Temperature Dependence of Threshold Current of Semiconductor Lasers
This is a continuation from the previous tutorial - how to estimate the threshold current density of a semiconductor laser.
In this tutorial we address the important issue of the high-temperature performance of semiconductor lasers.
The threshold current of double-heterostructure lasers is found to vary with temperature \(T\) as
\[\tag{3-6-1}I_\text{th}(T)=I_0\exp(T/T_0)\]
where \(I_0\) is a constant and \(T_0\) is a characteristic temperature often used to express the temperature sensitivity of threshold current.
For AlGaAs lasers the observed \(T_0\ge120\text{ K}\) near room temperature, while for InGaAsP lasers, \(T_0\) values lie in the range of \(50-70\text{ K}\). A lower \(T_0\) value implies that the threshold current increases more rapidly with increasing temperature.
The high temperature sensitivity of the threshold current of InGaAsP lasers limits their performance performance under high-temperature operation.
Furthermore, under CW operation at room temperature, the maximum power emitted by these lasers is limited by a thermal runaway process: more and more current is required to offset the effect of the internal temperature increase and this in turn further increases the temperature.
Because of these practical limitations, a considerable amount of experimental and theoretical work has been done to understand the higher temperature sensitivity of the threshold current of InGaAsP lasers.
In some InGaAsP laser structures, a part of the injected current can flow around the active region, the magnitude of which may vary with temperature; this results in an anomalously low or high temperature sensitivity of the threshold current.
The purpose of this tutorial is not to consider such structure-related effects but to concentrate on the fundamental aspects that can give rise to a high temperature dependence of the threshold current. For this reason, most results are presented for broad-area or stripe-geometry lasers.
Figure 3-26 shows the measured threshold current of a broad-area 1.3-μm InGaAsP-InP laser as a function of the operating temperature.
The threshold current can be represented by Equation (3-6-1) with \(T_0\approx110\text{ K}\) for \(100\text{ K}\le{T}\le240\text{ K}\) and \(T_0\approx60\text{ K}\) for \(240\text{ K}\le{T}\le340\text{ K}\). At higher temperatures, even lower \(T_0\) values are observed.
Similar \(T_0\) values have been reported by optical pumping using a YAG laser or a pulsed dye laser as the excitation source.
Several researchers have measured the threshold current as a function of temperature in the temperature range of \(10-70^\circ\text{C}\), which is generally the operating temperature range of these devices when they are used in practical systems.
Figure 3-27 show the estimated \(T_0\) obtained using Equation (3-6-1) from these measurements for InGaAsP-InP lasers as a function of the emission wavelength.
The measured \(T_0\) values generally lie in the range of \(40-70\text{ K}\). Several mechanisms have been proposed to explain the observed high temperature sensitivity of the threshold current of InGaAsP lasers. These are carrier leakage over the heterojunction, Auger recombination, and intervalence band absorption.
The differences between the temperature dependences of other lasing characteristics (e.g., carrier lifetime at threshold, external differential quantum efficiency, and optical gain) of GaAs-AlGaAs and InGaAsP-InP lasers have been extensively studied.
The results of these studies are consistent with the observed higher temperature dependence of the threshold current of InGaAsP-InP lasers compared with that of GaAs-AlGaAs lasers.
Carrier-Lifetime Measurements
The carrier lifetime at threshold \(\tau_\text{th}\) has been measured by the turn-on delay technique for both GaAs-AlGaAs and InGaAsP-InP lasers. Figure 3-28 shows the measured \(\tau_\text{th}\) as a function of temperature.
The results obtained are analyzed in the following fashion.
The threshold current density \(J_\text{th}\) of a broad-area laser is given by Equation (2-6-3) [refer to the emission characteristics of semiconductor lasers tutorial], or
\[\tag{3-6-2}J_\text{th}=qdn_\text{th}/\tau_\text{th}\]
where \(d\) is the active-layer thickness and \(n_\text{th}\) is the carrier density at threshold.
The observed decrease of \(\tau_\text{th}\) with increasing temperature (in the high temperature range) is more rapid for 1.3-μm InGaAsP lasers than for AlGaAs lasers; this is consistent with the observation that \(J_\text{th}\) increases with increasing temperature more rapidly in InGaAsP lasers than in AlGaAs lasers.
Furthermore, it is possible to conclude that the threshold carrier density \(n_\text{th}\) does not increase as rapidly with increasing temperature as does \(J_\text{th}\). This is consistent with the measurements of \(n_\text{th}\) using short electrical or optical pulse excitation.
Optical-Gain Measurement
The temperature dependence of the optical gain has been measured by both current injection and optical pumping.
In the current-injection technique, the net optical gain is obtained from measuring the intensity modulation in spontaneous-emission spectra that are observed from the facet of a laser at currents below threshold.
The modulation is caused by the Fabry-Perot resonances (the longitudinal modes) of the cavity. The net gain \(G\) is negative below threshold and is given by
\[\tag{3-6-3}G=\frac{1}{L}\ln\left(\frac{r^{1/2}-1}{r^{1/2}+1}\right)\]
where \(G=\Gamma{g}-\alpha_\text{t}\), \(r=P_\text{max}/P_\text{min}\), and \(\alpha_\text{t}\) is the total loss in the cavity including mirror losses. The quantities \(P_\text{max}\) and \(P_\text{min}\) are the maximum and minimum intensities in the spontaneous-emission spectrum. \(G\) is found to vary linearly with the current \(I\).
The measured slope of the gain-current curve \(\text{d}G/\text{d}I\) is shown in Figure 3-29 for both InGaAsP-InP and GaAs-AlGaAs lasers. As the temperature increases, the quantity \(\text{d}G/\text{d}I\) decreases more rapidly for InGaAsP (for \(T\gt230\text{ K}\)) than for GaAs.
An explanation for these results is that a fraction of the injected current in InGaAsP lasers is lost (by nonradiative recombination or carrier leakage) at high temperatures and that this fraction does not contribute to radiative recombination or optical gain.
Measurements of the optical gain have been reported using excitation from a pulsed N2-laser-pumped dye laser. The gain is determined by measuring the dependence of the amplified intensity on the length of the excited region.
Measurements of both the gain spectra and its temperature dependence have been reported. Figure 3-30(a) shows the measured gain spectra at \(300\text{ K}\), and Figure 3-30(b) shows the optical pump intensity required to maintain a constant gain as a function of temperature.
The measured gain spectrum is similar to that calculated in Figure 3-7 [refer to the radiative recombination in semiconductor lasers tutorial]. The optical pump power needed to maintain a constant gain is found to vary with temperature \(T\) as \(P=P_0\exp(T/T_0)\).
The \(T_0\) values are noted in Figure 3-30(b). The observed lower \(T_0\) above a certain temperature (\(T=265\text{ K}\)) is consistent with the higher temperature dependence of threshold current in the same temperature range (see Figure 3-26).
External Differential Quantum Efficiency
The external differential quantum efficiency for a laser with cleaved facets is given by Equation (2-6-11) [refer to the emission characteristics of semiconductor lasers tutorial], or
\[\tag{3-6-4}\eta_\text{d}=\eta_\text{i}\frac{\alpha_\text{m}}{\alpha_\text{m}+\alpha_\text{int}}\]
where \(\eta_\text{i}\) is the fraction of injected carriers that recombine to produce a stimulated photon, \(\alpha_\text{m}=\ln(1/R_\text{m})/L\) is the mirror loss, \(L\) is the length of the laser, \(R_\text{m}\) is the facet reflectivity, and \(\alpha_\text{int}\) is the sum of internal losses in the active and cladding layers.
A measurement of \(\eta_\text{d}\) as a function of temperature may be used to infer the variation of \(\alpha_\text{int}\) with temperature. However, for an absolute determination of \(\alpha_\text{int}\), \(\eta_\text{i}\) must be known, and for a determination of the temperature dependence of \(\alpha_\text{int}\), the variation of \(\eta_\text{i}\) with temperature must be known.
Incomplete knowledge of \(\eta_\text{i}\) may lead to misleading conclusions. For example, in some laser structures a large fraction of current can flow around the active region; as a result the observed \(\eta_\text{d}\) is small.
The measured \(\eta_\text{d}\) as a function of temperature for GaAs and InGaAsP lasers is shown in Figure 3-31. The lasers are oxide-stripe devices that do not have significant current leakage paths. The temperature dependence of \(\eta_\text{d}\) is somewhat steeper for InGaAsP lasers than that for GaAs lasers.
Discussion
The experimental observations on the temperature dependence of the threshold current, the carrier lifetime at threshold, the optical gain, and the sub linearity of spontaneous emission [refer to the experimental results of radiative and Auger recombination coefficients in semiconductor lasers tutorial] suggest that InGaAsP lasers suffer from a nonradiative carrier loss at high temperatures.
This carrier loss may be due to heterobarrier leakage that, as shown in the how to estimate the threshold current density of a semiconductor laser tutorial, increases with increasing temperature.
Heterobarrier leakage can be a major carrier loss mechanism for InGaAsP-InP lasers with emission wavelengths less than 1.1 μm due to a small heterobarrier height.
For lasers emitting near 1.3 μm and 1.55 μm, which is the region of interest for optical communication applications, the calculated drift-and-diffusion type of leakage is small, as shown in Figure 3-25 [refer to the how to estimate the threshold current density of a semiconductor laser tutorial].
Experimentally, the leakage current is about 10-30% of the total current and is mostly due to electron leakage.
Since the magnitude of the conventional drift-and-diffusion-type heterobarrier leakage depends on the doping and thickness of the p-cladding layer, laser structures can be designed with very small carrier leakage. The threshold current in such lasers nonetheless exhibits a high temperature dependence, suggesting that other mechanisms are also operative.
Another mechanism for carrier loss at high temperatures is Auger recombination. The measured Auger coefficient is large enough to account for a lower \(T_0\) value for 1.3-μm and 1.55-μm InGaAsP lasers than that observed for AlGaAs lasers.
The threshold current density of a broad-area laser can be calculated using Equation (3-5-1) [refer to the how to estimate the threshold current density of a semiconductor laser tutorial]. The calculated value is determined principally by the magnitudes of coefficients \(B\) and \(C\) and the threshold current density \(n_\text{th}\) if we assume that \(A_\text{nr}=0\) and \(J_\text{L}=0\).
The value of \(n_\text{th}\) depends on the threshold gain \(g_\text{th}\) which is determined by the laser structure (e.g., through the mode confinement factor) and optical absorption.
There have been several suggestions based indirect measurements that intervalence band absorption in the active layer due to transitions between the split-off band and the heavy-hole band is large and may be responsible for the strong temperature sensitivity of \(J_\text{th}\).
However, direct measurements yield small values. Henry et al. obtained values of \(14\text{ cm}^{-1}\) and \(12\text{ cm}^{-1}\) for intervalence band absorption in p-type InP and p-type InGaAsP, respectively, at \(\lambda=1.3\) μm for a carrier concentration of \(10^{18}\text{ cm}^{-3}\). When \(\lambda=1.6\) μm, these values are \(24\text{ cm}^{-1}\) and \(25\text{ cm}^{-1}\) for p-type InP and p-type InGaAsP, respectively, at a carrier concentration of \(10^{18}\text{ cm}^{-3}\).
Casey and Carter reported similar values of intervalence band absorption in p-type InP. These measurements show that intervalence band absorption is significantly smaller than what is needed to explain the observed temperature dependence of the threshold current.
The internal absorption losses are determined by free carrier absorption in addition to intervalence band absorption, which is determined by the carrier concentration in the active and cladding layers. Waveguide scattering losses are also included among the internal losses.
For the purpose of calculations described in this tutorial, we assume that a temperature-independent total optical loss \(\alpha_\text{a}\Gamma+(1-\Gamma)\alpha_\text{c}=30\text{ cm}^{-1}\).
Figure 3-32 shows the calculated radiative and Auger components of the threshold current density plotted as a function of temperature for 1.3-μm and 1.55-μm InGaAsP-InP broad-area lasers with an active-layer thickness of 0.2 μm.
The radiative component of the current is calculated using the gain-versus-nominal-current-density relation of Figure 3-9 [refer to the radiative recombination in semiconductors tutorial].
Figure 3-32(a) shows that the threshold current density of 1.55-μm InGaAsP lasers should be lower than that for 1.3-μm InGaAsP lasers in the absence of Auger recombination.
The Auger component of the total current density as calculated from Equation (3-5-5) [refer to the how to estimate the threshold current density of a semiconductor laser tutorial] is shown in Figure 3-32(b).
The total calculated threshold current density \(J_\text{th}\) is shown in Figure 3-32(c).
If the calculated threshold current \(I_\text{th}\) is expressed as \(\sim{I_0}\exp(T/T_0)\), the calculated \(T_0\) values of the radiative component \(J_\text{r}\) are \(T_0\approx100\text{ K}\) for \(100\text{ K}\lt{T}\lt200\text{ K}\) and \(T_0\approx200\text{ K}\) for \(270\text{ K}\lt{T}\lt350\text{ K}\).
The calculated temperature dependence of \(J_\text{r}\) in the low temperature range agrees with the measured temperature dependence characterized by \(T_0\) values in the range of \(100-110\text {K}\).
However, the radiative component alone cannot explain the measured temperature dependence of \(J_\text{th}\) in the high temperature range.
If Auger recombination is included, the calculated values of \(T_0\) in the high temperature range (\(270\text{ K}\lt{T}\lt350\text{ K}\)) using Figure 3-32(c) are \(70\text{ K}\) and \(\sim61\text{ K}\) for 1.3-μm and 1.55-μm InGaAsP lasers, respectively. (These values increase to \(90\text{ K}\) and \(72\text{ K}\) if a temperature-independent Auger coefficient is used in the calculation.)
Experimental \(T_0\) values are slightly lower than the values calculated above. Considering many uncertainties in the calculation, it is possible to conclude that the Auger processes, which become increasingly dominant with decreasing band gap, play a significant role in determining the observed high temperature sensitivity of long-wavelength InGaAsP lasers.
It has been pointed out that the carrier leakage can also take place due to Auger recombination. In the CCCh Auger process, hot electrons with energies far in excess of the heterobarrier height are produced. A fraction of these electrons can "leak" out of the active region to the cladding layers, constituting a leakage current, the value of which may not depend strongly on barrier height.
In some experiments the carrier temperature is found to be considerably higher than the lattice temperature near threshold in InGaAsP lasers. However, other measurements show that the two temperatures are nearly equal.
An understanding of the interaction of the hot Auger electrons with the lattice will be helpful in estimating the importance of Auger recombination for carrier leakage in InGaAsP laser structures.
The next tutorial introduces what is liquid-phase epitaxy.