Different than the Bardeen and Brattain transistor (1947) with the current gain depending on the ratio of the base carrier spontaneous recombination lifetime to the emitter-collector transit time, the Feng and Holonyak transistor laser current gain depends upon the base electron-hole (e-h) stimulated recombination, the base dielectric relaxation transport, and the collector stimulated tunneling. For the n-p-n transistor laser tunneling operation, the electron–hole pairs are generated at the collector junction under the influence of intra-cavity photon-assisted tunneling, with electrons drifting to the collector and holes drifting to the base. The excess charge in the base lowers the emitter junction energy barrier, allowing emitter electron injection into the base and satisfying charge neutrality via base dielectric relaxation transport (∼femtoseconds). The excess electrons near the collector junction undergo stimulated recombination at the base quantum-well or transport to the collector, thus supporting tunneling current amplification and optical modulation of the transistor laser.

The transistor (point-contact) invented by Bardeen and Brattain in 19471 revealed the operating principles of the emitter current injection, the base electron–hole recombination, and the collector current output. The three-terminal transistor replaced the fragile vacuum tube for fast reliable electrical signal switching and amplification, and has made possible a revolution in modern electronics, communications, and computer technologies. The integration of transistors into microchips (Noyce and Kilby2–4) and later of low power CMOS into VLSI created a revolution in microelectronics and the information industry. To improve the emitter injection efficiency and the overall performance, a wide bandgap emitter transistor has been proposed, yielding a heterojunction bipolar transistor (HBT) (Shockley and Kroemer5,6) that has been widely used in high speed mixed signal ICs and wireless communications. Besides its use in microelectronics, the electron–hole recombination has now become the basis of a variety of powerful semiconductor light sources. It has established a basis for III–V compound semiconductor lasers, light-emitting diodes (LEDs), and now a transistor laser. When Hall realized a GaAs diode laser and Holonyak realized a visible–spectrum (red) GaAsP alloy laser (1962),7,8 it had become evident at once that the III–V alloy would prevail in the form of diode lasers, LEDs, transistor lasers, and much more that lies ahead. Then quantum-wells (QWs) were inserted into the diode laser and LED (1977), thus improving the light conversion efficiency9,10 and aiding the revolution of LED lighting, TV, displays, and the birth of Big Data with QW laser optical communication infrastructure.

Today, direct modulated laser (DML) optical links prove to be the most energy-efficient and error-free data transmission. The uncooled oxide-VCSEL has demonstrated the record modulation bandwidth of 29 GHz and error-free data transmission at 57 Gb/s.11,12 However, the modulation bandwidth of a diode laser is thermally limited by the spontaneous recombination lifetime, the photon lifetime, and the cavity photon field. Clearly, the fast radiative recombination and the efficient junction heat transfer in the semiconductor laser are important for intensive study to enhance the direct modulation bandwidth and the high speed energy-efficient data transfer.

The two-port microwave HBT inevitably takes the form of a compact, high current density device.13,14 Feng and Holonyak (2004) realized the radiative recombination at the base of a III–V HBT could be modulated to be a three-port device.15 The radiative recombination lifetimes could be reduced by heavy base doping and the insertion of quantum-wells (QWs) in the base near the collector.16 The incorporation of an optical cavity (high Q) in QW-HBT aids the invention of the transistor laser demonstrated in 2004.17,18 The highly efficient base current modulation via fast stimulated recombination in the transistor laser provides the path to 10× bandwidth enhancement of the transistor and transistor laser. Furthermore, the transistor laser opens the frontier of direct voltage modulation laser via intra-cavity photon-assisted tunneling (ICPAT) for much more bandwidth enhancement.19,20 The transistor laser operates as a three-port device with both electrical (I–V) and optical (L-V) outputs as functions of the base current and the collector voltage inputs.21 The electrical and optical outputs are modulated by the base QW stimulated recombination for optical generation and by the collector tunneling for stimulated optical absorption.22,23

This work establishes the principles of operation for tunneling modulation of a QW transistor laser with current amplification and optical output via intra-cavity photon-assisted tunneling (ICPAT). The absorbed photon energy assists tunneling electron–hole pair generation at the collector junction creating excess electron drift to the collector as well as excess hole drift to the base. The excess hole charges at the base lower the energy barrier of the emitter junction, permitting minority carrier electron injection from the emitter and moving through the base via dielectric relaxation, resulting in the tunneling current amplification.

For an n-p-n III–V HBT, the base carrier distribution is illustrated in Fig. 1. The excess electron distribution (Δn1) in the base can be calculated by the current continuity equation with boundary conditions at the emitter-base (E-B) and the base-collector (B-C) junctions. The large valence band offset at the E-B junction in an HBT can effectively suppress the base hole current injection (IEp) into the emitter, thus improving considerably the emitter injection efficiency.5,6 The base current Ir1 is estimated from the ratio of the base stored charge to the recombination lifetime τB. The base transport current It1 is determined by the slope of the carrier distribution at the B–C interface and is approximately equal to the base stored charge divided by the base transit time τtB if the base recombination current is relatively small compared to the collector current. The Kirchhoff current law is satisfied by IEn=Ir1+It1 where IEnIE, It1IC, and Ir1IB, which leads to the transistor current constraint IE=IB+IC. The transistor current gain is defined as β=IC/IBIt1/Ir1. The injected minority carriers (electrons) will attract an equal number of holes via dielectric relaxation transport from the base terminal to satisfy charge neutrality and similarly the corresponding excess hole distribution (Δp1) in the valence band. Since the base of a microwave III–V HBT is heavily doped to ∼1019 cm−3, the radiative recombination lifetime is calculated from the measured current gain to be ∼134 ps.23 

FIG. 1.

Excess carrier distribution in the base of an n-p-n heterojunction bipolar transistor (HBT). For base-emitter forward bias, the emitter injects current IEn into the base as excess minority carriers (Δn1) and the excess electron charge lowering base contact potential, providing majority carrier (Δp1) injection into the base satisfying charge neutrality via dielectric relaxation. In steady-state operation, IEn is the sum of the base recombination current Ir1 and the base transport current It1. The HBT collector current IC=It1.

FIG. 1.

Excess carrier distribution in the base of an n-p-n heterojunction bipolar transistor (HBT). For base-emitter forward bias, the emitter injects current IEn into the base as excess minority carriers (Δn1) and the excess electron charge lowering base contact potential, providing majority carrier (Δp1) injection into the base satisfying charge neutrality via dielectric relaxation. In steady-state operation, IEn is the sum of the base recombination current Ir1 and the base transport current It1. The HBT collector current IC=It1.

Close modal

The excess minority carrier distribution in the base of a QW light-emitting transistor (LET) is shown in Fig. 2. The quantum-well in the base can be considered as an “optical collector” with efficient photon generation for an optical output. Thus, the QW LET becomes a three-port device with base current input (IB), collector current output (IC), and optical output (L0). Although the base recombination energy of the transistor was previously ignored as waste (heat), Feng and Holonyak realized for a direct-gap semiconductor, this could be a useful optical signal output.15 When quantum-wells are incorporated in the base of a III–V HBT, the radiative recombination lifetime of the device is reduced to ∼35 ps, which sets the foundation for a higher modulation bandwidth of the QW LET.23 The enhanced optical modulation bandwidth of a QW LET has been measured as f3dB∼ 7 GHz, confirming the fast radiative recombination lifetime of ∼23 ps.24 

FIG. 2.

Excess carrier distribution in the base of a quantum-well light-emitting transistor (QW LET). The incorporation of the base quantum-well in the HBT reduces the carrier recombination lifetime. QW recombination can be treated as an optical collector for photon generation and modulation.16 

FIG. 2.

Excess carrier distribution in the base of a quantum-well light-emitting transistor (QW LET). The incorporation of the base quantum-well in the HBT reduces the carrier recombination lifetime. QW recombination can be treated as an optical collector for photon generation and modulation.16 

Close modal

The incorporation of an optical cavity enclosing a QW-HBT enhances the photon field for stimulated recombination at the QW, yielding transistor laser coherent light output.17–27 For a diode laser, the carrier pile-up is due to the slow recombination lifetime (∼0.5 ns), a consequence of a laser resonance peak in the frequency response.28 In contrast, the transistor laser with a fast recombination lifetime (∼30 ps) reduces carrier “choking” and the laser resonance peak. The fast radiative recombination lifetime allows transistor lasers to reach critical damping; thus, the transistor laser has demonstrated a nearly resonance-free modulation frequency response up to 20 GHz.25,26

The electron–photon interaction inside the cavity requires modifications to the original Kirchhoff current law such that the conservation of both carrier and energy are correctly accounted for.27 The quantum-well transistor laser base carrier distribution of the optical cavity is illustrated in Fig. 3. The measured collector I–V and optical L-V characteristics of a transistor laser are shown in Fig. 4. The collector I–V exhibits three base operation regions, namely, the spontaneous, the QW ground-state stimulated, and the QW 1st excited state stimulated recombination. The collector I–V exhibits lasing threshold at Ith = 25 mA and displays a “1st gain-compression” due to base shifting the operation from spontaneous to ground-state stimulated recombination17,18 and a “2nd gain-compression” due to base shifting the operation from ground-state to 1st excited state stimulated recombination.19 The optical L-V displays two distinct regions of the quantum-well laser emission, namely, the ground state at wavelength λ0, and the 1st excited state at wavelength λ1 exhibiting also a higher optical gain due to the faster recombination rate. The fast stimulated recombination in the base of the transistor also reveals fast electrical switching and bandwidth enhancement.

FIG. 3.

Excess carrier distribution in the base of a transistor laser where the base QW shifts its operation from spontaneous to stimulated recombination and coherent emission inside the cavity. The stimulated enhanced recombination rate (reducing lifetimes) in the transistor laser increases the base recombination current Ir1 and reduces the base transport current It1. The excess carrier distribution shows the slope towards the QW is steeper due to higher QW recombination current and is smaller at the collector junction due to lower base transport current.22 

FIG. 3.

Excess carrier distribution in the base of a transistor laser where the base QW shifts its operation from spontaneous to stimulated recombination and coherent emission inside the cavity. The stimulated enhanced recombination rate (reducing lifetimes) in the transistor laser increases the base recombination current Ir1 and reduces the base transport current It1. The excess carrier distribution shows the slope towards the QW is steeper due to higher QW recombination current and is smaller at the collector junction due to lower base transport current.22 

Close modal
FIG. 4.

(a) Collector I–V characteristics of a transistor laser illustrating a first gain (β) -compression due to the shift of the base operation from spontaneous to stimulated recombination at ground state and a second gain (β) - compression due to the shift of the base recombination from (ground state) λ0 to the first excited state λ1. (b) The optical L-V characteristics of a transistor laser illustrating in the laser output and the transition from the ground state λ0 to the first excited state λ1 with optical gain enhancement revealing fast recombination lifetime in the first excited states.

FIG. 4.

(a) Collector I–V characteristics of a transistor laser illustrating a first gain (β) -compression due to the shift of the base operation from spontaneous to stimulated recombination at ground state and a second gain (β) - compression due to the shift of the base recombination from (ground state) λ0 to the first excited state λ1. (b) The optical L-V characteristics of a transistor laser illustrating in the laser output and the transition from the ground state λ0 to the first excited state λ1 with optical gain enhancement revealing fast recombination lifetime in the first excited states.

Close modal

Intra-cavity photon-assisted tunneling (ICPAT) reveals further high speed modulation mechanisms of the transistor and the laser operation (Fig. 5). In addition to the transistor laser base recombination current Ir1 and the base transport current It1, the tunneling electrons drift to the collector as an additional current IICPAT; the corresponding tunneling holes drift into the base as a base injection current IICPAT and then diffuse to the QW for stimulated recombination. Under steady-state operation, the hole current IICPAT is equal to the 2nd base recombination current Ir2. When the excess holes (Δp2) enter the base, the E-B energy barrier lowers to allow emitter electron injection and via dielectric relaxation transport towards the collector junction on a time scale of a few femtoseconds. For a transistor laser, the base is doped to ∼2×1019cm3 and the resistivity calculated to be ∼4.3×103Ωcm; thus, the dielectric relaxation time is estimated to be τ=εrε0ρ = 4.9 fs. The excess electrons (Δn2) correspond to the excess holes (Δp2) in the base via femtosecond dielectric relaxation transport. The Δn2 near to the collector junction (Fig. 5) drift to the collector and contribute to the 2nd base transport current It2. The carriers diffuse toward the QW and contribute Ir2 to stimulated recombination at the base. This is the operating mechanism of tunneling modulation of a quantum-well transistor laser with collector junction tunneling and QW stimulated recombination for tunneling current gain and optical modulation.

FIG. 5.

Excess carrier distribution in the base of a transistor laser under the influence of tunneling (ICPAT, red circle). Transistor laser operation with emitter current injection IEn, base recombination current Ir1, and base transport and collector drift current It1=IC1. The intra-cavity photon-assisted electron-hole tunneling at the B-C junction produces the local electron tunneling current IICPAT. The tunneling-generated holes accumulate as Δp2 in the base and thus the corresponding electron Δn2 due to dielectric relaxation transport from the emitter towards the collector junction. This leads to the increase of the base transport current It2 and the increase of the base recombination current Ir2. The sum of IICPAT and It2 accounts for the collector current increase of IC2. The ratio It2/Ir2 is the transistor laser tunneling current gain β2. The inset at the top right illustrates the photon-assisted tunneling process.29 

FIG. 5.

Excess carrier distribution in the base of a transistor laser under the influence of tunneling (ICPAT, red circle). Transistor laser operation with emitter current injection IEn, base recombination current Ir1, and base transport and collector drift current It1=IC1. The intra-cavity photon-assisted electron-hole tunneling at the B-C junction produces the local electron tunneling current IICPAT. The tunneling-generated holes accumulate as Δp2 in the base and thus the corresponding electron Δn2 due to dielectric relaxation transport from the emitter towards the collector junction. This leads to the increase of the base transport current It2 and the increase of the base recombination current Ir2. The sum of IICPAT and It2 accounts for the collector current increase of IC2. The ratio It2/Ir2 is the transistor laser tunneling current gain β2. The inset at the top right illustrates the photon-assisted tunneling process.29 

Close modal

The collector current IC can be separated into the collector current IC1 due to the base QW stimulated recombination and the tunneling collector current IC2 due to the stimulated optical absorption. Hence, IC=IC1+IC2 and IC2 can be expressed as

IC2=It2+IICPAT.
(1)

The base recombination current IB=Ir1 is set constant during device measurement, and the tunneling current equal to base QW stimulated recombination current at steady-state leads to IICPAT=Ir2. The transistor laser current gain due to the base recombination without tunneling is defined as β1=IC1/IBIt1/Ir1. A tunneling current gain can be defined as β2=It2/Ir2 to account for the tunneling-induced carrier transport associated with Δn2 and Δp2. This leads to

IC2=It2+IICPAT=It2+Ir2=(β2+1)Ir2=(β2+1)IICPAT.
(2)

The currents IC2 and IICPAT are determined from the measured collector I–V and optical L-V; the tunneling current gain β2 is then calculated from Eq. (2).

In the present work, the transistor laser collector IC-VCE and optical L-VCE output characteristics under ICPAT for a device of 200 μm cavity length are measured in Figs. 6(a) and 6(b) displaying Ith = 32 mA. The transistor small-signal current gain ΔIC/ΔIB and the laser optical conversion gain ΔL/ΔIB as a function of the collector voltage VCB are plotted in Figs. 6(c) and 6(d); VCB is calculated from VCE=VCB+VBE, and VBE is measured. Since ICPAT is related to the collector junction bias, it is more convenient to use VCB than the collector-to-emitter bias VCE as the variable. When the collector is biased VCB from −1 V to +1.0 V for weak tunneling, the current gain (β) exhibits β-compression near the lasing threshold Ith = 32 mA, which is due to the base shifting the operation from slower spontaneous to faster stimulated recombination as shown in Fig. 6(c). When the collector is biased above +1.5 V for stronger tunneling, the β-compression is overshadowed by the ICPAT tunneling collector current. The laser optical conversion gain (ΔL/ΔIB) of Fig. 6(d) exhibits weaker stimulated optical absorption under lower bias (VCB < +1.0 V) and stronger stimulated optical absorption under higher bias (VCB > +1.5 V). Similar to transistor laser current gain modulation, this is the laser optical gain modulation as a function of base current and collector voltage due to ICPAT.

FIG. 6.

Electrical and optical output characteristics of a transistor laser (200μm cavity length; Ith=32mA) under the influence of ICPAT: (a) collector I–V characteristics with transistor operating in spontaneous recombination when IB<Ith (subthreshold, gray area), under stimulated recombination when IB>Ith (colored region), and coherent breakdown at higher VCE; (c) transistor laser small-signal current gain β=ΔIC/ΔIB extracted from the collector I–V and β-compression under the influence of ICPAT tunneling; (b) Coherent light output (L-V) increasing with base stimulated recombination and decreasing with collector voltage under ICPAT tunneling; (d) laser optical conversion gain ΔL/ΔIB extracted from the L-V plot. Note that VCE=VCB+VBE and VBE2V, thus VCE=1V (or VCB=1V) marks the onset of ICPAT.

FIG. 6.

Electrical and optical output characteristics of a transistor laser (200μm cavity length; Ith=32mA) under the influence of ICPAT: (a) collector I–V characteristics with transistor operating in spontaneous recombination when IB<Ith (subthreshold, gray area), under stimulated recombination when IB>Ith (colored region), and coherent breakdown at higher VCE; (c) transistor laser small-signal current gain β=ΔIC/ΔIB extracted from the collector I–V and β-compression under the influence of ICPAT tunneling; (b) Coherent light output (L-V) increasing with base stimulated recombination and decreasing with collector voltage under ICPAT tunneling; (d) laser optical conversion gain ΔL/ΔIB extracted from the L-V plot. Note that VCE=VCB+VBE and VBE2V, thus VCE=1V (or VCB=1V) marks the onset of ICPAT.

Close modal

The transistor laser collector IC1-VCE and optical L0-VCE output characteristics without the effect of tunneling can be extrapolated based on the slope at VCE = 1.0 V (VCB = −1.0 V) as shown in Figs. 7(a) and 7(b). The collector I–V and the light output is dependent solely on the base recombination current IB and independent of the collector voltage. In this case, the β-compression is clearly revealed and the laser optical conversion gain is nearly independent of the base current and collector voltage as shown in Figs. 7(c) and 7(d).

FIG. 7.

Electrical and optical output characteristics of the transistor laser extracted from Fig. 6 without the influence of ICPAT: (a) collector IC1-VCE; (c) transistor small-signal current gain β1 = ΔIC1/ΔIB with observed current gain compression; (b) Optical light output L0-VCE; (d) laser optical conversion gain ΔL0/ΔIB extracted from the L0-VCE plot.

FIG. 7.

Electrical and optical output characteristics of the transistor laser extracted from Fig. 6 without the influence of ICPAT: (a) collector IC1-VCE; (c) transistor small-signal current gain β1 = ΔIC1/ΔIB with observed current gain compression; (b) Optical light output L0-VCE; (d) laser optical conversion gain ΔL0/ΔIB extracted from the L0-VCE plot.

Close modal

Isolating the tunneling ICPAT process from Fig. 5, Fig. 8 illustrates the unique base majority and minority carrier distributions (Δp2 and Δn2), carrier transport dynamics, and QW recombination due to the transistor laser collector tunneling current (IICPAT). The e–h pairs are generated at the collector junction under photon-assisted tunneling inside the optical cavity. Electrons drifting to the collector contribute to the excess collector current (IICPAT). Holes drifting to the base contribute as majority carrier injection and diffuse to the base QW for stimulated recombination (Ir2). Under steady-state operation, IICPAT=Ir2, the excess hole distribution (Δp2) is established. The excess hole charge (+qΔp2) lowers the emitter junction energy barrier and induces minority carrier (electron) injection via femtosecond dielectric relaxation transport at the collector junction to establish the excess electron distribution (Δn2) satisfying charge neutrality. The excess electrons that do not recombine (stimulated or spontaneous) will drift to the collector and contribute as additional collector current It2. These carrier transport and redistribution processes inside of the transistor laser establish the tunneling current gain (β2). Finally, the collector current due to tunneling can be expressed as IC2=It2+IICPAT=(β2+1)IICPAT, where β2 can be determined from the measured IC2 (from IC2-VCB) and IICPAT (from ΔL-VCB).

FIG. 8.

Graph showing only the tunneling process from Fig. 5: ICPAT (red circle), excess carrier transport, and carrier distribution under collector tunneling (ICPAT) assuming steady-state cavity photon density (constant IB). Electrons drifting to the collector contribute an excess collector current (IICPAT). Holes drifting to the base contribute majority carrier injection to the base and diffuse toward the base QW for stimulated recombination. The excess hole distribution in the base region is shown as Δp2. The excess hole charge lowers the emitter-base energy barrier permitting emitter electrons injection and dielectric relaxation transport (∼5 fs) toward the collector junction establish giving (Δn2) satisfying charge neutrality. The excess electrons that did not recombine (both stimulated in QW and spontaneous) drifting to the collector contribute as an additional collector current It2. These carrier transport and redistribution processes establish the transistor laser tunneling current gain β2.

FIG. 8.

Graph showing only the tunneling process from Fig. 5: ICPAT (red circle), excess carrier transport, and carrier distribution under collector tunneling (ICPAT) assuming steady-state cavity photon density (constant IB). Electrons drifting to the collector contribute an excess collector current (IICPAT). Holes drifting to the base contribute majority carrier injection to the base and diffuse toward the base QW for stimulated recombination. The excess hole distribution in the base region is shown as Δp2. The excess hole charge lowers the emitter-base energy barrier permitting emitter electrons injection and dielectric relaxation transport (∼5 fs) toward the collector junction establish giving (Δn2) satisfying charge neutrality. The excess electrons that did not recombine (both stimulated in QW and spontaneous) drifting to the collector contribute as an additional collector current It2. These carrier transport and redistribution processes establish the transistor laser tunneling current gain β2.

Close modal

The tunneling collector IC2-VCB and optical output light loss ΔL-VCB shown in Figs. 9(a) and 9(b) due to collector voltage (VCB) and base recombination current (IB) are extracted from the difference between Figs. 6 (with tunneling) and 7 (without tunneling). The method of extracting the ICPAT absorption coefficient from the ΔL-VCB optical output relation was described in the previous work.22 In this work, we require to derive the tunneling current IICPAT from measured laser output reduction (photon absorption by ICPAT) and we treat this current IICPAT as the “new source” of current injection into the base of transistor for tunneling base current modulation to complete the analysis on the IC2-VCB electrical characteristics and correlate the transistor laser electrical and optical operations. Next, we compare the light absorbed at the collector junction LICPAT (inside the cavity) to the measured optical light output loss ΔL (outside the cavity) based on Eq. (4) as shown in Fig. 9(c). Hence, the tunneling current IICPAT can be converted from the light absorption LICPAT as a function of the collector voltage VCB as shown in Fig. 9(d). Note that both LICPAT and IICPAT saturate at high voltage, which is due to a large collector junction bias leading to increased optical absorption coefficient and decreased cavity photon population. The products determine the total number of tunneling transitions.

FIG. 9.

(a) The collector current increase due to ICPAT (IC2) and (b) optical output reduction due to ICPAT (ΔL) are extracted from the difference of Figs. 6 and 7. Plot (c) shows the light loss LICPAT(inside the cavity) extracted from measured ΔL(outside of cavity) based on Eq. (4). Plot (d) shows the tunneling current IICPAT can be extracted from LICPAT.

FIG. 9.

(a) The collector current increase due to ICPAT (IC2) and (b) optical output reduction due to ICPAT (ΔL) are extracted from the difference of Figs. 6 and 7. Plot (c) shows the light loss LICPAT(inside the cavity) extracted from measured ΔL(outside of cavity) based on Eq. (4). Plot (d) shows the tunneling current IICPAT can be extracted from LICPAT.

Close modal

We have reported previously that the stimulated optical absorption coefficient ΓαICPAT due to intra-cavity photon-assisted tunneling22 is different from regular optical absorption coefficient due to photon-assisted tunneling.29 The confinement factor Γ accounts for the partial illumination of the collector junction by the laser beam. Therefore, the transistor laser cavity can be characterized by the three loss terms: the intrinsic loss αi, the mirror loss αm, and the ICPAT tunneling loss αICPAT. Both the intrinsic loss and the mirror loss are assumed to be constant with respect to the collector bias, but the ICPAT loss is field-dependent and varies with both IB and VCB. The transistor laser uses ICPAT modulating cavity absorption coefficient to control the cavity photon population, which is the foundation for a direct voltage modulation laser. It has been shown22 that

ΔL=12ωqηi[ αmαi+αm(IIth)αmαi+αm+ΓαICPAT(IIth,ICPAT) ],
(3)

where ΔL is the light output reduction, ηi is the internal quantum efficiency, and Ith,ICPAT is the voltage-dependent current threshold, a phenomenon unique to the transistor laser. Hence, the stimulated light absorption at the collector junction due to ICPAT LICPAT(inside the cavity) can be obtained from the measured laser output reduction ΔL by

LICPAT=12ωqηiΓαICPATαi+αm+ΓαICPAT(IIth,ICPAT)=ΔL(αi+αm)αm/2×ΓαICPATIIthIIth,ICPAT(αi+αm+ΓαICPAT)(αi+αm).
(4)

ΔL shown in Fig. 9(b) is obtained from the difference of the measured L-V plots in Figs. 6(b) and 7(b); αm=59cm1 for the device under discussion. The resulting LICPAT is plotted in Fig. 9(c). When Ith,ICPATIth at lower VCB, the proportionality factor on the right hand side of Eq. (4) approaches a constant value. The tunneling current IICPAT shown in Fig. 9(d) is obtained from IICPAT/q=ηiLICPAT/hv. If the ICPAT internal quantum efficiency ηi equals “one,” each absorbed photon assisted by ICPAT producing one electron–hole pair.

The transistor laser tunneling current gain β2=IC2/IICPAT1 can be derived from the extracted IC2 and IICPAT in Figs. 9(a) and 9(d), and plotted in Fig. 10 after removing the coherent breakdown region. β2 is always greater than zero as long as the collector junction is reverse biased, indicating each absorbed photon in the B-C junction can produce more than one electron at the collector terminal, and is the tunneling current gain of the transistor laser. β2 derived above is related to the ratio of stimulated QW recombination lifetime to collector drift time. Figure 10 shows that β2 increases with collector VCB for a given base current IB, indicating the increase of stimulated recombination lifetime due to the reduction of cavity photon density under ICPAT at higher collector voltage.

FIG. 10.

Transistor laser tunneling current gain β2 under ICPAT operation. Referring to Eq. (8), β2 is related to the ratio of stimulated recombination lifetime to collector drift time. For a given base current IB, β2 increases with collector VCB indicating the increase of stimulated recombination lifetime due to the reduction of cavity photon density under ICPAT at higher collector voltage.

FIG. 10.

Transistor laser tunneling current gain β2 under ICPAT operation. Referring to Eq. (8), β2 is related to the ratio of stimulated recombination lifetime to collector drift time. For a given base current IB, β2 increases with collector VCB indicating the increase of stimulated recombination lifetime due to the reduction of cavity photon density under ICPAT at higher collector voltage.

Close modal

The ratio of the tunneling current gain β2 compared to the base recombination current gain β1 is shown in Fig. 11. The 18 times enhancement is due to fast base transport of dielectric relaxation. In the transistor laser without tunneling, the injected minority electrons require a delay of base transit time (τtB) across the entire base in order to reach the collector. However, in the transistor laser with tunneling, the minority electrons respond to the injected majority holes (due to tunneling) and are able to transport through the base to the collector junction via dielectric relaxation in femtoseconds (τrelaxB ∼ 5 fs). The β2=It2/Ir2 will increase with respect to the collector voltage increases. The strong dependence on the collector junction bias VCB indicates that β2 increases are due to the QW stimulated recombination lifetimes increases due to higher ICPAT at higher collector voltage. The signal delay is limited approximately by the carrier drifting time at the collector junction and QW stimulated recombination lifetime at the base since both the tunneling time (∼20 fs) and the dielectric relaxation time (∼5 fs) are negligible. The measured IC and IC2 compare well to the extracted results from IICPAT of the transistor laser shown in Fig. 12. The tunneling current IICPAT is amplified by the tunneling current gain β2 and contributes to the tunneling collector current IC2. Thus, the total collector current of the transistor laser is IC=IC1+IC2.

FIG. 11.

The ratio of the transistor laser tunneling current gain β2=It2/Ir2=IC2/IICPAT1 to the base recombination current gain β1=It1/Ir1=IC1/IB. Transistor laser ICPAT operation can improve the current gain by as much as 18 times, due to the fast tunneling and dielectric relaxation transport and QW stimulated recombination. The increase of β2 at higher collector voltage is due to the increase of the QW stimulated recombination lifetime with the cavity photon density reduction.

FIG. 11.

The ratio of the transistor laser tunneling current gain β2=It2/Ir2=IC2/IICPAT1 to the base recombination current gain β1=It1/Ir1=IC1/IB. Transistor laser ICPAT operation can improve the current gain by as much as 18 times, due to the fast tunneling and dielectric relaxation transport and QW stimulated recombination. The increase of β2 at higher collector voltage is due to the increase of the QW stimulated recombination lifetime with the cavity photon density reduction.

Close modal
FIG. 12.

Summary of transistor laser operation under ICPAT: (a) the extracted tunneling current IICPAT as a function of the base current IB and the collector voltage VCB; (b) the measured collector tunneling current IC2 (dashed lines) compared to calculated IC2=(β2+1)IICPAT. Due to coherent breakdown at high voltages, IICPAT cannot be obtained at the full voltage range; (c) the measured collect current IC (dashed lines) compared to the calculated IC=(β2+1)IICPAT+β1IB.

FIG. 12.

Summary of transistor laser operation under ICPAT: (a) the extracted tunneling current IICPAT as a function of the base current IB and the collector voltage VCB; (b) the measured collector tunneling current IC2 (dashed lines) compared to calculated IC2=(β2+1)IICPAT. Due to coherent breakdown at high voltages, IICPAT cannot be obtained at the full voltage range; (c) the measured collect current IC (dashed lines) compared to the calculated IC=(β2+1)IICPAT+β1IB.

Close modal

The Bardeen transistor current gain β1, depending on the ratio of collector current output to base current input modulation and the use of the charge control model in the base, can be expressed as

β1=ICIB=QτECQτB=τBτEC=τbulkτtB+τdrift.
(5)

In Eq. (5), τbulk is the bulk base recombination lifetime which is proportional to the base majority carrier concentration, τEC is the emitter-to-collector minority carrier transit time, τtB is the base transit time, and τdrift is the carrier drift time at the collector junction. For a high speed HBT with thin base thickness (small τtB), the collector junction drift time τdrift needs to be accounted for.

When QWs are inserted in the base of the HBT, the base carrier recombination lifetime τB can be reduced further.23 Thus, the QW transistor current gain β1QW(spon) is derived as

β1QW(spon)=τBτtB+τdrift=11τbulk+Q1Q21τt,EQWτtB+τdriftQ2Q1τt,EQWτtB+τdrift,
(6)

where Q1 is the base storage charge for QW recombination, Q2 is the base stored charge for the collector transport, and τt,EQW is the base transit time from the emitter to the QW. The numerator in Eq. (6) describes the reduction of the total base recombination lifetime τB due to the QW fast recombination lifetime of (Q2/Q1)τt,EQW.

In transistor laser operation, the base recombination lifetime τB is reduced due to the QW shifting from spontaneous to stimulated recombination, which analytically takes the form

β1QW(stim)=τBτtB+τdrift=11τbulk+Q1Q21τstim+Q1Q21τt,EQWτtB+τdriftQ2Q1τstimτtB+τdrift.
(7)

The fact that τstim is proportional to the cavity photon density and the QW carrier density is owing to the device operation shifting from spontaneous to stimulated recombination and is given by the β-compression in Fig. 4.

For the transistor laser under ICPAT operation, the transistor current gain β1QW(stim) is the same as Eq. (7), and the tunneling current gain β2(tunnel) can be expressed as

β2(tunnel)=It2Ir2=qΔn2υdrift12LQWqΔp2τstim=υdrift12LQWτstim=LCτdrift12LQWτstimLQWLCτstimτdrift.
(8)

LQW is the distance between the QW to the base-collector junction and LC is the distance to collector junction. The tunneling current gain β2 is approximately the ratio of the QW stimulated recombination lifetime to the carrier drift time at collector junction. β2 increase with collector VCB increase for a given base current IB shown in Fig. 10. The stimulated recombination lifetime increases due to the reduction of cavity photon density under ICPAT at higher collector voltage.

We have studied here the transistor laser, going beyond the original Bardeen e-h spontaneous recombination bipolar transistor (1947), with stimulated e-h recombination operating under the influence of quantum-well assistance in the base, and stimulated optical modulation under the influence of intra-cavity cavity photon-assisted tunneling at the collector. The tunneling gain mechanism is the result of the unique transistor laser base transport properties under the influence of ICPAT and base dielectric relaxation, which yields fast carrier base transport and recombination than the original Bardeen transistor. The voltage and current dependence of the tunneling current gain and optical modulation have been revealed in detail. Although the analysis is carried out for the transistor laser intra-cavity photon-assisted tunneling, the operation mechanism should apply in general to tunneling collector transistors of various design configurations.

This work has been supported in part by the Air Force Office Scientific Research under Grant No. AF FA9550-15-1-0122. N. Holonyak, Jr., is grateful for the support of the John Bardeen Chair (Sony) of Electrical and Computer Engineering and Physics, and M. Feng for the support of the Nick Holonyak, Jr., Chair of Electrical and Computer Engineering. After December 23, 1947 and John Bardeen's identification (at BTL) of the transistor and the importance of the electron and hole, i.e., e and h conductance bipolarity, we remain indebted to John Bardeen, our mentor, for his lifelong continuing interest in the transistor (parallel to the BCS theory), the effect of the electron and the hole (e-h) in helping to originate the diode laser and LED, and in addition now leading to the e-h recombination (electrical and optical) transistor laser. N.H. is especially grateful to John Bardeen for bringing transistor research to Urbana (1951) and changing all of our lives world-wide with the new quantum-physics and solid state devices.

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