electrons an n-typesemiconductor.B. BIAS-INDUCED DOPINGThe applied electric

electrons and holes, control the current. However, for an idealunipolar Schottky type operation, it is essential to limit theband bending such that for an n-type semiconductor, at theinterface, the intrinsic fermi level EFI falls below the Fermilevel EF, which implies that ?b ? uT ·ln(Nc/ni), where Nc isthe conduction band effective density of states, ni is theintrinsic carrier concentration, and uT is the thermal voltage(=kT/q, where k is Boltzmann’s constant and T is thetemperature). Excessive band-bending at the MS interfacemay result in a p-n junction-type operation. Therefore, thelimiting conditions at the MS interface (x = 0) for a unipolarSchottky-type operation can be expressed as(Ec ? EF)|x=0 = q?b ? kT · ln (Nc/ni) -(1)for an n-type semiconductor,and(EF ? Ev)|x=0 = q?b ? kT · ln (Nv/ni) -(2)for a p-type semiconductor.Ec and Ev represent the conduction band edge and valenceband edge, respectively, and Nv is the valence band density ofstates. The terms kT · ln (Nc/ni) and kT · ln(Nv/ni) areapproximately equal to Eg/2 for most semiconductors.Fig. 1. Schematic energy band diagrams for (a) traditional n-typeSchottky contact. A depletion layer is formed at the MS interface. (b)n-type Schottky contact with excessive band-bending near theinterface resulting in inversion (p-type) charge in an n-typesemiconductor.B. BIAS-INDUCED DOPINGThe applied electric fields at the MS interface play adecisive role in governing the electrostatics and therebycharge induction in the UTB semiconductor. It can be arguedwhether the principle of bias-induced doping is not simplybased on the conventional field effect. However, inconventional FETs, the charge carriers originate from dopedsemiconductor regions in close vicinity (like doped S/Dregions), whereas in the ED concept, the charge carriersoriginate from a metal electrode, which is in direct contactwith the semiconductor body with an additional term toaccount for nonzero VGB?s = VGB + ?s/q ? ?m/q ? uT · ln (ni/Nc) – (3)For a bulk or partially depleted channel, similar relationscan be obtained using a nonzero Vox term. The term(?s/q ? ?m/q ? uT · ln (ni/Nc)) is actually the workfunctiondifference (?m ? ?s)/q, which is zero in the case of a purelybias-induced ED. In this case, it is easy to understand that apositive VGB will induce n-doping, while a negative VGB willinduce p-doping. Furthermore, the effect of interface traps canbe accounted for as?s = VGB + ?s/q ? ?m/q ? uT · ln (ni/Nc ) + (Qit + Qinv)/Cox – (4)with Qinv is the mobile inversion charge. Again, the interface -traps mainly affect the electrostatics, hence ED, but ideally,only the mobile charge should be controlled by the gate.Fig. 2. Schematic cross section of a UTB device with 2-D gatedSchottky contact for workfunction or bias-induced ED (left). Theenergy band diagram for a p-type formed region perpendicular to thegate along the red dashed line (right).The simultaneous induction of p-type and n-typecharged regions in a semiconductor body via an applied fieldcan be realized using a dual (or multiple) gate structure. Bybiasing two gates with opposite polarities, electrons and holescan be simultaneously induced in a semiconductor body asanalytically explained by (3) and (4). Depending on therelative position of such gates, electrostatically induced localbipolar regions have been reported both in lateral 30 and invertical structures.1) Lateral p-n Junction: Bias-induced ED was firstexperimentally demonstrated in a CNT system 2 where alateral p-n junction diode was formed adopting a split gateconfiguration as shown in Fig. 3. Biasing a first gate electrodewith a positive voltage with respect to the CNT body resultedin an n-type doping of a CNT channel region adjacent to it.Similarly, a negative voltage with respect to the CNT body ata second gate resulted in a p-type doping. This led to theformation of a lateral p-n junction diode in the CNT channel.The experimentally fabricated device showed rectifyingcharacteristics of a p-n junction diode with an ideality factorclose to one. In addition, the same polarity biases at both gateelectrodes resulted in an n-channel or p-channel FET. BTBT3was also observed in CNTs, demonstrating an ED p-njunction, which could be interesting for the TFET.Fig. 3. Schematic cross section of the CNT p-n diode 2. The splitgate configuration was used to electrostatically induce a lateral p-njunction. BiasingVGS1 < 0would give a p-type region in the adjacentCNT channel and VGS2 > 0 would result in an n-type region.2) Vertical p-n Junction: Electron–Hole Bilayer: Anopposite polarity gate bias configuration in the verticaldirection can be utilized to form bias-induced electron-holebilayer (EHB) as shown in Fig. 4.Fig. 4. Schematic cross section of the EHB concept (left). Energyband diagram perpendicular to the gates along the red dashed line(right). By enforcing an opposite polarity bias between the top andthe bottom gate, a tunnel junction can be formed. The wave functioncurves represent the electron (left) and hole (right) distribution in theEHB structure for illustration purposes.Thus it can be established that a high carrier density of both pandn-type (1018–1020 cm?3) Fig (7) can be electrostaticallyinduced in UTB devices, particularly for narrow bandgapsemiconductors.C. BTBT OPTIMIZATION- (6)- (7)Fig. 5. BTBT characteristicsIII. APPLICATION ON GRAPHENEElectrostatic doping of graphene through ultrathinhexagonal boron nitride films.Fig. 6. Electrostatic doping of graphene. Electrostatic potential, asmodeled across Cu/h-BN/graphene sandwich, showing induce shift ofgraphene Fermi energy.When combined with graphene, hexagonal boron nitride(h-BN) is an ideal substrate and gate dielectric with which tobuild metal |h-BN| graphene field-effect devices 3. Apredicted intrinsic doping of graphene is particularlyprominent for ultrathin h-BN layers and should be observablein experiment. It is dominated by novel interface terms that weevaluate from DFT calculations for the individual materialsand for interfaces between h-BN and Cu or graphene.As opposed to chemically doped graphene, electrostaticdoping of the graphene layers by using supercapacitorarchitectures allows dynamical control of the Fermi levelposition and hence the level of loss. In the case of graphenebasedsupercapacitors, the capacitor structure is formed withgraphene-graphene or graphene-metal electrodes 1. Thesupercapacitor architecture can electrostatically dope thegraphene electrodes, this is similar to the operation of solidstate graphene-base capacitors. Due to the electrical doublelayer (EDL) formation low bias voltages of the order of fewvolts are sufficient to produce a large enough shift of theFermi level to modulate the absorption up to the visiblewavelengths.