Fatemeh (Samira) Soltani University of Victoria June 11 th

Semiconductor Devices n-type semiconductorp-type semiconductor (Electrons like to fall downhill)(Holes want to drift upward) Depletion Layer : Potential Barrier, X : Distance from surface 2

Rectifying Contacts : Work function needed to transport an electrons from to infinity n-type : 3

: Contact Potential p-type : 4

Biasing It is the estimation of the net current that flows across the potential barrier when a metal and an n-type semiconductor are connected to a D.C. source. 5

Current flows from metal into semiconductor : ( : area of contact, : constant ) Current flows from semiconductor to metal : ( : bias voltage ) Saturation current : For forward bias (+V) the net current increases exponentially with voltage. For reverse bias (-V) the current is essentially constant and equal to. The saturation current is about three orders of magnitude smaller than the forward current. 6

p-n Rectifier (Diode) 7

Diode modes 8

Bipolar Junction Transistor 9

Amplifying transistor 10

Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) 11

MOSFET is a device used for amplifying or switching electronic signals. The threshold voltage of a MOSFET is usually defined as the gate voltage where an inversion layer forms at the interface between the insulating layer (oxide) and the substrate (body) of the transistor. 12 No conduction between source and drain Switch is off Gate attracts electrons, including an n-type conductive channel in the substrate below the oxide Electrons flow between n-doped terminals The switch is on

Graphene 13 Graphene is a one-atom-thick planar sheet of carbon atoms that are densely packed in a honeycomb crystal lattice. The name comes from graphite + -ene; graphite itself consists of many Graphene sheets stacked together. In Graphene electrons / holes are confined to a plane of atomic thickness. This makes Graphene devices sensitive to the surrounding environment such as substrate and the dielectric media in contact with Graphene.

Graphene-FET 14 Metal electrodes : Ti Distance between source and drain : 5 um The center of the device was exposed to each solvent. After measurement, the solvent was removed and dried with Nitrogen gas. The source – drain bias was kept constant at 10 mV.

Related works AuthorsMethodImpurity ( cm^(-2)) Mobility ( cm^2/v.s) Temperature (k) Tan et. al (2007) Charged Impurity on SiO2 substrate 2-15 x 10^(11) 1-20 x 10^31.6 Chen et. al (2008) Doping Graphene with potassium atoms 40 x 10^3 room Bolotin et. al (2008) Suspended Graphene - etched SiO2 substrate 1-20 x 10^45 Chen et. al (2009) Organic solvent with dielectric constant x 10^4 room 15

Dielectric Screening Effect 16 Minimum position : Dirac point On both sides of Dirac point, the conductivity increases linearly with the carrier density and then slows down. Eventually, it approaches a constant conductivity.

The role of charged impurities The scattering by charged impurities leads to a linear dependence of conductivity on carrier density. In addition charged impurities are believed to generate potential fluctuations that create electron and hole puddles in Graphene. : residual density – determines the conductivity of Graphene and also responsible for observed finite conductivity at Dirac point. ( : impurity concentration, : coupling strength of dielectric, : normalized voltage fluctuation correlation ) calculations predict that the density of effective charged impurities reduces as increases and the induced scattering in Graphene decreases accordingly. 17

Mobility 18 Slopes of linear regions on both sides of the conductivity minimum : electron / hole mobility in each dielectric medium : back gate capacitance a) Both hole mobility (filled circles) and electron mobility (empty circles) increase with (decreasing with ) before reaching a plateau value. (phonon scattering) b) Asymmetry factor is the ratio of electron to hole mobilities and at high asymmetry in the electron and hole mobilities diminishes. This explains screening effect of charged impurities for scattering.

Dirac point changes 19 : position of minimum conductivity and it is a function of, which reduces as increases. : width of minimum conductivity plateau decreases with. : magnitude of minimum conductivity decreases from 18 to 3.5.

Summery Transport properties of Graphene FET in different dielectric solvents have been studied. Screening effect of charged impurities (esp. at high κ) improves device performance. Upon increasing the dielectric constant : Both electron and hole mobilities increase a few orders of magnitude The width of the conductivity minimum decreases sharply and approaches zero in high κ solvents. The position of minimum conductivity tend to shifts positively The minimum conductivity value decreases from 18 to 3.5 The conductivity saturation occurs at lower carrier densities, and the short range conductivity changes little 20

References : Fang Chen, Jilin Xia; Nano Lett. Vol. 9, No. 7, 2571 – 2574 (2009) Rolf E. Hummel; Electronic Properties of Materials; Springer; New York; Third Edition;