Characterization of Multi-Carrier Heterostructure Devices with Quantitative Mobility Spectrum Analysis and Variable Field Hall Measurements

Transcription

1 Characterzaton of Mult-Carrer Heterostructure Devces wth Quanttatve Moblty Spectrum Analyss and Varable Feld Hall Measurements J. R. Lndemuth, Gang Du, and B. C. Dodrll Lake Shore Cryotroncs, Inc., 575 McCorkle Boulevard, Westervlle, OH 4382, USA K. Vargason and Y. C. Kao Intellgent Eptaxy Technology, Inc., 21 East Arapaho Rd., Ste 2, Rchardson, TX 7581, USA I. Vurgaftman, and J. R. Meyer Code 5613, Naval Research Lab, Washngton, DC 2375, USA Abstract. Hall measurements at a sngle appled magnetc feld are ncapable of characterzng the mult-carrer propertes of heterostructure devces such as HEMT and mult-quantum wells because the measured parameters are averaged over all carrers. In ths paper, we demonstrate a novel characterzaton technque, Quanttatve Moblty Spectrum Analyss (QMSA) n conjuncton wth varable magnetc feld Hall measurements that provdes for the extracton of ndvdual carrer mobltes and denstes for mult-carrer devces. Temperature (2-4 K) and magnetc feld ( - 9 T) dependent Hall measurements and QMSA results for InP HEMT devces wll be presented. For the HEMT devce, the hgh moblty 2DEG carrer n the quantum well channel layer and the doped cap layer carrer are clearly dstngushed and ther propertes are extracted by QMSA. Temperaturedependent propertes of the ndvdual carrers may also be determned usng ths technque, and such measurements provde nsght nto the mult-quantum well devce propertes at low temperatures. The relablty and senstvty of QMSA and varable feld measurements show that ths technque s a powerful measurement methodology for routne electrcal characterzaton of mult-carrer semconductor devces for both research and ndustral QC/QA applcatons. Introducton Advances n compound semconductors have resulted n novel heterostructure devces wth superor performance. These devces are wdely used n RF, mcrowave, and optcal applcatons today. The rapd pace wth whch these devce technologes have advanced have, n turn, necesstated the development of new measurement and data analyss technques. For example, conventonal sngle magnetc feld Hall characterzaton s ncapable of provdng a precse determnaton of the electronc transport propertes of a mult-layered devce such as a phemt. The key parameters of a phemt are moblty and densty of the 2DEG carrer (or carrers) n the quantum well channel layer. In order to characterze the 2DEG carrer n a phemt devce wth sngle feld Hall measurement technques, one has to ether repeat the steps of etchng and characterzng untl the doped cap layer s removed, or termnate the ep growth process before the cap layer s formed. Even f these steps are taken, the accuracy of the characterzaton cannot be guaranteed f addtonal carrer(s) such as surface and nterface charges exst n the measured sample. In ths paper, we demonstrate a novel mult-carrer characterzaton technque, the quanttatve moblty spectrum analyss (QMSA), 1-6 whch s an mprovement over prevous spectrum data analyss approaches. 7,8 Smlar to two other mxed conducton analyss technques, fnte number carrer least-square ft 9 and Shubnkov-de Haas (SdH) effect, 1 ths technque analyzes varable magnetc feld Hall data. QMSA complements these two methods, but also provdes sgnfcant advantages. For example, the fnte number carrer ft method requres knowledge of the number of carrers n advance, whereas fully automated QMSA requres no advance sample nformaton and s capable of provdng mobltes and denstes wth accuracy comparable to the fnte number ft technque. Although the SdH technque can n some cases extract ndvdual carrer denstes n

2 a mult-carrer sample that dsplays multple oscllaton perods, unlke QMSA t cannot provde moblty values. In ths work, we apply QMSA to synthetc mult-carrer Hall data, and also to varable feld Hall measurement data for an InP phemt devce from Intellgent Eptaxy Technology. The results show that ths technque extracts ndvdual carrer mobltes and denstes for mult-carrer materals, and s especally relable and senstve for hgh moblty heterostructure devces such as phemts. Data for devces wth cap layers wll be compared to devces wthout cap layers. Ths wll demonstrate QMSA s ablty to resolve mult-carrers n phemts. Comparson wth the results of SdH measurements wll be dscussed. QMSA 1. Theoretcal background For a sngle carrer materal, the measured Hall coeffcent and resstvty are gven by, 11 1 R H ( B) = (1) nq 1 ρ( B) =, (2) nqµ and the conductvty tensor s gven by, nqµ xx = (3) 1+ µ B xy 2 nqµ B =. (4) 1+ µ B Here n s the carrer concentraton, µ s the moblty, q s the charge of the carrer, and B s the magnetc feld. It s apparent from Eqs. (1) and (2) that for sngle carrer materals the Hall coeffcent and resstvty are feld ndependent. The sngle feld Hall characterzaton s therefore suffcent for such materals. However, for mult-carrer systems the moblty and densty calculated from Eqs. (1) and (2) wll be averaged over all carrers. For such materals, conductvtes of the ndvdual carrers are addtve, and the total conductvty tensor (of a N-carrer system) s gven by: 2 N nqµ xx = (5) + 1 µ B N 2 nqµ B xy = (6) + 1 µ B The fnte number carrer analyss performs a least-square ft of the measured data to a preset number of carrers. In ths approach, the number of carrers N must be defned n advance and (µ j, n j ) of each carrer are fttng parameters. Ths shortcomng can be overcome by usng the ``moblty spectrum" concept. In ths approach, dscrete carrers are generalzed by a conductvty densty functon that spreads over a contnuous moblty range. The conductvty tensor s gven by: 12 p n s µ s µ xx ( ) + ( ) (7) = dµ 1+ µ B p n ( s ( µ ) s ( µ )) µ B dµ (8) 2 1 µ B xy = 2 + where s p (m), s n (µ) are hole and electron conductvty densty functons, respectvely. The QMSA analyss technque mproves greatly over earler efforts utlzng the spectrum concept. 7,8 For detaled dscussons of QMSA and ts applcatons, please refer to References A two-carrer test of QMSA Fgure 1 shows synthetc Hall data for a two-electron-carrer case over the magnetc feld range.5-5 T. The mobltes and denstes of the two electron carrers are lsted n Fg. 1. A random uncertanty of.5% s added to the data. A sngle feld measurement at.35 T (usng the data from Fg. 1a) would have yelded a moblty of -3.98x1 3 cm 2 /Vs and densty of x1 13 cm -3, whch clearly do not reflect ether of the two carrers. Hall Coeffcent (m 3 /C) (a) Two electron carrer case (wth.5% random uncertaty) µ 1 = -1, cm 2 /Vs n 1 = cm -3 µ 2 = -8, cm 2 /Vs n 2 = cm B (T) Fgure 1. Synthetc Hall data of the two-carrer case. Fgure 2 plots the QMSA spectrum result for ths example. Two well-separated electron peaks representng the two carrers are shown n the spectrum. The moblty and densty values (lsted n Fgure 2) of these two peaks extracted by QMSA match the two set carrers to wthn 1%. Fgure 2 also shows a small hole peak. Ths s an analyss artfact due to the lmted feld range and measurement uncertanty. Increasng the range of magnetc felds over whch measurements are conducted tends to mnmze the occurrence of such artfacts. Furthermore, these artfacts are usually much smaller n Resstvty (Ωm)

3 magntude than the domnant peaks and ther contrbuton to the total conductvty s neglgble. Electron and Hole Moblty Spectra (a.u.) (b) 1 2 Two carrer QMSA B =.5-5 T m 1 = -9.97x1 2 cm 2 /Vs n 1 = -1.1x1 14 cm -3 m 2 = -8.2x1 3 cm 2 /Vs n 2 = -1.1x1 13 cm -3 analyss artfact Moblty (cm 2 /Vs) Fgure 2. QMSA spectrum results for data n Fgure 1. The sold curve represents electrons and dashed curve represents holes (same for all the QMSA plots below). 3. A four-carrer test of QMSA Fgure 3 plots the QMSA spectrum result for a synthetc four-carrer case (three electrons and one hole wth a random uncertanty of.5%). The magnetc feld range for ths data set extends from.9 to 9 T. In addton to mnmzng the artfacts dscussed above, hgher feld strength s needed to mprove the QMSA resoluton when a large number of carrers are present, partcularly when ther mobltes are smlar n value. For ths model case, all four carrers are readly extracted by QMSA. The set mobltes and denstes of the four carrers and the correspondng QMSA results are lsted n Table I. The accuracy of the QMSA results n ths case s slghtly poorer than n the two-carrer case, but s stll qute reasonable. Electron and Hole Moblty Spectra (a.u.) e1 h e Moblty (cm 2 /Vs) e3 Four carrer QMSA B =.9-9 T Fgure 3. The four-carrer case QMSA spectrum. µ set cm 2 /Vs µ QMSA cm 2 /Vs n set cm -3 n QMSA cm -3 e e14-1.e14 e2-1e4-1.2e4-5e12-5.1e12 e3-3.7e4-3.75e4-1e e11 h 3e3 3.3e3 1e13 1.e13 Table I. The four-carrer case set mobltes and denstes and ther correspondng QMSA results. Experment Varable feld Hall and SdH measurements were conducted on InP PHEMT devces, fabrcated by Intellgent Eptaxy Technology, usng the Lake Shore Hall Measurement System (HMS) Model 959. One devce was fabrcated wth a cap layer; the other was fabrcated wthout a cap layer. HMS 959 s a superconductng cryogenc system wth a maxmum feld of 9 T and temperature range of 2-4 K. A van der Pauw sample confguraton wth four contacts was used to conduct the measurements. Gold wres were heat-bonded to gold contact pads, provdng ohmc contacts as assured va two-probe I-V curve measurements, whch were lnear. Measurement results 1. Varable feld Hall measurements and QMSA results. Varable feld Hall measurements were conducted for felds from 2 G to 85 KG (.2 to 8.5 T) and at varous temperatures. Fgures 4 and 5 show the measured sheet resstvty and the measured sheet Hall coeffcent data at 5 K and 3 K. for a sample wth a cap (fgure 4) and a sample wthout a cap (fgure 5). For the sample wth out a cap, the feld dependency of the data s small. From the observaton we would conclude that one carrer s contrbutng to the conducton. However for the devce wth a cap (fgure 4) the feld dependency s qut large and we would expect more than one carrer to contrbute to the conductvty. Fgures 6 (sample wth cap) and 7 (sample wth out cap) shows the derved conductvty tensor and the ftted results from QMSA. The near perfect ft (sold lnes) to the data s a good ndcaton of the valdty of the QMSA spectrum results presented below.

4 Sheet Hall Coeffcent (1^6 cm^2/c R H (3 K) R H (5 K) ρ (5 K) ρ (3 K) Feld (kg) Fgure 4. Measure sheet resstvty and sheet Hall coeffcent of devce wth cap layer. The lnes are gudes for the eyes. Sheet Hall Coeffcent (1^6 cm^2/c R H (5 K) R H (3 K) ρ (3 K) ρ (5 K) Feld (kg) Fgure 5. Measured sheet resstvty and sheet Hall coeffcent of devce wth no cap layer. As expected ths devce shows less feld dependency than the devce n Fgure 4. Applcaton of QMSA to the measured Hall data shown n the fgures results n the mult-carrer moblty spectra plotted n Fgure 8. As expected, the spectrum for the sample wthout a cap shows only one electron carrer. At a temperature of 5K the moblty s 21 cm 2 /(V s) and the sheet densty s 1.75 X 1 12 cm -2 However, at 3 K the moblty has decreased to 66. The sheet densty remans relatvely constant at 1.89 X Ths decrease n moblty wth temperature s consstent wth electronphonon scatterng. In contrast, the sample wth the cap shows the same carrer as the sample wthout the cap, but there s now a second electron carrer, n the cap layer, wth low moblty. At 5K ths carrer has a oblty of 11 cm 2 /(V s) and a Sheet Resstvty (ohm/sqr Sheet Resstance (ohm/sqr) Sheet conductvty (1/ohm) xx 5 K xx 3 K xy 3 K xy 5 K Feld (kg) Fgure 6. Conductvty calculated from the data n Fgure 4. The symbols are the expermental data and the lnes are the fts from QMSA. Sheet conductvty (1/ohm) xx 5 K xy 3 K xy 5 K xx 3 K Feld (kg) Fgure 7. Conductvty calculated from the data shown n Fgure 5. The symbols are the expermental data and the lnes are fts from QMSA. Sheet conductvty (1/ohm Cap 3 K Cap 5 K No cap 3 K Cap 3 K No cap 5 K Cap 5 K Moblty (cm 2 /(V s)) Fgure 8. QMSA spectrum for both InP samples, wth cap and wthout cap. The sample wth out a cap shows one carrer wth a temperature dependent moblty. The moblty changes from 21 (at 5 K temperature) to 66 (at 3 K temperature). The sample wth a cap has only two carrers. One wth moblty of about 1 and a second wth moblty of about 1. The second carrer (the one n the cap) shows lttle temperature dependence

5 sheet densty of 3.77 X 1 13 cm -2. At 3 K ts moblty s 1 cm 2 /(V s) and sheet densty s 3.8 X 1 13 cm -2. The hgh moblty carrer changes slghtly wth the applcaton of the cap. At 3 K the moblty s 94 cm 2 /(V s) and the sheet densty s 3.4 X 1 12 cm -2. Although these are two dfferent samples whch could account for the dfference, there s also a fundamental dfference that s due to the changes n the electrostatc felds n the devce because of the cap. The moblty of the hghest moblty peak ncreases wth decreasng temperature, ndcatng that electron-phonon scatterng domnates the charge transport n the channel layer. The temperature dependence of the moblty of the 2DEG carrer n the sample wth the cap s shown n Fgure 9. Sheet Resstvty (Ω/ ) HEMT wthout cap layer T = 4.2 K B (Gauss) Fgure 1. SdH measurement at 4.2 K. Sngle oscllaton s consstent the one carrer model of the sample wthout cap. The correspondng sheet densty s 1.6 X 1 12 cm -2. 2DEG Carrer Moblty (cm 2 /Vs) HEMT wthout cap layer HEMT wth cap layer T (K) Fgure 9. Temperature dependence of hghest moblty carrer. Ths ndcates that electron-phonon scatterng domnates the transport process. 2. SdH effect measurement results Fgure 1 shows the SdH measurement result at 4.2 K. Ths measurement was done on the sample wth out a cap. A Fourer transform analyss of these data reveals, as expected, one frequency, that yelds a carrer densty of n1=1.6 X 1 12 cm -2. Ths carrer agrees wth the denstes correspondng to the two hghest moblty features n the QMSA spectra of Fgure 8. Concluson We have demonstrated that varable feld Hall measurements and the fully automated QMSA are capable of provdng much more nformaton than sngle-feld data when appled to mult-carrer devces. QMSA s especally powerful n characterzng hgh moblty devces such as phemts and mult quantum wells. For the present InP phemt devce, QMSA easly separates the hgh moblty 2DEG carrer(s) from the low moblty speces. Measurements on two phemt samples, one wth a cap and one wth out, clearly demonstrate QMSA ablty to accurately determne the number of carrers and the densty and moblty of each carrer. The advantage of usng varable feld Hall measurements and QMSA n routne producton QA/QC and devce R&D for heterostructure materals, rather than conventonal sngle-feld Hall characterzaton methods, has been clearly demonstrated. Acknowledgments Dscusson wth Fred Pollak s gratefully acknowledged. Work at the Naval Researcher Lab was supported n part by a Cooperatve Research and Development Agreement wth Lake Shore Cryotroncs, Inc.

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