Renewable Energy and Advanced Materials (CREAM) of Norfolk State University, Virginia.

References:

[1] Xu, Y., He, K. T., Schmucker, S. W., Guo, Z., Koepke, J.C., Wood, J.D., Lyding, J.W., Aluru, N.R., “Inducing electronic changes in graphene through silicon (100) substrate modification” Nano Letters, vol.11, pp.2735-2742 (2011)

[2] Yang, H., Heo, J., Park, S., Song, H.J., Seo, D.H., Byun, K.E., Kim, P., Yoo, I. Chuang, H. J., Kim, K., “Graphene barrister a triode device with a gate-controlled Schottky barrier” Science, vol.336, pp.1140-1143 (2012)

[3] Card, H. C., and Rhoderick, E. H, “Studies of tunnel MOS diodes I. Interface effects in silicon Schottky diodes” Joumal of Physics D: Applied Physics, vol.4, no.10, p. 1589 (1971)

[4] Henry, M. B., and Das, S., “SPICE-compatible compact model for graphene field-effect transistors” IEEE International Symposium on Circuits and Systems, pp. 2521-2524 (2012)