Measurements carried out on thick Al/sub x/Ga/sub 1-x/As (x  0.63

Airey, R.J.

David, J.P.R.

Hopkinson, M.

Ng, B.K.

Rees, G.J.

Tozer, R.C.

English

White Rose Research Online

This is a repository copy of Avalanche multiplication and breakdown in AlxGa1-xAs (x < 0-9) .White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/901/Article:Ng, B.K., David, J.P.R., Rees, G.J. et al. (3 more authors) (2002) Avalanche multiplication and breakdown in AlxGa1-xAs (x < 0-9). IEEE Transactions on Electron Devices, 49 (12). pp. 2349-2351. ISSN 0018-9383 https://doi.org/10.1109/TED.2002.805570eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 49, NO. 12, DECEMBER 2002 2349Avalanche Multiplication and Breakdownin Al Ga AsB. K. Ng, J. P. R. David, G. J. Rees, R. C. Tozer, M. Hopkinson, andR. J. AireyAbstract—Measurements carried out on thick Al Ga As ( 0 9)diodes showed that the ionization coefficients of Al Ga As becomewidely different when 0 63 and are virtually independent offor 0 72. A strong dead space effect is also observed in thickAl Ga As structures with 0 6. The breakdown voltage is foundto increase at a slower rate with when 0 63.Index Terms—Al Ga As, avalanche breakdown, avalanche multipli-cation, impact ionization, ionization coefficients.I. INTRODUCTIONAvalanche multiplication in AlxGa1 xAs (x  0:6) is relativelywell characterized [1]–[7]. In this alloy range the electron and hole ion-ization coefficients, and respectively, decrease withx and the=ratio (1=k) in bulk material approaches unity asx increases [6]. Bycontrast, very little is known about the behavior forx > 0:6. We haverecently investigated the avalanche behavior in Al0:8Ga0:2As [8] andfound that its ionization coefficients are very different in magnitudesuch that its/ ratio deviates markedly from the trend observed inAlxGa1 xAs (x  0:6). These results are somewhat surprising and in-dicate that it is not appropriate to extrapolate the avalanche behavior ofAlxGa1 xAs (x > 0:6) from that of material withx  0:6. It is there-fore of interest to investigate the avalanche behavior in AlxGa1 xAswith x > 0:6.II. EXPERIMENTA series of ten AlxGa1 xAs homojunction p-i-n/n-i-p structureswith nominal i-region thickness,w, of 1 m (w = 0:8 m forx = 0:6) andx ranging from 0.4 to 0.9 were used in this study. TwoAl0:8Ga0:2As layers reported previously [8] are included here forcompleteness. All p-i-n (n-i-p) structures were grown by conventionalsolid-source molecular beam epitaxy on n+ (p+) (100) orientedGaAs substrates. The p-i-n (n-i-p) structures comprise a thin n+ (p+)GaAs buffer, an n+ (p+) AlxGa1 xAs cladding layer, an undopedAlxGa1 xAs i-region, a p+ (n+) AlxGa1 xAs cladding layer anda thin p+ (n+) GaAs cap. The p+ and n+ cladding layers werenominally between 0.5m and 1m thick and were doped with Beand Si respectively to levels of 1–2 1018 cm 3. Table I lists thealuminum fractions, the breakdown voltages(Vbd) and the parametersobtained from modeling the capacitance–voltage profiles of the layers.All layers, except P70a, had windows etched in the substrate so thatboth electron and hole initiated multiplication characteristics,Me andMh respectively, can be measured on the same diode. Excitation lightfrom a laser source was focused to a small spot (10 m) on eitherthe top or back cladding layer of the diodes to inject carriers into thehigh field regions. An increase in the primary photocurrent prior toavalanche multiplication was corrected using the method of WoodsetManuscript received July 15, 2002. This work was supported by EPSRC(U.K.) and by the Nanyang Technological University, Singapore, through ascholarship to B. K. Ng. The review of this brief was arranged by Editor M.Anwar.The authors are with the Department of Electronic and ElectricalEngineering, University of Sheffield, Sheffield S1 3JD, U.K. (e-mail:bkng@ieee.org; j.p.david@sheffield.ac.uk).Digital Object Identifier 10.1109/TED.2002.805570TABLE IMEASUREDPARAMETERS OF THEAl Ga As DIODESal. [9]. Excess noise measurements were performed at a center fre-quency of 10 MHz and a noise effective bandwidth of 4.2 MHz, asdescribed by Liet al. [10].Virtually pure carrier injection was achieved by illuminating theAl0:4Ga0:6As and Al0:5Ga0:5As diodes with 542 nm light froma HeNe laser, since more than 97% of this incident light [11] isabsorbed in the 1m thick cladding layers. For the AlxGa1 xAsdiodes withx  0:6, 442 nm light from a HeCd laser was used.Such light is strongly absorbed (>98%) in the cladding layers ofdiodes with0:6  x  0:8 and pure carrier injection is ensured. Themultiplication characteristics of the AlxGa1 xAs (x > 0:6) diodesunder strongly mixed carrier injection condition were also investigatedusing weakly absorbed 542 nm light.III. RESULTS AND DISCUSSIONSFig. 1 shows the typicalMe andMh of layers P50, P60, P65, P70b,P80, and P90. Forx < 0:61,Me andMh are observed to converge asxincreases, consistent with previous investigations [6]. By contrast thereis a significant difference betweenMe andMh of the AlxGa1 xAsdiodes withx  0:63. Me andMh of P90 appeared slightly closerthan those of P70b and P80 because of a slightly contaminated injectionconditions resulting from the 442 nm light. Multiplication characteris-tics similar to those of P90 are also observed in N90. The multiplicationcharacteristics from mixed carrier injection(Mmixed), resulting fromtop illumination with 542 nm light, forx  0:63 lie between those ofMe andMh, as expected. It is also noted thatMe > Mh in all layers,indicating that >  for all x. The conventional local model [12] wasused to extract the ionization coefficients from the multiplication char-acteristics of the AlxGa1 xAs diodes. The layers P40, P50, and P65have relatively low cladding doping levels (Table I) and the depletionregions extend considerably into the cladding layers. Consequently, thenonideal electric field profiles of these layers were taken into accountwhen calculating the ionization coefficients.Fig. 2(a) and (b) depict the ionization coefficients forx  0:61 andx  0:63 respectively. The parameterized coefficients of Al0:8Ga0:2As[8] are shown in both Fig. 2(a) and (b) for comparison. The coefficientsobtained forx  0:61 are in qualitative agreement with those reportedpreviously [6]. It can be seen from Fig. 2 that decreases with in-creasingx for x  0:61 but remains virtually constant for all higherx.On the other hand, while also decreases slightly with increasingx upto x = 0:61, it suffers a sudden large drop atx = 0:63, beyond whichit changes very little. Consequently, the= ratio approaches unity asx increases from 0.36 to 0.61 but becomes much greater than unity for0018-9383/02$17.00 © 2002 IEEE2350 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 49, NO. 12, DECEMBER 2002Fig. 1. (Solid lines) and (dashed lines) of back-etched AlGa Asp-i-n diodes. (Dot-dashed lines) measured using 542 nm light for P65,P70b, P80, and P90 are also shown.x  0:63. As a result the= ratios in AlxGa1 xAs with x  0:63are found to be larger than those of most other III–V materials.The excess noise characteristic of each alloy composition from pureelectron injection is shown in Fig. 3. The excess noise of P40 and P50correspond tok = 0:7 andk = 0:6 respectively and are in good agree-ment with the= ratios deduced from the ionization coefficients. Inthe case of P60 a lower excess noise, corresponding tok = 0:4, isobtained and appears to contradict the value of=  1 deducedfrom photomultiplication measurements. This apparent disagreementis due to nonlocal dead space effects which have become significantin a w  0:8 m Al0:6Ga0:4As structure [13]. The excess noise ofthe AlxGa1 xAs (x  0:63) diodes is even lower and correspondsto 0:15  k  0:3. These results broadly corroborate the= ratiosextracted from photomultiplication measurements. Although the=ratio is almost constant in AlxGa1 xAs (x  0:63), the excess noiseis seen to fall with increasingx. This suggests that the nonlocal effectsin 1m thick AlxGa1 xAs (x  0:63) diodes are also significant andincrease withx. We believe the increasing significance of dead spacein AlxGa1 xAs (x  0:63) follows from the increase in threshold en-ergy for impact ionization withx.Allam [14] showed that the breakdown voltage in wide gap semi-conductors scales linearly with a Brillouin-zone-averaged energy gap,hEind:i, given byhEind:i =18(E  + 3EX + 4EL) (1)whereE , EX andEL are the conduction-band energies at the , XandL extrema, measured from the valence band edge. WhenE  isFig. 2. (Open symbols) and (dotted symbols) deduced from theAl Ga As diodes with (a) = 0 36 ( ), 0.47 ( ), 0.61 ( ), and(b) = 0 63 (hexagon), 0.72( ), 0.89 ( ). For = 0 80, theparameterized (solid line) and (dashed line) reported in [8] are used.Fig. 3. Excess noise factor measured in P40( ), P50( ), P60( ), P65( ), P70( ), P80( ), and P90( ) from electron initiated multiplication.Dashed lines are McIntyre’s local prediction for= 0 to 1 in steps of 0.1.particularly large such that it has a negligible effect on the high-fieldtransport, a modified zone-average energy [14] ignoringE  given byhEind:im =17(3EX + 4EL) (2)is used instead. A phenomenological relation given byVbd = 45:8(hEind:i   1:01) (3)is found to predict accurately the breakdown voltage of 1m struc-tures of several wide gap semiconductors. To test the phenomenolog-ical expression in (3),Vbd of ideal AlxGa1 xAs diodes withw = 1m are plotted as a function ofx in Fig. 4. The ionization coefficientsof Plimmeret al. [6] and those deduced in this work are used calcu-lated the values ofVbd for x  0:3 andx  0:36 respectively. Thepredictions ofVbd from the work of Davidet al. [1] and from (3) areIEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 49, NO. 12, DECEMBER 2002 2351Fig. 4. Comparison of the of 1 m Al Ga As diodes, calculated usingand deduced in this study( ) and those of Plimmeret al. ( ) [6], withDavid’s (dashed line) [1], and Allam’s (solid line) [14] predictions. Inset showsthe equivalent average energies corresponding to the calculatedof 1 mAl Ga As diodes in Allam’s expression [14] plotted against.(solid line), (dashed line) and (dotted line) as a function ofare also shown in the inset.also included in Fig. 4 for comparison. The values ofhEind:i in (3) forvariousx are computed using (1).While the calculatedVbd of the AlxGa1 xAs (x  0:47) diodes arein qualitative agreement with the empirical expression of Davidet al.[1], a better agreement is achieved with Allam’s expression forx up to0.63. However, the calculatedVbd departs from both predictions andincreases at a slower rate withx for x > 0:63. The results suggest thatthe additional improvement in the potential breakdown performance ofAlxGa1 xAs devices obtained from increasingx saturates at aroundx = 0:63. The equivalent average energies corresponding to the cal-culatedVbd of 1 m AlxGa1 xAs diodes in Allam’s expression areplotted as a function ofx in the inset of Fig. 4. The variation ofhEind:i,hEind:im andEX with x are also shown. The average energy requiredto produce the calculatedVbd in (3) is identical to that ofhEind:i forx < 0:63, but approacheshEind:im for x = 0:72 and tends towardEX whenx > 0:72. This suggests that the -valley may have becomeunimportant in determining theVbd of AlxGa1 xAs whenx > 0:63and that even the influence of theL-valleys onVbd becomes decreas-ingly important forx > 0:72.IV. CONCLUSIONThe ionization coefficients of AlxGa1 xAs are found to convergeasx increases from 0.36 to 0.61 but become very different at higherx,resulting in a large= ratio in AlxGa1 xAs with x  0:63. Excessnoise measurements corroborated the observation of large= ratiosin AlxGa1 xAs (x  0:63) and revealed a strong dead space effectin thick AlxGa1 xAs diodes withx > 0:6. The breakdown voltageof 1 m AlxGa1 xAs diodes is found to vary linearly with the zone-averaged energy forx < 0:63, but increases more slowly withx whenx > 0:63. The results suggest that the dependence ofVbd on the -andL-valleys of AlxGa1 xAs diminishes whenx > 0:63.REFERENCES[1] J. P. R. David, J. S. Marsland, H. Y. Hall, G. Hill, N. J. Mason, M. A. Pate,J. S. Roberts, P. N. Robson, J. E. Sitch, and R. C. Woods, “Measuredionization coefficients in Ga Al As,” in Proc. 1984 Symp. GaAs Re-lated Compounds, Inst. Phys. Conf. Ser., 1985, p. 247.[2] G. E. Bulman, V. M. Robbins, and G. E. Stillman, “The determina-tion of impact ionization coefficients in (100) gallium arsenide usingavalanche noise and photocurrent multiplication measurements,”IEEETrans. Electron Devices, vol. 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Avalanche multiplication and breakdown in AlxGa1-xAs (x < 0-9)

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Avalanche multiplication and breakdown in AlxGa1-xAs (x < 0-9)

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