Epitaxial Structure Design of a Long-Wavelength InAlGaAs/InP Transistor Laser

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Epitaxial Structure Design of a Long-Wavelength InAlGaAs/InP Transistor Laser Yong Huang, Jae-Hyun Ryou, Senior Member, IEEE, and Russell D. Dupuis, Fellow, IEEE

Abstract— The threshold condition in long-wavelength InAlGaAs/InP transistor lasers is theoretically and numerically investigated. The optical gain in the In0.58 Ga0.42 As/In(Al0.4 Ga0.6 )As strained quantum well is calculated using a simplified k-selection model while intervalence band absorption is considered as the major intrinsic optical loss in the transistor lasers. It is found that room-temperature lasing of an N-InP/ p-In(Al0.4 Ga0.6 )As/N-InP double heterostructure transistor laser is achieved only when the base thickness and doping level are within a specific narrow range. However, the selectable range is significantly expanded by means of facet coating, structure engineering, and quantum well design. By using a more compressively-strained or thicker quantum well as the active region in a separate confinement heterostructure transistor laser, it is possible to obtain a threshold current density as low as sub-100 A/cm2 . Index Terms— Chemical vapor deposition, heterojunction bipolar transistors, semiconductor device modeling, semiconductor lasers.

I. L ONG -WAVELENGTH T RANSISTOR L ASERS

T

RANSISTOR lasers (TLs) are newly-emerging optoelectronic devices capable of continuous-wave emission of stimulated light while simultaneously performing transistor action, as demonstrated by Feng, et al., in 2006 [1]. In the form of a heterojunction bipolar transistor (HBT) with a quantum well (QW) incorporated in the base, TL offers a potential high modulation speed [2]–[4], suppressed relaxation oscillation [5], and a low turn-on delay [4] owing to the reduced carrier lifetime in the base/active region. In addition, thanks to its dual functionality as a conventional HBT and a laser source [6], the complexity associated with monolithic integration of an HBT and a TL is significantly reduced compared to the integration of an HBT with a p-i -n laser diode (LD) in terms of structure design, material growth, and device fabrication. The TLs demonstrated to date have been predominantly fabricated from GaAs-based materials,

Manuscript received October 7, 2010; revised November 30, 2010; accepted January 17, 2011. Date of current version March 25, 2011. This work was supported in part by the Defense Advanced Research Projects Agency University Photonics Research Center under Contract HR0011-04-1-0034 (Hyper-Uniform Nanophotonics Technologies Center). Y. Huang and J.-H. Ryou are with the Center for Compound Semiconductors, and School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: [email protected]; [email protected]). R. D. Dupuis is with the Center for Compound Semiconductors, School of Electrical and Computer Engineering, and School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2011.2108636

e.g., AlGaAs(InGaP)/GaAs heterostructures [1], [2], [5]– [9]. Room-temperature continuous-wave (CW) operation has been achieved in the TLs using strained InGaAs QW in the GaAs base layer and thereby the emission wavelength is limited to the near-infrared region (λ ∼ 980 nm). For fiber optical communication applications, the operating wavelength should be extended to either ∼1.3 μm or ∼1.55 μm and highspeed direct modulation of TLs can be a critical benefit at those wavelengths. The InP-based material system has been the dominant material technology in producing LDs at these wavelengths as well as in making high-speed HBTs and thus becomes the best candidate for long-wavelength TLs (LWTLs). However, successful transfer of the TL technology from GaAs-related materials to InP-related materials is nontrivial. Despite the TL demonstration based on InAlGaAs/InP operating near λ ∼1.55 μm at liquid-nitrogen temperature [10], [11], the real progress of the TL development has been hampered by a number of technological difficulties related to InP material system including relatively low material and modal gain [12], limited material selection, limited effectiveness of the p-type doping [13], and strong intervalence band absorption (IVBA) in base at long wavelengths [14], [15]. In particular, p-type doping in the base region poses unique challenges. Unlike a conventional p-i -n LD, where the light emission relies on simultaneous injection of both electrons and holes into the active region, TLs utilize the minority-carrier recombination in the QW with the majority-carrier concentration staying almost constant in the base. Using an NpN TL as an example (here, capital letter N denotes wider band gap n-type material). Fig. 1 depicts schematically the carrier distribution profile in the TL in forward active mode. In this graph, N0 , NQW and NB are unbounded carrier density, bounded/captured carrier density in the QW, and base doping level, respectively, which will be examined in detail later. By incorporating a QW in the base region, electrons injected from the emitter are trapped in the QW where the radiative recombination is significantly enhanced. While the electron quasi-Fermi level in the QW is controlled by the base-emitter voltage, the hole concentration is essentially pinned by the base doping level and its quasi-Fermi level is hardly changed during device operation. In order to achieve population inversion and subsequent stimulated emission, the base doping must be high enough to preset the hole quasi-Fermi level in the QW and boost the optical gain. On the other hand, a high p-type doping level inevitably leads to strong absorption of optical field mainly by IVBA and a high optical loss, which eventually prohibits the device from lasing. Therefore, optimization of the base doping

0018–9197/$26.00 © 2011 IEEE

HUANG et al.: DESIGN OF A LONG-WAVELENGTH InAlGaAs/InP TRANSISTOR LASER

Electron level

NQW N0 BE junction

QW

BC junction

hv

Hole level

NB

Fig. 1. Schematic representation of the carrier distribution profile in an N p N TL in forward active mode.

level could be of critical importance in realizing low-threshold LW-TLs. In this work, we present theoretical analysis and numerical calculation on the threshold condition of an InAlGaAs/InP LW-TL using a rather simple yet effective approach. Based on the steady-state condition that gain is balanced by loss, the base doping level and thickness are numerically investigated through evaluating the threshold carrier and current densities, which reveals only a narrow working range of supporting lasing. We show that the facet coating, structure engineering, and QW design affect the threshold and output characteristics, which provides insightful guidance in designing a highperformance LW-TL. II. O PTICAL G AIN AND L OSS IN A T RANSISTOR L ASER As illustrated in Fig. 1, when electrons injected from the base-emitter (BE) junction diffuse across the QW, a fraction of them are captured to the two-dimensional (2D) bound states in the QW, which forms a 2D carrier density of NQW . The average unbounded (3D) carrier density around the QW is N0 , which can be calculated by the classical continuity equation and boundary conditions. Below threshold, NQW is related to N0 through the expression of [16] d NQW N0 d NQW d NQW = − − dt τcap τr τesc

(1)

where τcap is the capture lifetime, τr is the recombination lifetime in the QW, and τesc is the carrier thermionic escape lifetime. Since τr is much larger than τesc [3], [16], under steady state condition, we have ∼ τesc N0 . NQW = (2) τcap In a TL, the profile of N0 is tilted, set by the boundary condition at the reverse-biased base-collector (BC) junction. As a result, if more than one QW is employed in the active region, the 2D bound carrier density in the second QW will be lower than that in the first one close to the BE junction given the same τ cap and τ esc , and may not contribute to the optical gain. Therefore, the tilted charge distribution in the

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TL necessitates the use of a single QW (SQW) to mitigate the effect of nonuniform carrier distribution, which has been normally adopted in the GaAs-based TLs [1], [2], [5]– [9]. In an HBT or a TL, the base current (IB ) resupplies holes and maintains the charge neutrality in the base region. As the base is usually highly doped, the hole concentrations insensitive to any hole injection and fixed at the doping level of NB [17]. The confined hole density in the undoped QW region can be obtained based on self-consistent solutions of both Poisson’s and Schrödinger’s equations. For simplicity, we assume that the hole concentration level in the QW is also NB considering its small volume relative to the base region. As we will see, this approximation gives a direct and critical link between the optical gain and loss while introducing minimal error. The dominant base current component of a TL is the radiative recombination current [1]. Now the active region of a TL can be regarded as a SQW sandwiched by two heavily-doped p-type layers with a variable electron density of NQW and a fixed hole density of NB in the QW. The p-type region also serves as the waveguide of the TL. Based on this simple scenario, we carry out calculations on the optical gain and loss in steady state close to the threshold condition. Assuming that in the SQW all sub-bands are parabolic and that optical transitions obey rigorous k-selection rules, the peak gain gp occurs at the band edge transition, i.e., when h¯ ω = E g + E el + E hl

(3)

where h¯ ω is the photon energy, E g is the bandgap energy, and E el and E hl are the first quantized energy levels of electrons and holes, respectively [18]. Neglecting transition broadening, gp can be expressed as gp = g0 [ fc (n) − f v ( p)]

(4)

where f c (n) and f v ( p) are the Fermi electron occupation factors at the conduction and valence band edges, respectively. fc (n) = f v ( p) =

1 1 + e(Eel −Fc )/ kB T 1 1 + e(Fv −Ehl )/ kB T

(5)

(6)

where Fc and Fv are the electron and hole quasi-Fermi levels, respectively. g0 is a material constant given by     mr μ 2 Rcv (7) g0 = ω ε h¯ 2 L z where ω is the angular frequency of light, μ is the permeability, ε is the dielectric constant, m r is the reduced effective mass given by (m e * m h *)/(m e * + m h *), m e * and m h * are the effective masses of electrons and holes, respectively, L z is 2  is the matrix element of the dipole the QW width, and Rcv moment [14], [19]. To get a more clear relationship of gp on the carrier density, (4) can be rewritten as [18]– [20]   gp = g0 1 − e−n/Nc − e− p/Nv (8)

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where Nc = Nv =

∞ m ∗e kB T (Eel −Een )/ kB T e π h¯ 2 L z n=1 ∞ m ∗h kB T (Ehl −Ehn )/ kB T e . π h¯ 2 L z n=1

and InP

InAlGaAs

InP

Lz



αi = WG + QW kp NB (11)   1 1 ln and αm = . (12) 2L R1 R2 α i is the intrinsic loss and αm accounts for mirror loss (optical output). In (11) and (12), WG and QW are the optical confinement factors of the waveguide and QW, respectively, kp is the IVBA coefficient, L is the cavity length, and R1 and R2 are the facet reflectivity. Then the threshold condition QW gp = αi + αm becomes

  QW g0 1 − e−NQW /Nc − e−NB /Nv

 

 1 1 ln . (13) = WG + QW kp NB + 2L R1 R2 The recombination lifetime τr in (1) is given by [21]

 1 (14) = A + B NB + C NB NB + NQW τr where A is the nonradiative recombination coefficient related to the local defects, B is the radiative recombination coefficient, and C is the Auger recombination coefficient. Neglecting A in high-quality materials [22], at threshold when NQW = Nth we obtain the threshold current density as

 q L z Nth Jth = = q L z Nth B NB + C NB NB + NQW (15) τr where q is the electron charge. It should be pointed out that Jth accounts for the net current that flows into the QW, which is exactly the difference between the emitter current (IE ) and collector current (IC ) if the recombination current in base bulk region is neglected. In this case, the base current is (16)

Ev = 0.3 eV

Cladding

Waveguide/ active

Cladding

n = 0.18 n = 0.24

(a) QW

1.0

1.0

0.5 Energy (eV)

(10)

where

where AE is the emitter size.

dWG

QW

As the highly p-doped region serves as the waveguide in a TL, IVBA is considered as the main intrinsic loss mechanism. Assuming that other losses such as free-carrier absorption in the cladding layers or photon scattering at the interfaces are negligible, the total optical loss (α T ) of a TL is

IB = IE − IC = AE Jth

Collector

Ec = 0.04 eV

E en and E hn are the nth quantized energies in conduction band and valence band, respectively. Equation (8) is the exact expression of gp if only one conduction and one valence subbands are occupied. Only the heavy-hole band and TE mode are considered in the derivation. With independent control over electron and hole densities, in a TL we have   (9) gp = g0 1 − e−NQW /Nc − e−NB /Nv .

αT = αi + αm

Base

Emitter

0.5 Fermi Level

0.0

0.0 Ec

−0.5

−0.5 −1.0

−1.0 Ev

−1.5 0

1400

1600 1800 Position (nm)

2000

−1.5

2200

(b) Fig. 2. (a) Schematic electronic band diagram and refractive index profile for an N -InP/ p-In(Al0.4 Ga0.6 )As/N -InP DH TL and (b) calculated equilibrium electronic band diagram.

Starting from these equations, we study the threshold condition in TLs. Two structures have been examined, i.e. double heterostructure (DH) TLs and separate-confinement heterostructure (SCH) TLs. III. D OUBLE -H ETEROSTRUCTURE T RANSISTOR L ASERS Fig. 2(a) shows the schematic band diagram and refractive index profile for an N-InP/ p-In(Al0.4 Ga0.6 )As/N-InP DH TL. In the structure, the InP emitter and collector serve as the cladding layers and In0.53 (Al0.4 Ga0.6 )0.47 As base serves as the waveguide layer. An 8 nm undoped compressively-strained In0.58Ga0.42 As QW is placed in the middle of the base. The substrate in the epitaxial structure design is semi-insulting InP. In practice, silicon (Si) can be used as the n-type dopant while carbon (C) can be used as the p-type dopant [11], [13]. The collector region includes (towards the growth direction) a Si-doped InP (InP:Si) subcollector (300 nm, n = 1 × 1019 cm−3 ), an In0.52 Al0.48 As:Si etch stop (20 nm, n = 1 × 1019 cm−3 ) and an undoped InP collector/cladding (300 nm) and the emitter region includes an InP:Si emitter spacer (75 nm, n =2×1017 cm−3 ), an InP:Si emitter/cladding (1500 nm, n = 5×1018 cm−3 ) and an InP:Si+ contact (50 nm, n = 1×1019 cm−3 ). A highly-doped thin InAlAs layer in the collector is to achieve a precise etching control, while minimizing the series resistance. The In0.53 (Al0.4 Ga0.6 )0.47 As waveguide thickness

HUANG et al.: DESIGN OF A LONG-WAVELENGTH InAlGaAs/InP TRANSISTOR LASER

100

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20

100

18

10

10

1

QW

NB (×1018 cm−3)

 (%)

16

1

40

60

−200

12 10 8

−80.0

6

WG 20

14

4

80 100 120 140 160 180 200 dWG (nm)

20 Fig. 3.

QW and WG as a function of dWG in the DH TL.

Gain or loss (cm−1)

1000

Gm at dWG = 15 nm αT at dWG = 15 nm

Fig. 5.

40

60

80 100 dWG (nm)

120

140

160

2-D contour plot of for the DH TL with as-cleaved mirrors.

1000

Gm at dWG = 40 nm αT at dWG = 40 nm

100

Gm at dWG = 100 nm αT at dWG = 100 nm

10

100

10

If G m > αT , then there will be a solution for NQW :   QW g0 NQW = Nth = Nc ln

(19)

where 1 0.1

Fig. 4.

−18.0

0

2

1 10 1 NB (×1018 cm−3)

G m and αT as a function of NB at dWG = 15, 40, and 100 nm.

dWG and base doping level NB are variables to be determined. The whole structure is symmetric. Fig. 2(b) illustrates the calculated band diagram for a DH TL with dWG = 50 nm and NB = 1×1019 cm−3 . Experimentally we have demonstrated a TL based on this structure operating at 77 K in CW mode [11]. The optical confinement factors are a single function of dWG . Fig. 3 is a plot of QW and WG against dWG for the DH TL [23]. Note WG takes into account the confinement in the whole waveguide region. It is clear that QW increases with dWG and then saturates at 1.6% while WG is much larger than QW . From (13), one can tell that the solution of NQW is strongly dependent on the choice of NB and dWG . In certain circumstances, there is no solution for NQW , which means that the total loss is larger than the maximum gain even when NQW approaches infinity. Therefore, we define maximum available gain G m as   (17) G m = QW g0 1 − e−NB /Nv to account for the modal gain when the pumping level is very high and the term, exp(-NQW /Nc ), is negligible. The total loss is again  

 1 1 ln . (18) αT = WG + QW kp NB + 2L R1 R2

≡ G m − αT .

(20)

If is negative, there will be no solution for Nth . To reduce Nth , it is necessary to maximize by optimizing NB and dWG . For a specific example, we consider a TL with a cavity length L = 800 μm and as-cleaved mirrors of R1 = R2 ∼0.3, which gives a mirror loss of 15 cm−1 . kp is chosen to be 4×10−17 cm−2 [14], [15] and g0 is 4847 cm−1 for an 8 nm SQW [19]. m e * and m h * are 0.051 m 0 and 0.217 m 0 , respectively [24], where m 0 is the electron rest mass. Nc and Nv are computed to be 7×1017 cm−3 and 3×1018 cm−3 , respectively using a finite-barrier model assuming E c = 0.72 E g. The emission wavelength is λ ∼1.56 μm from the band-edge transition. By plugging in QW and WG from Fig. 3 for a certain dWG , we are positioned to evaluate G m and α T at different NB . Fig. 4 shows G m and α T as a function of NB at dWG = 15, 40, and 100 nm, respectively. NB spans from 1×1017 to 5×1019 cm−3 . At low NB , α T approaches α m while at high NB, G m saturates at QW g0 . It is evident that α T is larger than G m in most cases. At dWG = 15 nm, G m is too low to overcome α T resulting from a small QW . On the other hand, at dWG = 100 nm, α T is too high for G m due to a large WG . Only at dWG = 40 nm, G m and α T have intersections in a certain range of NB , which indicates that is positive and Nth exists only in this narrow range. To get a full picture of the “living zone” for the DH TL, a 2-D contour plot of on dWG and NB is generated, as displayed in Fig. 5. dWG is varied from 10 to 160 nm and NB is from 1×1017 to 2×1019 cm−3 . Clearly only a narrow zone with positive will support lasing, with the maximum of 0.6 cm−1 obtained at dWG = 35 nm and NB = 4×1018 cm−3 . Thus, to achieve a long wavelength DH TL at room temperature, the base doping and thickness should be stringently and precisely controlled. As implied from

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20

Base

Emitter

16 NB (×1018 cm−3)

Collector

Ec = 0.04 eV

18 InP

14

InAlGaAs

QW

−200

12 10 8 6

Ev = 0.25 eV

−80.0

12.0

Cladding

4 7.00

2

SCH

−18.0

0

Ev = 0.3 eV

WG/ active

n = 0.18

SCH

Cladding

n = 0.03

n = 0.21

20

40

60

80 100 dWG (nm)

120

140

160

(a) QW

1.0

Fig. 6. 2-D contour plot of for the DH TL with coated mirrors having reflectivities of 0.95 and 0.7.

1.0

Fig. 4, one way to ease the lasing condition and expand the selectable range is to lower the mirror loss α m . For example, if coated mirrors are employed for higher mirror reflectivity with R1 = 0.95 and R2 = 0.7, the mirror loss will be reduced to 2.5 cm−1 . Fig. 6 shows the 2-D contour plot of for a DH TL in this condition. The region with positive is significantly extended and the maximum is 13.1 cm−1 , much larger than in the uncoated as-cleaved mirror case. Consequently, the threshold current density will be remarkably reduced. However, the highly-reflective mirrors also bring about reduced optical output. The threshold current density and optical output of these devices will be discussed later. IV. S EPARATE -C ONFINEMENT H ETEROSTRUCTURE T RANSISTOR L ASERS In the DH TL structure, the confinement factors in the QW and waveguide are dependent on the waveguide thickness as revealed in Fig. 3. Whereas increasing dWG leads to enhanced QW and G m , it also results in a large WG and thus a large α T . This apparent trade-off can be eliminated by moving part of the waveguide layers into the emitter and collector regions to form a SCH TL. In this case, the SCH layer thickness can be chosen to maximize QW , while not affecting WG . Shown in Fig. 7(a) is the schematic band diagram and refractive index profile for a SCH TL. In the structure, In0.52 (Al0.47 Ga0.53 )0.48 As is chosen as the SCH material. When the Al mole fraction in In0.53 (Alx Ga1−x )0.47 As alloys (nearly lattice-matched to InP) increases, the electronic band alignment between In0.53 (Alx Ga1−x )0.47 As and InP changes from the straddling lineup (type-I band alignment) for InGaAs to the staggered lineup (type-II band alignment) for InAlAs, and a nearly continuous conduction band heterostructure is formed at the Al mole fraction of x Al ∼0.47 [25]. As a result, no effective barrier for electron transport is expected if part of the InP cladding is replaced by In0.53 (Al0.47 Ga0.53 )0.47 As alloy. The SCH layer is either n-type doped in emitter or undoped in collector and the optical loss in these layers is neglected since the free-carrier absorption in n-type materials

Energy (eV)

0.5

0.5 Fermi Level

0.0

0.0 EC

−0.5 −1.0

−2.0

−1.0

Hole barrier EV

−1.5 0

1400

1800 1600 Position (nm)

−0.5

−1.5

−2.0 2000

(b) Fig. 7. (a) Schematic electronic band diagram and refractive index profile for a SCH TL and (b) calculated equilibrium electronic band diagram.

are significantly smaller than IVBA in p-type materials in this III–V material system [26]. Thus WG still refers to the optical confinement in the highly-doped base/waveguide layers. The structure employs a short base/active region and an extended cladding, similar to a SCH LD. The continuous conduction band in the emitter facilitates electron transport while holes are blocked by a thin (20 nm) InP layer. With both In0.53 (Al0.47 Ga0.53 )0.47 As and InP being the emitter, the structure exemplifies a composite emitter concept [27]. The thin InP layer severs as an emitter, etch stop, and base passivation layer. The base/active region is similar to that in the DH TL with NB and dWG to be determined. Fig. 7(b) illustrates the calculated electronic band diagram for a SCH TL with dWG = 50 nm and NB = 1×1019 cm−3 . The whole structure is nearly symmetric. Fig. 8 shows the dependence of QW and WG on dWG in the SCH TL. The SCH layer thickness is chosen in the way that a maximum QW is obtained. Not surprisingly QW remains almost constant at maximum value of 1.6%. The 2-D contour of for the SCH TL with the same cavity length (L = 800 μm) and as-cleaved mirrors is generated, with the results displayed in Fig. 9. Area with positive is conspicuous in this map. increases significantly as dWG decreases, which is a result from reduced WG . The SCH TL promises improved threshold characteristics than the DH TL.

HUANG et al.: DESIGN OF A LONG-WAVELENGTH InAlGaAs/InP TRANSISTOR LASER

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10

 (%)

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1

QW

1

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60

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4

4

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2500

QW and WG as a function of dWG in the SCH TL.

Jth (A/cm−3)

20 18

NB (×1018 cm−3)

16 14

2500 2000

1500

1500

1000

1000

500

500

0

10 8 12.0 0

7.00

2 20

0

2

40

60

Fig. 10. TLs.

−18.0

80 100 dWG (nm)

120

140

Dependence of (a) Nth and (b) Jth on NB for the DH and SCH

160

1.0

1.0 DH TL as cleaved DH TL coated SCH TL as cleaved

0.8

2-D contour plot of for the SCH TL with as-cleaved mirrors.

With being known, Nth can be calculated using (19), and subsequently Jth can be obtained using (15). B and C are assumed to be 1×10−10 cm3 /s and 5×10−29 cm6 /s, respectively [22], [28]. To compare the threshold characteristics of the DH TL and SCH TL, we calculate Nth and Jth as a function of NB at a fixed dWG = 40 nm. Fig. 10 summarizes the results for the DH TLs with as-cleaved and coated mirrors and the SCH TL with as-cleaved mirrors, with Nth in Fig. 10(a) and Jth in Fig. 10(b). The DH TL with as-cleaved mirrors shows the highest Nth and narrowest NB range. The lowest Nth attainable with the as-cleaved DH TL is 3.0×108 cm−3 . By using coated mirrors or SCH structure, the selectable NB range is significantly expanded and lowest Nth attainable is around 1.0×108 cm−3 . Jth exhibits a similar trend for the DH and SCH TLs. The lowest Jth attainable with the DH TLs with as-cleaved and coated mirrors and the SCH TL with ascleaved mirrors are 642.8, 31.4, and 111.6 A/cm2 , respectively. In all the devices Jth increases significantly with NB owing to a reduced carrier lifetime. Reducing the mirror loss by using either facet coating or longer cavity helps to reduce the threshold current density, but it also limits the optical output power. For a given current injection level above threshold, the optical output of a LD

0

4 6 8 NB (×1018 cm−3) (b)

−80.0

22.0

4

Fig. 9.

10

−200

12

6

4 6 8 NB (×1018 cm−3) (a)

DH TL as cleaved DH TL coated SCH TL as cleaved

2000

αm/(αi + αm )

Fig. 8.

2

80 100 120 140 160 180 200 dWG (nm)

6

5

WG 20

DH TL as cleaved DH TL coated SCH TL as cleaved

6

Nth (×1018 cm−3)

100

647

0.8

0.6

0.6

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0.4

0.2

0.2

0.0

0

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4

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8

10

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14

0.0 16

NB (×1018 cm−3) Fig. 11.

Dependence of αm /(αi + αm ) on NB for the DH and SCH TLs.

or a TL is proportional to α m /(α i + α m ), which is exactly equal to the ratio of differential quantum efficiency to internal quantum efficiency. Fig. 11 shows the dependence of α m /(α i + α m ) on NB for the DH and SCH TLs. dWG is again kept at 40 nm. The value of α m /(α i + α m ) drops rapidly with NB , with the coated DH TL being minimal. Considering both threshold and output characteristics, the SCH TL design represents an optimal balance between the threshold current density and optical output power. The SCH TL could also enhance the transient characteristics in the optical modulation by reducing base thickness and thus diffusion-related time delay.

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TABLE I S UMMARY OF THE TL AND LD P ERFORMANCES WITH D IFFERENT QW D ESIGNS

Structure QW material

SCH LD 8 nm In0.58 Ga0.42 As SQW

SCH TL 8 nm In0.58 Ga0.42 As SQW

SCH TL 8 nm In0.68 Ga0.32 As SQW

SCH TL 12 nm In0.58 Ga0.42 As SQW

SCH TL 12 nm In0.68 Ga0.32 As SQW

NB [cm−3 ]

—

1.5 × 1018

1.3 × 1018

1.3 × 1018

0.9 × 1018

α i [cm−1 ]

5

9.6

8.3

8.8

6.1

α m /(α i + α m )

0.75

0.61

0.64

0.63

0.71

[cm−3 ]

0.93 × 1018

0.65 × 1018

0.64 × 1018

0.43 × 1018

0.49 × 1018

Nth [cm−3 ]

1.51 × 1018

2.08 × 1018

1.75 × 1018

1.28 × 1018

1.19 × 1018

Jth [A cm−2 ]

73.3

111.6

73.5

72.9

42.3

Ntr

V. Q UANTUM W ELL D ESIGN For a conventional LD with lossy waveguide, one way to boost the optical gain is to use multiple QWs (MQWs). However, the non-uniform distribution of electrons in the base in the TLs requires us to use a SQW. Another way to reduce the threshold current density is to incorporate a certain amount of strain in the QW active region, which modifies the hole effective mass and thus lowers the value of Nv in (8) [18], [24]. We calculate the Nth and Jth as a function of NB for SCH TLs at a fixed dWG = 40 nm with an 8-nm compressively-strained Inx Ga1−x As QW. The indium (In) mole fraction, x In varies from 0.58, 0.60, 0.63, to 0.68, corresponding to a compressive strain of 0.32%, 0.47%, 0.68%, and 1%, respectively. As expected, both Nth and Jth decrease steadily with increasing In mole fraction. The lowest Jth of 73.5 A/cm2 is obtained for the TL with an In0.68Ga0.32 As SQW. When it comes to the epitaxial material growth of highly strained QW, however, generation of misfit dislocation needs to be prevented, which may pose a limitation to use of a highly strained rather thick QW. QW thickness, L z , is also an important parameter to deal with. The dependence of Nth and Jth on L z in QW LDs is rather complicated [29]. On the one hand, although an enhanced QW resulting from increasing L z is completely offset by the 1/L z factor in g0 , leading to little variation of QW · g0 product, increasing L z does increase the modal gain by reducing Nc and Nv and thus filling band more effectively. On the other hand, Jth may rise as it is proportional to L z from (15). Fig. 12 shows the calculated Nth and Jth as a function of NB for the same SCH TL structure with L z of 8, 12, and 16 nm consisting of an In0.58 Ga0.42 As SQW. While Nth is generally shown to decrease with increasing L z , Jth is minimal at L z = 12 nm. The lowest Jth attainable is 72.9 A/cm2 for the TL with a 12 nm SQW. It should be pointed out that the calculation does not consider the variation of emission wavelength caused by the change of strain or QW thickness. With improved performance achieved through the active region design, comparison is made between the TLs and a conventional LD. We consider a p-i -n SCH SQW LD with a similar structure to Fig. 7(a) except the doping profile, i.e., the waveguide is undoped and top cladding is p-doped. Again,

dWG is fixed at 40 nm and an 8 nm strained In0.58 Ga0.42 As QW is employed. The intrinsic loss in the LD is assumed to be 5 cm−1 [30]. Table 1 summarizes the performances of the LD and SCH TLs with different QW designs. As-cleaved mirrors are considered for all the devices. NB is chosen such that the minimal Jth is achieved in each TL. The transparent carrier density Ntr is solved by setting gp to zero in (9). As compared to the LD, Ntr is reduced in SCH TLs due to the base doping. Jth is higher in the TL with the same SQW because of higher α i . However, by having more strain or increasing the QW thickness, Jth can be made as low as ∼73 A/cm2 , which is almost the same as that in the LD. If a 12 nm In0.68 Ga0.32 As SQW is employed, Jth is as low as 42.3 A/cm2 and α m /((α i + α m )) factor is also close to that in the LD. These results suggest that the LW-TLs be able to achieve similar DC performance compared to the LDs by means of structure engineering, proper selection of base doping, and improved design of the QW. VI. D ISCUSSION In this paper, we have taken a simplified approach to the gain-loss relationship to avoid time-consuming calculations as well as to provide a direct analytical expression about the effects of structural parameters on the lasing condition. In the gain spectrum, the transition broadening due to the interband relaxation process is neglected, which both lowers the peak gain and shifts it to higher energy [19]. The actual hole concentration in the QW is verified to be lower than NB (within an error less than 20%), which also leads to an overestimate of the optical gain especially in TLs with a thin base or a thick QW. In addition, the TL structure needs to be examined and validated from the perspective of an HBT, where metal contact will be made on the base. Consequently, a thin highly-doped base contact layer is required in the structure and the product of base doping and base thickness has to be large enough to ensure a low sheet resistance. Nevertheless, this is the first theoretical attempt to tackle the LW-TLs that combine both LD and HBT device physics. With the improvement in the performances of LW-TLs, more complicated and accurate models will be necessary to account for the detailed structural parameters of these novel devices.

HUANG et al.: DESIGN OF A LONG-WAVELENGTH InAlGaAs/InP TRANSISTOR LASER

10

10 Lz = 8 nm Lz = 12 nm

Nth (×1018 cm−3)

Lz = 16 nm

and transistor lasers with F. Dixon, G. Walter, M. Feng, and N. Holonyak, Junior of the University of Illinois at UrbanaChampaign, Urbana. R EFERENCES

1

1

0

1

2

3

4 5 6 NB (×1018 cm−3)

7

8

9

(a) 400

400 Lz = 8 nm

300

300

Lz = 12 nm Lz = 16 nm

Jth (A/cm−3)

649

200

200

100

100

1

2 3 NB (×1018 cm−3) (a)

4

Fig. 12. Dependence of (a) Nth and (b) Jth on NB for SCH TLs with different L z of the SQW.

VII. C ONCLUSION In summary, this paper presents theoretical investigation and numerical evaluation of InP/InAlGaAs TL structures in terms of the threshold and output characteristics from the perspective of a pure light emitter. The NpN TL can be regarded as a SQW inserted into a highly-doped p-type layer with an electron density controlled by emitter injection and a hole density fixed at the base doping level. The optical gain is calculated using a simplified k-selection model and IVBA is assumed to the main intrinsic optical loss. It is revealed that room-temperature lasing of an N-InP/ p-In(Al0.4 Ga0.6 )As/NInP DH TL can be achieved only if the waveguide thickness and base doping level of the TL are within a specific narrow range centered around dWG = 35 nm and NB = 4 × 1018 cm−3 . The selectable working range is significantly expanded by using facet coatings or a SCH design, where part of the waveguide is moved into the emitter and collector regions. The SCH TL is shown to have an optimal balance between the threshold current density and optical output characteristics. In addition, the performance of SCH TLs can be improved by employing more compressively-strained or a thicker QW as the active region, and the threshold current density can be lowered to sub-100 A/cm2 level similar to that in a SCH LD. ACKNOWLEDGMENT The authors would like to acknowledge useful technical discussions and collaborations on light-emitting transistors

[1] M. Feng, N. Holonyak, Jr., G. Walter, and R. Chan, “Room temperature continuous wave operation of a heterojunction bipolar transistor laser,” Appl. Phys. Lett., vol. 87, no. 13, pp. 131103-1–131103-3, Sep. 2005. [2] M. Feng, N. Holonyak, Jr., A. James, K. Cimino, G. Walter, and R. Chan, “Carrier lifetime and modulation bandwidth of a quantum well AlGaAs/InGaP/GaAs/InGaAs transistor laser,” Appl. Phys. Lett., vol. 89, no. 11, pp. 113504-1–113504-3, Sep. 2006. [3] B. Faraji, D. L. Pulfrey, and L. Chrostowski, “Small-signal modeling of the transistor laser including the quantum capture and escape lifetimes,” Appl. Phys. Lett., vol. 93, no. 10, pp. 103509-1–103509-3, Sep. 2008. [4] L. Zhang and J.-P. Leburton, “Modeling of the transient characteristics of heterojunction bipolar transistor lasers,” IEEE J. Quantum Electron., vol. 45, no. 4, pp. 359–366, Apr. 2009. [5] M. Feng, H. W. Then, N. Holonyak, Jr., G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett., vol. 95, no. 3, pp. 033509-1–033509-3, Jul. 2009. [6] R. Chan, M. Feng, N. Holonyak, Jr., A. James, and G. Walter, “Collector current map of gain and stimulated recombination on the base quantum well transitions of a transistor laser,” Appl. Phys. Lett., vol. 88, no. 14, pp. 143508-1–143508-3, Apr. 2006. [7] G. Walter, N. Holonyak, Jr., M. Feng, and R. Chan, “Laser operation of a heterojunction bipolar light-emitting transistor,” Appl. Phys. Lett., vol. 85, no. 20, pp. 4768–4770, Nov. 2004. [8] R. Chan, M. Feng, N. Holonyak, Jr., and G. Walter, “Microwave operation and modulation of a transistor laser,” Appl. Phys. Lett., vol. 86, no. 13, pp. 131114-1–131114-3, Mar. 2005. [9] M. Feng, N. Holonyak, Jr., H. W. Then, C. H. Wu, and G. Walter, “Tunnel junction transistor laser,” Appl. Phys. Lett., vol. 94, no. 4, pp. 041118-1–041118-3, Jan. 2009. [10] F. Dixon, M. Feng, N. Holonyak, Jr., Y. Huang, X. B. Zhang, J. H. Ryou, and R. D. Dupuis, “Transistor laser with emission wavelength at 1544 nm,” Appl. Phys. Lett., vol. 93, no. 2, pp. 021111-1–021111-3, Jul. 2008. [11] Y. Huang, J. H. Ryou, R. D. Dupuis, F. Dixon, N. Holonyak, Jr., and M. Feng, “InP/InAlGaAs light-emitting transistors and transistor lasers with a carbon-doped base layer,” J. Appl. Phys., to be published. [12] P. Bhattacharya, Semiconductor Optoelectronic Devices, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1997. [13] Y. Huang, X.-B. Zhang, J.-H. Ryou, R. D. Dupuis, F. Dixon, N. Holonyak, Jr., and M. Feng, “InAlGaAs/InP light emitting transistors operating near 1.55 μm,” J. Appl. Phys., vol. 103, no. 11, pp. 1145051–114505-6, Jun. 2008. [14] M. Asada, A. Kameyama, and Y. Suematsu, “Gain and intervalence band absorption in quantum-well lasers,” IEEE J. Quantum Electron., vol. 20, no. 7, pp. 745–753, Jul. 1984. [15] J. Taylor and V. Tolstikhin, “Intervalence band absorption in InP and related materials for optoelectronic device modeling,” J. Appl. Phys., vol. 87, no. 3, pp. 1054–1059, Feb. 2000. [16] N. Tessler and G. Eisenstein, “On carrier injection and gain dynamics in quantum well lasers,” IEEE J. Quantum Electron., vol. 29, no. 6, pp. 1586–1595, Jun. 1993. [17] M. Friedrich and H.-M. Rein, “Analytical current-voltage relations for compact SiGe HBT models. I. The ‘idealized’ HBT,” IEEE Trans. Electron Devices, vol. 46, no. 7, pp. 1384–1393, Jul. 1999. [18] S. L. Chuang, Physics of Optoelectronic Devices. New York: Wiley, 1995. [19] T. Makino, “Analytical formulas for the optical gain of quantum wells,” IEEE J. Quantum Electron., vol. 32, no. 3, pp. 493–501, Mar. 1996. [20] K. J. Vahala and C. E. Zah, “Effect of doping on the optical gain and the spontaneous noise enhancement factor in quantum well amplifiers and lasers studied by simple analytical expressions,” Appl. Phys. Lett., vol. 52, no. 23, pp. 1945–1947, Jun. 1988. [21] W. Liu, Fundamentals of III–V Devices: HBTs, MESFETs, and HEMTs. New York: Wiley, 1999. [22] R. Olshansky, C. Su, J. Manning, and W. Powazinik, “Measurement of radiative and nonradiative recombination rates in InGaAsP and AlGaAs light sources,” IEEE J. Quantum Electron., vol. 20, no. 8, pp. 838–854, Aug. 1984.

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[23] M. J. Mondry, D. I. Babic, J. E. Bowers, and L. A. Coldren, “Refractive indexes of (Al, Ga, In)As epilayers on InP for optoelectronic applications,” IEEE Photon. Technol. Lett., vol. 4, no. 6, pp. 627–630, Jun. 1992. [24] T. Ishikawa and J. E. Bowers, “Band lineup and in-plane effective mass of InGaAsP or InGaAlAs on InP strained-layer quantum well,” IEEE J. Quantum Electron., vol. 30, no. 2, pp. 562–570, Feb. 1994. [25] W.-C. Liu, H.-J. Pan, S.-Y. Cheng, W.-C. Wang, J.-Y. Chen, S.-C. Feng, and K.-H. Yu, “Applications of an In0.53 Ga0.25 Al0.22 As/InP continuousconduction-band structure for ultralow current operation transistors,” Appl. Phys. Lett., vol. 75, no. 4, pp. 572–574, Jul. 1999. [26] R. J. Deri and E. Kapon, “Low-loss III–V semiconductor optical waveguides,” IEEE J. Quantum Electron., vol. 27, no. 3, pp. 626–640, Mar. 1991. [27] R. Driad, W. R. McKinnon, S. P. McAlister, T. Garanzotis, and A. J. SpringThorpe, “Effect of emitter design on the dc characteristics of InP-based double-heterojunction bipolar transistors,” Semicond. Sci. Technol., vol. 16, no. 3, pp. 171–175, Mar. 2001. [28] J. Piprek, J. K. White, and A. J. SpringThorpe, “What limits the maximum output power of long-wavelength AlGaInAs/InP laser diodes?” IEEE J. Quantum Electron., vol. 38, no. 9, pp. 1253–1259, Sep. 2002. [29] B. Saint-Cricq, F. Lozes-Dupuy, and G. Vassilieff, “Well width dependence of gain and threshold current in GaAlAs single quantum well lasers,” IEEE J. Quantum Electron., vol. 22, no. 5, pp. 625–630, May 1986. [30] A. Kasukawa, R. Bhat, C. E. Zah, M. A. Koza, and T. P. Lee, “Very low threshold current density 1.5 μm GaInAs/AlGaInAs graded-index separate-confinement-heterostructure strained quantum well laser diodes grown by organometallic chemical vapor deposition,” Appl. Phys. Lett., vol. 59, pp. 2486–2488, Nov. 1991.

Yong Huang was born in Chongqing, China. He received the B.S. degree in materials science and engineering from Tsinghua University, Beijing, China, in 2002, and the M.S. degree in electronics and optoelectronics from the Institute of Semiconductors, Chinese Academy of Sciences, Beijing, in 2005. He is currently pursuing the Ph.D. degree at the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. His current research interests include epitaxial structure design, metalorganic chemical vapor deposition growth, and characterization of III–V compound semiconductor materials and devices.

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 47, NO. 5, MAY 2011

Jae-Hyun Ryou (M’01–SM’07) was born in Cheongjoo, Korea. He received the B.S. and M.S. degrees in metallurgical engineering from Yonsei University, Seoul, Korea, in 1993 and 1995, respectively, and the Ph.D. degree in materials science and engineering from the University of Texas, Austin, in 2001, in the area of solid-state materials. He worked at the Honeywell Technology Center, Minneapolis, MN, and the Honeywell VerticalCavity Surface Emitting Lasers Optical Products, Richardson, TX, as a Research Scientist from 2001 to 2003. He is currently a Senior Research Engineer with the Center for Compound Semiconductors, Georgia Institute of Technology, Atlanta. He has authored or co-authored three book chapters and more than 100 technical journal papers, and has presented more than 160 papers in various conferences. He holds eight U.S. patents. His current research interests include photonic and electronic materials, devices, and nanostructures based on III–V compound semiconductors. Dr. Ryou is a recipient of the Korean Government Overseas Scholarship in 1995. He is a member of the Optical Society of America, the Minerals, Metals and Materials Society, and the Materials Research Society.

Russell D. Dupuis (SM’84–F’87) received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Illinois at UrbanaChampaign, Urbana. He worked at Texas Instruments Incorporated, Dallas, from 1973 to 1975. In 1975, he joined Rockwell International, Seal Beach, CA, where he was the first to demonstrate that metalorganic chemical vapor deposition (MOCVD) growth could be used for the growth of high-quality semiconductor thin films and devices. He joined AT&T Bell Laboratories, Murray Hill, NJ, in 1979, where he extended his work to the growth of InP-InGaAsP by MOCVD. In 1989, he became a Chair Professor in electrical and computer engineering at the University of Texas, Austin. In August 2003, he accepted a chaired professorship in electrical and computer engineering and materials science and engineering at the Georgia Institute of Technology, Atlanta. Dr. Dupuis has received many awards and distinctions throughout his career, including the National Medal of Technology in 2002, the John Bardeen Award of the Minerals, Metals and Materials Society in 2003, and the IEEE Edison Medal in 2007. He currently holds the Steve W. Chaddick Endowed Chair in Electro-Optics and is a Georgia Research Alliance Eminent Scholar. He is a member of the National Academy of Engineering, the American Physical Society, and the Optical Society of America.