Optical pulse generation in a transistor laser via intra-cavity photon-assisted tunneling and excess base carrier redistribution

The invention of the transistor in 1947 by Bardeen and Brattain¹ and semiconductor diode laser and light-emitting diode in 1962 by Hall et al.² and Holonyak³ have been instrumental in revolutionizing microelectronics, photonics, and solid-state lighting, in fact, now has become the basis of a fast growing industry. The insertion of the quantum well (QW) in the semiconductor diode laser in 1977⁴ tunes and confines the radiative recombination inside the quantum well, resulting in lower threshold and higher speed modulation. The transistor base and base current (I_B) separate the low impedance input, the minority “emitter” current (I_E), from the high impedance output, the “collector” current (I_C), thus yielding a “transfer resistor” under the current constraint I_E + I_B + I_C = 0. Hence, the transistor can produce signal amplification with the current gain, β = |I_C/I_B|. Further improving the emitter injection efficiency in the transistor with a wider gap was identified in 1948⁵ and the heterojunction bipolar transistor (HBT) was proposed still later in 1957.⁶ The laser operation of a transistor was reported later (1980) as a laser transistor,⁷ but only lased in the transistor saturation mode (both base and collector junctions in forward bias). Hence, it operates as a “double injection diode laser” and cannot simultaneously operate as a laser with transistor collector output.

Since 2000 in developing the “sub-micron emitter” HBT toward THz operation,^8,9 the HBT is operated at much higher base current density. We realized that there is enough base recombination current and light emission, a large signal in a small base region, to shift transistor spontaneous into stimulated operation (Feng and Holonyak, the transistor laser (TL), 2003).^10–12 This is particularly the case if quantum wells are inserted into the base region to tune and control the radiative recombination, and an optical resonator is included to enhance the cavity Q. Recently, vertical-cavity transistor lasers (high Q) with a low threshold I_TH < 2 mA have been realized.^13,14 Of further interest in a TL, the nonlinear signal mixing occurring at the collector tunnel junction makes possible high impedance and low power modulation.^15,16

An optical pulse can be generated in the transistor laser via collector junction modulated intra-cavity photon-assisted tunneling (ICpaT), resulting in re-supply of holes in the base and inducing excess base electron redistribution and recombination. 1 and 2 GHz optical pulse generation is demonstrated in a transistor laser using collector voltage control. With additional signal modulation at the base, 2 GHz pulse multiplication is demonstrated here. We incorporate the modulated intra-cavity photon-assisted tunneling absorption coefficient into the laser electron-hole coupled rate equations to provide a convenient basis for analysis.

The n-InGaP/p⁺-GaAs/n⁺-GaAs HBT layer structure of the present work is grown by Dupuis MOCVD. The HBT structure consists of a 40 nm In_0.49Ga_0.51P emitter Si-doped to 3 × 10¹⁷ cm⁻³, an 85 nm GaAs base C-doped to 1 × 10¹⁹ cm⁻³, a single undoped 15 nm In_0.15Ga_0.85As base-region quantum well at wavelength λ ≈ 980 nm, and a 60 nm GaAs collector with Si-doping to 2 × 10¹⁶ cm⁻³. The devices are fabricated as previously described.^11–13 The edge-emitting TL cavity length is 200 μm.

Figure 1 shows the band diagram of the TL with the collector junction tunneling under reverse bias as previously described.^15,16 The base recombination current, I_Br, is expressed as the sum of the hole components, I_Br = I_B + I_paT + I_rT. I_B is the re-supply of holes by the base ohmic contact. I_paT is the re-supply of holes by the ICpaT. I_rT is the base re-supply of holes by the direct tunneling of electrons. Since ICpaT is a more efficient tunneling process (lower gap) than direct tunneling, I_Br ∼ I_B + I_paT. The collector current I_C is expressed as the sum of the electron components, I_C ∼ I_t + I_paT. I_t is the minority carrier current of injected electrons from the emitter that cross the base and I_paT is the ICpaT portion of the electron current. Figure 2 shows the (a) TL collector I_C-V_CE and (b) TL optical L-V_CE characteristics with a threshold I_TH = 32 mA. Four distinct regions are evident. Below threshold, the transistor operates under spontaneous recombination as indicated by the “black lines” of the collector I-V and the optical L-V. Above threshold, the transistor operates as a laser (stimulated recombination) as indicated by “red lines” of the collector I-V and the optical L-V. The collector tunneling is negligible when collector voltage V_CB ≤ 0 V. Since V_CE = V_CB + V_BE, we can determine V_CB = 0 V by setting V_CE = V_BE under laser operation (I_B > I_TH = 32 mA) from the measured transistor laser V_BE-V_CE family curves (data not shown here) as a threshold for the collector tunneling (IC_PAT) process. The ICpaT threshold V_CE, when V_CB = 0 V, is in the range of 1.77 V to 2.12 V for I_B changes from 35 to 60 mA. Hence, for V_CB ≤ 0, I_C ≈ I_t (the usual collector current) and optical power remains constant limited by constant base current. When the TL operates under high collector bias (V_CB > 0 V), the tunneling process occurs predominantly via ICpaT absorption. Thus, excess collector current increases and optical power reduces as a function of V_CE, I_C ≈ I_t + I_paT shown as “blue lines” for the collector I-V and the optical L-V. Notice that the base recombination current, I_Br = I_B + I_paT, also increases due to IC_PAT. In addition, excess base electrons are induced into the base from emitter. Further increase of V_CE, the photon loss via ICpaT exceeds the photon gain by the QW, the laser ceases operation (laser breakdown) and results in spontaneous operation shown as orange lines for the collector I-V and the optical L-V. The collector junction, as a result, enables the laser output to be controlled effectively by the use of a third terminal (control) voltage. This enables the TL to be directly modulated via base current (δI_B) as well as by collector voltage control (δV_CE and δV_BC).

For optical pulse generation as shown in Fig. 3, the TL is arranged in a two-port microwave electrical common-emitter configuration with a bias of I_B = 40 mA and V_CE = 2.5 V. The RF signal power P_LO drives the collector port with various input powers (P_LO = −10, −4, and +12 dBm). The laser output power is collected through optical fiber and linked to a Newport detector and Picosecond Pulse Lab's amplifier. Figure 4 illustrates the TL optical pulse generation of (a) 1 GHz and (b) 2 GHz waveforms with various input power levels of collector modulation. For low level modulation P_LO = −10 dBm, the optical waveform (blue line) shows an approximate linear relation with the collector modulated sine wave. By increasing P_LO = −4 dBm, the optical waveform (red line) shows more distortion with a small pulse peak. Further increasing the input power, P_LO = +12 dBm (15.8 mW), the optical output shows an optical waveform (black) with a strong optical pulse followed with a modulated waveform. As the TL is biased at I_B = 40 mA and V_CE = 2.5 V with the collector junction modulated at 12 dBm (corresponding to ΔV_CE = ± 1.25 V), the collector voltage swing will be between 1.25 and 3.75 V, as shown in Fig. 2. At V_CE = 3.75 V, the laser breakdown is due to the net cavity photon density below threshold; photon generation in QW is less than photon loss by IC_PAT. The TL shifts the base operation from coherent stimulated to incoherent spontaneous recombination. When the GHz modulation returns to 2.5 V and 1.25 V, the cavity photon density increases and shifts from the incoherent to coherent state. The IC_PAT excess base carriers redistribute and, as a result, a sharp optical pulse is generated, followed with a steady-state modulated waveform. The modulation bandwidth for a 200 μm TL with V_CE = 2.5 V is 2 GHz at I_B = 40 mA and 7.2 GHz at I_B = 60 mA. The highest modulation bandwidth for a 400 μm TL with V_CE = 1.5 V is 13.4 GHz at I_B = 145 mA.

The electric field dependence of the semiconductor fundamental absorption edge is referred to as the Franz-Keldysh effect. With the coherent photon-assisted tunneling absorption, the barrier height is reduced to E_g - hv. The photon-assisted tunneling is known to exhibit high nonlinear absorption. An analysis of electro-absorption assuming uniform electric field (DC) can be expressed^17,18 by $αpaT∼F1/3∫B∞|Ai(z)|2dz$⁠, where Ai (z) is the Airy function, F is collector junction electrical field, and $B∼F−2/3•(Eg(GaAs)−hv)$ is a constant determined by the GaAs bandgap and photon energy (hv) absorption.

For the transistor laser, Then et al.¹⁶ modify the Statz-deMars laser electron-photon coupled rate equations¹⁹ to include intra-cavity photon-assisted tunneling absorption, α_paT relating to collector voltage modulation. The collector current increases I_C = I_t + I_rT + I_paT ∼ I_C(α_paT, P) with I_paT/q = vα_paTP. The emitter current, I_E = I_E(I_C), is coupled to the collector current, I_C, as a result of the tunneling re-supply of holes to the base. The coupled equations in the notation used in Refs. 16 and 19 are

and

Using small-signal analysis, we obtain for the minority carrier population, N = N_o + δN(ω); for the optical gain, g = g_o + (∂g/∂N)·δN(ω); a photon population, P = P_o + δP(ω); the expressions I_E = I_E,o + δI_E(ω); I_C = I_C,o + δI_C(ω); α_paT = α_paT,o + δα_paT(ω); and the transistor current constraint, δI_E(ω) = δI_C(ω) + δI_B(ω). Equation (1) can be re-written in small-signal nonlinear form as

with the intra-cavity photon-assisted tunneling absorption modulation, δα_paT Taylor-expanded as

Thus, the nonlinear modulation of laser output can be realized in Eq. (3) with two nonlinear IC_PAT terms [vP_oδα_paT] and [vδα_paTδP].

Figure 5 shows the multiplier characteristics of a common-emitter TL with both base current and collector voltage modulation. The collector is modulated at 2 GHz with P_LO = +12 dBm and the base is modulated at 100 MHz with P_IF = −4 dBm. The multiplication waveforms illustrate 2 GHz pulse trains with a modulation signal of 100 MHz, agreeing with the frequency up-conversion measured.

In conclusion, we demonstrate that 1 and 2 GHz optical pulses can be generated in a transistor laser using collector junction modulation via intra-cavity photon-assisted tunneling. Excess base carrier redistribution as well as cavity photon density modulation shift the laser operation from stimulated to spontaneous. We include the IC_PAT absorption coefficient into laser electron-photon coupled rate equations to explain the nonlinear effect of laser pulse generation. Contrary to current modulation at the quantum-well in diode laser, the IC_PAT modulation in transistor laser is a light absorption process via voltage modulation at the base collector junction. Hence, the steady-state laser output is not affected by the relaxation oscillation caused by current modulation. The bandwidth of IC_PAT modulation can be estimated as a PIN detector bandwidth, which is limited by capacitance associated with detector area and depletion width as well as carrier transit time. Thus, the intrinsic transistor laser modulation bandwidth via IC_PAT can be extended toward 0.3 THz.

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. We are also thankful for GGB Industries, Inc., for supplying high speed GSG probes for testing the Transistor Laser.