On the temperature dependence of the barrier height and the ideality factor in high voltage NinGaAs schottky diodes

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Solid-State Electronics Vol. 39, No. 10, pp. 1457-1462, 1996

Pergamon

P l h S0038-1101(96)00060-3

Copyright © 1996ElsevierScienceLtd Printed in Great Britain.All rights reserved 0038-1101/96 $15.00+ 0.00

ON THE TEMPERATURE D E P E N D E N C E OF THE BARRIER HEIGHT A N D THE IDEALITY FACTOR IN HIGH VOLTAGE Ni-nGaAs SCHOTTKY DIODES M. N A T H A N j, Z. S H O S H A N I l, G. A S H K 1 N A Z I 2, B. M E Y L E R 2 and O. Z O L O T A R E V S K F ~Tel-Aviv University, Faculty of Engineering, Department of Electrical Engineering-Physical Electronics, Tel-Aviv 69978, Israel 2G.A,D. Semiconductors, P.O.B. 505, Migdal Ha'emeq 10500, Israel (Received 20 October 1995; in revised form 11 January 1996)

Abstract--The temperature dependence of current-voltage (I-V) Schottky barrier heights (SBH) and ideality factors (n) in Ni-nGaAs high voltage (No = 5 × 10~4-10~5cm -3) diodes was measured in the temperature range 298-473 K. The I - V SBH qSB,increases slightly (by about 3.5%), and n decreases by about 5% when T is increased from 298 to 473 K. Consequently, the flat-band SBH ~bFB,approximated by the product $B x n decreases slightly with increasing temperature, in agreement with the capacitance-voltage SBH (Ckcv) behavior in similar diodes. The temperature coefficient of q~rBis doping dependent, and equals ~(1 + 0.3) × 10-4eV/K for No = 5 x 10~4cm-~ and (2.2 + 0.1) x 10-4 eV/K for No = 10~5cm -5. Most of these results can be satisfactorily explained by the existence of laterally inhomogeneous barriers, as modelled previously. The most likely inhomogeneities are due to Ni-nGaAs reaction phases and interfacial crystallography. When literature data are re-evaluated using ~b~Binstead of ~bB,much more consistent results are obtained, indicating that ~b~Balways decreases (or at most stays constant) with increasing measurement temperature. Copyright © 1996 Elsevier Science Ltd

~b(T) in Au-nGaAs[7] and Ni-nGaAs[8] in the range 300--470 K are exceptions. The understanding of operating mechanisms at usage temperatures (300600 K for GaAs), and in particular the question of whether the electron transport at the metal-semiconductor (M-S) interface in these low doped, large area diodes is determined by inhomogeneities, has practical aspects, and may contribute to improved design. The present study was undertaken with these considerations in mind.

1. INTRODUCTION The technology of high voltage, high current GaAs Schottky diodes has recently advanced to the point that they are becoming serious competitors to Si diodes at voltages up to 200V[1,2]. The diodes operate at temperatures up to about 500 K, and in forward conduction clearly deviate from the ideal behavior predicted by the standard thermionic emission (TE) model: I = A A ** T 2 exp( - qq~s/kT)

x exp[q(V- IR)/nkT-

2.EXPERIMENTAL

1] (1)

where A is the area, A** is the Richardson constant, R is the series resistance (affecting I only at significant forward voltages), ~bs is the I - V barrier height (uncorrected for image force effects), n = 1 for an ideal diode and the rest of the symbols have their normal meaning. The non-ideal behavior is reflected in n > 1 and temperature dependent ideality factors n(T) and Schottky barrier heights (SBH), ~b(T). Recent models[3-5] explain such dependencies by invoking spatially inhomogeneous Schottky barriers. Although there are a n u m b e r of published studies of n(T) and ~b(T), most of them documented by Werner and Giitler[3], they were in general restricted to low voltage diodes and low temperatures, normally below room temperature. The studies on n(T) and ~b(T) on N i - n G a A s diodes in the range 100-434K[6], and

Schottky diodes were prepared on commercially available (100)GaAs NON+ epitaxial structures consisting of a 400/~m N ÷ substrate doped to No = 2 x 10 TMcm -3 and a 14-20 # m NO layer doped to about 5 × 10~4--1 x 10 ~5cm -3. A N i A u G e ohmic contact was vacuum deposited on the N ÷ side and rapid thermal annealed in forming gas at 643 K for 60 s. After contact formation, the wafer was cleaned, etched in a 1 H 2 0 + 3 H 3 S O 4 + 1H202 etch and immersed in an electrolyte containing nickel salt and hydrazine. A 0.1-0.2 tim Ni Schottky barrier was then chemically deposited at ~373 K, and the structure rapidly annealed again in forming gas at 623 K for 60 s. Square mesas of 3 x 3 and 4 x 4 mm 2 were defined by photolithography and etched through the Ni and down to the N ÷ layer. The sides of the mesas were covered with a special polyimide to

1457

M. Nathan et al.

1458

Table 1. Nolayer thicknessesand doping levelsfor wafersused in this study Process

N~ thicknesslayer (~m)

Doping level (cm-3)

14 16 20

8.91 × 10~a 1.06 × 10~5 5.18 x 10t4

252 253 254

Table 2. Electrical parameters (vs T) extracted from forward I-V characteristics of all Schottky diodes in this study. The data correspond to those exhibited in Figs 1-3. The (Ocvwas measured only at room temperature. The ~bBand n values are averages from three mesas. The third character after the decimal point reflectsthis averaging, and is used in plotting the figures.The third character has no meaning in terms of accuracy T [K] 298

avoid excessive leakages and surface breakdown. Other details are given in Ref.[1]. Temperature dependent I - V measurements were performed with a Tektronix 371A High Power Curve Tracer connected with a probe assembly and heating stage capable o f reaching 600 K. The temperature during measurement was stable within + 1 K. The curve tracer uses rapid short current pulses, thus avoiding self heating in the diode. A Richardson constant o f 8,6 A cm -2 K--', experimentally verified by a modified Richardson plot[9], was used in the calculation o f the I - V SBH. " D a r k " C - V characteristics were measured at 1 M H z with a H P 4192 L F Impedence Analyzer and a probe having a parasitic capacitance o f 0.5-1 pF. Only r o o m temperature C - V barriers were obtained. The M - S interface and N ~ concentrations determined from the C - V plots matched values provided by the substrate manufacturers. A l t h o u g h the trends o f n(T) and q~(T) were identical in all diodes, which came from a large n u m b e r o f wafers and processes, the absolute values at a given value o f T could vary by 5-10%. We thus concentrated on the best three processes, n u m b e r e d 252, 253 and 254. N ~ layer doping levels and thicknesses are shown in Table 1 and mesa areas in Table 2. 3. RESULTS

3.1. Ideality f a c t o r n vs T The forward I - V characteristics o f our diodes are given in Ref.[1]. The behavior o f n vs I / T is shown in Fig. 1 and Table 2. A l t h o u g h the absolute values

1.20

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¢8 (eV) 0.868 0.873 0.850 0,852 0.844 0.845 0.872 0.875 0.853 0.857 0.848 0.846 0.879 0.879 0.859 0.861 0.857 0.852 0.886 0.883 0.871 0.864 0.866 0.862 0.893 0.887 0.876 0.866 0.873 0.867

n 1.080 1.095 1.105 1.080 1.130 1.120 1.070 1.080 1~087 1,065 1.120 1.100 1.060 1.060 1.060 1.045 1.106 1.085 1.050 1.045 1.040 1.030 1.090 1.070 1.040 1.030 1.025 1.020 1.080 1.060

~FB (eV)

~c~ (eV)

0.937 0.917 0.956 0.935 0.939 0.906 0,920 0,901 0.953 0.906 0.946 0.931 0.933 0.945 0.927 0.913 0.949 0.930 0.931 0.932 0.910 0.899 0.947 0.924 0.930 0.923 0.905 0.889 0.943 0.922 0.928 0.914 0.897 0.883 0.942 0.919

change slightly from mesa to mesa, the trend is identical. W h e n T increases from 298 to 476 K, n decreases by 5 + 1%. This behavior is in agreement with H a c k a m and Harrop's[6] data on N i - n G a A s , and would be expected if the Scottky barrier is inhomogeneous[3-5]. F o r example, Werner and Giitler give the following expression: p3 n-~(T) - 1 = pz = - p 2 + 2 k T / q '

(2)

where p~, 02 and p3 are voltage coefficients which quantify the voltage d e f o r m a t i o n o f the i n h o m o geneous barrier distribution. This expression correctly predicts the decrease o f n with increasing T. F o r an inhomogeneous barrier c o m p o s e d o f low SBH " p a t c h e s " o f radius R0 surrounded by high SBH material (the difference in the SBH being A), having a Gaussian distribution o f values 7 -= 3(AR~/4) ~/3with a standard deviation a, Sullivan et a/.[5] predict a similar dependency o f n(T): n=l

~ 0 ,

Area P r o c e s s (ram2)

~ - ~1 rR'~~2 1f 'Tf11'3~2/3 bb'l •

(3)

Here /3 = q / k T , tl = e d q N o , Vbb is the total b a n d bending (diffusion potential) for a uniform barrier at a given applied bias Va, ~s is the permittivity o f the semiconductor and all other symbols have their accepted meaning. Both expressions have the form o f n = 1 + To~T, in which To is the well k n o w n " a n o m a l y factor" which

High voltage Ni-nGaAs Schottky diodes is independent of temperature. Werner and Giitler[3] identify To as ~ - q p { 2 k , while in Sullivan's model[5], To = qa2/3k~l:/3V~/b3.

3.2. I - V barrier dpB vs T The dependence q~8(T) is fairly linear whether plotted vs T or I/T in the given T range. We chose to plot <#Bvs 1 / T i n Fig. 2, to be consistent with n vs 1/T in Fig. 1. Figure 2 shows a slight linear increase of the barrier (by approximately 3.5%) between 298 and 473 K. This trend of increasing ~bn with T is also in agreement with the predictions of Refs[3-5]. Similar behavior is observed in A l - n G a A s diodes[9], while in one of the previous N i - n G a A s studies[6], as well as in A u / A g - n G a A s diodes[10] the trend was opposite. One should note that the barrier obtained from capacitance-voltage (C-V) measurements, d~cv, always decreases with increasing T. In fact, to reconcile ~bB with ~c~, some authors[6,9] have suggested multiplying ~b~ by n(T) to obtain the "true" ~ . The product is a close approximation of the "flat-band" barrier (~br,) obtained at zero electric field[l 1]: l'kTlnNC, )~- ~

~rs=n~.-(n-

(4)

where Nc is the density of states in the conduction band. Calculated ~bFa= ~b~(T)n(T) values are shown in Fig. 3 and Table 2. ~bpa follows the dependence ~bFs(T) = ~bps(0)- ~T, i.e. decreases with T (in contrast with ~n), with the temperature coefficient ~, apparently doping dependent, shown in Table 3. • is smallest at the lowest doping, (1 + 0.3) × 10 -4 eV/K at N~ = 5 X 10 ~4cm -3, and increases to ( 2 . 2 + 0 . 1 ) × 10-4eV/K at N n = 1 x 10~cm -~. The C~cvtemperature coefficient in Goldberg's[8] study on diodes very similar to ours, 2.4 x 10-4eV/K at No = (1 - 2 ) x 10 t~ cm -~, is in excellent agreement with our ~bp~ data; his r o o m temperature ~bcv, 0.89 eV, is 0.04 eV smaller than our q ~ but matches

Table 3. Values of ~bfBat 0 K and the temperature coefficient ~ of the F-B barrier 10~B(T)= 0Fe(0) -- ~T) for each process and mesa size. The 0rB(0)and ~ valueswere obtained by linear regression using the data in Table 2. The results for the 9 mm2 mesas in process sample #252 do not fit the general trend, for reasons unknown Mesa area No ~b~e(0) Process (turn2) (crn-J) (eV) (eV/K) 252 9 8.91 x 10 ~4 0.95 - 4 . 3 x 10 -5 16 1.02 -23 x 10 -4 1.06 × 10 ~5 1.00 - 2 . 3 x 10 -4 253 9 16 0.98 - 2 . 1 x 10 -4 254 9 5.18 x 10 ~4 0.97 - 6 . 0 x 10 -~ 10 0.98 - 1 . 3 x 10 -4

our dPcvwell. Other temperature coefficients found in m e t a l - n G a A s diodes are 5.8 x 10-4eV/K[6] in N i - n G a A s (Am = 1 × 10 ~6cm -3) and 7 × 10 -4 eV/K in Al-nGaAs[9] (No = 2 x 10 t6 cm-3), Note that the combined data of this study plus Refs[6] and [8] indicate clearly that ct increases with decreasing No. The bandgap in GaAs decreases with T at a rate of about 5 . 4 x 10-4eV/K[12]. Thus, the ~bF~ (T) dependence in these N i - G a A s diodes is unlikely to be related to the bandgap dependence. 4. DISCUSSION The temperature dependence of both the ideality factor and I - V barrier in our diodes can be satisfactorily explained by the inhomogeneous barrier models. Specifically, in the absence of interfacial oxides (unlikely due to the low temperature reaction between Ni and GaAs, see below), tunneling (for which our dopings are too low), or generation-recombination currents (unlikely because forward C - V measurements are frequency independent and the I - V curves are smooth[l]), no other models provide a satisfactory explanation for n > I, its temperature dependence, and the difference between the ~bB and ~bcv[3]. Moreover, since neither ~b, nor ~bFBfollow the T-dependence of the bandgap in our diodes, Fermi

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1000/T [K-q Fig. 2. I-V barrier heights vs measurement temperature in Ni-nGaAs diodes. Each point is an average of three mesas.

Fig. 3. Flat-band barrier height vs temperature in Ni-nGaAs diodes. The ~bFedecreases slightly with increasing T for epilayers with No = 2 x 10~5cm -3 and stays almost constant for epilayers with No = 6 x 10J4cm-3. ~bBFwas plotted vs lIT for convenience, to match Figs 1 and 2.

1460

M. Nathan et al.

level pinning due to interface states is unlikely, as increasing evidence seems to indicate[4]. Due to the low- T reactions (see below), it is extremely likely that the interface, and therefore the SBH in our diodes, is inhomogeneous. A key requirement in the latest inhomogeneity models[3-5] is that the scale of the inhomogeneity is small compared with the depletion layer thickness. We shall see that due to the low doping and the small metal thickness in our diodes, this condition is easily fulfilled. In order to obtain the high voltage ( ~ 150-200 V, Ref.[1]), the epitaxial n o layer under the Ni has to have both low doping and a relatively large thickness, of the order of a few microns. For a doping level of 10 ~ cm -3 in GaAs, the depletion width W under the barrier at zero bias is given by[12]: W = (2esVb~/qNo) °5,

(5)

where Vb, = Ck,~-- (kT/q)ln(Nc/N~,). Ignoring for now the dependence of 4~B on T and using the room temperature value of 0.93 V, and given that N c = 4.7 × 10 ~7cm -3 at 300 K[12], we get Vbi = 0.77 V and W = 1.05/am. The depletion region thus resides entirely in the NO layer. As pointed out by Tung[4], the barrier metal is normally polycrystalline, with grain size of the order of the thickness, which in our Ni films would be about 0.1/am. It is also well known that Ni is "reactive" on GaAs, forming Ni-As compounds and N i - G a alloys[13]. Specifically, a ternary compound NixGaAs (x ~ 3) forms already upon deposition at ambient (room to 353 K) temperature in minutes[14,15], and is likely to consume a significant amount of our Ni film under the barrier annealing conditions (623 K, 60 s). Thus it is easy to envisage the SBH as composed of "patches" with a scale smaller than the depletion width, due to various crystallite orientations as well as varying local chemistry and phases. This inhomogeneity will lead to a "pinch-oft" of the conduction path in front of low SBH areas, and the effect will become more significant as the ratio between W and the size of the patches increases[4]. It is also clear that the pinch-off will increase at lower doping levels. How likely is it that pinch-off will occur in our diodes? For a circular patch geometry, (other geometries will yield similar results[5]) pinch-off will occur when A, the local SBH deviation from the average SBH, is larger than a critical Acre,defined[4] by: (Acr~¢/Vbb)= 2 R o / W .

(6)

With W = 1.05/am, assuming R0 = 0.05/am, and with Vbb at zero bias equal to V = 0 . 7 7 V , A,~, = 2 V b b R o / W = 0.075V (we assumed implicitly that the uniform barrier is that of the high SBH phase). For a smaller R0, or under a forward bias, A would be smaller, while for a larger uniform SBH (i.e. Vbb), A will be larger.

The question now turns to the likelihood of the SBH being different by A at different points on the N o layer. We have stated that the barrier is probably a mixture of Ni, Ni3GaAs and possibly other NixGaAs phases. While there are no data on the SBH of each one of these materials on GaAs, a number of studies in the literature have dealt with the dependence of the SBH in metal/GaAs systems on heat treatments. We assume that with non-reactive metals on GaAs, Ag being a good example[16], the room temperature SBH is that of the "as-deposited" (unreacted) metal-GaAs system. If the SBH changes after heat treatments, there must be either reactions, extensive interdiffusion, or changes in the GaAs substrate. A significant difficulty in comparing the data on the same metal-GaAs system from different studies arises from the fact that most supply only ~bB but not the ideality factor. Another error may arise when "as-deposited" barriers are inadvertently reacted during the preparation of an ohmic contact. It is clear by now that a comparison of I - V SBHs is meaningless, and that either F-B or C-V barriers should be used. Regarding the Ag-nGaAs system, we can deduce from the careful study of Newman et a/.[16], that the thFB (i.e. n ~ s ) remains constant at 0.95 eV after heating between room temperature and 633 K. Van de Walle et a/.[17] report a rather constant q~s of about 0.88 eV after l0 min annealing up to 623 K (in agreement with Newman), and then a drop of about 0.2 eV for annealings between 623 and 773 K. Since no ideality factors are given, their results cannot be compared with those of Newman. Wang et a1.[18], investigating MBE grown epitaxial A g - n G a A s diodes, measured the "in situ" qhB after growth at 453K. With ~bB=0.856eV and n = 1.03, their "as-deposited" ~FB is 0.88 eV. As in previous studies, they found that rapid thermal annealings (20 s) up to 623 K did not change ~bs. Above 623 K, ~B decreased, but n increased significantly, so that a ~FB of 0.92, 1.12 and 1.19 eV can be calculated for 623, 723 and 823 K, 20 s treatments respectively. For the same diodes, C~cz decreased slightly from 0.99 eV in the as-grown sample to 0.95 eV in the 823 K annealed one. The reason for the discrepancy between the ~bFB and the ~bcvis not clear, since normally the two are in excellent agreement[16]. We can deduce however from the comparison of Refs[16] and [18] that the "intrinsic" SBH of Ag-nGaAs is approximately 0.92 + 0.03 eV, and that the SBH due to polycrystalline Ag[16,17] is probably at the higher end of the range, while that due to single crystal Ag is at the lower end. Thus, in the context of the inhomogeneity models, the crystallography does play a part. Another and possibly larger part is played by the chemistry changes, in particular formation of new phases (in Ref.[18], AgGa and GaAg3 form after 823 K, 50 s annealings). Interestingly, even in "reactive" systems such as Al-nGaAs, the thFB of epitaxial A1 at 300 K--0.75 eV[19]--is significantly lower than that

High voltage Ni-nGaAs Schottky diodes ofpolycrystalline A1---0.87 eV[20] (on similarly doped (100) substrates, 1.6 x 10 z6and 6 × 1016cm -3 respectively). A somewhat analogous situation exists for metal/silicide SBHs on Si. The ~b~Bof W on nSi(100) at 300 K is 0.67 eV, while that of WSi2 on nSi(100) (obtained after annealing at 1073 K for l h) is 1.19 eV[21]. The ~bFBof Ti on nSi(100) at 300 K is 0.51 eV, while that of TiSi2 on nSi(100) (1 h annealing at 773K) is ~0.60eV[22]. Both W and Ti are non-reactive with Si at 300 K. Another epitaxial system, NiSiz-Si also exhibits strong inhomogeneity, with a ~FB of 0.40 eV (for No = 1.6 × 10 ~scm -3) for uniform silicide layers, and 0.65eV for heavily faceted layers on Si(100) or Ni Si2 on Si(111)[23]. Regarding Refs[21] and [22], one can conclude that the silicide-nSi SBH in both cases is higher than the "intrinsic" metal-Si SBH by a significant percentage. The evidence[16,23] thus indicates that reactions and the creation of new phases can increase ~bFRand lead to significant inhomogeneity due to a mixture of different phases or different crystalline orientations at the M - S interface. Returning to Ni-nGaAs, our room temperature ~bFBis 0.94 + 0.02 eV vs 0.834 eV in [6] and 0.80 eV in [15]. The differences are probably due to our "as-deposited" films (prepared chemically at 373 K and after a second anneal at 623K) being significantly more reacted than the "as-deposited" films in Refs[16] and [15]. Interestingly, after 1 h annealing at 643 K, the q~vB in [15] increased to 0.85 eV. (Lahav et al. annealed the films further at higher temperatures, and showed the q~s to decrease to 0.48 eV at 823 K. Unfortunately, they did not measure the ideality factor, which however, according to their Fig. 14, increased significantly. Thus, it is very likely that their q~FBincreased further at higher annealing temperatures.) The evidence is thus strong that interfacial reactions in the N i - n G a A s system, as in other metal-nGaAs systems, increase the "true" barrier ~bFs. Note that while the average ~bFBincreases with annealing temperature, ~bFa decreases with increasing measurement temperature. The former results from interfacial reactions, while the latter is a consequence of the barrier inhomogeneity. Some of our results remain unexplained. In Table 2, at each T, n is slightly higher for a lower doped substrate (sample #254), while ~B is roughly constant. The differences are small, but the trend contradicts the No dependency predicted by Sullivan et al.[5]. The No dependency of the ~bFBtemperature coefficient is also not addressed by either model[3-5]. However, following Werner and Giitler's[24] analysis of ~ in metal-Si systems, one sees that the differences in ~t, about 120/IV/K between no = 5 x 10 ~4 and 1 x 10~Scm-3, and ,,,480 pV/K between 5 x 10~4and 1 x 10 z6 cm -3, are extremely large and probably quite significant. The No effect on n can only be speculated upon as being due to impurity effects on reaction kinetics, similar to those in Pt silicide formation[25],

1461

where both increasing boron and arsenic concentrations in Si lead to a small decrease of the pre-exponent factor, i.e. slows the reaction. A similar effect of the Si doping in our nGaAs substrate on the metal-GaAs reaction may slow the reaction and the grain growth of all phases in the film. Thus, the smaller W at a larger no may be (over)compensated by a smaller Ro. This is admittedly quite speculative, and other factors, including measurement error (of the order of 1%), dopant segregation to the interface and its effect on the local chemistry, etc., may be involved. Further modelling is needed to explain the or(No) dependency. In conclusion, by measuring the temperature dependence of ~bs and n, we have found that most of the electrical characteristics of high-voltage N i nGaAs Schottky diodes can be explained by, and lend support to, inhomogeneous barrier models. Moreover, when literature data are re-evaluated using flat-band (~FB) instead of regular ~bss, the consistency of results among different studies is increased significantly. It is important to realize that the inhomogeneity models deal with measurement temperature dependencies, and cannot predict the effects of reactions leading to products with unknown barriers. Also, the strong influence of crystallography on barrier properties is established[24], complicating matters further. Thus, while it is true that metal-nGaAs reactions resulting in polycrystalline compounds lead to increased barriers, no generalization can be made to other systems. Some results, particularly the dependence of the ~bFBtemperature coefficient on No need to be investigated further. Acknowledgement--One of us (Z.S.) wishes to thank Dr L.

Zolotarevski for his help and guidance throughout this work.

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