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Numerical investigationof the effects of gradedlayer on the performance ofAlGaAs/GaAs heterojunctionbipolar transistorsNacer Debbar & Hamad Al-HokailPublished online: 09 Nov 2010.

To cite this article: Nacer Debbar & Hamad Al-Hokail (2000) Numericalinvestigation of the effects of graded layer on the performance of AlGaAs/GaAsheterojunction bipolar transistors, International Journal of Electronics, 87:10,1153-1162, DOI: 10.1080/002072100415594

To link to this article: http://dx.doi.org/10.1080/002072100415594

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INT. J. ELECTRONICS, 2000, VOL. 87, NO. 10, 1153 ± 1162

Numerical investigation of the eŒects of graded layer on the performanceof AlGaAs/GaAs heterojunction bipolar transistors

NACER DEBBARyz and HAMAD AL-HOKAILy

The e� ects of grading on the performance of heterojunction bipolar transistors(HBTs) are studied by numerically solving the basic semiconductor equations.The numerical modelling is based on the extended drift± di� usion formulationwith inclusion of thermionic emission current at the heterointerface of abruptemitter HBTs. The results of the simulation show that the graded layer improvessigni® cantly the current driving capability of the HBT and lowers its o� set voltage.However, owing to the increase in the recombination in the graded layer, thecurrent gain of the graded HBT is lower and depends strongly on the bias at lowand medium bias range. The simulation also reveals the presence of a potentialminimum in the conduction band of the graded emitter HBT, which results in anelectron accumulation in the region. This accumulation increases the emitter-basecapacitance and its charging time, leading to a smaller unity-gain frequency fT.

1. Introduction

Recently heterojunction bipolar transistors (HBTs) have received great interestbecause of their potential use in high speed and microwave applications (Kroemer1982) . In fact, excellent performance HBTs fabricated from AlGaAs/GaAs and InP/InGaAs have been reported to have unity-gain frequencies (fT ) of 170 GHz and186 GHz, respectively (Ishibashi et al. 1990, Song et al. 1994) . The superior perfor-mance of HBTs over their counterpart homojunction transistors is attributed to theuse of a wide bandgap emitter, which suppresses hole injection into the emitter and,therefore, allows high base doping and low emitter doping without sacri® cing emitterinjection e� ciency. Hence, reducing the base series resistance and the base± emittercapacitance, both of which are important for high-speed operation.

The presence of a conduction band spike is believed to degrade the injectione� ciency of the abrupt emitter HBT. This is because the spike causes the electronsin the heterojunction to transport by means of thermionic emission and tunnelling(Perlman and Feucht 1964, Lundstrom 1984, Horio and Yanai 1990, Yang et al.1993) . This impedes the electron injection from emitter to base and results in adecrease in the collector current. Generally the problem is overcome by the intro-duction of a thin layer of graded AlGaAs in the emitter side adjacent to the base.E� ectively, this will smooth out the conduction band spike and make the injectionmore e� cient. However, the graded layer will lead to a much higher recombinationin the emitter± base space charge layer. It will be shown that this will degrade thecurrent gain in the low current range where the recombination dominates the basecurrent.

Internationa l Journal of Electronics ISSN 0020± 7217 print/ISSN 1362± 3060 online # 2000 Taylor & Francis Ltdhttp://www.tandf.co.uk/journals

Received 19 May 1999. Accepted 8 February 2000.yElectrical Engineering Department, King Saud University, PO Box 800, Riyadh 11421,

Saudi Arabia.z Corresponding author. e-mail: debbar@ksu.edu.sa

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Various computational methods have been developed to help us understand theoperational mechanism of these devices, and hence optimize their design. Theextended drift± di� usion formulation, developed by Sutherland and Hauser (1977),Lundstrom and Schuelke (1983) and Marshack and Van Vliet (1984), for composi-tionally non-uniform semiconductors can describe very well the transport of carriersin graded emitter HBTs. However, the presence of abrupt band discontinuities inabrupt emitter HBT has led to the inclusion of thermionic emission and tunnellingmechanisms in describing the carrier transport over the heterojunction (Perlman andFeucht 1964, Lundstrom 1984, Horio and Yanai 1990, Yang et al. 1993).

In this paper, a comprehensive analysis of the e� ect of a graded layer on theperformance of AlGaAs/GaAs HBTs is carried out using a one-dimensional numer-ical model that incorporates thermionic emission transport mechanisms across theabrupt heterojunction and drift± di� usion in the remainder of the structure. Thestudy focuses on the most important parameters that characterize the performanceof HBTs. These are the device gain, the current drive capability, the cuto� frequencyand the o� set voltage.

2. Numerical model

In abrupt emitter HBTs, thermionic emission over the energy band discontinu-ities can describe electron and hole transport mechanism across the heterointerface(Perlman and Feucht 1964, Lundstrom 1984, Horio and Yanai 1990, Yang et al.1993) . The basic equations based on the extended drift± di� usion model areemployed for the remaining parts of the structure where the material compositionis uniform.

Thermionic emission can be incorporated by designating two nodes at either sideof the heterointerface separated by very small mesh spacing. The current densities forelectrons and holes between these interface nodes can be expressed as (Horio andYanai 1990, Yang et al. 1993)

Jn;i ˆ ¡q¸n1n1…0¡†exp ¡ D Ec

kT… †‡ q¸n2n2…0‡† …1†

¸n1;2 ˆ A*eT2

qNc1;2…2†

Jp;i ˆ q¸p1p1…0¡†exp ¡ D Ev

kT… †¡ q¸p2p2…0‡† …3†

¸p1;2 ˆ A*hT 2

qNv1;2…4†

where A*e and A*h are the e� ective Richardson constant for electrons and holes,respectively; ¸n1;2 and ¸p1;2 are the mean electron and hole thermal velocities, respec-tively ; Nc1 ;2 and Nv1;2 are the e� ective density of states in the conduction and valenceband in each region, respectively; n1…0¡), n2…0‡ ) and p1…0¡), p2…0‡) are the electronand hole densities at each side of the heterointerface, respectively.

The basic drift± di� usion equations are modi® ed to handle position dependentmaterial composition. These modi® cations use the band parameter approach

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introduced by Sutherland and Hauser (1977). For the one-dimensional steady state,the modi® ed equations are expressed as

ddx

"dÁ

dx… †ˆ ¡q…p ¡ n ‡ ND ¡ NA† …5†

dJn

dxˆ q…R ¡ G† …6†

dJp

dxˆ ¡q…R ¡ G† …7†

Jn ˆ ¡q·nnd

dx…Á ‡ Án†‡ kT ·n

dndx

…8†

Jp ˆ ¡q·ppd

dx…Á ¡ Áp† ¡ kT ·p

dpdx

…9†

Án ˆ À…x† ¡ Àr

q‡ kT

qln

Nc…x†Ncr

… † …10†

Áp ˆ ¡…x† ¡ Àr

q¡

Eg…x† ¡ Egr

q‡ kT

qln

Nv…x†Nvr

… † …11†

where Á is the electrostatic potential, Án and Áp are the composition dependent bandparameters, ND and NA are the donor and acceptor concentrations, respectively, Ncand Nv are the density of states in the conduction and valence bands, respectively, Egis the bandgap energy, and À is the electron a� nity. The subscript r represents theparameter value at a reference point in the device structure, taken to be the GaAs.The electron and hole recombination (R) processes are described by the Shockley±Read± Hall statistics

R ˆ pn ¡ n2i

½n…p ‡ ni†‡ ½p…n ‡ ni†…12†

where, ni is the intrinsic concentration and ½n and ½p are the lifetimes for electronsand holes, respectively.

For AlxGa1¡xAs, the electron and hole mobilities are reduced by 12.7 and 6.7%per Al composition of 0.1 from the values in GaAs. The other material parametersare listed in table 1 as a function of the Al mole fraction.

The structure modelling is carried out by a simultaneous numerical solution ofPoisson’ s equation, continuity equations for holes and electrons, and the auxiliarycurrent equations describing the carrier generation± recombination process. The

Performance of AlGaAs/GaAs heterojunction bipolar transistors 1155

Parameter Formula …0 µ x µ 0:45)

Band gap (eV) Eg¡ ˆ Eg¡;GaAs ‡ 1:247xElectron a� nity (eV) À ˆ 4:07 ¡ 0:6…Eg¡…x† ¡ Eg¡;GaAs)Electron e� ective mass mn ˆ …0:067 ‡ 0:083x†m0

Hole e� ective mass mp ˆ …0:48 ‡ 0:31x†m0

Dielectric constant " ˆ …13:1 ¡ 3x†"0

Electron and hole life times ½n ˆ ½p ˆ 10¡8 s

Table 1. Material parameters used in the simulation (Yang et al. 1993).

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® nite di� erence method is used to discretize equations (5)± (9) on a non-uniformmesh consisting of 300 points. The Scharfetter± Gummel (1969) technique is usedto discretize the continuity equations. The resulting system of equations is linearizedusing Newton’s method, and then solved using an iterative approach. After theprogram reaches convergence, the potential and carrier concentration pro® les arereadily available, from which the variables of interest are computed.

3. Results and discussions

Figure 1 shows the structure of the Npn HBT simulated in this study. TheAl0:3Ga0:7As emitter has a doping of 5 £ 1017 cm¡3 and a thickness of 0.2 mm thatincludes the 300 AÊ linearly graded layer for the graded emitter case. The p-type GaAsbase thickness and doping are 0.13 mm and 5 £ 1018 cm¡3, respectively. The collectoris 0.40 mm thick and has a doping of 5 £ 1016 cm¡3. The collector± emitter voltageV CE is ® xed at 3 V throughout this work except for the JC-V CE curves, and thesimulations are done at room temperature.

The investigation focuses on comparing the previously mentioned ® gure of meritsof the graded emitter HBT (g-HBT) to those of the abrupt emitter HBT (a-HBT).The presence of the graded layer changes the potential pro® le in the vicinity of theheterojunction, as shown in ® gure 2, and, consequently, it alters the current trans-port across the heterojunction, which gives rise to several changes in the JC and JBvs. V BE curves, as shown in ® gure 3. The turn on voltage at a given collector currentis smaller, leading to a lower o� set voltage, as will be shown later. The ideality factorfor JC is equal to 1 while that of the a-HBT is 1.11; this was also observed experi-mentally (Tiwari et al. 1987, Asbeck et al. 1989) . The current driving capability of theg-HBT is higher at low and medium current level but becomes comparable to that ofthe a-HBT at very high current levels. The base current also shows certain di� er-ences: JB is larger at low and medium bias and becomes smaller at high bias, therecombination dominates the base current for a more extended region in the low biasrange as evidenced by the n ˆ 2 region in the JB-V BE curves.

These di� erences are generally attributed to the presence of the conduction bandspike at the emitter± base junction (Yang et al. 1994) . In the g-HBT, the composi-tional grading, as is shown in ® gure 2, smoothes out the conduction-band spike.Therefore, the electron transport across the heterointerface is governed purely bydrift± di� usion; this gives rise to an ideality factor of 1 and a smaller o� set voltage.While in the case of a-HBT, the electron transport across the spike will be deter-mined by thermionic emission mechanism, which impedes the electron injection,leading to a larger turn-on voltage and a slightly higher ideality factor. Figure 4

1156 N. Debbar and H. Al-Hokail

Figure 1. Schematic structure of Npn HBT simulated in this investigation.

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Performance of AlGaAs/GaAs heterojunction bipolar transistors 1157

Figure 2. Simulated conduction band pro® le in the emitter± base region vs. distance of the a-HBT and g-HBT at a collector current density of 102 A cm¡2 . The heterojunction islocated at x ˆ 0:2 mm.

Figure 3. Simulated collector and base current densities as a function of emitter± basevoltage. The collector-emitter voltage is maintained at 3 V.

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1158 N. Debbar and H. Al-Hokail

Figure 4. Common emitter characteristics of the g-HBT and a-HBT.

Figure 5. Simulated electron and hole concentration pro® le at a collector current density of102 A cm¡2.

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shows the JC ¡ V CE characteristics where we can see clearly a much lower o� setvoltage as explained and a higher current driving capability as expected.

The base current consists mainly of three components, namely the recombinationcurrent in the emitter± base space charge region, JSCR , the recombination current inthe neutral base region, JBR , and the back injected holes, JBI. It was shown that atlow bias JSCR dominates the base current while JBI and JBR dominate at high biases(Liou et al. 1993, Yang et al. 1994) . Figures 5 and 6 show the carrier concentrationand the recombination rate, respectively, vs. distance in the vicinity of the E± Bheterojunction. The heterojunction is located at x ˆ 0:2 mm. In the g-HBT theback injected hole current is much lower as suggested by the lower injected holeconcentration beyond the space charge region, as shown in ® gure 5. While therecombination rate is larger, as can be seen in ® gure 6, in the gradedregion. These observations remain valid in many simulations at di� erentcurrent levels. These results explain the fact that the base current of the g-HBT ishigher at low biases, where it is dominated by the recombination current, and getssmaller at high biases when the back injected hole current dominates as discussedabove.

Figure 7 shows the common emitter current gain ­ vs. collector current densityJC. It is shown that the g-HBT exhibits a higher gain at high current levels due tobetter current driving capability and lower base current. However, its gain getssmaller and more bias dependent at low and moderate current levels due to thelarger recombination in the E± B space charge region.

The cuto� frequency fT of the HBT is important for analysing the bandwidth ofthe small-signal ampli® er and the power gain of power ampli® er. It is calculatedusing the de® nition

Performance of AlGaAs/GaAs heterojunction bipolar transistors 1159

Figure 6. Simulated recombination rate vs. distance in the emitter-base region at di� erentcollector current density levels.

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1160 N. Debbar and H. Al-Hokail

Figure 7. DC current gain as a function of collector current density.

Figure 8. Cuto� frequency vs. collector current density.

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fT ˆ 12º

D JC

D QT V cEˆCONST

…13†

where, D QT is the incremental excess charge corresponding to the increment D JCand D JC is the incremental collector current density.

Here, QT represents the total charge of one type of carrier in the entire device.The results for the abrupt and graded case are shown in ® gure 8. The a-HBT exhibitshigher fT over the entire useful current range. By reference to ® gures 2 and 5 we canexplain this result as follows. In the g-HBT a potential energy minimum results in theconduction band within the graded region. This minimum contributes to a substan-tial electron concentration in the region, which signi® cantly increases the E± B capa-citance and its charging time leading to a reduction in fT. At high current levelsabout 105 A cm¡2, the velocity overshoot e� ects occurring in the collector regioncause the collector transit time to be very small for a narrow collector currentrange which leads to a peak in the cuto� frequency (Horio et al. 1989).

These results suggest that abrupt emitter design is advantageous over the gradedemitter HBT. Similar conclusions have been reached from experimental results(Enquist et al. 1987) and from numerical simulation (Yang et al. 1994).

4. Conclusions

In this paper, the performance of graded emitter HBT has been studied andcompared with that of abrupt emitter HBT. The study was done using numericalsimulation that combines the drift± di� usion and thermionic emission transport in asingle formulation for the abrupt HBT. The results of the simulation show that thegraded layer e� ectively removes the conduction band spike. This has resulted in alower o� set voltage, an ideality factor for JC equal to unity, and a higher currentdriving capability. However, the simulation shows that the a-HBT is more e� ectivein reducing the space charge region recombination and hence, maintaining a highcurrent gain at lower operating biases. In addition, the simulation also reveals thepresence of a potential energy minimum in the conduction band of the gradedregion. This energy minimum has resulted in an accumulation of electrons thatincreases the E± B capacitance and its charging time, which resulted in a lower cuto�frequency over the whole useful current levels.

In conclusion, the results of the simulation suggest that the abrupt emitter HBTdesign is advantageous over the graded emitter HBT.

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ENQUIST, P. M., RAMBERG, L. P., and EASTMAN, L. F., 1987, Comparison to compositionallygraded to abrupt emitter± base junctions used in the heterojunction bipolar transistor.Journal of Applied Physics, 61, 2663± 2669.

HORIO, K., IWATSU,Y., and YANAI, H., 1989, Numerical simulation of AlGaAs/GaAs hetero-junction bipolar transistors with various collector parameters. IEEE Transactions onElectron Devices, 36, 617± 624.

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