Organization of this thesis - 發光二極體於功能性頻譜照明之研究

1 Introduction

1.6 Organization of this thesis

The thesis is organized as following: The complete treatment of LED spectrum characterization is provided in Chapter 2, including the junction temperature detection and determination, the LED spectrum modeling in terms of junction temperature and drive current, and the validation of the simulated spectrum model. In Chapter 3, the methodology of the multispectral mixing optimization is presented, which has six steps that in all aspects can correspond to the design flow of the

conventional lens system. By using the proposed methodology into practical LEDs system, we demonstrate two design cases for general lighting application in Chapter 4. The first example follows the design flow step-by-step to produce a color tunable LEDs cluster with high color rendering property as well as high efficiency. In the second design case, we further release the constraint of the constant ambient temperature, so that a more practical multispectral mixing platform can be realized.

Furthermore, detailed analyses and comparison for different LEDs combination are also provided in this chapter. Finally, discussions and summary of this doctoral dissertation, and recommendations for the future works are given in Chapter 5.

Chapter 2 LED Spectral Characterization

2.0 Goal

In the traditional optical design, the dioptre, or diopter ϕ, is a unit of measurement of the optical power for a single lens, which can be expressed in terms of refractive index n and surface curvatures r1, r2. In the first order optics, the expression for a thin lens can be written as:

1 2

1 (n 1)(r r)

 f    (2-1)

where f is the focal length. The refractive index of optical glasses, in general, changes with ambient temperature, the extend of which depends on the glass type and on the wavelength ^. Therefore, the diopter of a lens can be characterized by temperature and surface curvatures. One benefit of using diopter (reciprocal of focal length) rather than focal length is that the linearity exists in power calculation of thin lens system.

For example, a doublet system with a thin 2-dioptre lens close to a thin 0.5-dioptre lens would have the focal length approximated to that of a singlet with 2.5-dioptre.

For an additive mixing system, the corresponding assumption of narrower spectral bandwidth yields the linear property in chromaticity calculation as mentioned in Section 1.1. In addition, the factors conceptually analogous to the surface curvature and ambient temperature in lens system are the drive current IDC and junction

temperature T_j. As we have known that I_DC and T_j are crucial bases for spectral model.

The process that establishes the connection of spectrum power distribution SPD with drive current I_DC and junction temperature T_j can be named as the LED spectral characterization. In this chapter, we have an intention to provide a complete process and formalism in spectral characterization.

2.1 Junction temperature measurement

Due to the p-n junction located deep inside the commercial LEDs package, real time junction temperature determination is almost impossible ^. Many researches therefore reported several junction temperature measurement techniques, including the forward voltage method ^{}, the peak wavelength shift method ^, the high energy slope method ^, the nematic liquid crystal method ^{}, and the radiation energy method ^{}. Among these methods, the forward voltage method is utilized in this research because it is the most convenient way to incorporate the junction temperature detection into the control of drive current.

2.1.1 Forward voltage method

There are two main steps for the forward voltage method. The first one is to launch the pulsed calibration measurement to obtain the database of forward voltage Vf

subject to a set of two parameters: junction temperature T_j and pulsed drive current I_p. By interpolating the data in the first step, it is likely to precise estimate the junction temperature from the corresponding forward voltage.

For the calibration measurement, five commercial available single-die high- power LEDs are selected, consisting of red, amber, green, blue, and cool-white emitters with the maximum input power of 1 watt. The sample LEDs are mounted

inside TeRchy HRMB-80 isothermal oven with active air circulation ^. The oven temperature is predefined by every 10°C increment. To ensure the thermal steady state between the air in the oven and chip junction, at least thirty minutes delay between the settled temperature and the measurement is needed. Each sample LED then is driven by a pulsed current with low duty cycle (e.g. 0.1%), so that the additional thermal effect from the power dissipated in the chip junction can be neglected. Therefore, the junction temperature is logically equivalent to the oven temperature. During the pulse current applied, the voltage measurement is performed with the Keithley 2400 SourceMeter that controlled by our GUI program.

2.1.2 Junction temperature estimation

A typical forward current-voltage Ip−Vf characteristic at different junction temperature T_j is shown in Figure 2-1. According to different current level, the current-voltage character reveals three different tendencies. When the drive current ≤ 100uA, the current exceeds the exponential fit (dashed line) because the measured character is dominated by various leakage currents. For example, one of these leakages is the carrier tunneling transport across the quantum-well structure ^. For drive current ≥ 10mA, the effect of the internal series resistance gradually dominate the character of the current-voltage curve, which results in a lower drive current ^. In the ideal exponential fit region 100uA ≤ Ip ≤ 10mA, the current-voltage characteristic of the p-n junction diode can be described by the Shockley equation ^:

exp( ^f )

saturation currents under diffusion and recombination process. n_ideal is the ideality factor with a theoretical value between 1 and 2.

Figure 2-1 Typical semi-log current-voltage characteristic of a green InGaN LED (HELIO Optoelectronics Corp., HMHP-E1HG)

Subsequently, we attempt to establish the relation between forward voltage V_f and junction temperature Tj by examining five current levels, 10uA, 100uA, 1mA, 10mA, and 100mA from Figure 2-1. As shown in Figure 2-2, despite slight deviations from the linearity due to the effects of leakage current (see the high junction temperature side for current I_p = 100uA) and internal series resistance (see the low junction temperature side for current Ip = 10mA), a linear approximation has proven to be sufficient for junction temperature prediction for 100uA ≤ Ip ≤ 10mA ^, which is given as:

( ) ( )

f j P j

V T  I T  (2-3)

where γ and δ are the slope for a specific pulsed current I_P and the current independent intercept, respectively.

Figure 2-2 The voltage-temperature characteristic of a green InGaN LED (HELIO Optoelectronics Corp., HMHP-E1HG) at five current levels.

With the linear approximation, the slope γ and intercept δ of Equation (2-3) can be obtained from measuring only two voltage-temperature characteristics, V_f(T₁) and Vf(T2), which prevents a time-consuming measurement. Where T1 and T2 can be the two extreme cases as the thermal boundary, i.e. T₁ = 20 °C and T₂= 110 °C respectively. Therefore, acalibration curve that profiles the relationship between the forward voltage V_f and junctiontemperatures T_jcan be rewritten as:

2 1

1 1

2 1

[ ( )]

( ) ( )

j f f

f f

T T

T V V T T

V T V T

   

 (2-4)

For the pulsed drive current Ip > 100mA, the behavior of the internal series resistance (Rs) should be taken into account. Thus the Equation (2-3) can be modified

( ) ( ) ( )0

f j p s j j

V T I R T  I T  (2-5)

In fact, junction temperature dependence of the internal series R_s(T_j) for I_p > 100mA, like V(Tj) in the region of 100uA ≤ Ip ≤ 10mA, is often approximated by a linear expression as well, which could be simply written as R_s(T_j) =γ’T_j +δ’ with slope and intercept γ’ and δ’. The new slope γ’’ = γ’ + γ and intercept δ’’ = δ’ + δ will be generated to fit the behavior in this region. Consequently, it is more convenient to stick with Equation (2-4) for practical junction temperature estimation, via only two measurements to obtain a set of parameters (γ, δ) or (γ’’, δ’’). The results of the best fitting for all measured LEDs are gathered in Table 2-1. A good agreement between the experimental measurement and linear model can be obtained with R² exceeding 0.99.

Table 2-1 Pentachromatic LEDs, specific pulsed current Ip , slopes γ and γ’’, and intercepts δ and δ’’ of the linear approximation.

LED (HELIO

Optoelectronics Corp.)

I_p = 1mA I_p = 100mA

γ δ γ’’ δ’’

HMHP-E1HR (red) -1.91E-03 1.72 -1.82E-03 2.13

HMHP-E1HA (amber) -2.19E-03 1.80 -1.74E-03 2.06

HMHP-E1HG (green) -2.91E-03 2.68 -2.48E-03 3.18

HMHP-E1HB (blue) -1.35E-03 2.43 -1.39E-03 2.82

HMHP-E1HW (cool-white)

-1.54E-03 2.56 -2.04E-03 2.98

2.2 Junction temperature determination

To this point, we have completed junction temperature estimation from the current-temperature calibration measurement. In the following step, sample device is operated under normal conditions, which is exposed to variant ambient temperature T_a and subjected to a series of DC drive current IDC. With the help of previous calibration, the junction temperature determination can be achieved in terms of ambient temperature Ta and DC drive current IDC directly.

We firstly apply a constant drive current IDC through the sample LED mounted on a fixture (Arroyo Instruments, TEC 264-BB-DB9). The entire module is placed inside the cavity of an integrating sphere. The temperature of the fixture controlled by the thermoelectric cooler (Arroyo Instruments, TEC Source 5310) can be regarded as the ambient temperature Ta. As the thermal steady state has been reached, the DC forward voltage V_DC is recorded, and the emitted spectral power distribution SPD as well as the overall optical power Φ of each sample LED can be captured by the spectrometer (SR-UL1R, Topcon) attached to the integrating sphere. The junction temperature Tj can be determined by the interpolation of the DC forward voltage VDC

according to the pulsed calibration measurement. Finite sampling points are measured in a normal operation range (10 ^oC ≤ Ta ≤ 100 ^oC and 0 mA ≤ IDC ≤ 350 mA), in which the incensements of ambient temperature and DC drive current are programed to be 10 ^oC and 35 mA, respectively.

Based on the experimental setup, we could have measured results composed of one M x N spectral matrix S and several M x 1 parameter vectors, i.e. tj (junction temperature), ta (ambient temperature),ϕ (optical flux), vDC (DC forward voltage) and iDC (DC drive current). Where M represents the number of experimental modulations

380nm to 780nm in steps of 10nm (N = 41). It is noted that vectors are denoted by bold-faced lower-case letters and matrices are represented by bold-faced capital letters.

With the sufficient database, the junction temperature T_j now can be related to ambient temperature Ta and DC drive current IDC via the introduction of the equation developed by A. Keppens ^: importing variant known input data set (I_DC, T_a) and corresponded output data T_j, the fitting values for all sample devices at Ta = 50 ^oC are shown in Table 2-2. In Equation (2-6), the thermal resistance R_t between the junction and the reference point can also be predetermined by inserting known values of Tj, Ta, Pe (= IDCVDC), and Φ to the

In which the denominator, the difference of the input electric power Pe and the radiant flux Φ, indicates the power dissipated in the LED. The measurement results for red AlInGaP LED (HELIO Optoelectronics Corp., HMHP-E1HR) are shown in Table 2-3, where the resistance of 48.1 ^oC/watt can be determined.

Table 2-2 The values of fitting parameters c1, c2, c3, and c4 for pentachromatic LEDs at ambient temperature Ta = 50 ^oC.

LED (HELIO

Optoelectronics Corp.)

Fitting parameters

c1 c2 c3 c4

HMHP-E1HR (red) − 0.0420 0.0685 − 2.8118 − 1.4573 HMHP-E1HA (amber) − 0.0996 0.1972 − 2.8791 − 7.3223 HMHP-E1HG (green) − 0.5543 0.7596 21.2939 − 35.8853 HMHP-E1HB (blue) − 0.0039 − 0.0107 3.8395 1.7290 HMHP-E1HW

(cool-white)

− 0.0669 0.0927 − 1.5967 − 3.0327

Table 2-3 The DC drive current I_DC, electrical power P_e, optical power Φ and junction temperature T_j for red AlInGaP LED (HELIO Optoelectronics Corp., HMHP-E1HR) at ambient temperature T_a = 50 ^oC.

I_DC(mA) P_e(watt) Φ (watt) T_j (^oC)

70 0.143 0.202 56.9

140 0.307 0.429 64.8

210 0.495 0.676 73.8

280 0.697 0.935 83.5

350 0.915 1.208 94.0

2.3 LED spectrum modeling

2.3.1 Double Gaussian model

Generally, the spectral power distribution SPD can be fitted by a single Gaussian function, which incorporates three the power (p), peak wavelength (^ˆ) and spectral width (Δλ) with junction temperature. However, in most of cases, practical spectrum is not perfectly symmetric, which will lead to the numerical error by single Gaussian fitting. In order to overcome this issue, in this chapter, we proposed a double Gaussian function with two sets of parameters: ^{( ,}^p  ^ˆ^,  ⁾ and ^{( ',}^p ^ˆ^', ^'). On the basis of the discussion in Section 1-2, all parameters related to the spectrum are supposed to be functions of both junction temperature Tj and DC drive current IDC. The estimated spectrum composed by the double Gaussian function, in contrast with the measured spectrum S, is denoted as S. Therefore, an estimated M x N spectral matrix S (e.g.

M = 100 and N = 41 respectively) for a single-color LED can be expressed as:

  '

S G G (2-8)

where G^ g



1^,^^,gM



^T and G^'^ g



^{' ,}1 ^^{, '}gM



^T represent two Gaussian bases of the double Gaussian spectral matrix. Here we can temporarily omit G' and solely focus on G due to the same treatment for both of them from Equation (2-8) to Equation (2-10). The base matrix G has M spectral vectors g₁ to g_M, each of them has N sampling wavelengths. The value for the nth point of mth row vector gm, named as gmn, can be given by:

2 2

exp{ [ ( ) ] /ˆ }

mn m n m m

g  p     (2-9)

where three parameters p_m, ^ˆ_m, and Δλ_m refer to the mth Gaussian power, peak wavelength, and spectral width of the base matrix G, whose values could be found by satisfying the minimization of Equation (2-10) :

2 ˆ ˆ

arg min[ | s_ms_m| , {p_m, _m, _m, p' ,_m ' ,_m ' }]_m (2-10)

where sm is the mth measured spectrum (mth vector) of the spectral matrix S, and

  '

m m m

s g g is the estimated spectrum, corresponding to sm , of the spectral

matrix S .

2.3.2 Single-colour spectral function

After applying the minimization of Equation (2-10) though the spectral matrix, we have three M x 1 vectors including Gaussian power p, peak wavelength ˆλ , and spectral width Δλthat can empirically be related to junction temperature tj and DC drive current iDC:

ln(  _{p p}

p) M c (2-11a)

ˆ λ λ

λM c (2-11b)

ln(Δλ)M c_{Δλ Δλ} (2-11c)

whereMp^^[tj^T^{ln( ) ln(}t j iDC^{) ]} l ,Mλ ^^[t j ^ln(iDC⁾ l] and MΔλ^^{[ ln( )}tj tj ^¹ i⁽ DC⁾^{1/ 2} l^] are

M x 3 basis matrices for p, ˆλ and Δλ, respectively. The vector element l indicates

the M x 1 all-ones vector. cp, cλ, and cΔλ refer to 3x1 coefficient vectors, whose values could be calculated by linear least square method, e.g. power coefficient vector^c^p ^^{M M}



^p^T ^p



^¹^M^p^T^{ln( )}^p ^{. For the}red AlInGaP LED (HMHP-E1HR), Figure 2-3 shows the distribution of all elements in Gaussian power p and its coefficient values cp1, cp2 and cp3. The corresponded goodness of fit, shown in Figure 2-4, reveals that the Gaussian power distribution is well fitted by Equation (2-11a).

Similarly, applying the above regularized process Equation (2-9) − Equation (2-11) to the other Gaussian function G' will lead to coefficient vectors

', ', and '

p λ Δλ

c c c . By obtaining all of the coefficients, the complete double Gaussian

function ^S^{( )} for single-color LED spectrum can be given in respect of the junction temperature T_j and DC drive current I_DC:

Figure 2-3 The distribution of all elements in Gaussian power p and its fitting

coefficient values c_p1, c_p2 and c_p3.

Figure 2-4 The deviation and goodness of fit for Gaussian power distribution fitting.

2.3.3 Phosphor-converted spectral function

For the spectrum of phosphor-converted white LED SW^{( )} , the estimated spectrum

W( )

S  is simply assumed to be composed of two double Gaussian functions SB^{( )} and SF^{( )} :

( ) ( ) ( )

W B F

S  S  S  (2-13)

where SB^{( )} GBGB^' and SF^{( )} GFGF^' denote the double Gaussian in the blue region and the fluorescence region, respectively. Here a cutoff wavelength λBF should be defined to denote the boundary in the middle of blue and fluorescence component, whose value can be pointed when the slope of measured spectrum just changes from negative to positive. Therefore, the modeling of the spectrum S_B( ) follows the same mathematical treatment in single-color case from Equation (2-9) to Equation (2-12).

The other spectrum SF^{( )} , however, can subsequently be found by the same way but using the modified target spectrum^|SW^{( )} SB^{( ) |} .

2.4 Validation of the spectral model

In order to validate the spectrum models presented in Equation (2-12) and Equation (2-13). The simulation results as well as the measurement data for green and phosphor-converted LED emission spectra at T_j = 25 ^oC and I_DC = 350 mA are correspondingly illustrated in Figure 2-5. The results show that a good agreement between the experiment and numerical approximation could be obtained with R² exceeding 0.98. The fitting parameters of estimated phosphor white light spectrum, determined from Equation (2-11), are to be listed in Table 2-4. Furthermore, the luminous flux and CIE colour coordinates for all sample LEDs are calculated and compared in Table 2-5.

Figure 2-5 The illustration of the simulation model and the experimental measurement

Table 2-4 The parameters of approximated phosphor-converted LED spectrum. The blue and fluorescence components should be individually considered.

( ) ( ) ( )

W B F

S  S  S 

GB G_F G_B' G_F'

cp -4.1322 -4.8712 ^c^p¹^' -4.5411 -4.5641

cp -0.0051 0.0003 ^c^p²^' -0.0010 -0.0009

cp 2.0739 2.2380 ^c^p³^' 2.1244 2.1370

c_1 450.0824 539.5471 c_1' 453.8196 561.7751

c_2 0.0552 0.0340 c_2' 0.0330 -0.0375

c_3 -2.0052 0.4289 c_3' -2.5025 -4.3316

c__1 2.0876 2.9537 c__1' 3.6268 4.4596

c__2 -0.0030 0.0038 c__2' 0.0079 0.0022

c__3 0.0047 0.0020 c__3' 0.0023 0.0053

Table 2-5 The comparison of the simulation and measurement on luminous flux and CIE colour coordinates for all sample LEDs.

LED (HELIO

Current-voltage characteristics for five sample LEDs have been measured at four junction temperatures from 20^oC to 110^oC. By examining different current levels, a

temperature T_aand DC drive current I_DC by Equation (2-6).

In the section of spectrum modeling, a double Gaussian function has been proposed to numerically fit practical spectra that are usually not perfectly symmetric.

The features of the Gaussian function, the power (p), peak wavelength (^ˆ) and spectral width (Δλ), can empirically be related to junction temperature T_j and DC drive current IDC as given by Equation (2-11). Once all of the related coefficients are obtained, the double Gaussian function ^S^{( )} for single-color LED spectrum will be completed as Equation (2-12). The spectrum of phosphor-converted white LED

W( )

S  , however, can subsequently be found by individually imposing the same mathematical treatment to blue region and fluorescence region. A good agreement between the experiment and numerical approximation could be achieved with R² exceeding 0.99.

Chapter 3 Multispectral Mixing Optimization as Lens Design Techniques

3.0 Goal

The solution of lens design is a typical inverse problem. Given the effective focal length (EFL) and degree of correction for an optical system, it is always possible to determine the curvatures, the thicknesses, and the number of lenses accordingly. For example, if we aim to design a lens system with a specified EFL and correct three Seidel aberration coefficients, it can be analytically resolved by a set with two singlet lenses, that leaves four degrees of freedom, two powers and two shape factors [the shape factor is defined as (R2 + R1) / (R2 − R1), where R1 and R2 are the radii of the first and second surfaces, respectively] ^. However, due to the complexity of multiple lenses that increases the computational cost, the more efficient method in lens design would resort to an iterative process ^, as shown in Figure 3-1(a).

In multispectral mixing, a similar problem inspired us to borrow this process by replacing the lens set with a number of LEDs for a certain predefined requirements.

The corresponded design procedure is proposed in Figure 3-1(b), including six steps:

(3.1) initial system, (3.2) define boundary condition, (3.3) optimization, (3.4) aberration or merit analysis, (3.5) judgment, and (3.6) tolerance analysis. The aim of this chapter is to step by step complete the optimization process.

Figure 3-1 Design procedure of (a) lens design and (b) spectral synthesis of a LED cluster. Both flow charts include six steps: (3.1) initial system, (3.2) define boundary condition, (3.3) optimization, (3.4) aberration or merit analysis, (3.5) judgment, and (3.6) tolerance analysis.

3.1 Initial system

Like the glass map with variant lenses in lens design, a “LED map” with broad range of LEDs could be accordingly generated based on the manufacturers’ datasheets that offer different available materials and peak wavelengths ^{}. Because it is known that the LEDs with higher luminous efficiency possess higher emission flux, the luminous efficiency of a LED can be conceptually analogous to the refractive index, the y-axis of the glass map, of a lens. On the other hand, we replace the Abbe number, the x-axis of the glass map, by the peak wavelength for no good reason. Thus a LED map can be subsequently plotted as Figure 3-2. It is obvious that green (505nm) and amber (595nm)-colour LEDs would serve as the appropriate candidates in the consideration of high luminous efficiency,.

Figure 3-2 Normalized luminous efficiency of visible LED made from GaInN and AlGaInP series versus individual peak wavelength. The LED with high LE is analogous to the lens with high refractive index.

If we plan to mix two single-colour LEDs for a specific color temperature CT, the most straightforward solution is to select two complementary peak wavelengths on the chromaticity diagram. However, the question becomes more complex while multiple figures of merit are considered by a number of LEDs. To pick appropriate LED set in a systematic way, we list three suggestions for initial system ^:

1. A mental guess. This way is workable for an expert while it is laborious for a beginner.

2. A designed case in previous literatures. It is the most common way to choose a design close to your requirements.

3. A search through the patent files. This is also a time-consuming work and the consideration of avoiding the patent’s claims in your design is necessary.

At this moment, the second approach is easier to follow and, fortunately, many previous literatures have disclosed their experience for specific merits, e.g., the trichromatic source composed of primary emissions (630 nm, 530nm, and 450nm) makes surface colors appear more saturated, whereas the continuous spectrum designed to mimic daylight will have better color rendering ability ^. In addition to single-colour LEDs, the rapid progress in efficiency of phosphor based LEDs will certainly drive the solid state lighting into more composite possibility ^.

3.2 Define boundary conditions

Before optimizing a predetermined initial system, the designer must define the domains of input variables. Such step not only ensures a reasonable result but also reduces the computational time. In lens design we usually set the curvatures and the thicknesses of lenses as the free variables to be optimized, whose domains are mainly

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