Methods to study carrier dynamics of LEDs are mainly categorized as optical and electrical techniques. The aim is usually to measure the carrier recombination lifetime in the active region and/or the radiative efficiency of the LED in order to study the mechanisms affecting the efficiency of the LEDs. In this section, first, a widely known model that is used to describe efficiency droop is presented and then the common optical and electrical measurement methods used to extract the parameters for this model are listed.
1.6.1 ABC model
To investigate the efficiency droop, the mathematical model known as ABC model has been widely used. The most advanced form of this model describes the rate of carrier loss from the QW as 𝑅 = 𝐴𝑛 + 𝐵𝑛2 + 𝐶𝑛3+ 𝑓(𝑛) where 𝑅 is the rate of carrier loss, 𝑛
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is carrier density in the QW, 𝐴 is SRH coefficient, 𝐵 is bimolecular coefficient, 𝐶 is Auger recombination coefficient, and 𝑓(𝑛) is a 4th or higher order function of 𝑛 representing carrier leakage [15]. Based on the definition of the rate of carrier loss, radiative efficiency (𝜂𝑅𝐸) of the LED is 𝜂𝑅𝐸= 𝐵𝑛2
𝑅 , total carrier lifetime is 𝑛 𝑅 = 1 𝐴+𝐵𝑛+𝐶𝑛2+𝑓(𝑛) 𝑛 , and the DLT is 𝑑𝑛 𝑑𝑅 = 1 𝐴+2𝐵𝑛+3𝐶𝑛2+𝑑𝑓(𝑛) 𝑑𝑛
. Measurement of these three
quantities in the lab and estimation of 𝑛 is used to fit the associated equations to find the unknown coefficients. The behavior of the coefficients is studied as a function of 𝑛 and temperature to investigate the role of individual processes in efficiency and thermal droop. However, use of this model in its different forms has often showed different results and it is one of the reasons efficiency droop is still the subject of debate. Some studies have shown that often by neglecting the carrier leakage term (𝑓(𝑛)), Auger recombination is the dominant process in efficiency droop due to extracted large C coefficients [16]. On the other hand, groups that are considering the leakage term in the equations have shown that the leakage is partially responsible for efficiency droop [17]. Thus, the community has not consented to a single cause for droop.
An entirely different approach that simultaneously considers both Auger process and carrier leakage is essential to understand efficiency droop. In chapter 4 it will be shown that although both carrier leakage and Auger recombination increase with increasing current density, Auger recombination is the dominant cause of efficiency droop.
In the following sections, common methods used to measure carrier lifetime in order to extract the unknown parameters of the ABC model are listed.
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1.6.2 Time-resolved photoluminescence (TRPL)
TRPL is the most common method to measure the carrier lifetime. It is done by tracking the photoluminescence intensity as a function of time for various optical pumping powers [18-20]. Carrier lifetime is then found by fitting the data to a mono- exponential or bi-exponential decay function [20]. Carrier lifetime vs. 𝑛 is used to study carrier dynamics of the LEDs. The pump wavelength is usually chosen so that it only excites the QWs. Thus, carriers are resonantly generated and recombined in the QWs. Although TRPL is well-established and common, there are several limitations with this method. First, due to optical pumping, the carrier density in the QWs is hard to quantify unless detailed absorption properties of the active region are known. Second, TRPL does not capture the effect of carrier transport in cladding layers and subsequent interaction between carriers in the cladding layers and the QWs [21]. Third, it is shown that although carriers are generated resonantly in the QW, carrier escape does take place which it would affect the studies using resonant pumping to study carrier dynamics [22]. Fourth, TRPL does not achieve the flat-band conditions achieved under electrical injection, resulting in a different electron-hole wavefunction overlap [23]. Thus, TRPL represents an incomplete picture of dynamics of LEDs under electrical injection.
1.6.3 Previous small-signal methods
Small-signal methods have been previously used to obtain the DLT. An optical technique is to small-signal modulate the intensity of the pump laser and track the phase difference between the modulation signal and the PL signal. The phase delay is then attributed to the DLT in the QW [24]. This method has most of the limitations that TRPL faces including the difficulty in estimation of 𝑛 and neglecting of the transport effects.
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To more accurately characterize the DLT in electrically injected LEDs under typical operating conditions, small-signal RF methods have previously been used. An early method applied a time-variant small-signal modulation to the DC current and tracked the phase difference between the input electrical signal and the modulated light output of the LED [25, 26]. One limitation of this method is the assumption that the frequency modulation bandwidth is only governed by the carrier recombination process [16, 27], while studies have shown it is also affected by carrier transport [28-30]. An alternative method to extract the carrier lifetime involves fitting of the small-signal impedance characteristics to simple circuit models representing only the active region of the LED [21, 26, 31]. However, by using extracted parameters from only the impedance data, one cannot reconstruct the modulation response of the device. In addition, more recent simulations have shown that transport effects should also be considered in the circuit model [32]. David et al. recently included transport effects using a method similar to the method developed in chapter 2 to study the temperature dependence of carrier recombination and introduced Coulomb-enhanced capture as a new process in c-plane InGaN LEDs [33].
Chapter 2 presents a powerful method considering all the carrier mechanisms under electrical injection to study the DC and dynamic properties of III-nitride LEDs which aids in the understanding of efficiency challenges and enables the design of high-speed, high-efficiency LEDs. This differential method provides accurate information about the differential carrier lifetimes, carrier density, and radiative and non-radiative rates in the QW. Furthermore, a differential analysis of recombination rates instead of the ABC model is used to study the droop phenomenon.
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