Observation of the Linear Stark Effect in a Single ...

1 Observation of the Linear Stark Effect in a Single acceptor in SiL. E. Calvet,1,2,*R. G. Wheeler,2and M. A. Reed21 Institut d Electronique Fondamentale, Ba timent 220, Universite Paris-Sud, 91405 Orsay Cedex, France2 Departments of Applied Physics and Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA(Received 22 March 2006; published 2 March 2007)The Stark splitting of a Single fourfold degenerate impurity located within the built-in potential of ametal-semiconductor contact is investigated using low temperature transport measurements. A model isdeveloped and used to analyze transport as a function of temperature, bias voltage, and magnetic field. Ourdata is consistent with a boron impurity.

2 We reportgfactors ofg1=2 1:14andg3=2 1:72and a linearStark splitting2 of numbers: , , +y, investigation of Single dopant atoms, or atomic-scale electronics, seeks to manipulate the charge and/orspin at the individual impurity level. Fundamentally, thereis a deep analogy between natural atoms, typically studiedin large ensembles using light and a Single impurity con-fined in a semiconductor, measured by current transport[1]. The Stark Effect has been explored in large ensemblesof atoms [2,3], but an investigation of an individual con-fined impurity is lacking. Recent quantum computing pro-posals [4,5] make such explorations particularly relevant,especially those of Single dopants in silicon situated in acomplex environment [6,7].

3 Here we rely on traditionalelectron transport measurements of randomly placed shal-low acceptors [8 11] and a novel geometry to explore theStark splitting of an individual transport measurements involving a gate, changingVgenergetically moves a localized impurity level with respectto the contacts, and subsequent tunneling typically exhibitsa Lorentzian spectral shape as it passes through the Fermilevel. Here the gate is used to probe the energy position andconductance spectrum of the impurity and thus cannot beused to tune the Stark Effect . The required low tempera-tures and equilibrium source-drain voltage necessary forobserving Single impurities are in apparent conflict withthe high electric field one might apply perpendicular to thegate to probe such a perturbation.

4 We resolve this byinvestigating a resonant impurity embedded in the built-in potential of a Schottky barrier and thus subject to a largeelectric field even at impurity is located near the metallic electrode of aSchottky barrier metal-oxide-semiconductor field-effecttransistor (SBMOSFET) [12 16], in which the sourceand drain are made from the metallic silicide PtSi [asdepicted in (a)]. At low temperatures and smallbias voltages current transport is governed by direct tun-neling through the Schottky barriers formed at the metal-semiconductor interface, whose resistance is much largerthan that of the channel [14]. An acceptor impurity locatednear this interface modifies the potentialVat the contact,enhances tunneling via its resonant level and is easilyobservable in low temperature transport use a 1D model forV x [15,16] that takes into accountthe perpendicular (z) electric field from the gate with theeffective carrier concentration at the MOS surface,ns.

5 Thetotal 1D potentialV x [ (b)] includes a hydrogenicimpurity and a standard metal-semiconductor depletionpotential: FIG. 1. (a) Schematic of the device. S, D, and G signify,respectively, the source, drain, and gate. The impurity (notshown) is located in the semiconductor near the metallic sourceor drain. A black and white contour plot of the depletionpotential is drawn near the source and drain, where the scaleranges from (black) to 0 (white) eV relative to the valenceband. (b) The different potentials from the 1D model calculatedusing the parameters from ,096805 (2007)PHYSICAL REVIEW LETTERS week ending2 MARCH 20070031-9007=07=98(9)=096805(4)096805-1 2007 The American Physical Society V x qN"s wx x22 ib q4 "sja xj q16 "sx q16 "s a x ;(1)wherew 2"sqns ibqis the depletion width,ais the dis-tance from the impurity to the metal, ibis the SB height,andVtis the threshold voltage.

6 The last two terms in thisequation are the image charge due to an electron tunnelingthrough the potential and the charged acceptor . The SBheight ( ib 0:225 eV) was determined from a fit to thethermionic emission equation in the 180 250 K range. Theelectric fieldESB V a rB V a rB 2rB, whererBis the in silicon have a fourfold degenerate groundstate and belong to the 8representation. Here, the poten-tial at the metal-semiconductor interface adds a largeelectric field across the impurity, potentially lifting thezero field fourfold degeneracy. We consider the linearStark Effect , which results in a splitting2 for a fieldEapplied parallel to theh100idirection [7,17]: jp8jE;(2)wherep8is the Linear dipole moment of a 8level.

7 In amagnetic field the impurity is mainly affected by theZeeman Effect , [17,18] with Ez Emj Eres B 0 gjmjj BmjB, wheremj 3=2, 1=2, 1=2, and 3=2,for a magnetic field applied parallel to addition to quadratic effects, the model neglects strainthat may result from the PtSi source and conductance of a resonant impurity is given by theLandauer formalismG E 2e2hT E . Here the transmis-sion coefficientT E jt t j2, wheretx ; xL xRp E i x2are the probability amplitudes of the positiveand negative Stark split levels, x xL xRis the totalleak rate of each Stark split peak, and E E Eresis thedifference between the Fermi level and the zero fieldresonant level. When2 > xthe conductance consistsof two Lorentzian peaks located atE Eres.

8 At largeenough temperatures ( 2 2 <3:53kBT), the Starksplit peaks experience a broadening due to the temperaturedependence of the Fermi function [9,11,19].The devices consist of ann-type polysilicon gate, aboron doped substrate (5 1021m 3), a nm gate ox-ide, and 30 nm metal silicide PtSi regions as the source anddrain [13]. Devices sizes were sufficiently small that indi-vidual impurities are easily identifiable and well of the band bending at the SB the energeticposition of impurities situated near the metal varies andresonances can be observed over a large range of gate were performed in a dilution conductancedI=dVdswas measured using astandard lock-in technique withVdsapplied in theh100idirection.

9 Characteristics were investigated as a function oftemperature, bias voltage, and magnetic field. The mag-netic field was applied perpendicular to the two-dimensional hole gas (2 DHG) in (a)shows thedI=dVdsversusVgat different biasvoltages. AtVds 0V, a splitting is clearly visible as theresonance exhibits a double peak with2 V gres V gres 0:6mV 0:1 meV. The parameters from thezero bias Landauer fit are shown in TableIand indicatevery asymmetric barriers. The fit is not unique since Lxand Rxare symmetric inT E ; however, to observe thetransport of a Single impurity over that of the direct tunnel-ing current (along the20 mdevice width), the impuritymust be close to the metal.

10 One striking characteristic atequilibrium is the peak height difference between the Starksplit peaks. To understand this, we performed detailedsimulations of the leak rates for a wide range of values ofaandnsusing a WKB approximation (Ref. [20]): 0 "!0 exp 21"ZxLx0dx 2m V x E 1=2 exp 21"Zx0xRdx 2m V x E 1=2 ;(3)where!0is the attempt frequency andV x is given byEq. (1). We find that the peak height difference cannot beexplained by the difference in energy levels of the Starksplit peaks. Instead, it is attributed to the anisotropy of thesilicon bands near the impurity. In a traditional SB withimage force, tunneling occurs within the semiconductor inthe same energy band and thusm is the semiconductoreffective mass in the direction of emission [21].