Extraction of Schottky barrier height insensitive to temperature via forward currentvoltage- temperature measurements
11 Extraction of Schottky barrier heightinsensitive to temperature via forward current-voltage-temperature measurements
Liu ChangshiNan Hu College, Jiaxing University, Zhejiang, 314001, P. R.China, E-mail: [email protected] thermal stability of most electronic and photo-electronicdevices strongly depends on the relationship between SchottkyBarrier Height (SBH) and temperature. In this paper, thepossible of thermionic current depicted via correct and reliabilityrelationship between forward current and voltage isconsequently discussed, the intrinsic SBH insensitive totemperature can be calculated by modification on Richardson-Dushman`s formula suggested in this paper. The results ofapplication on four hetero-junctions prove that the methodproposed is credible in this paper, this suggests that the I–V–Tmethod is a feasible alternative to characterize these hetero-junctions.Keywords: Schottky barrier height; Thermionic current;Insensitive to temperature; Calculation.1. Introduction
Because the SBH controls the current flow to in electronicand photo electronic device based on junctions, obviously, theSBH of each new junctions most be calculated. One typicalmethod to estimate the SBH is voltage-and temperature-current(I-V-T), by employing the SBH, , )(),(
I TRALnqkTTI ⋅⋅=ϕ ϕ of junctions were commonly extracted. The quantity I s is thesaturation current, k is the Boltzmann’s constant, q is theelectronic charge, A and R are the area of hetero-junction andthe effective Richardson's constant of semiconductor injunctions, Hence, one barrier height at fixed temperature , T ,can be calculated by each pair of data in from of (I ,T ).Therefore, there was temperature-dependent barrier height inmany references [1-5]. As can be seen in references, the valuesof increase with increasing temperature [6-10], however, as ϕ the temperature increases, the barrier height of GaAs:Cr andPd/n-GaSb start to decrease [11,12]. In the voltage-depend SBH,the effective SBH is less than the flatland SBH on n-typesemiconductor, due to interface-state-derived short-range bandbending. The effective p-type SBH does not depend on theapplied bias. Our abilities to understand of the deferenceresponse to temperature of the SBH at hetero-junctions haveadvanced little in the past years. Existing SB technology invariably resort to mechanisms not directly linked to thetemperature-depend SBH, not because such a connection doesnot exist, but because this relationship is too complicated tostudy. SBH measured by internal photoemission for most ofthese hetero-junctions are very close to unity, insensitive to themeasurement temperature [13].One therefore looks for a technique which is free from theabove limitation. In this paper, a simple method based on themodification on Richardson-Dushman’s formula and thermioniccurrent is developed for the determination of the barrier heightinsensitive to temperature of Schottky barrier diodes. Themethod leads to a reasonable estimation of the thermioniccurrent because one reliability and correct function to calculateforward current by voltage is recommended in this paper. Themethod is successfully used to determine the barrier height offour Schottky contacts.2. Methodology and applicationsIt is tactful to calculate SBH insensitive to temperaturethrough Richardson-Dushman`s formula [14], in according withthe Richardson-Dushman`s formula, the intrinsic Schottkybarrier height of individual junction can be derived fromthermionic current, I , defined as the zero-electrical field current at different temperatures and the temperature, T. (1) )exp()( kTqARTTI ϕ−= where is the intrinsic SBH of hetero-junction. According to ϕ the principle of nonlinear least-square fitting, parameters A, Rand can be optimized when the curve of T-dependent I is the ϕ best fitted. Hence, SBH, , can be known based on equation (1). ϕ The key answer to SBH insensitive to temperature is I . Ifjunction current is described by the thermionic emission theoryas [15] (2) ]1)-[exp(),( −= nkTqVITVI Hence, the thermionic current or zero-electrical field (V=0)current I given by Eq. (2) is always is zero at any temperatures.However, when there is series resistance, R s , in I-V model, it isimpossible to reckon I via the function in form ofbecause it is not analytically invertible ]1-)-[exp(),( nkTIRqVITVI s = [16].For experimental current-voltage of hetero-junctions, thegrowth rate does not steadily decline in the forward direction,but rather increases very quickly. This is shown in the growthcurve by an S-shaped, or sigmoidal. Here, the data of current-voltage for hetero-junctions in the forward direction is may bemodeled using three-parameter model based sigmoidal as below [17] (3) )0())(exp(1)( max ≻ VVVIVI c −+= α the so-called logisitc model, where and in ≻ α max ≺≺ the forward direction. The curve has asymptotes I=I min as V→0and I=I max as V→∞, which is, of course, never actually attained.This cause few difficulties in practice, because at the voltage atwhich growth begins to be monitored we have . From (3) ≻ I it is easily seen that the current is at half of the maximum currant(I=I min /2), this occurs when V=V c . Again α acts as a scaleparameter on V, thus influencing the growth rate.As examples of potential application we calculate the I-V forfour experimental hetero-junctions from different sources. Thesehetero-junctions are: Au/n-Si [18], Ni/CdSe/p-Si(001) [19],Se/n-GaN [20], and CoSi2/n-Si(100) [21] published in papers.The experimental I-V curves of these hetero-junctions areillustrated in Figs. 1-4, the best parameters to calculate thecurrent by voltage at high level accuary ? were obtained byfitting the experimental I-V with logisitc model (3) andsummarized in Table 1. In Figs. 1-4 the theoretical I-V curves ofthese four hetero-junctions are compared with experimentalresults, Figs. 1-4 indicate that the calculated results are in goodagreement with experimental data. Because logisitc model (3) reproduce the I–V characteristics of those experiments,according to the logisitc model (3), the thermionic current (zero-field) I at different temperatures can be estimated from thefunction (3), the thermionic current is (4) )exp(1),( max00 cV VITVII ⋅+== = α Fig. 5 shows the experimental I vs T plots for the above hetero-junctions. Nevertheless, the results of traditional Richardson’sformula (1) fitting on experimental I and the temperature, T, israther unsatisfactory to describe thermionic emission fromhetero-junctions, hence, modification of Richardson-Dushman`sformula is carried out, a scaling of T β is suggested which isdifferent from the traditional R-D scaling of T , (5) )exp()( kTqARTTI ϕ β −= where β is an adjustable parameter. In Fig. 5 the modeledthermionic current against temperature is depicted fordetermining the SBH of the four hetero-junctions. The values ofA ╳ R, β , and are optimized from the best nonlinear kq / ϕ least-square fitting in the above figures and the SBH of thedevices insensitive to temperature are calculated using Eq. (5).3. ConclusionsIt is apparent from the above discussions that the proposed method may be used as an accurate technique to determinebarrier height of Schottky contacts via forward current-voltage -temperature, the method is useful for evaluating barrier heightinsensitive to temperature. The proposed I–V–T method beginsby exploring the real response of forward current to voltage attemperature, it then proves mathematically that the calculationof the thermionic current is correct and reliability. Our findingssuggest that the traditional thermionic emission law governed bythe well-known R-D equation is no longer valid, results in ourmethod predicts a scaling of T β , which is different from theclassical R-D scaling of T , and β is variable. It may bementioned here that the efficient utilizations of both thethermionic current extracted by good explanation on forwardcurrent via voltage and modification on Richardson-Dushman’sformula are emphasized. The suggested method can be easilyapplied to either homoginity or inhomoginity hetero-junctions.Clearly, the proposed technique is not complicate and can beapplied by simply knowing the D.C. current-voltagecharacteristics of the device. References [1] Halil Özerli, Ibrahim Karteri, Şükrü Karataş, ŞemsettinAltindal, The current–voltage and capacitance–voltagecharacteristics at high temperatures of Au Schottky contact to n-type GaAs, Materials Research Bulletin, 2014, 53, 211–217[2] I. Jyothi, V. Janardhanam, HyobongHong, Chel-JongChoi,Current–voltage and capacitance–voltage characteristics of AlSchottky contacts to strained Si-on-insulator in the widetemperature range, Materials Science in SemiconductorProcessing, 2015, 39, 390–399[3] A.Gümüş, Ş. 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Van Meirhaeghe, F.Cardon, Guo-Ping Ru, Xin-Ping Qu, Bing-Zong Li, Electrical characteristics of CoSi /n-Si(100) Schottky barrier contactsformed by solid state reaction, Solid-State Electronics, 2000, 44,1807-1818 Table 1 The best parameter to reproduce experimental current-voltage of hetero-junctions at various temperature, T.
Junctions T(K) I max V c α Au/n-SiNi/CdSe/p-SiSe/n-GaNCoSi2/n-Si ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -3 ╳ -4 ╳ -4 ╳ -3 ╳ -4 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -5 ╳ -4 ╳ -3 ╳ -3 ╳ -3 ╳ -1 ╳ -1 Figure caption:Fig. 1 . Forward current as a function of voltage for Au/n-Sijunction at different temperature via experiment and theory. Fig. 2.
Forward current as a function of voltage for Ni/CdSe/p-Si(001) junction at different temperature via experiment andtheory. Fig. 3
Forward current as a function of voltage for Se/n-GaNjunction at different temperature via experiment and theory. Fig. 4
Forward current as a function of voltage for CoSi2/n-Si(100) junction at different temperature via experiment andtheory.8