Equivalent Circuit Establishments of a GaN High-Electron-Mobility Transistor and 635 nm Laser Diode for a Short-Pulsed Rising Current Simulation

Abstract

In this paper, a dynamic operational linear regulator (DOLR) based on a GaN high-electron-mobility transistor (HEMT) and wide-bandwidth operational amplifier was developed and implemented. The driving current could be regulated and controlled by the DOLR for 632 nm laser diodes. The constant-current mode for the continuous-wave laser and the pulse-width modulation (PWM) mode for the short-pulsed laser were realizable using this DOLR. This study focused on the rising-edge time change on the laser driving current when the DOLR was operated under the high-frequency PWM mode, because the parasitic components on the GaN HEMT, laser diodes, printed circuit board, and power wires could influence the current’s dynamic behavior. Therefore, the equivalent circuit models of the laser diode and GaN HEMT were applied to establish a DOLR simulation circuit in order to observe the rising-edge time change on the laser driving current. A DOLR prototype was achieved, and so experimental waveform measurements could be implemented to verify the DOLR simulation and operation.

1. Introduction

GaN semiconductor devices can implement higher-frequency operation than conventional Si-based semiconductor devices because two-dimensional electron gas (2DEG) can be formed inside GaN semiconductor devices. Two-dimensional electron gas has high electron mobility, which accelerates electronic conduction in lateral GaN semiconductor devices. Because of the epitaxial growth of GaN layers on Si, SiC, or sapphire substrates, the electric field occurs on the surface of a lateral active layer. Therefore, laterally configured GaN semiconductor devices can withstand a rating voltage of <650 V; however, a new cascode GaN-FET (field-effect transistor) raised the withstand voltage to 900 V [1,2].

“Laser” is a word formed from the initial letters of “light amplification by stimulated emission of radiation”. According to the various materials used for configuration, lasers can be classified as semiconductor lasers, fiber lasers, gas lasers, or solid-state lasers. Figure 1 illustrates a simple semiconductor laser configuration. In Figure 1, the active layer of the laser semiconductor is the second p-type semiconductor, which is placed in between the first p-type and n-type semiconductors. The first p-type semiconductor can be regarded as the positive (+) electrode, while the bottom of the n-type semiconductor can be regarded as the negative (−) electrode. When the positive/negative electrodes apply the electric field, the active layer can be excited to emit a stream of light that can be amplified by mirror surfaces to enhance emitting a laser beam [3]. When a power source is applied to the positive/negative electrodes and the laser semiconductor is in forward-bias operation, the electrons from the n-type semiconductor are injected into the second p-type semiconductor, and the wide bandgap of the heteroisolation junction between the first and second p-type semiconductors can restrict the amount of electron compounding in the active layer; as a result of the carrier confinement, the population inversion probabilities can be increased to promote high-intensity light emission [4].

Semiconductor lasers are equipped with several excellent characteristics, such as monochromaticity, high directionality, high coherence, and high energy density. Diode lasers with wavelengths of 635 nm have been applied to noncontact treatments such as photodynamic therapy groups for toluidine blue and the stability of orthodontic mini-implants [5,6].

Table 1. Crucial technology of linear regulators.

Citation	[7]	[8]	[9]	[10]	[11]	This Study
Light source	LED	LED	LED	LED	Not mentioned (NM)	Laser diode
Transistor	MOSFET	MOSFET	BJT	BJT	GaN HEMT	GaN HEMT
Dimming method	PWM	PWM	PWM	PWM	Undescribed	Undescribed
Optical power adjustment	NM	NM	NM	NM	NM	PWM and constant-current
PWM frequency (Hz)	1k	0.4k	2k	NM	NM	200k
Minimum short-pulsed time	NM	NM	NM	NM	NM	2 µs

lists relevant studies on optoelectronic semiconductors with linear regulators. In the literature [7,8,9,10], light-emitting diodes (LEDs) were typically used as the light source, and bipolar junction transistors (BJT) and metal-oxide-semiconductor field-effect transistors (MOSFET) were used as the linear regulators. Only in [11] was a GaN HEMT used. In addition, in [11], a dimming function was implemented using pulse-width modulation (PWM) with a frequency of <2 kHz.

Optical output power adjustment for a laser diode (LD) is similar to illumination dimming for LEDs. Therefore, in this study, high-frequency PWM and constant-current modes were implemented to adjust the optical output power of a laser diode; the PWM frequency was adjustable to 200 kHz, while the minimum short-pulsed time was 2 µs to reach the maximum operating current.

LEDs associated with GaN materials have many benefits, such as high luminous efficiency, low energy consumption, long operation lifetime, and broad spectral range. Hence, GaN-based LEDs have been applied usefully in disinfection, automotive front lighting, solid-state lighting, and full-color displays [12,13,14,15]. Moreover, combinations of GaN devices and laser diodes have been used in a few practical applications, such as photoconductive semiconductor switches, light detection and ranging (LIDAR) systems, and plasma-assisted molecular beam epitaxy systems [16,17,18].

2. Equivalent Circuits of Laser Diode and GaN HEMT

2.1. Laser Diode

A laser diode with a wavelength of 635 nm (model number: HL63193MG, Oclaro Inc., San Jose, CA, United States) was used in this study, the specifications of which are listed in

Table 2. Laser diode specifications.

Description	Specification
Device package	TO−52
Wavelength range	632 to 643 nm
Operating voltage range	2.2 to 2.6 V
Maximum operating current	1 A
Optical output power	700 mW (at −10 to 30 °C and 1 A)

[19].

The physical configuration and equivalent circuit (EC) of the laser diode are illustrated in Figure 2. In Figure 2a, T_ld1 and T_ld2 are the metal terminals. The outside of the physical configuration could connect with the power source to drive the laser chip. The inside of the physical configuration here included the p-contact, n-contact, bonding wires, active layer, and substrate.

In Figure 2b, the equivalent circuit of the laser diode is depicted. It had package and chip parasitic components. The package parasitic components included the bonding wire resistance R_pld, bonding wire inductance L_pld, and extracted submount capacitance C_pld. The chip parasitic components included the intrinsic diode D_cld, chip resistance R_cld, and chip electrode capacitance C_cld [20,21]; the diode property is presented using D_cld.

2.2. GaN HEMT

The GaN HEMT device used was a GS61004B (GaN Systems Inc., Ottawa, ON, Canada);

Table 3. GaN HEMT device specifications.

Parameter	Specification	Unit
Package	GaNPX package
Drain–source withstand voltage	100	V
Turning-on drain–source resistance	16	mΩ
Drain–source threshold voltage	1.7	V
Internal gate resistance	0.9	Ω
Input capacitance (Ciss)	260	pF
Output capacitance (Coss)	110	pF
Reverse transfer capacitance (Crss)	5	pF

lists its specifications.

The physical configuration and equivalent circuit of the GaN HEMT are illustrated in Figure 3. A particular package (flat no-lead package) was developed and used for the GaN HEMT from the design of GaN Systems Inc; using this physical package, the intrinsic parasitic inductance was reduced. Figure 3a illustrates the physical package configuration, and Figure 3b is the GaN HEMT equivalent circuit. The electrical components included a substrate, Si substrate, GaN buffer layer, two-dimensional electron gas channel, AlGaN buffer layer, p-GaN contact, gate, drain, source electrodes, the bottom of the chip package, and contact pads [22,23].

The equivalent circuit of the GaN HEMT had intrinsic and extrinsic parts, as shown in Figure 3b [24,25,26,27]. The intrinsic part components included the resistances (R_gs and R_ds), capacitance (C_ds), and dependent current source (g_mv_g); g_m is the transconductance value, and v_g is the across voltage on C_gs. The extrinsic part components include the inductances (L_pd, L_pg, and L_ps), capacitances (C_pd and C_pg), and resistances (R_pd, R_pg, and R_ps).

Because of the air–bridge source connection, the pad connection, electrode, and cross capacitance formed the C_pd and C_pg. The parasitic resistances (R_pd, R_pg, and R_ps) represent the contact resistance and semiconductor bulk resistance on the drain, gate, and source terminals. The parasitic inductances (L_pd, L_pg, and L_ps) are at the GaN HEMT with contact pads on the bottom of the chip packages.

The gate electrode and drain-source channel formed the parallel-plate capacitance C_gs. The drain and source electrodes were installed along the two-dimensional electron gas channel, which formed C_ds and C_gd. R_ds is a channel resistance between the drain and source terminals.

3. Dynamic Operational Linear Regulator

Figure 4 is the circuit block diagram of the DOLR based on the GaN HEMT controlling the 635 nm-wavelength laser diode. The DOLR included the operational amplifier (OP), current buffer, GaN HEMT, current detection resistance (Rcs), and the differential amplifier. The control circuit of the DOLR included the microcontroller unit (MCU), voltage buffer, integral circuit, GaN HEMT off switch (GHOS), and GHOS driver; the three laser diodes (L_a1, L_a2, and L_a3) could be controlled by the DOLR.

PWM ports 1 and 2 of the MCU output two signals (V_pwm1 and V_pwm2). The integral circuit could transfer the PWM voltage V_pwm2 to become a direct-current (DC) voltage. Via the voltage buffer preventing the loading effect, that DC voltage can be regarded as a reference voltage V_iref for stabilizing the laser diode operating current I_rld. The OP could compare the differential amplifier output voltage (V_da) with V_iref to control the GaN HEMT. In order to enhance the driving ability of the OP output for V_op, the current buffer was used for the GaN HEMT turning-on operation. Then, the operating current of La₁ to La₃ could be controlled by the DOLR.

The drain–source channel resistance of the GaN HEMT could be regulated by the DOLR to control the drain terminal current. In addition, a short-pulsed current can be fulfilled from a high-frequency’s V_pwm1. Therefore, the high-bandwidth component must be used for the differential amplifier and current buffer.

The driving ability of V_pwm1 could be enhanced by the GHOS driver, as V_pwm1 synchronizing with V_ghos could control the GHOS turning on/off to further manipulate the GaN HEMT. When V_ghos was at the high-voltage level, the GHOS was turned on; then, the gate terminal of the GaN HEMT would become the low-voltage level, which is less than the threshold voltage, resulting in the GaN HEMT turning off. When V_ghos was the low-voltage level, the GHOS could be turned off; then, the gate terminal of the GaN HEMT would become a high-voltage level, because the OP output voltage V_op through the current buffer could control the GaN HEMT. Meanwhile, the DOLR could be controlled to regulate I_rld.

3.1. DOLR Device List

Table 4. DOLR component list.

Component	Model Number
Microcontroller unit	S9S12G48F1MLC: NXP Semiconductors, AG Eindhoven, Netherlands
Voltage buffer	LM258: Texas Instruments Inc., Dallas, TX, United States
Integral circuit	Resistors and capacitors using surface mount devices
OP, current buffer anddifferential amplifier	LT1818CS8#TRPBF: Analog Devices, Wilmington, Massachusetts, United States
GHOS and its driver	TPS2819: Texas Instruments Inc., Dallas, TX, United States PD84002: STMicroelectronics, Geneve, Switzerland
GaN HEMT	GS61004B
Current detection resistance	WSLT2512R1000FEA: Vishay Intertechnology Inc., Malvern, Pennsylvania, United States

lists the practical devices used for the DOLR shown in Figure 3.

3.2. DOLR Specification

The DOLR’s specifications are listed in

Table 5. DOLR specifications.

Description	Circuit Symbol	Range
Three laser diode operating voltages	Vrld	6.6 V
Laser diode operating current	Irld	0–0.8 A
DOLR supply power	Vsp	7 V
PWM signal 1	Vpwm1	5 V, 0 to 100%, 200 kHz
PWM signal 2	Vpwm2	5 V, 5 V, 0 to 100%, 10 kHz
Reference voltage	Viref	0 to 0.8 V

.

3.3. Simulation Circuit

The circuit simulation software POWERSIM (Powersim Inc., Rockville, MD, United States) was used. Based on Figure 4 and considering the parasitic components, the circuit block diagram of the simulation circuit is illustrated in Figure 5.

Figure 5 depicts the parasitic components from the printed circuit board and power source. L_pcb1, L_pcb2, L_pcb3, and L_pcb4 are the parasitic wire inductances; R_pcb1, R_pcb2, R_pcb3, and R_pcb3 are parasitic wire resistances; L_pcb1 and R_pcb1 are on the printed circuit board between T_{g_g} and the current buffer; L_pcb2 and R_pcb2 are on the printed circuit board between T_{g_g} and the GHOS; L_pcb3 and R_pcb3 are on the printed circuit board between T_{g_s} and R_cs; and L_pcb4 and R_pcb4 are on the printed circuit board between T_{g_d} and the third laser diode equivalent circuit of the cathode terminal T_k3.

The parasitic wire inductance and resistance on the power cable of the DOLR supply power (V_sp) were also considered. The parasitic wire inductance and resistance on the printed circuit board are L_pw and R_pw, respectively; the parasitic inductance from the V_sp is the L_pp. L_pw, R_pw, and L_pp were connected in series between V_sp and the anode terminal (T_a1) of the first laser diode equivalent circuit.

3.4. Parameter Considerations and Calculations for GaN HEMT

Because the physical package of the GaN HEMT (GS61004B) used a new preplated Au configuration rather than the conventional bonding wire, the parasitic inductances between the three electrodes (gate, source, and drain) and contact pads [28,29] were reduced. From [29,30], these parameter values were referenced, including L_pd = 1.3 nH, L_pg = 1.2 nH, and L_ps = 0.45 nH; moreover, R_pd = R_pg = R_ps = 1 mΩ was assumed. According to the GS61004B specification list in Table 3, R_gs = 0.9 Ω, R_ds = 27 mΩ, C_gs = 295 pF, C_gd = 6.2 pF, and C_ds = 133.8 pF.

The parameter g_m was the rate of change from the drain-to-source current i_ds (Figure 3b) and gate-to-source voltage V_gs [31,32]. g_m was calculated and expressed as

$$g_m=\Delta i_{ds}/\Delta v_{gs}$$

(1)

From the GS61004B datasheet [22], the i_ds and v_gs values were found on the device’s characteristic curve; therefore, both (4 V, 61 A) and (3 V, 39 A) could be substituted into (1) to obtain g_m = 22 S.

From [17,18], C_pd and C_pg were tiny, at approximately 10⁻¹⁵ F; therefore, this study assumed C_pd = C_pg = 1 pF.

3.5. Parasitic Components on Printed Circuit Board

In this study, the copper wire on the printed circuit board was regarded as a rectangular conductor to evaluate the resistance and inductance values. From [33], the inductance of a rectangular conductor can be calculated and expressed as

$$L_{pcb}=0.2m\times l\times \left\{\ln \left[2l/(w+h)\right]+[2.35m\times (w+h)/l]+0.5\right\}$$

(2)

where l, w, and h, represent the length, width, and thickness of the rectangular conductor, respectively. The length, width, and thickness units are millimeters (mm); the inductance L_pcb unit is the microhenry (μH). In this paper, the copper conductor thickness was 0.035 mm. Moreover, the parasitic resistance of the copper conductor on the printed circuit board can be calculated and expressed as

R_pcb = R_pw = ξ × l/A

(3)

where ξ represents the resistivity (in the present study, ξ = 1.73 × 10⁻⁵ Ω-mm at 20 °C) and A is the cross-sectional area of the copper conductor (A = w × h).

In the GaN HEMT turning-on loop (Figure 5), the parasitic components on the printed circuit board were L_pcb1 and R_pcb1. In the GaN HEMT turning-off loop, the parasitic components on the printed circuit board were L_pcb2 and R_pcb2. Because the copper wire in the GaN HEMT turning-on loop had a length of 49.5 mm and a width of 1.5 mm, substituting the length = 49.5 mm and the width = 1.5 mm into (2) and (3) led to R_pcb1 = 16 mΩ and L_pcb1 = 46.2 nH. Moreover, because the copper wire in the GaN HEMT turning-off loop had a length of 42 mm and a width of 1.5 mm, substituting the length = 42 mm and the width = 1.5 mm into (2) and (3) led to R_pcb2 = 13.2 mΩ and L_pcb2 = 37.5 nH.

A copper wire between T_{g_s} and R_cs on the printed circuit board had a length of 27.3 mm and a width of 5.5 mm; substituting the length = 27.3 mm and width = 5.5 mm into (2) and (3) led to L_pcb3 = 15.9 nH and R_pcb3 = 2.5 mΩ. Moreover, the practical R_cs was 100 mΩ.

The copper wire between the T_{g_d} and the third laser diode equivalent circuit on the printed circuit board had a length of 1 mm and a width of 1 mm; substituting length = 1 mm and width = 1 mm into (2) and (3) led to L_pcb4 = 8.9 nH and R_pcb4 = 6.1 mΩ.

The power wire was connected to the first laser diode equivalent circuit with V_cc. Because the power wire can be regarded as a cylindrical conductor, according to [33,34], its parasitic inductance can be calculated and expressed as

$$L_{pw}=2l_w\times \{\ln [\left(2l_w/d\right)\times \left(1+\sqrt{1+{\left(d/2l_w\right)}^2}\right]-\sqrt{1+{\left(d/2l_w\right)}^2}+\left(\beta /4\right)+\left(d/2l_w\right)$$

(4)

where l_w and d represent the length and diameter of the power wire (cm); β represents the relative permeability of copper (β was set to 1 in this paper), and the units of L_pw are nanohenries (nH). In this study, the power wire had l_w = 20 cm and d = 0.2 cm; substituting l_w = 20 cm and d = 0.2 cm into (3) and (4), L_pw = 209.9 nH and R_pw = 2.7 mΩ can be obtained. Moreover, the parasitic inductance L_pp inside V_cc was also considered, and L_pp was set as 1.2 μH.

4. Circuit Simulation and Experiment

The simulation circuit using the PSIM is shown in Figure 6. The simulation results are presented in Figure 7. In Figure 7, V_pwm1 is the GHOS operating signal, V_iref is the reference voltage for the constant-current operation, V_gs is the gate-to-source voltage of the GaN HEMT, and I_rld is the operating current for the three laser diodes.

In the present study, V_pwm1 was zero, which represented no PWM signal. When V_iref was 0.4 V, the V_gs of the DOLR could be controlled to regulate I_rld and maintain it at 0.4 A, as shown in Figure 7a. When V_iref was 0.8 V, the V_gs of the DOLR could be controlled to regulate I_rld and maintain it at 0.8 A, as shown in Figure 7b. Figure 7 displays results for a simulation of the constant-current mode operation of the DOLR.

Figure 8 shows results for the simulation the PWM-mode operation of the DOLR. The frequency of V_pwm1 was 200 kHz, V_iref was 0.8 V, and I_rld spent 2.2 µs rising to the rated operating current at 0.8 A. In Figure 8a–c, the short-pulsed times of I_rld were 2.25, 3, and 4 µs, respectively.

In accordance with Figure 4, critical experimental waveforms are presented in Figure 9and Figure 10, including V_pwm1, V_iref, V_gs, and I_rld.

In the experimental waveform shown in Figure 9a, when the microcontroller unit stopped outputting the PWM signal from the PWM port 1, V_pwm1 was a low voltage level. When V_iref was set at 0.4 V, V_gs could be regulated to control the GaN HEMT; hence, I_rld was operated in the constant current of 0.4 A. In the experimental waveform shown in Figure 9b, V_pwm1 was also at a low voltage level; however, V_iref was set at 0.8 V, V_gs could be regulated to control the GaN HEMT, and I_rld could be operated in the constant current of 0.8 A.

In the experimental waveform shown in Figure 10, the PWM mode was implemented for the laser diodes. I_rld could be operated in different PWMs. Because the microcontroller unit outputted the PWM signal from the PWM port 1, V_pwm1 became a pulse signal, and both V_gs and I_rld followed the change of V_pwm1. V_iref was set at 0.8 V, and the rising time of I_rld was 2 µs to reach the maximum operating 0.8 A. In Figure 10a–c, the duty cycle ratios of the PWMs were 40% (2 µs/5 µs), 60% (3 µs/5 µs), and 80% (4 µs/5 µs), respectively.

The DOLR prototype driving the three 635 nm laser diodes is shown in Figure 11.

5. Conclusions

In this study, a GaN HEMT was incorporated with wide-bandwidth operational amplifiers to achieve a DOLR. Three 635 nm laser diodes were controlled by the DOLR; therefore, the laser diodes could be operated in the PWM mode to achieve a short-pulsed laser or in the constant-current mode to achieve a continuous-wave laser. In order to understand the operating current changes in laser diodes, this study used the equivalent circuits of the laser diode and GaN HEMT to simulate DOLR operations and observe the critical waveforms. From the simulations and experimental results, it was concluded that the operating current of the laser diode was influenced by critical factors including the device parasitic components and PCB layout. Using the developed DOLR prototype, three 635 nm laser diodes were controlled to achieve short-pulsed and continuous-wave lasers.