Calculated energy distribution of electrons in the active region at 3 different junction temperatures: 500, 700, and 1000 K. A flat band diagram schematic is used just to show the barrier height of the p-GaN and for a comparative picture of the three distributions, which actually correspond to three different band diagrams. The integrated tail of the Fermi–Dirac distribution makes up only 0%, , and of the total current at the junction temperatures of 500 K, 700 K, and 1000 K, respectively.
Schematic of electron overflow caused by ballistic or quasiballistic electron transport across the InGaN active region. The electrons gain a kinetic energy after being injected into InGaN, which equals to . These hot electrons will either traverse the active region ballistically and quasiballistically, escape recombination inside InGaN, and contribute the electron overflow current, or be thermalized and captured inside the active region through interactions with LO phonons.
(a) Calculated ratio of the overflow electron current to the total current as a function of the EBL barrier height in nonpolar -plane LEDs, assuming flat band conditions in the active region (i.e., 0 V net potential drop across the InGaN active region after the applied external voltage compensates the built-in potential, which is ), corresponding to 3.8, 4.0, and 4.7 V externally applied bias for the LEDs with 15%, 8%, and 0% Al in the EBL, respectively. (b) Calculated ratio of overflow electron current to the total current as a function of the applied voltage (forward direction) across the -plane LEDs with three types of EBLs: 0% Al, 8% Al, and 15% Al. The symbols in (a) and (b) represent the calculated points whereas the lines are guides to the eye.
Calculated (overflow electron current/total electron current) as a function of the applied forward voltage across the LED without the SEI and without EBL, and the LED with a 1-layer InGaN SEI and without EBL. Symbols represent the calculated values and solid lines are guides to the eye. The inset shows the simplified conduction band edge for the LEDs with and without (dashed line) the SEI.
Calculated conduction band edge of -plane (solid line) and -plane (dotted line) InGaN LEDs with a 6 nm active region and a 10 nm EBL. The injection current density for both LEDs is .
Calculated electron overflow current as a function of the voltage applied across the device for -plane DH LEDs (6 nm active region) with different EBL heights (i.e., Al and 15% Al in ) and without SEI as well as a -plane DH LED with SEI and without any EBL. Any voltage drop across metal/semiconductor contacts is neglected.
(a)Relative EQE of -plane LEDs grown on freestanding -plane GaN substrates with varying Al composition (15%, 8%, and 0%) in the EBL layers, measured under pulsed current, pulse width and 0.1% duty cycle. The inset shows the current-voltage dependence for the LED with 15% Al in EBL. (b) The EL efficiency loss as a function of the external applied voltage across the p-n junction of the LEDs, assuming negligible electron overflow at the current density corresponding to the peak efficiency for the LED with 15% Al in EBL, which is very reasonable according to our calculations.
Relative EQE of -plane DH LEDs grown on -plane GaN templates on sapphire with and without an EBL layer. The LEDs were measured under pulsed current, pulse width and 0.1% duty cycle.
(a) Schematic for the two -plane LEDs with InGaN SEI before the active regions (to thermalize the injected electrons from the n-GaN layers), one of which has a 10 nm EBL with 15% Al and the other one without any EBL in the -region. (b) Relative EQE of the two -plane LEDs with SEI: one with and one without EBL. The LEDs were measured under pulsed current, pulse width and 0.1% duty cycle.
Relative EQE of two -plane LEDs with SEI inserted under the active region: one with and one without EBLs. The LEDs were measured under pulsed current with pulse width and 0.1% duty cycle. The SEI includes three intermediate InGaN layers with In compositions of 3%, 6%, and 10%, in the given order.
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