DC parameter extraction of equivalent circuit model in InGaAsSb heterojunction bipolar transistors including non-ideal effects in the base region

Solid-State Electronics 61 (2011) 69–75

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DC parameter extraction of equivalent circuit model in InGaAsSb heterojunction bipolar transistors including non-ideal effects in the base region Yang-Hua Chang ⇑, Zong-Tai Cheng Graduate School of Optoelectronics, National Yunlin University of Science & Technology, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 24 July 2010 Received in revised form 12 December 2010 Accepted 24 January 2011 Available online 19 February 2011 The review of this article was arranged by Prof. E. Calleja

a b s t r a c t This paper presents the DC parameter extraction of the equivalent circuit model in an InP-InGaAsSb double heterojunction bipolar transistor (HBT). The non-ideal collector current is modeled by a non-ideal doping distribution in the base region. Then several consequent non-ideal effects, which have always been neglected in typical HBTs, are studied using Medici device simulator. Moreover, the associated DC parameters of VBIC model are extracted accordingly. The equivalent circuit model is in good agreement with the measured data in IC–VCE characteristics. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: InGaAsSb HBT VBIC model

1. Introduction Heterojunction bipolar transistors (HBTs) exhibit a number of advantages due to the wide-bandgap emitter. The bandgap difference at the B–E junction increases the emitter injection efficiency significantly, so the base doping concentration can be increased to reduce the base resistance without the adverse effect on current gain. The high base doping concentration also allows a thinner base layer to improve the electron transit time and fT while the Early voltage is not affected significantly. Besides, the high base doping concentration virtually eliminates emitter current crowding and high-injection effects. Another result of high base doping is that the depletion region at the B–E junction locates mostly in the emitter. Only a narrow depletion region is present on the base side. In the case of an abrupt B–E heterojunction, where there is a conduction band discontinuity (DEC), the narrow depletion region in the base still results in a collector current ideality factor that is slightly larger than unity (1.1), as opposed to a homojunction BJT or a graded-junction HBT which typically shows a collector current ideality factor of unity. In a non-ideal case that base doping is lower than the nominal value, depletion region in the base will be wider, making an even larger collector current ideality factor (>1.1). InP-based HBT technology usually incorporates In0.53Ga0.47As in the base, which is lattice-matched to InP substrate, for its high ⇑ Corresponding author. Address: 123 University Road, Sec. 3, Douliou, Yunlin 64002, Taiwan, ROC. Tel.: +886 5 534 2601x4329; fax: +886 5 531 2063. E-mail address: [email protected] (Y.-H. Chang). 0038-1101/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2011.01.044

electron mobility and low bandgap. The low bandgap in the base layer results in low turn-on voltages of the devices. Recently, InP HBTs with InGaAsSb base has been studied due to its lower bandgap and lower conduction band offset (DEC) at the base–emitter as compared to the InGaAs counterpart [1,2]. Consequently, the turnon voltage VBE of the HBT is further reduced. Thus the InGaAsSb base HBT has great potential for low-power and high-speed applications. To realize the potential of the transistor, the equivalent circuit model has to be established. In this paper, the DC characteristic of an HBT with InGaAsSb base layer grown on InP substrate is analyzed, and DC parameters of an equivalent circuit model are extracted. The VBIC model is chosen for parameter extraction because it provides the modeling of more non-ideal effects. Several non-ideal effects, which are often neglected in conventional HBTs, are included in this study. In particular, the non-ideal effects arising from a lower base doping level near the emitter are considered and studied with a device simulator Medici. The extracted parameters are verified with ADS (Advanced Design System). 2. Parameter extraction Extraction procedure and the associated Medici simulation are described in this section. The experimental data was measured from a DHBT grown by a molecular beam epitaxy (MBE) system on a semi-insulating (1 0 0) InP substrate. The InGaAsSb HBT consists of a 450 nm n+-In0.53Ga0.47As subcollector, a 200 nm n-In0.53Ga0.47As collector, a 25 nm p+-In0.2Ga0.8As0.7Sb0.3 base

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layer, a 52.5 nm n-In0.52Al0.48As emitter, and an n+-In0.53Ga0.47As emitter cap. The base doping is 4  1019 cm3. Silicon and beryllium are the n- and p-type dopants, respectively. The emitter size is 1  10 lm2. Current–voltage characteristics are measured with an Agilent HP4155B semiconductor parameter analyzer. 2.1. VBIC model overview

Therefore, WBE can be any value between 0 and 1 at this stage, but optimization may be necessary during the extraction of base resistance. More discussion on WBE is given in Section 2.3.2. The collector current is modeled by a voltage-dependent current source IC, also shown in Fig. 1. The current can be expressed by

IC ¼

The complete VBIC equivalent circuit is complicated, including a parasitic pnp transistor resulting from a conducting substrate. For HBTs grown on semi-insulating substrates, the parasitic transistor is usually negligible. This work focuses on the base region and the B–E junction. A simplified equivalent circuit is shown in Fig. 1. The B–E junction is divided into ‘‘internal’’ and ‘‘external’’ diodes, and each diode is represented by ideal and non-ideal current components. The associated parameters are extracted from base current in the low-to-medium VBE bias region. 2.2. Parameters for low-bias currents The low-bias currents are concerned with the base and collector currents up to the most ideal region (lowest ideality factor) in the Gummel plot. Base current is divided into ‘‘internal’’ and ‘‘external’’ components to account for emitter crowding and the distributed base resistance. The ‘‘internal base current’’ is expressed as a function of Vbei:

    q  V bei 1 IBðintÞ ¼ IBEI exp NEI  kT     q  V bei 1 þ IBEN exp NEN  kT

ð1Þ

where IBEI and NEI correspond to the ideal current, and IBEN and NEN correspond to the non-ideal current. The ‘‘external base current’’ IB(ext) can be expressed by the same equation, except the bias Vbei being replaced by Vbex. Both Vbei and Vbex are indicated in Fig. 1, and they are calculated by the simulator at each external bias VBE. The proportion of IB(int) and IB(ext) is determined by a user-definable parameter WBE. When WBE = 1, all the base current flows through the internal B–E junction, and is equal to IB(int). Then the base resistance is the sum of the constant RBX and the variable RBI/qb, where ‘‘qb’’ is the normalized base charge calculated by the simulator. On the other hand, when WBE = 0, all the base current flows through the external B–E junction, and is equal to IB(ext). Then the base resistance is RBX only. Since WBE determines the proportion of base current flowing through the variable resistor RBI/qb, it is difficult to extract WBE from the base current in low-to-medium bias region, where the base resistance is not significant in device characteristics.

        IS q  V bei IS q  V bci  exp  1   exp 1 qb qb NF  kT NR  kT

ð2Þ

The corresponding parameters are IS, NF, and NR, where NF and NR are the ideality factor of forward and reverse operations, respectively. ‘‘qb’’ is the normalized base charge, a bias-dependent internal parameter that accounts for the Early effect, high-injection effect, and space-charge capacitors at the B–E and B–C junctions. Under forward-active operation, the reverse component can be neglected, so only IS and NF are extracted. The measured Gummel plot is shown in Fig. 2, from which the collector current parameters IS, NF, and base current parameters IBEI, NEI are extracted in the biasing range of VBE = 0.5  0.6 V. Non-ideal base current, which usually results in a higher base ideality factor in low-bias region, is not present in the measured result, so the non-ideal parameters IBEN and NEN are not extracted. The extraction result is listed in Table 1. The collector current ideality factor 1.32 in Table 1 is apparently higher than normal values. The ideality factor is close to unity for conventional BJTs. For HBTs, which have a larger energy bandgap in the emitter than in the base, the collector ideality factor can be larger than unity (1.1 or higher) under one of the following two conditions: (1) Base doping impurities out-diffuse into emitter in a graded B–E heterojunction, which causes a conduction band hump near the junction so that collector current is reduced, and its ideality factor is larger than unity [3]; (2) Base doping concentration drops below the designed value at an abrupt B–E heterojunction, creating a larger space-charge region on the base side. A significant portion of the forward bias contributes to barrier reduction in the base region, not in the emitter, so it does not help the injection of electrons. The larger base space-charge region, the larger portion of forward bias will be wasted, further increasing the collector ideality factor. Fig. 3a shows the reduction of conduction band barrier for electrons crossing an abrupt junction. For an assumed base doping of 4  1018 cm3, when a forward bias of

VCB = 0 V

C

IS , NF IBEI , NEI Rc

B

RBX

Bx Vbex Cjex

RBI/qb

Cjc Bi

Ibci-Igc

IB(ext) Vbei

Cje

IB(int)

Fig. 2. A measured Gummel plot.

IC

Re E Fig. 1. A simplified equivalent circuit of the VBIC model.

Table 1 Low-bias VBIC model parameters extracted from the measured Gummel plot in the biasing range of VBE = 0.5–0.6 V. IS (A)

NF

IBEI (A)

NEI

1.236  1014

1.32

4.937  1013

1.95

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(a)

1

Energy (eV)

ing profile decreasing as a Gaussian function toward the emitter. The characteristic length of the Gaussian profile is optimized to 0.0075 lm so that the simulated collector ideality factor is also 1.32, identical to the measured value. The ideality factor of 1.32 from simulation is caused by the larger depletion width in the base region with the hypothetical doping profile. The lower doping in the base also results in a larger base resistance and other non-ideal effects. The values of base resistance from measurement and from Medici simulation is evaluated and compared in Section 2.3.2.

1.2

B

E

0.8

e-

0.6 0.4

0.53 eV

VBE = 0.6 V

0.2

VBE = 0 V 0

0

0.02

0.04

0.06

0.08

Position (µm)

Non-ideal effects at high biasing condition include emitter and base parasitic resistances, as well as high-injection effect. Although high-injection effect is usually not considered in HBTs due to high base doping concentrations, we evaluated its existence at high biases due to the assumed lower base doping near the emitter.

(b) 1.2

Energy (eV)

1

B

E

2.3. Parameters for high-bias currents

0.8

e-

0.6

2.3.1. Extraction of emitter resistance Emitter resistance of 210 X was determined with the RE-flyback measurement [4], and can be optimized later in the high current region of Fig. 2 if it is necessary.

0.4

VBE = 0.6

0.59 eV 0.2

VBE = 0 V 0

0

0.02

0.04

0.06

0.08

Position (µm) Fig. 3. The reduction of conduction band barrier at a forward bias of 0.6 V. (a) Only 0.53 eV for base doping concentration of 4  1018 cm3, and (b) 0.59 eV for base doping concentration of 4  1019 cm3. Emitter doping concentrations: 3  1017 cm3. Data were calculated from Medici.

0.6 V is applied, the reduction of barrier for electrons is only 0.53 eV due to the non-negligible space-charge region on the base side. It causes a slower increase of collector current in the Gummel plot, or an ideality factor significantly larger than unity. In Fig. 3b, for base doping of 4  1019 cm3, the reduction of barrier for electrons reaches 0.59 eV, indicating that almost all of the applied bias is used to reduce the barrier. The DHBT under test has an abrupt B–E heterojunction, so we adopt the second case to account for the collector ideality factor of 1.32. Then, in Medici simulation, the nominal base uniform doping of 4  1019 cm3 is modified to a non-uniform profile having a lower concentration near the emitter, as shown in Fig. 4. The doping profile consists of two regions: a 0.005 lm uniform profile of 4  1019 cm3 near the collector, and a 0.02 lm non-uniform dop-

Thickness = 0.02 µm

2.3.2. Extraction of base resistance The base resistance, as shown in Fig. 1, consists of a constant part RBX and a variable part RBI/qb, which decreases at high current levels to describe the current crowding effect. The internal base current IB(int) passes both RBX and RBI/qb, whereas the external base current IB(ext) passes RBX only. The proportion between IB(int) and IB(ext) is determined by the parameter WBE. When WBE = 0, IB(ext) accounts for 100% of the total base current, so the base resistance is RBX. On the other hand, when WBE = 1, IB(int) accounts for 100% of the total base current, so the base resistance is (RBX + RBI/qb), which results in the maximum effect from RBI/qb in base current. Therefore, when the current crowding effect is expected, WBE should be set to a value close to one. In this condition, the base resistance is (RBI + RBX) at low biases, and reduces to RBX at high current levels. Considering the assumed lower base doping near the emitter, we expected the current crowding effect and chose WBE = 1. Extraction of RBX and RBI requires measurement and/or simulation. Base resistance can be extracted by measurement of S11 in a frequency range. Alternatively, a DC measurement technique similar to the RE-flyback (collector open) can be used to extract the minimum base resistance, which appears at high base current levels. Fig. 5 shows the measurement configuration. Collector terminal is open so IE = IB (<0), and VC = VC0 . The base resistance is derived as follows:

Thickness = 0.005 µm C B

RB

RC

C

(open)

B +

IB

E

B

C

Fig. 4. The assumed doping profile with a lower concentration near the emitter. E, B, and C stand for emitter, base, and collector, respectively.

+

VBE

-

VB E

E

VCE RE

E

Fig. 5. Measurement configuration for determination of minimum base resistance at high base current. A current source IB is varied at the base terminal, and VBE and VCE are measured accordingly.

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V BE  V CE ¼ V BE0  V CE0 ¼ V BE0  V C0 E0 ¼ IB RB þ V B0 E0  V C 0 E0 ¼ IB RB þ V B0 C 0

ð3Þ

(a)

1 µm

0.2 µm

E

The derivation can be summarized as:

V BE  V CE ¼ IB RB þ V B0 C 0

0.5 µm

B

ð4Þ

Dividing (4) by IB yields:

C

V BE  V CE V 0 0 ¼ RB þ B C IB IB

ð5Þ

(b)

1 µm

0.2 µm

0.5 µm E B C

Fig. 7. The half cross-section of base layer. Voltage drops were applied between the bold lines to simulate the base resistance.

108 X. It is probably due to other parasitic in the measured device, such as contact resistance, which was not included in Medici simulation. Note that the same deficiency also exists in Fig. 7a, so it is canceled out in the resistance difference of 11.2 X between Fig. 7a and b. The technique suggested here provides a physicsbased solution to the extraction of base resistances. Following the non-zero RBI, the emitter current crowding was also verified by Medici. Using the same condition of non-uniform base doping distribution as depicted in Fig. 4, current density along the B–E junction was simulated and is shown in Fig. 8. The current density resulted from ideal uniform base doping (4  1019 cm3) is also plotted for comparison. The lower base doping concentration and high base resistance indeed cause a much higher current density at the emitter edge, which is the condition of emitter current crowding. Therefore, the importance of determining RBI is justified.

2.3.3. High-injection effect The high-injection effect is a phenomenon at high VBE forward bias when the injected minority carrier concentration in the base is close to or even higher than the doping concentration. Usually,

VBE - VCE IB

The left-hand side of (5) can be calculated from measured data. When its value is plotted as a function of 1/IB, as shown in Fig. 6, the extrapolated intersect on the y-axis is defined as RBM, which represents the base resistance at IB ? 1. The validity of extrapolation requires a nearly constant slope, as can be verified from Fig. 6. This results from the condition that the VB0 C0 in (5) remains nearly constant during the measurement. Note that this measurement technique yields the minimum base resistance only, which appears at very high base current levels. Under normal operations where IB is finite, the theoretical base resistance should be higher than the RBM. We followed this procedure and obtained 108 X for the minimum base resistance. This value corresponds to RBX mentioned earlier in this section. The determination of RBI is relatively difficult, since it is present only at lower base current levels, where the base resistance is hard to measure. Alternatively, we did Medici simulation to study the base resistance at low bias and high bias, under the assumed condition of non-uniform base doping distribution. Fig. 7a and b show the half cross-section of base layer. Voltage drop was applied between the electrode pairs (bold lines), and the simulated current was scaled up in the direction of emitter length and also doubled to match the actual symmetrical HBT. Then the base resistance was determined by the ratio of voltage drop and current. A low bias was applied to the electrode pair in Fig. 7a to resemble an ideal low-bias condition, where we expected a nearly uniform current distribution across the B–E junction and thus RBI was present. In this case, the total resistance between the electrodes was 68 X. The electrode pair in Fig. 7b resembled the hypothetical condition of an extremely high bias, where base resistance RBI/qb vanished. In this condition, the resistance between the electrodes was 57 X. The resistance difference in Fig. 7a and b corresponds to RBI, and is equal to 11.2 X. Therefore, we set RBI = 11.2 X. Along with the RBX = 108 X as described in the previous paragraph, the total base resistance is therefore 119.2 X at low biases, and is reduced to 108 X at very high biases. The determination of RBX and RBI combines a simple measurement and a simple Medici simulation. It is noticed that the simulated resistance of 57 X from Fig. 7b is lower than the measured minimum base resistance of

RBM

1/IB Fig. 6. Extrapolation to the minimum base resistance RBM according to (5).

Fig. 8. Electron current density along half B–E junction under a VBE forward bias of 0.8 V. The position at 1.2 lm is the emitter edge, and the position at 1.7 lm is the emitter center. The total emitter width of the device is 1 lm. solid line: result from the non-uniform base doping as shown in Fig. 4. Line with symbols: result from a uniform base doping of 4  1019 cm3.

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73

1E+20

Concentration (cm-3 )

1E+19 1E+18 1E+17 1E+16 1E+15 1E+14 1E+13 1E+12 0.0525

HOLES ELECTRONS 0.0575

0.0625

0.0675

0.0725

Position (µm) Fig. 9. Electron and hole concentrations in the base region, simulated by Medici at VBE = 0.8 V. The position at 0.0525 lm is the B–E junction.

this is unlikely to happen in an HBT because the base doping concentration is very high. However, in the special case where the base doping level near the emitter is lower than the designed target, the high-injection effect may occur. We used Medici to evaluate whether the condition of high-injection had been reached. Fig. 9 shows the simulated electron and hole concentrations in the base at VBE = 0.8 V. The electron concentration exceeds the hole concentration near the B–E junction, indicating that the onset of high-injection is reached. As a result, the high-injection parameter IKF in the VBIC model must take effect at this bias. The highinjection effect causes a reduction in collector current, similar to the emitter resistance RE. Therefore, special care is needed to differentiate the effect of IKF from that of RE. Fig. 10a shows the effects of IKF and RE (the emitter resistance of 210 X extracted earlier) on collector current calculated by VBIC model. It can be observed from dashed lines 1–3 that the collector current starts being affected before its value reaches IKF. Besides, the RE of 210 X has a stronger effect on collector current than IKF, as the dashed line 4 (with RE = 210 X only) nearly overlaps the solid line (with both RE = 210 X and IKF = 1.60  103 A). Therefore, it is not straightforward to extract the IKF from the IC–VBE curves when the RE is present. Fig. 10b shows the effects of IKF and RE on current gain b. When only IKF is present (dashed lines 1–3), b peaks at a different bias as IKF is varied. This differs from the effect of RE = 210 X along (dashed line 4), which does not causes the b peak. Therefore, b is clearly a better indicator for IKF extraction. Besides, the solid line (simultaneous presence of IKF and RE) does not overlap the dashed line 4 (RE only), showing the distinct effect of IKF with the presence of RE. Since RE is already determined by the flyback method, IKF can be determined by fitting the measured current gain in Fig. 10b. The optimized IKF is 1.60  103 A.

Fig. 10. (a) Collector current, and (b) b, calculated by VBIC model at various IKF (dashed lines 1, 2, and 3 with RE = 0), or RE = 210 X (dashed line 4, without IKF). Solid line: IKF = 1.6  103 A and RE = 210 X. Measured data are plotted with symbols.

2.4. Early effect The Early effect is usually neglected in HBTs due to the high base doping concentration, so the Early voltage can be assumed infinite. However, for HBTs with a thin base, base width modulation may become more significant, so the Early voltage should be evaluated. VEF is the parameter in VBIC model. Conventionally it can be readily determined by the slope of the IC–VCE curve, but the slope may lead to an overly estimated Early effect if weak avalanche breakdown coexists in the same biasing range. To prevent the weak avalanche breakdown from happening, the value of VCE must be kept very low, but such a small range of VCE potentially results in a large fluctuation in the Early voltage during extrapolation. Therefore, we adopted another approach. Firstly, collector current was measured as a function of VBE under two VCB biases

Fig. 11. (a) Collector current measured at two VCB biases. (b) The ratio of collector currents.

(ex. 0 and 1 V). The result is plotted in Fig. 11a. Secondly, the ratio of current in Fig. 11a is calculated and plotted in Fig. 11b, which is a U-shaped curve. The higher ratio at low VBE results from the

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(a) 6E-4

(b) 1E-2

Measurement

5E-4

IB step: 2 µA

Simulation

4E-4

VCB = 0 V

Simulation

1E-4

IC , IB (A)

IC (A)

Measurement

1E-3

3E-4 2E-4 1E-4

1E-5 1E-6 1E-7

0E+0 0

0.5

1

1.5

2

1E-8

0

0.2

0.4

VCE (V)

0.6

0.8

1

1.2

VBE(V)

Fig. 12. (a) IC–VCE characteristics and (b) Gummel plot from measurement and VBIC model simulation.

2.6. Avalanche breakdown parameters

Table 2 The complete DC model parameters. IS (A) 1.236  10

NF 14

IBEI (A)

NEI 13

1.32

4.937  10

IBCN (A)

NCN

WBE

1.95 RBX (X)

4.7  1011

1.276

1

108

RBI (X)

RE (X)

RCI (X)

IKF (A)

11.2

210

90

1.6  03

PC

MC

AVC1

AVC2

0.246

0.101

0.007

0.98

reverse-bias leakage current at the B–C junction, while the higher ratio at high VBE may result from the weak avalanche breakdown or reduction of collector series resistance. The minimum ratio of 1.00147 at a median bias is dominated by base width modulation with lowest contribution from other effects. Thus the minimum ratio of collector current is used to derive the Early voltage. Assume that IC1 is the current at VCE1 (=VBE + VCB1), and IC2 is the current at VCE2 (=VBE + VCB2). Then, at a certain VBE, the slope in the IC–VCE curve is expressed as:

IC1 dIC IC2  IC1 ð1:00147  1ÞIC1 ¼ ¼ ¼ V CE1 þ V A dV CE V CE2  V CE1 V CB2  V CB1

ð6Þ

where VA is the Early voltage to be derived. In (6), IC2 is equivalent to 1.00147 IC1 based on the minimum ratio in Fig. 11b. The VA obtained with this technique is 216 V. Although the large value indicates a negligible base width modulation, this technique provides a reliable extraction of the Early voltage.

2.5. Intrinsic collector resistance The collector resistance in VBIC model consists of intrinsic collector resistance RCI and extrinsic collector resistance RCX. RCI is associated with the quasi-saturation behavior [5] in IC–VCE characteristics, where the transistor is biased between linear and fully-saturation region. A larger RCI results in a lower slope in the quasi-saturation region of the IC–VCE characteristics. Although quasi-saturation is not the focus of this work, it is necessary to optimize RCI so that the low-bias region of the IC–VCE characteristics is modeled properly. The optimized value of RCI is 90 X.

Due to the low bandgaps in InGaAsSb base and InGaAs collector layers, weak avalanche breakdown is more likely to occur in the HBT. VBIC model describes this effect with Igc at base–collector junction, as shown in below equation:

Igc ¼ ðIC  Ibc Þ  AVC1  ðPC  V bci Þ h i  exp AVC2  ðPC  V bci ÞMC1

ð7Þ

AVC1 and AVC2 are weak avalanche parameters; PC is the base– collector built-in potential; MC is the grading coefficient of the base–collector space-charge capacitance. Vbci is the internal forward bias at the B–C junction. Theoretically, AVC1 and AVC2 can be determined accurately based on (7). In reality, however, even if the IC–VCE characteristics is measured by setting a VBE value for each curve, the VBC calculated by VBC = (VCE  VBE) is not the internal bias Vbci. Since the determination of Vbci is not straightforward, the approximate values of AVC1 and AVC2 were determined empirically by fitting procedure. The best biasing range used for the extraction is VBE > 0.7 V, to be differentiated from the biasing range used for Early voltage extraction shown in Fig. 11. 2.7. The complete model The complete DC model parameters are listed in Table 2, except WBE and the Early voltage of 216 V. The ICVCE characteristics and Gummel plot calculated by VBIC model are plotted in Fig. 12. It shows that the model is in good agreement with the measurement. Therefore, it has been confirmed that the WBE is 1 for this device. 3. Conclusion A procedure of DC parameter extraction in VBIC model has been presented. Non-ideal base doping distribution has been hypothesized to account for the high ideality factor in the measured collector current. With a combination of measurement and Medici simulation, internal and external base resistors have been identified, and the high-injection effect has been evaluated. Finally, Early voltage and avalanche breakdown parameters have been extracted. The VBIC model agrees well with the measurement. Acknowledgments The authors would like to thank Prof. Jen-Inn Chyi and Dr. Shu-Han Chen at National Central University, Taiwan, ROC for experimental data and valuable discussion. This work was

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supported by the National Science Council, Taiwan, ROC under Contract No. NSC 98-2221-E-224-068. References [1] Chen Shu-Han, Wang Sheng-Yu, Teng Kuo-Hung, Chyi Jen-Inn. High current and low turn-on voltage InAlAs/InGaAsSb/InGaAs heterojunction bipolar transistor. Proceedings of the IEEE 19th international conference on indium phosphide and related materials, Matsue, Japan. 2007;14–18:141–4.

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