Deep levels in semiconductors — Influence of hydrostatic pressure

Physca I l 7B & 118B (1983) 188-190 North-HollandPubhshmgCompany

188

DEEP LEVELS IN SEMICONDUCTORS - INFLUENCEOF HYDROSTATICPRESSURE~ W.Jantsch+, K.Wunstel§, O.Kumagal&andP.Vogl§ + Johannes Kepler Unwers~tat, A-4040 LlnZ, Austria § Max-Planck-lnStltut fur Festkorperforschung, 7 Stuttgart 80, F.R.G. & Sony Corporation - Research Center, Yokohama,Japan Isothermal transient capacitance measurements provide a s~mple and yet extremely sensltive tool for the determination of pressure coefficients of deep level energies. Results for the chalcogen donors S, Se and Te in Sl are in good agreementwlth predictlons from the semiempirlcal model by Hjalmarson et al. In contrast to the chalcogen donors, the levels of ~nterstit~al Fe, Mn, V and T1 ~n S~ move towards the valence band under pressure. A qualitative explanation is given for this anomaly. 1.

INTRODUCTION

Experimental investigations of deep states in semiconductors are malnly concerned with the m croscopic characterization of defects and thelr actlvatlon energles.(1-3) In thls paper we show that hydrostatic pressure provides a valuable extension In defect level spectroscopy: (i) Hydrostatlc pressure discrlmlnates shallow and deep states independent of their activation energy: deep states are predlcted and verified to exh i b i t pressure coefficients of their blnding energy, which are larger by two orders of magmrude than those of shallow traps. ( i i ) In testlng theoretical models, pressure dependences are b e t t e r s u i t a b l e than, e . g . , the influence of temperature because of the additional compllcatlon due to electron-phonon Interactlon ~n the l a t t e r case. Experimental results for S, Se and Te are in good agreementwlth results from the semlemp l r i c a l LCAO-Koster-Slater model by H3almarson et a l . (HVWDmodel).(4) For the i n t e r s t i t i a l transltion metal impurltles Fe, Mn, V and TI ~n St we provide a q u a l i t a t w e explanatlon of the observed ~rregular s~gn of the pressure coeff~clent. 2.

EXPERIMENTALRESULTS

The influence of hydrostatlc pressure P on deep level energles is investigated here by means of translent capacitance measurements on abrupt p-n junctions or Schottky barriers at a temperature T. After appllcatlon of a voltage pulse, whlch sets the blas voltage to zero for a perlod a, the capacitance of a reverse biased dlode shows a transient aC(t) due to emlssion of carrlers from deep traps w~thin the space charge region, At a suitable temperature only a s~ngle trap is involved. The transient is then exponentlal and Its tlme constant is just the ~nverse of the thermal emlsslon rate e(T,P). The capture cross section, o(T,P), of the trap can be determined from the dependenceof the transient amplitude, aC(t~O), on the f i l l l n g pulse length ~.(5) The pressure coefficient Is obtalned from (5,6):

where AG stands for the change of G1bb's free energy, G, due to emission of a trapped carrier to the majority carrier band. Sample preparatlon has been descrlbed elsewhere. (7-9) For the capacitance measurements a conventional 1MHzbridge connected to a dlgital slgnal averager Is used. The sample is placed in a Cu-Be c e l l , which is pressurized with He-gas. The temperature stab11~ty of 0.05 K enables a resolution of better than ± 10-12eV/Pa.

c; ! <

Si:S

c; < l.-

z __. z < Q: ~1 11 z

0.I _N ~[ :E

"B"-I,,,I

\ "4 S x lOePa

E c - 0.32mY

z TIME

[sec]

Fig.l; Normallzed capacltance translents due to the B-level of S in Sl for varlous pressures. ~AG/BP = -kBT. @/BP.{In e(T,P)-ln ~(T,P)}, (I) ~) Work performed at the Max-Planck-lnstltut fur Festkorperforschung, Stuttgart. 0 378-4363/83/0000-0000/$03.00 © 1983 North-Holland

IV. Jantsch et al

/ Deep

levels m semiconductors

In Fig.1 experlmental results+for the normalized capacitance transients of a p -n Si diode doped with S are given for various pressures. From a comparison of the zero pressure emission rates to results from conventional DLTS, (7) we attrlbute the translents gwen in Fig.1 to the B-level of S, which is most l i k e l y due to the neutral substltutlonal donor (D°÷D+).(7) From the slope of the straight lines in Fig.1 the emlsslon rate is obtained as a function of pressure.

n-Si 0 a.

Si : S

~" 07 E | 06 \. "t. ~o d 05 o ' \ \~ • (.) Q4 ~1

,.%S /

#o

! U,I U. Lt. UJ 0 ¢.)

I I ! I

tU tw

I I

I

/

I

I I

#

! /

T=~TKo 03

I I

Tg

-1

tU nO.

/ AS1"/

2 0 x t OePa , 3 07 . 400

.

I I

I

o

D°--~D"

•

D*.-~D°+

I

I

I

I

I

0,2

03

O~

(IS

06

E¢ - E T

(eV)

Fig.3: Pressure coefficients of the D°+D+ and the D++D++ transitions of S, Se and Te in $1 as a functlon of the level energies ET relative to the conduction band edge Ec. For comparison the value of As is also gwen.(11)

~.~ 02 I

0

/

Se

(Ec-O32eV)

o"

01

-2

o

Fig. 2 shows results for the normallzed capacitance amplitude as a function of the f i l l i n g pulse length, whlch, in p r i n o p l e , enable a determnatlon of the capture cross section.(lO) The data in Fig.2 do not depend on pressure withln experlmental accuracy. Therefore ~(T,P) in Eq.1 08

189

I 1

I 2

I 3

I 4

Tab.I: Trap level energies; ET and t h e i r pressure coefflclents for transition metal impurities in Sl relative to the valence band edge, Ev.

5 FILLING PULSE LENGTH 5 I~secl Fig.2: Normalized capacitance amplitude due to

Level

the B-level of S in Si as a functlon of the f111ing pulse length ~. does not depend on pressure either.(lO) The second term in Eq.1 thus vanlshes and @AG/@Presults slmply from the variation of e wlth pressure. Withln the experimentally accesslble temperature range of about 501( for each level investlgated, no temperature dependenceof BAG/@Pis observed. The pressure coefflclent of AG ~s thus identical to that of the change in enthalpy.(lO) In Fig.3 we present results for the pressure coefficients of chalcogen donors in Si re]at~ve to the conduction band edge, Ec, as a function of the binding energy AG=Ec-ET. Tab.I summarizes our results for transition metal impurltles in Si. The data in Tab.I are given with respect to the va]ence band edge, Ev. For comparison, the pressure coefficient of the energy gap is also gwen. The double donor ]evels of S, Se, and Te exhibit capture cross sections larger than lO'ZScm2. For these levels the f i n i t e rise time of our apparatus prevents a determination of the influence of pressure on ~. In these cases o is assumed to be independent of pressure.

(ET-Ev) (eV)

~(ET-Ev)/BP (lO-zZeV/Pa)

T.++ _ + 1 ÷11 .-++ , + v ÷v Mn++~n+ Fe+ ~Fe°

0.29 0,45 0.31 0.39

-2,0 -2.5 -0.5 -3.3

E c - Ev

1.12

-1.5

3.

DISCUSSION

3.1

ChalcogenDonors in Si

The levels observed in S-, Se- and Te- doped Si have been attributed to substitutional donors. (7) Their pressure Coefficients are larger by two orders of magnitude than the value of -5xlO-13eV/Pa of the shallqw As-donor.(11) The l a t t e r value has been explained quantitatively within the framework of hydrogenlc effective mass theory by considenng the pressure dependences of the effective mass and the dielectric oonstant.(ll) The essenti~1 property of a deep trap is i t s short-range potential n i l e its long-range Coulomb potenti~1 plays only a secondary role. Within effectivCmass theory, the

loaalJzation in r-space requires the inclusion o f higher conduction band ,iinima. I f the Lz -

190

I¢ Jantsch et al /Deep levels m semwonductors

and F15c-mlnlma of Sl are taken ~nto account, the resultlng pressure coefficient is s t i l l too small by an order of magnitude.(5) The multlband character of deep chalcogen traps is thus ewdent from our experimental data. Chemcal trends of deep, substltutlonal donors have been successfully predicted by the HVWDmodel.(4) In this model an impurlty is deflned to be a deep trap theoretlcally, i f its central cell potentlal alone, without any long range Coulomb potential is suff4clently strong to bind a state within the band gap of the host. The HVWD model employs a tlght-blndlng-Koster-Slater scheme. The effect of pressure arlses from the change in_2 the lnteratom~c transfer matrix elements, M=Mo.a , wlth bond length a.(5) In the case of S and Se, the short range potentlal is sufflclently strong in order to blnd a localized, deep state, whereas Te is predicted to be borderline shallow. The resulting theoretical pressure coefficient for S and Se is B(ET-Ev~BP=+I.5xIO-~V/Pa or B(Ec-ET)/ ~P =-3xI~ ~V/Pa, whlch is reasonable agreement with our experimental data. Fo~ Tea s~gnlflcantly smaller value is found experiment a l l y (see Fig.3) reflecting the borderline situation. The As-donor is predicted and verlfled to be shallow in agreement with its small pressure coefflclent. (11) 4.2

Transltlon Metals in S1

The translt~on metal levels g~ven in Tab.I have been attributed to the double donor level of i n t e r s t i t i a l Te,V, and Mn, respectively.(8) The Fe-level has been identlf~ed as single ~nterstit~al donor.(9) As can be deduced from our experimental data, the trap levels formed by these ~nterstlt~al 3d-ions move towards the valence band under pressure in contrast to the subst~tutlonal chalcogen trap levels and other substitutional 3d-~mpur~ty levels ~n III-V - and II-VI - compounds.(12) In order to explaln th~s anomalous behavlour, we apply a recently developed self-consistent t~ght-blndlng model for 3d-~ons in sem?conductors, which w i l l be described ~n detail elsewhere. This model provides the following qualitative explanation for the observed pressure dependence of transition metal ~mpur~tles: Hydrostatlc pressure affects the 3d-levels in two ways: (1) The ~ncrease of hybr~dlzat~on between ~mpur~ty- and host (T2-) states pushes the antlbonding hostllke states further up ~n the gap. (I~) The kinetic energy of the ~mpurlty d-electrons and of the host s-and p-electrons increases. Since the d-electrons are more localized, however, the host s- and p-states move up faster ~n energy than the metal d-states.(13) The mechanism (1) leads to a positive pressure coefficient of the trap levels w~th respect to the valence band. The k~net~c energy term (11) on the other band, leads to an effectlve lowering of the 3d-energies under pressure and also lowers the trap energies w~th respect to E,. For substitutional defects the calculatlon ~hows, that the hybridization effect (1) dominates. For i n t e r s t i t i a l 3d-~mpur~ties, however, the hybridization with the host ~s much weaker and ( ~ ) domnates, which explains the negatlve pressure coefficient.

ACKNOWLEDGEMENTS Part of this work is supported by the "Fonds zur Forderung der Wlssenschaftllchen Forschung", Austrla, Project No.4236. I t is a pleasure to thank E.Janz~n, B.Skarstam, C.Holm, K.Graff, E. Bauser and K.Ploog for generously provlding samples. Many helpful discusslons wlth H.J.Queisser, M.Altarelll, H.G.Grimmeiss, P.Wagner and H.D. Hochhelmer are gratefully acknowledged. REFERENCES (1) Ludwig G.W. and Woodbury H.H. in: Solid State Physio813,p223, Seitz F. and Turnbull D. (eds.),(Aca~-emlc Press, N.Y. and London, 1962) (2) Kaufmann U. and Schneider J., in: F e s t k ~ e r probleme, VoI.XX,p87, Treusch J.,(ed.),(Vleweg, Braunschwelg 1980) (3) Chen J.W. and M11nes A.G., Ann.Rev.Mater. Sc1., 10, 157 (1980) (4) Hjalmarson H.P., Vogl P., Wolford D.J. and Dow J.D., Phys.Rev.Lett. 44, 810 (1980), and Vogl P., in: Festkdrperpro-~leme, VoI.XXI, p 191, Treusch J. (ed.), (Vieweg, Braunschwelg 1981) (5) Jantsch W., Wunstel K., Kumagal O. and Vogl P., Phys.Rev.B2_SB, 5515, (1982) (6) Wallls R.H., Zylberstejn A. and Besson, Appl. Phys.Lett.38, 698 (1981) (7) Grlmmelss H.G., Janzen E. and Skarstam B., J.Appl.Phys. 51,3740 (1980) and ibld.,p4212. Grlmmelss H.G-.-~Janzen E., Ennen E., Schlrmer 0., Schnelder J., Worner R., Holm C., S i r t l E., and Wagner P., Phys.Rev.B 2_44,4571 (1981) (8) Graff K. and P1eper H., in: SemCoonductor Silioon 1981, Huff H.R. and Kriegler R.J. (eds.) p331, (Electrochem.Soc., Pennington 1981) (9) Wunstel K. and Wagner P., Appl.Phys.A2_77,207 (1982) and references thereln. (10) Wunstel K., Kumagal 0., Wagner P. and Jantsch W., Appl.Phys. A2~7, 251 (1982) (11) Holland M.G. and Paul W., Phys.Rev.12___BB, 30 (1962) (12) Nichols D.N., Odeh I. and Sladek, Solid State Commun.34,621(1980), and: Hennel A.M., Martlnez GT~,J.Phys.Soc.Japan 4g,Suppl.A, 283 (1980), and: Kocot K. and ~ranowskl J.M., Phys.stat.sol. b 8_!1,629 (1977) (13) Glotzel D., ~n: Physics of Solids under High Pressure, p263, Schilllng J.S. and Shelton R.N. (eds.) (North Holland Publ., 1981) and private communicatlon.