REVISTA MEXICANA DE FislCA 44 SUI'L~;M~;NTO 3. 165-167 DICIEMBRE 199H A simple model for atomic layer doped field-effect transistor (ALD-FET) electronic sta tes M.E. Mora-Ramos Celltro de Investigaciones en Óptica, Unidad Aguascalientes. Juan de M01lloro 207. Zona Cefllro, 20000 AguasClllientes, Ags., Mexico L.M. Gaggero-Sager Escuela de F':'iica,Uni\'ersidad Autónoma de Zacatecas Av. PreparalOria 301.98060 Zacatecas, Zac .. Mexico Recibido ellO de enero de 1998; aceptado el 13 de enero de 1998 We propose a simple potential rnodel based on the Thomas-Fcrmi approximation (o reproduce the main propenics of the elcctronic slructure of an atomic layer dopcd ficld effccl transistor. Prcliminary nurncrical rcsults fUf a Si-bascd ALD-FET justify why bound electronir stalcs are nol observed in the experiment. Keywords.' Field effcet transistor (FET's): delta-doping quantum wells Se propone un modelo sencillo para la descripción de las principales propiedades de la estructura electrónica de un transistor de efecto de campo con dopamiemo de capas atómicas. basado en la aproximación de 'Il1omas-Fcrmi. Los resultados numéricos iniciales realizados para un ALD-FET de Si justifican el que no se observe experimentalmente la existencia de estados ligados para los electrones de conducción. Descriptores: Transistores de efeclo de campo (FETs); pozos cuánticos delta dopados PAes: 73.30; 73.61; 55.11 lo Introduction SpaliaIly loealized impuriJies can be seeded lo a high degree of confincmcnt wilh lhe use of modcrn epitaxial rcchniques. Currenlly, 6 doping has been sueeessfuIly used lo produce Si layers in GaAs and AI:rGat_zAs, Sb laycrs in Si and S layers in In? [1-6]. The syslem of our eoneem, lhe atomie layer doped field effeel Iransislor (ALD-FET), is oblained by lhe growing of two delta-doped quantum wells; one of Il.rypc and one of 1'_ lype [7-9] (see Hg.I). The device conduelion ehannel should be, fundamenlaIly, lhe f1-1ype quanlum weIl; lhus we are going to base the explanation of rhe elccrronic propertics in sludying how the bands bend due lo Ihe presenee of lhe Iwo delta layers. Qur purpose is lo presenl a simple model lo describe the main characteristics of rhe clectronic gas observcd in lhis kind of syslem. The main point in Ihe model is Ihallhe eonduelion band is deseribed by Ihe deplelion approximalion in lhe proximily of the interface, and by two isolaled 6-weIls in the region nOl so c10se lo the interfacc. The eontael pOlenlial is delermined by lhe presenee of inlerface states, the Fermi level, rhe bias volrage, tcmperalure, defecrs, etc. Wc focus our attention on rhe semiconductor so thar wc assume fixed known values fOf rhe conlacr potcnti al and Fermi leve!. In this siruarion the carriers reach lhe equilibrium nor only by the ionizarion 01"impuritics, but 3150 by moving from the Il-typc well lO the metal-semiconductor interfacc. The 6 wcll is no longer a ncutral systcm. This alle. ration of neutralily does not prevent the conduction band lo / GATE \ SDURCE DRAIN doped luyers SUBSTRATE FIGURA l. ALD-FET: cross-scctional view. be fla! at long disranccs becausc [he whole system (wclls plus interface) rcmains neutral. The depletion layer lhickncss. t, decreases in such a way lhar the interface potential (\'~) rcmains unchangcd. 2. Model From the pcrspectivc of lhe reconstruclion of the condUClion band, Ihe p-doped delta well simply aets as a potenlial barrier for thc electrons localizcd in the n-type well. In a model 166 ME MORA-RAMOS previously proposed for 6-FET [10), lhe semiconduclor conduction band is descrihed lhrough a pOlenlial which has lhe form al' a Schottky barrier plus a simple Thomas-Fcrmi cxpression for lhe ¡solaled n-Iype 6-well which was lirsl proposed in Ref 11. The question is lhal lhe p-Iype 6-well can also he veey weH dcscrihcd within (he Thomas-Fermi approximalion as has becn shown in Ref. 12. Thcrcfore. wc propase (he following cxprcssion as a pOlcntiai moJel lo dcscrihe the semiconductor conduction band in the ALD-FET: V(=) = + [\~,(=) + I'p(Z)]8(/d - z). I'sch(Z) if=2:0, if Z < 0, fr\'c lf bound-negativc cnergy-states occur in the systcm. the quantity Id will represcnt the zera potcntial position, l.e.. we assumc that the well docs not contributc to the total potential in the region of the ionized impuritics. Thereforc, in our mode11d is also thc depletion layer width because alzcro tempcraturc only the impuritics helow the Fermi level (£1') are ionized. Thc proposed potential model satisfies the boundary conditions and describes in a simple way the esscntials of the actual physical system. Il will be used to sludy the elcctranic structure and can be the starting potential for a more exaet selfconsistent calculation. Since' the tcmperature to he considereJ is c10se 10 zera. the cnergy levels ¡hat we take ¡nlo account are only those bclow lhe Fenni level which, following ¡oriaui [111 wc lake al the conduction band edgc. (4) The pOlenlials 01'. lhe p- and n-lype delta-doped quanlum wclls in the Thomas-Fcrmi aproximation are. rcspcctively [10-121: (5) (6) \~.(z) - Ep = 3/2 mhh e' 11 =-- r,. 2r,,,3 ) 1/5 ( rre2]J2D (7) and e2 (m,;)3/2 = -r, =On = 157fh 3 ' with (8) mili are the cffectivc masscs of the hcavy and the Iight hales. rcspectivcly. m; is (he effcctivc mass 01'the conduction electrons. HeTe, m/¡f¡ and \Ve have slUdied a Si-based ALD-FET syslem, ano lhe 1'0lIowing values for the inpul parametcrs have beco used: IHh/¡ = 0.5211/0. mIh 0.161110; m; (m;l,nd)I/3 with J1Id = O.91G3mo and l11el O.1905mo (mo bcing free c1ectran l11ass). On the other hand, the valuc tr = 11.7 is taken. The ¡¡rst step in the nUl11crical calculation is to look for the non-trivial solutions of the trascendental cquation I'(ld) O. They indicale lhe exislance 01' a negalive pOlenlial region and, consequenlly, lhe presence 01' bound energy slates which will have an associated two-dirnensional electron gas responsible for a much higher speed operalion. For that search. we eonsidcred values 01'.vd ranging [rom 0.1 x 101M cm-3 to 1 x 1018 crn-3.the contaet potential Ve took values fmm 0.4 cV to 1 cV and the two-dimensional im+ purity conccntrations n2J) and J12D varied both fmm 3 x 1012 crn-:.l 10 ..¡ X 10H cm-2. Thc conclusion of the nurncrical calculation with this potcntial model is that within those inlervals a Si-hased ALD-FET syslem does nol exhibil lhe prescnec of elcctronic localized states; i.e., the minirnun value 01"\1(..:) always remains positivc and the system beeomes a Schottky barricr with an inhomogeneous distrihution 01"impuritics. = wilh on 3. Results and conclusions = the paramclcrs bcing ° concentra- (2) (he well known cxprcssion 2rre.2 Sd . impurity tiaos (l>2LJ and H2D. respcctivcly) are also two important pararneters to be fixed. Both usually have values bctwcen 1OJ:l and 9 x 10Bcm-2. Nd is the background impurily conccntralion; 1 is (he distance helween lhe inlerface and Ihe poinl heyond which Ihe field ceeated by the charge al the interface is zera, and is givcn by = = p- ano ll-typc (1) and 1 = Thc tWQ-dimensional where 8(=)={~ Thc lirsl question lo clarify is welher bolh wells are in faet too clase. In that case, the rccombination of donar ano acceptor impurilics might aCCUf, and (ha! is an undcsirablc cffect. So, the scparation distance betwccn both wclls has to be-al Icasl-grcater (han the sum of the cffeclivc Uohr radius corresponding la the f1-typc impurities plus the corresponding la the p-lypc impurities. In the work. wc fix lhis scparation as 200 Á. in such a way Ihat the nUlllcrical cvaluation has beco performed for 6" 300 A, and 6" 500 A. Re •.. Mex.l-"ís. +lS3(1998) 165-167 = = A SIMPLE MODEL FOR ATOMIC LAYER DOPED FIELD-EFFECTTRANSISTOR The existance of discrele energy levels for the conduction clcctrons would Icad to an important qualitalive changc in the physics of Ihis kind uf device. It is necessary lo explore olher physically realistic (and experimenlally achievahle) intervals (ALD-FET) ELECTRONIC STATES 167 for the paramClcrs as well as for the separation bctwccn the lO make a definitive conclusion. 01' coursc, another possibilily is lhe use of a differenl malerial (GaAs. for inslance) lo be lhe basis of Ihe ALD-FET syslelll. Ó laycrs. in order 1. E.F. Schubert. A. Fischcr. and Klaus Ploog, IEEE Transaclioll.S on Electron Del'ices ED-33 (1986) 625. 7. K. Yamaguchi, Y. Shiraki. y. Katayama. and Y. Murayamn. J,m. J. AI'I". I'hys. 5uppl. 22.( (1983) 267. 2. S.L. Wu. T.K. Carns. 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