PHOTOCONDUCTIVE SWITCH CHARACTERIZATION BY MEANS OF DEEP LEVEL SPECTROSCOPY

Transcription

1 PHOTOCONDUCTVE SWTCH CHARACTERZATON BY MEANS OF DEEP LEVEL SPECTROSCOPY R.P. Brinkmanna,b, T. Tessnowb, K.H. Shoenbahb, R.A. Rosh a: Siemens AC, ZFE BT ACM 31, D-8173 Miinhen b: PER, Old Dominion University, Norfolk, VA : Naval Srfae Warfare Center, Dahlgren, VA Abstrat DLTS (deep level transient spetrosopy), PCTS (photo-inded rrent transient spetrosopy), and EBCTS (eletron-beam inded rrent transient spetrosopy) are experimental tehniqes to determine the deep level spetrm of non-ideal semiondtors. These methods operate by externally exiting a sample of the material, and then monitoring the time onstants of the sbseqent retrn to eqilibrim. We analyze the onventional ("rate window") method of evalating the experimental data obtained by these tehniqes, and find it wanting in many respets. A new method (termed "spetral analysis") is then presented whih is sperior both in terms of aray and resoltion, and whih also makes the deep level spetrosopy tehniqes more sited for nmerial evalation. ntrodtion The performane of radiation (i.e., laser or eletron-beam) ontrolled solid state swithes depends strongly on the properties of the employed semiondtor material. Reent investigations have shown that not only the ideal featres of the material are of importane, bt also the non-ideal harateristis related to the natre and the onentration of imprities and other rystal flaws. By inding additional disrete states (so-alled deep levels or traps) into the band strtre of the semiondtor, one an drastially inflene the ritial performane measres like effiieny, hold-off voltage, and reovery time [1], and an even open the possibility of ompletely new swith onepts [2]. n this sitation, both the analysis and the design of solid state swithes reqire reliable information abot the loation, the ross setions, and the nmber densities of the deep levels in the employed material. Several experimental methods have been designed to obtain this information, the most widely sed are known by their aronyms as DLTS (deep level transient spetrosopy) (3], PCTS (photo-inded rrent transient spetrosopy) [4], and EBCTS (eletron-beam inded rrent transient spetrosopy) (?]. The priniples of these methods are very similiar, they operate by externally exiting a sample of the material, and analyzing the time onstants of the sbseqent retrn to eqilibrim as a fntion of the temperatre. The last two methods are partilarly similar, for they both se irradiation as means of exitation, and monitor the sample ondtane as a measre for the exitation. Both methods are espeially sited for the analysis of semi-inslating semiondtor materials whih form the basis of all optially ativated swith onepts. The priniple set-p of the methods is shematially depited in Fig. 1. A sample of the material nder onsideration is frnished with two oplanar Ohmi ontats of a few mm spaing, and then monted on a thermally isolated holder within an eletrially gronded ryostat. The temperatre of the ryostat an be adjsted in the range from 77 K (liqid nitrogen ooling) to 4 K (eletrial heating), it an be diretly monitored by means of at-type thermo element. Throgh an opening in the ryostat, the devie is sbjeted to an irradiation plse (laser light in the ase of PCTS, energeti eletrons in the ase of EBCTS) whih brings it into a state of high eletroni exitation; the inreased ondtivity and its sbseqent retrn to eqilibrim an be monitored by means of an external voltage sore and a rrent viewing resistor. The signal is then reorded by a transient digitizer and finally stored as a nmerial ompter file. The basi assmption of deep level spetrosopy is that the time onstants whih govern the retrn to eqilibrim ontain essential information on the level spetrm of the material. n general, the dynamis an be qite ompliated to analyze, let s ths fos on a sitation where only one isolated eletron trap of total onentration N is ative in a material with eletron lifetime T. n this ase, the arrier kinetis an be desribed in terms oftwo rate eqations for nand nr, the density of the eletrons in the valene band and in the trap, respetively, dn dt dnr dt n K(ennT- n(n- nr))- -, T K(n(N- nr)- ennr). J( and en desribe the onstants of eletron aptre and thermal emission of the trap, they depend on the ross setion a, the ionization energy b.e and the temperatre T. (Frthermore, g is the statistial weight of the level, m the effetive eletron mass, k and h denote Boltzmann's and Plank's onstant, respetively.) (1) (2) J( (J' y-;:;;; /skt, (3) ~ (mkt) ~ exp (-b.e). g 21r1i 2 kt To desribe the reovery, the eqations an be even more simplified: The term~ n(n- Nr) representing bak-trapping beomes negligible, and the term~ on the left of (1) an be dropped (nder the assmption that J( N ~ T- 1, i.e., that the trap is dominated by other hannels of eletron reombination.) We an then solve the eqations expliitly; assming that the trap is filled at t =, the eletron density is (4) n(t) = ATNexp(-At). (5) (The sample rrent i is proportional to this qantity, times a fator whih depends on the geomety of the sample, the applied voltage, and on the speifi mobility of the arriers.) The time onstant A eqals Ken, in terms of the ross setion and the energy level of the trap it is, _ 2amk 2 T 2 ( _ b.e) A- 2 3 exp kt. 7r g1i (6) COMPUTER Fig. 1: Priniple set-p for deep-level spetrosopy, with "irradiation sore" denoting either a laser (PCTS) or an eletron-beam (EBCTS). Under the assmption that the deep level parameters ontain no impliit dependene on the temperatre T, we an plot A/T 2 logarithmially and obtain a linear fntion in 1/T, the so-alled Arrhenis plot. The slope of this fntion is proportional to the ionization energy of the deep level b.e, and the absolte term ontains the ross setion a. So far, the evalation of the data obtained by deep level spetrosopy seems ompletely straightforward. We have, however, taitely glossed over a problem that is by no means trivial: How an one determine the rate onstants A from the atally observed rrent i(t), in partilar when there is a hane of more than one trap being ative in the data? 618

2 Report Domentation Page Form Approved OMB No Pbli reporting brden for the olletion of information is estimated to average 1 hor per response, inlding the time for reviewing instrtions, searhing existing data sores, gathering and maintaining the data needed, and ompleting and reviewing the olletion of information. Send omments regarding this brden estimate or any other aspet of this olletion of information, inlding sggestions for reding this brden, to Washington Headqarters Servies, Diretorate for nformation Operations and Reports, 1215 Jefferson Davis Highway, Site 124, Arlington VA Respondents shold be aware that notwithstanding any other provision of law, no person shall be sbjet to a penalty for failing to omply with a olletion of information if it does not display a rrently valid OMB ontrol nmber. 1. REPORT DATE JUN REPORT TYPE N/A 3. DATES COVERED - 4. TTLE AND SUBTTLE Photoondtive Swith Charaterization By Means Of Deep Level Spetrosopy 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNT NUMBER 7. PERFORMNG ORGANZATON NAME(S) AND ADDRESS(ES) Siemens AC, ZFE BT ACM 31, D-8173 Miinhen 8. PERFORMNG ORGANZATON REPORT NUMBER 9. SPONSORNG/MONTORNG AGENCY NAME(S) AND ADDRESS(ES) 1. SPONSOR/MONTOR S ACRONYM(S) 12. DSTRBUTON/AVALABLTY STATEMENT Approved for pbli release, distribtion nlimited 11. SPONSOR/MONTOR S REPORT NUMBER(S) 13. SUPPLEMENTARY NOTES See also ADM EEE Plsed Power Conferene, Digest of Tehnial Papers , and Abstrats of the 213 EEE nternational Conferene on Plasma Siene. Held in San Franiso, CA on Jne 213. U.S. Government or Federal Prpose Rights Liense. 14. ABSTRACT DLTS (deep level transient spetrosopy), PCTS (photo-inded rrent transient spetrosopy), and EBCTS (eletron-beam inded rrent transient spetrosopy) are experimental tehniqes to determine the deep level spetrm of non-ideal semiondtors. These methods operate by externally exiting a sample of the material, and then monitoring the time onstants of the sbseqent retrn to eqilibrim. We analyze the onventional ("rate window") method of evalating the experimental data obtained by these tehniqes, and find it wanting in many respets. A new method (termed "spetral analysis") is then presented whih is sperior both in terms of aray and resoltion, and whih also makes the deep level spetrosopy tehniqes more sited for nmerial evalation. 15. SUBJECT TERMS 16. SECURTY CLASSFCATON OF: 17. LMTATON OF ABSTRACT SAR a. REPORT b. ABSTRACT. THS PAGE 18. NUMBER OF PAGES 4 19a. NAME OF RESPONSBLE PERSON Standard Form 298 (Rev. 8-98) Presribed by ANS Std Z39-18

3 The Rate Window Tehniqe The traditional proedre of evalating deep levels spetrosopy data is known as the rate-window tehniqe (6). The method is based on the observation that the differene of the response rrent at two time points, tl.i = i(t 1 )- i(t2), is neqal from zero only when the time onstant lies within a ertain window (see Fig. 2). ndeed, for a single exponential mode of the form i(t) = Aexp( ->.t) the differene as a fntion of.x has a maximm at ). = ln(t2/t1). t2- tl Correspondingly, if the temperatre of the sample is sanned throgh a ertain interval, a peak in the plot of tl.i over T marks the passing of time onstant thogh the "rate window". l ~ j: _N-~ _N ~ ft._j 1., ~-----! n----t.. _ - -~ _r:----!-'--- ~ ~ _jr~j ' amplitde of transients Fig. 2: Signal differene tl.i as a fntion of the time onstant of a single-mode signal (itself being a fntion of the sample temperatre). To analyze the sensitivity and the resoltion of the rate window tehniqe, it is advantageos to swith to a different point of view. nstead of modifying the rate onstants embodied in i(t) (by hanging the temperatre of the sample), we onentrate on a single response rve and evalate tl.i as a fntion of the window interval [t1, h). Assming that the ratio tdt2 = 1) is onstant (:=.5 in the following examples), and introding a new independent variable.x via relation (7), we an express the signal differene as.3 :..;::, a.1 Ol Vi. 1-1 tl.i(.x) = i(11ln(1/1))) _ i( ln(1/1)) ). (1-17).X (1-17).X 2 J 4 1 oo 2 J 4 (7) (8) Rote Constant A. Fig. 3: Signal differene tl.i for a single-mode response i(t) = exp( -t), as fntion of the spetral parameter.x (an independent variable). We infer from the form of expression (8) that a hange of the temporal sale of the inpt signal, t ----> at, orresponds to a transformation ). ---->.Xja in the fntion tl.(.x). t is ths natral to plot the signal differene in logarithmi oordinates (where re-saling is eqivalent to a lateral shift); we will refer to sh a plot of tl.i over ln(.x) as the "rate ~indow spetrm" of i(t). For a single-modeo response i(t) = exp( -.Xt), the spetrm has a single peak loated at.x (the rate onstant of the signal), it falls to zero both for.x ----> and.x ----> oo. Fig. 3 illstrates this for the normalized ase =.X = 1, where the spetrm follows (for 1) =.5) the expliit form Bease of the linearity of definition (8), the spetrm of a sm of exponential modes onsists of the sperposition of the orresponding single-mode responses. Unfortnately, however, the width of the peaks is relatively broad, and they an be resolved individally only when the time onstants are sffiiently separated from eah other. Figs. 4 and 5 demonstrate this effet for two modes of the same amplitde, separated by fators >.2/>. 1 of 5, 1, 1 and 1, respetively. 4-J L.8 : Timet Fig. 4: A signal i(t) onsisting of two sperimposed mode of eqal amplitde (A= 1), with A1 = 1 and A2 = 5, 1,1,1, respetively E :.4 L... 8_.3 <.n a Rate Constant log(.\) Fig. 5: The rate window spetra for the for different ases of Fig. 4. The figres demonstrate that different modes an only be resolved when the separation between the time onstants exeeds a fator of ten. For traps with idential ross setions, this orresponds to an energy resoltion of not better than 2kT (abot 5 mev at room temperatre). Clearly, it is desirable to do better than that. (9) 619

4 Spetral Analysis Or alternative evalation method "spetral analyis" is motivated by the form of the data olleted in deep level spetrosopy experiments. Namely, what one atally obtains from a set-p like the one depited in figre 1 is not jst two data points i1 and i2 (nor a ontinos rve i(t) as assmed for or analyis), bt a disrete set of digitally reorded vales ik at eqally spaed timepoints tk = ( k - 1 )Llt, k = 1... N. Taking into aont that the measrement will also be sbjet to some sperimposed noise, the data (of a signal with M modes) has the form M ik = L ' exp( -.>.l'tk) + 8ik. (1) 1'=1 The task of any evalation method is to invert this relation, i.e., to determine the 2M mode parameters from the N measred data ik. Obviosly, bease of the sper-imposed noise, there annot be an exat soltion to that problem, the best we an hope for is an "optimal hoie" based on some appropriate statistial proedre. The first approah that omes to mind is a least-sqare fit, with the ' and.>.1' hosen sh that the total sqared deviation assmes its minimm: N M 2 Ll 2 = L(L~>exp(-.>.l'tk)- ik) ='=Min. (11) k=1 1'=1 For two reasons, however, this is not the optimal approah. First, the system of eqations derived from (11) is nonlinear (and ill-onditioned), so that a diret soltion is diffilt to obtain. And seondly, the nmber of modes present in the signal is not known a priori, so that M mst be treated as an additional nknown. Both diffilties an be overome if we allow not only for disrete modes, bt also for a ontinos mode distribtion (a "spetrm") (.>.) by making the ansatz (12) Clearly, it is not possible to allate the spetrm diretly by means of a least-sqare fit; the knowledge of a finite nmber of data points ( ik) is not sffiient to ompletely determine a ontinos fntion (). ndeed, there is an infinite nmber of possible spetra that represent the data eqally well. Most of these fntions, however, are highly irreglar, i.e., ontain strong (even disontinos) fltations and vales in the negative range. We an spress these nphysial soltions -whih have their origin in the fat that the inverse of the integral-operator in (12) is nbonded and hene not ontinos - with the help of a sitable reglarization of the problem. We proeed as follows: Standard variational alls allows s to niqely determine the minimizing spetrm as (.>.) = k=1 { th.xexp(-.>.tk).>. ~ S, where the Jk denote the soltion of the matrix eqation with M given as Mkl = j.>.exp( -.>.(tk + t1)) d.>.. s (17) (18) (19) n these eqations, the spport S is defined as that sbset of (, oo) where the exponential polynomial is greater than or eqal to zero, N S = {.>. E (O,oo) LJk.>.exp(-.>.tk) :2: } k=1 (2) For eah set of rrent data ik, eqations (17) to (2) determine a family of spetra (.>.), parametrized by the Lagrangian mltiplier A. For A =, the "smoothest" soltion is hosen, namely the one idential to zero, and no attention is paid to the data onstraint (15). For greater vales of A, the fit beomes inreasingly better, and orrespondingly the spetrm beomes more and more peaked; generally, it holds d 2 da> o, (21) d 2 da Ll <. (22) n the limit A -> oo, the spetrm onverges to a sm of 8-fntions, and one an reover the "optimal hoie" for the mode parameters of ansatz (1): Denoting by S~> (Jl = 1... M) the partition of the spport into its ompat sbsets, the relations are lim r d.>., A--~>oo JsJJ. lim f (.>.) d.x. A--+oo Js~-' (23) (24) nstead of seahing for the "best" fit, we speify a ertain qality level, i.e., a maximm qadrati deviation Ll 2, and then determine the "most physial" spetrm that meets the reqirement. n other words, we searh for the (in logarithmi sale) smoothest spetrm among all positive trial fntions whih sffiiently represent the data (13) (.>.) :2:,.>. E (O,oo), (14) (15) Clearly, this task is eqivalent to a variational problem with onstraints, represented by the Lagrangian fntion Fig. 6: Family of spetra (.>.) for the rrent data given in Fig. 7, parametrized by the Lagrangian mltiplier A (:::;.>.:::; 1, 1 :::; A:::; 1 1 ). where the fntion V(A) ensres the positivity of the soltion and the parameter A E [, oo) takes the data ondition into aont. t is interesting to note that this behavior (illstrated by Fig. 6) is atally the basis of or nmerial soltion strategy: While, for any given finite vale, the spetral eqations are rather diffilt to solve, we fond it very satisfatory to start at A = and follow the trajetory of 62 the Jk(A) throgh soltion spae (sing Newton's sheme).

5 Comparison of the Methods Having otlined the priniples both of the rate window method and of spetral analysis, we now proeed to ompare the tehniqes diretly. First, it is lear that or new approah reqires a onsiderably inreased mathematial and nmerial effort ompared to the rate window method; among other things it reqires the repeated iterative soltion of a opled set of N nonlinear eqations, with eah iteration involving an eigenvale/eigenvetor searh and the determination of all positive real zeros of a high-order exponential polynomial. To demonstrate that this inreased effort is really jstified, let s apply both shemes to a set of onstrted data with known harateristis. Fig. 7 shows sh a set of 5 data points, representing a two-mode spetrosopy signal sperimposed with some Gassian noise refleting measrement errors. Expliitly, we assmed a form (25) with tk eqally spaed at intervals of b..t =.1, tk =.1(k- 1) +.5, and oik drawn from a normal distribtion n(o,.5) with zero mean and.5 standard deviation (=relative error of abot 2.5%.)... '- ::l (.) Timet Fig. 7: Constrted spetr9sopy signal as basis of a method omparison, onsisting of two modes (.\ 1 = 2,.\ 2 = 5) with sperimposed noise. Let s first onsider the reslts of the original rate window method. Fig. 8 shows the spetrm b..i(.\) as defined in eqation (8), plotted logarithmially in thr~e <!_eades ranging from.\ =.1 to.\ = 1. As expeted (bease.\2/.\1 = 2.5 is smaller than the minimm resoltion of abot 1), it is not possible to separate the two modes present in the signal. nstead, the spetrm is represented as one single peak with the maximm loated.\~ 4.5. (Graphial evalation.).6.5 E :J.4 z ~.3 Vl.2.1 o.o L-..-:::::::::_L...l. L._.....:.:::::i:== Rote Constant log(-1.) Fig. 8: Rate window b..i spetrm for the two-mode signal diplayed in Fig. 7, with the separate single-mode spetra shown for omparison. 621 Now we trn to analyzing the reslts ofthe spetral analysis method. Fig. 9 depits the spetrm (.\) in the range of 1 to 1, evalated for A= 1 1 (Note that the interval spans only one deade, as opposed to three in Fig. 8.) The spetrm learly resolves the two modes present in the signal; both the rate onstants >. and the amplitdes are estimated with reasonable aray. Frther investigations onfirmed that the error of 5-1% is diretly related to the sperimposed noise, for oik = we were able to determine the onstants p to an aray of 1-6 :>.. :-= Ul Vl 8 ' ,\ = 1.93,\ = 4.82 A=.182 A=.31G ll Rote Constant log(a) Fig. 9: Spetrm (.\) of the spetral analysis method, with A= 1 1 A omparison of the two spetra learly shows the speriority of the spetral analysis tehniqe, both in terms of resoltion and ara:y. Extended nmerial experiments have shown that there are no prmiple bonds in this respet, the ahievable qality is only limited by sperimposed noise of the inpt data (and the aray of the emplo~ed floating point arithmeti). At a noise level of 2.5%, rate onstants whih differed by less than 1.5 old easily be resolved. This orresponds to an energy resoltion of better than 1 mev at room temperatre, an 5% improvement over the rate window method. An additional advantage of the new tehniqe is that it is also better adapted to the experimental set-p depited in Fig. 1: The atally olleted data are a finite nmber (typially 124) of vales ik sampled at eqidistant times tk; jst as reqired by the spetral analysis tehniqe. To se only two of these data points (as in the traditional rate window method) wold orrespond to wasting the blk of the alrea~y a~qired information; to exploit the knowledge of the omplete f~t1n ~(t) (as we did in or analysis) wold reqire the se of potentially nstable methods of extrapolation. Mh frther effort is reqired before or tehniqe an replae the rate window method as the standard tool of deep level spetrosopy: Tests mst be implemented to deide whether the data an be reasonably represented by an exponential sm in the first plae. A statistial analysis of the relation between the qality of the inpt and the onfidene limits of the otpt is needed, and an interative ser interfae mst be designed to allow onvenient maniplation and evalation of large amonts of data. Nonetheless, we believe that the demonstrated advantages of the new method will make this effort worthwhile. Referenes [1] R.P. Brinkmann, K.H. Shoenbah, D.C. Stodt, V.K. Lakdawala, and M.K. Kennedy, EEE Trans. Eletron Devies, 38, 71 (1991). [2] K.H. Shoenbah, V.K. Lakdawala, R.F.K. Germer, and S.T. Ko, J. Appl. Phys, 63, 246, [3] D.V. Lang and R.A. Logan, J. Appl. Phys, 47, 1533, (1976). [4] D.K. Shroder, Semiondtor Material and Devie Charaterization, New York (199). [5] T. Tessnow, K.H. Shoenbah, R.A. Rosh, R.P. Brinkmann, L. Thomas, and R.K.F. Germer, in Proeedings 2. nternational Symposim on GaAs and Related Componds, Freibrg, [6] D.V. Lang, in Thermally Stimlated Relaxation in Solids, P. Branlih ( ed. ), Berlin, 1979, p. 93.