Ž .Applied Surface Science 142 1999 481–484

Parameter extraction in non-ideal thermionic emission diodes

J.I. Lee a,) ,1, J. Brini a, J. Boussey a, C.A. Dimitriadis b

a LPCS, ENSERG, 38016 Grenoble Cedex, Franceb Department of Physics, UniÕersity of Thessaloniki, 54006 Thessaloniki, Greece

Abstract

Novel and simple, on-site extraction method of parameters; the ideality factor, series resistance, leakage resistance, andsaturation current, from both the forward and the reverse current–voltage characteristics and their derivatives of non-idealthermionic emission diodes is presented. The results of successful application of the method on sets of different metalrn-SiSchottky diodes and p–n junction diodes are reported and discussed. q 1999 Elsevier Science B.V. All rights reserved.

PACS: 73.30.qy; 73.40.Lq

Keywords: Parameter extraction; Thermionic emission; Schottky diode; p–n Junction diode; Series resistance; Leakage current

1. Introduction

Quick and accurate evaluation of device parame-ters is necessary especially in the process of develop-ing new materials for the devices, where non-idealcharacteristics are often encountered. The structuresand the process conditions are important as a first-hand diagnosis of the materials. In thermionic emis-sion diodes, such as Schottky barrier diodes, whenthere is a non-negligible series resistance R , thes

usual method of obtaining the ideality factor n, fromw xthe slope of dVrdln I cannot be used 1–3 . Also, for

) Corresponding author. Photonics Research Center, Korea In-stitute of Science and Technology, Cheongryang, P.O. Box 131,Seoul 130-650, South Korea. Tel.: q82-2-958-5786; Fax: q82-2-958-5709; E-mail: jil@kistmail.kist.re.kr

1 On leave from Photonics Research Center, KIST, Seoul 130-650, South Korea.

Ždiodes with low Schottky barriers i.e., large reverse.saturation current, I , the approximation, R ss dynw xdVrd IsnkTrIqR 4,5 , to extract R and n iss s

not valid. And if there is an appreciable leakagecurrent, I cannot be determined, and obtaining Rs s

Ž .and n from the plot of R vs. 1r Iq I is notdyn sw xpossible 6 . One way is to utilize the computer

fitting to find the parameters by reiteration, which,however, still takes considerable time and effort. Wehave developed a noble and simple analytic methodwhich can be executed on-site, at the current–volt-age measurement equipment with simple built-in userfunctions of data analysis, such as differentiation,and give quick and accurate results. Preliminaryresults on some Schottky diodes can be found in the

w xliterature 7 . In this work, application of the methodis extended from non-ideal to near-ideal diodes inregard to the barrier height of the diode, utilizingdifferent metalrn-Si Schottky diodes and some shal-low junction p–n diodes.

0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-4332 98 00724-7

( )J.I. Lee et al.rApplied Surface Science 142 1999 481–484482

2. Methods

Ž .The current–voltage I–V characteristic of aSchottky barrier diode with a series resistance, R ,s

and a parallel leakage resistance, R , is usually givenl

by,

1Ž .qrnkT VyR IŽ . sIs I e y1 q VyR I , 1Ž . Ž .Ž .s sR l

where n, R , R , and I are considered to be con-s l sŽ .stant. Differentiating Eq. 1 , we get the expressions

for the first and second derivatives, dVrd I'RdynŽsometimes called as the differential resistance or the

. 2 2dynamic resistance and d Vrd I 'd R rd I, re-dyn

spectively, as follows,

1R s qR , 2Ž .dyn sq 1

Žqr nkT .ŽVyR I .sI e qsnkT R l

d R q 1dyn 2sy 1y R yR R yR .Ž . Ž .dyn s dyn sd I nkT R l

3Ž .

So far, the procedure is straight forward, and anyrelations obtained from the above expressions of thederivatives with reasonable approximations are legit-imate so that the application of the relations on thecharacteristics of a real diode can test the validity of

Ž . Ž .Eq. 1 , in return. From Eq. 2 , one can see thatR is a monotonously decreasing function of thedyn

applied voltage V, limited by R in the reversel

direction and by R in the forward direction.sŽFor simplicity, we define, R ' yd R rsd dyn

.1r2 w Ž .x2 Ž .d I , and, R ' R r R yR . Eq. 3 can ber sd dyn s

rewritten as,

q 1R s 1y R yR . 4Ž .Ž .r dyn snkT R l

When R is much larger than R , R can bedyn s s

neglected, and by plotting R vs. R , the idealityr dyn

factor and the reverse leakage resistance can beobtained from the y- and x-intercepts, respectively.In the region where the leakage current is much

smaller than the total current, we can get the follow-Ž . Ž .ing useful relations from Eqs. 1 – 3 .

nkTR s R qR , 5Ž .dyn sd s( q

nkT 1Is y I . 6Ž .s( q Rsd

Now, by plotting R vs. R , and I vs. 1rR , thedyn sd sd

ideality factor can be determined from the slope, andR and I can be given by the intercepts, respec-s s

tively. The values of the derivatives and their basicfunctions are readily available from the measuredI–V curve, and the analysis can be done on-site. TheI–V measurements and the analysis were performedon HP-4155A semiconductor parameter analyzer, atroom temperature.

3. Non-ideal diodes

By non-ideal diodes, we mean the diodes withlow Schottky barrier, such that, qI rnkT41rR . Ins l

these diodes, the leakage current can be neglected inthe forward bias region including at around zerovoltage, where R , I and n can be determined froms s

Ž . Ž .Eqs. 5 and 6 . Typical results on 1 mm diametercircular TiNrn-Si Schottky diodes with the barrier

w xheight of about 0.5 eV 8 , are presented in Fig. 1.The reverse saturation current determined from the

Ž . Ž .plot of Eq. 6 was 0.39 mA. In Fig. 1 a , therelation between the derivatives, R vs. R , in Eq.dyn sdŽ .3 , is depicted. The bottom left part gives the linear

Ž .region, where Eq. 5 can be used to obtain theideality factor and the series resistance, as shown in

Ž .Fig. 1 b . R of 45.8 V and n of 1.14 were deter-s

mined from the intercept and the slope, respectively.In stronger forward bias, the ideality factor tend toincrease along with the decreasing series resistance.The increase of the ideality factor has been recentlydiscussed to be due to the dynamic occupancy of the

w xinterface states 9 . An external resistor of 56 V wasconnected in series with the diode and the resultingplot is compared with the original plot, showing aparallel shift by the value of the external resistor.The purpose of the external resistor was to confirmthe validity of the method and it is not necessary toconnect it to extract the parameters.

( )J.I. Lee et al.rApplied Surface Science 142 1999 481–484 483

Ž . Ž . Ž Ž 2 2 .1r2 .Fig. 1. a R 'dVrd I vs. R ' ydV rd I for adyn sd

TiNrSi Schottky diode with low barrier height, for the whole biasŽ .voltage range. b R vs. R in forward bias region, with anddyn sd

without 56 V external series resistor, the slope gives ns1.14 andŽ Ž .. Ž .the intercept gives R s45.8 V Eq. 5 . c R vs. R ins r dyn

reverse bias region, with and without 10 kV external parallelresistor, R s3.6 kV and ns1.10 were evaluated from thel

Ž Ž ..intercepts Eq. 4 .

Ž . Ž .Fig. 1 c shows the plot of Eq. 4 mainly in thereverse bias region, again compared to the resultwith an external resistor of 10 kV in parallel with

the diode to confirm the validity of the method. R l

of 3.6 kV and n of 1.10 were evaluated from the x-and y-intercepts, respectively. The ideality factorobtained was always smaller that the one obtained in

Ž .Fig. 2. a R vs. R for a PtSirSi Schottky diode with highdyn sdŽ .Schottky barrier height for the whole bias voltage range. b Rdyn

vs. R for V )300 mV, ns1.85 and R s36.0 V were deter-sd sŽ Ž .. Ž .mined from the slope and the intercept, respectively Eq. 5 . c

R vs. R from the rest of the bias region, R s257 kV andr dyn l

ns1.80 were evaluated from the intercepts.

( )J.I. Lee et al.rApplied Surface Science 142 1999 481–484484

the forward region, possibly due to the Schottkyw xbarrier lowering effect 10 .

4. Near-ideal diodes

For this category, we examined a group ofŽTiNrn-Si Schottky diodes with different process

.conditions than the ones in Section 3 , PtSirn-SiSchottky diodes, and shallow junction pq–n diodesw x11 . All of them had high barrier heights resulting inthe reverse saturation currents around 1 pA or muchless for our device geometry of 1 mm diameter. Inthese diodes, the reverse saturation current was sosmall, and the leakage current could not be neglectedup to moderate forward biases. Fig. 2 shows typicalresults of the analysis. The general feature of the

Ž .relation, R vs. R , is the same as in Fig. 1 a .dyn sd

The linear region in the low left part of the plotŽ .started above 300 mV of forward bias. Now Eq. 5

must be applied in stronger forward bias region andR and n were determined to be 36.0 V and 1.85,s

Ž .respectively, in Fig. 2 b . Also a tendency of theincrease in the ideality factor can be seen at strongerforward bias. The increasing tendency was less obvi-ous in diodes with smaller ideality factors. From theregion where the leakage current is relatively signifi-cant, R of 257 kV and n of 1.80 were evaluatedl

Ž . Ž .from the plot of Eq. 4 in Fig. 2 c . In somenear-ideal diodes, the leakage current was so smalland the tunnelling current was detected indicatingthe existence of thin layer of insulator at the inter-

Ž .face. In this case, Eq. 1 is no longer valid espe-cially near zero bias voltage, and R does not varydyn

monotonously with the applied voltage, requiringanother extraction method including the tunnellingcurrent.

5. Conclusions

We presented a simple and analytical methodswhich can be applied on-site, in I–V characteriza-

tion, to extract the fundamental parameters ofthermionic emission diodes, from the measured cur-rent–voltage characteristics and their derivatives.Results of successful application of the method onTiNrn-Si and PtSirn-Si Schottky diodes and shal-low junction pq–n diodes are presented and dis-cussed. This method provides useful and accuratemeans to evaluate the parameters on-site, thereby,enabling a first-hand diagnosis of the materials,structures and the process conditions for the fabrica-tion and development of thermionic emission diodes.

Acknowledgements

One of the authors, J.I. Lee, is grateful for helpfuldiscussions with G. Ghibaudo and S. Cristoloveanu,and technical assistances from F. Farmakis and S.Mercier, and supports from Ministry of Science andTechnology, Korea during his leave at LPCS.

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