Blue Light Gallium Nitride Laser Diode

SAN JOSÉ STATE UNIVERSITY
Thayer Watkins

A Blue Light Gallium Nitride Laser Diode

The Motivation

The search for a practical blue-light laser diode is driven by the prospects of profits and the economic benefits for society. Blue-light lasers based upon media such as ZnSe or argon have long been known but it is only the red light lasers that have been economical for use in general applications. The major advantage of the blue light lasers and laser diodes is that they will increase the information storage capacity of such devices as CD-ROMs. Some sources [Gunshor 1993] hold out the prospect of blue light lasers increasing storage capacity by a factor of four. This would mean that compact discs could store 2.6 gigabytes rather than 650 megabytes. This would be the case if a blue light laser produces light which has one half the wavelength of the red light lasers and hence the area for storing one bit of information would be reduced by a factor of one fourth. But the blue light laser diodes that appear to be practical are not reducing the wavelength by a full one half; instead the ratio of wavelengths is more like 60 to 65 percent. This would increase the storage capacity of devices by a factor of between 2.4 and 2.8 to 1. This is substantially less than four but still highly worthwhile.))

The History

As late as 1993 the most likely candidate for a practical blue LED was ZnSe on a GaAs substrate. But as a result of recent breakthroughs at Nichia Chemical in Japan the focus of attention is now on GaN as a medium for blue LEDs and laser diodes. These GaN LEDs are definitely now in the production stage. Nichia, as of April 1996, was shipping about two million GaN LEDs per month. The development of economical GaN laser diodes continues.))

The feasibility of GaN LEDs was publicized in 1971 by research at RCA. The research were able to create photoluminescence in the blue and the green range of the spectrum. The spectra for this photoluminescence is shown in Figure 1. An interesting aspect of the results is that the peaks of the spectrum depend upon the temperature. The spectrum also apparently depend upon some other uncontrolled factors. The work at RCA was based upon GaN doped with zinc and using indium contacts. Recent work has also made use of indium along with GaN.))

Technical Problems of Production

Although the RCA work demonstrated the feasibility of GaN lasers there were three technical problems to overcome before GaN LEDs could become practical:

1. Lack of a suitable substrate))
2. Thermal convection problem due to the high
(1000^oC) temperature needed to create the GaN
3. the failure of p-type doping.

Sapphire was used as a substrate but it was not completely satisfactory because of an approximately 15 percent mismatch of the lattices of GaN and sapphire. Researchers at Nichia solved the problem of the discontinuity in lattice structure at the boundary between the substrate and the GaN by creating a buffer layer of aluminum nitride (AlN) on the sapphire substrate before the GaN crystal is formed. Later they improved upon the method by using a buffer layer which is formed by deposit of GaN from an organometallic (metalorganic) vapor. Nakamura at Nichia Chemical Industries of Tokushima, Japan invented a dual-flow reactor that blows gas perpendicular to the substrate. Nakamura also solved the problem of achieving p-type doping. He used N₂ gas rather than ammonia (NH₃) in process of annealing the GaN-Sapphire diodes. Ammonia dissociates at high temperature (400^oC) producing hydrogen ions (H⁺) which interfers with the lasing processes. The dopant was also changed, from Zn to Mg. The resulting laser diodes are 200 times brighter than the previous versions.))

Operationing Characteristics and Problems

There are some other technical problems involved in producing a GaN laser diode. Laser diodes differ from the gas and crystal lasers in many significant ways. First of all, semiconductor diodes are physically much smaller than other lasers. Second, the amplification takes place in the junction of the semiconductor so only a small part of a small device is involved in the lasing processes. This means that the gain coefficients (amplification per unit length) have to be much higher than for other types of lasers.

The roughly elliptical cross-section of the junction region dictates that the beam will have an elliptical shape; i.e., it spreads much less (contrary to what one might at first think) in the plane of the junction than in the plane perpendicular to the junction. This means that the beam is not TEM_0,0. Third, the divergence angles are relatively large, on the order of a few degrees, and the divergence angles are different in the different planes.

Fourth, the bandwidth for laser oscillation is much higher than for other lasers and multimode oscillation often occurs.

Fifth, holes must be taken into account in the semiconductor processes as well as electrons. [Verdeyen p. 442]))

Sixth, the most effective way to create an optical cavity for creating feedback is to use mirrored sufaces of planes cleaved on the crystal planes. For GaN on a sapphire substrate there is a problem of a difference in the angle of the cleaved planes of GaN and sapphire of about 30°.))

Spectral Characteristics of GaN LEDs

In December of 1991 Nakamura et al. reported achieving a peak wavelength output from a p-n junction GaN-based diode of 430 nm with a Full-Width at Half Maximum (FWHM) of 55 nm. This laser diode had a power output ten times a comparable SiC blue-light diode.

The technical breakthroughs for GaN-based laser diodes have come quickly in the past few years. In July of 1995 Nakamura et al. reported the development of yellow, green and blue light- emitting GaN-based diodes. The FWHM for the green laser diodes was 45 nm for a peak wavelength of 525 nm. In March of 1996 Vaudo et al. reported electroluminescence from a GaN diodes which has a spectral peak at 400 nm. The FWHM is only 30 nm. This is a quite narrow range for a semiconductor. The location of the spectral peak depends upon the current density so that the effective output of the diode can be shifted all the way from orange to ultraviolet light by varying the current.

However, in January of 1996 Nakamura et al. had reported an even smaller FWHM of 1.6 nm for an InGaN multiwell laser diode using GaN/AlN buffer layers. This was at room temperature. The spectral peak was at 417 nm. In February Nakamura et al. reported a FWHM of only 0.05 nm for an InGaN multiwelllaser diode at room temperature. The peak was at 415.6 nm. This was a heterostructure as opposed to a homostructure of p-n junction GaN diode used by Vaudo et al..

Aggarwal et al. were able to create an ultraviolet laser from GaN with GaN/AlN buffering layers using optical pumping from a N₂ gas laser. The spectral peak ranged from approximately 359 nm at liquid nitrogen temperature (77 K) to 365 nm at room temperature (295 K). This was reported in February of 1996.

Obviously the technical obstacles to marketing a practical blue-light GaN laser diode are being rapidly surmounted and this device may well be an economic reality in the near future. Nichia Chemical Industries is at the leading edge of this technology.

References:

H.C. Casey, Jr. and M.B. Panish, H(S -1)_e(S -1)_t(S -1)_e(S -1)_r(S -1)_o(S -1)_s(S -1)_t(S -1)_r(S -1)_u(S -1)_c(S -1)_t(S -1)_u(S -1)_r(S -1)_e(S -1)_ (S -1)_L(S -1)_a(S -1)_s(S -1)_e(S -1)_r(S -1)_s(S -1)_, Part A,

Academic Press: New York, 1978.

D.E. McCumber, "Einstein Relations Connecting Broadand Emission and Absorption Spectra," P(S -1)_h(S -1)_y(S -1)_s(S -1)_i(S -1)_c(S -1)_a(S -1)_l(S -1)_ (S -1)_R(S -1)_e(S -1)_v(S -1)_i(S -1)_e(S -1)_w(S -1)_, vol. 136 (November 16, 1964), pp. A954-A957.

G.H.B. Thompson, P(S -1)_h(S -1)_y(S -1)_s(S -1)_i(S -1)_c(S -1)_s(S -1)_ (S -1)_o(S -1)_f(S -1)_ (S -1)_S(S -1)_e(S -1)_m(S -1)_i(S -1)_c(S -1)_o(S -1)_n(S -1)_d(S -1)_u(S -1)_c(S -1)_t(S -1)_o(S -1)_r(S -1)_ (S -1)_L(S -1)_a(S -1)_s(S -1)_e(S -1)_r(S -1)_ (S -1)_D(S -1)_e(S -1)_v(S -1)_i(S -1)_c(S -1)_e(S -1)_s(S -1)_,

John Wiley & Sons: New York, 1980.

Verdeyen, L(S -1)_a(S -1)_s(S -1)_e(S -1)_r(S -1)_ (S -1)_E(S -1)_l(S -1)_e(S -1)_c(S -1)_t(S -1)_r(S -1)_o(S -1)_n(S -1)_i(S -1)_c(S -1)_s(S -1)_, Prentice-Hall, 1995.

Appendix 2: The κ)Selection Rule

The periodic lattice structure of a crystal leads to a periodic potential function. A wave function _j((F 4)r(F 1 for an electron in the crystal lattice then has, according to the Bloch Theorem, the form:

_j((F 4)r(F 1 = V (F 2)(S 2)- (S 2)1 (S 2)/ (S 2)2u((F 4)r(F 1exp(iκ)(S 1).(F 4)r(F 1,

where V is the volume of the crystal specimen and V (F 2)(S 2)- (S 2)1 (S 2)/ (S 2)2 represents a normalization factor, u((F 4)r(F 1 is periodic with the periodicity of the crystal lattice and κ)is the wave vector representing the quantum mechanical state. The wave functions are indexed or labeled by the corresponding wavevector (F 4)k.

Consider a possible transition of an electron in state κ)_c in the conduction band to a hole with state κ)_v in the valence band. The wave functions are then

_{j (F 4)_k(S -3)c((F 4)r(F 1 = V (F 2)(S 2)- (S 2)1 (S 2)/ (S 2)2}u (S -1)c((F 4)r(F 1exp(iκ)(S -1)c (S 1).(F 4)r(F 1

_{j (F 4)_k(S -3)v((F 4)r(F 1 = V (F 2)(S 2)- (S 2)1 (S 2)/ (S 2)2}u (S -1)v((F 4)r(F 1exp(iκ)(S -1)v (S 1).(F 4)r(F 1.

The probability of a transition from state κ)_c to a state κ)_v with the creation of a photon radiated in the direction (F 4)A is determined by the value of

M(κ)_c,κ)_v) = (F 9)i_j*(F 4)_k(S -3)c((F 4)r(F 1(F 9)D (F 4)_{A_{j (F 4)_k(S -3)v((F 4)r(F 1d(F 4)r},}

where (F 9)D (F 4)_Ais the gradient in direction (F 4)A. When the Bloch wave functions are entered into this expression the result is:

M(κ)_c,κ)_v) = V (S 2)- (S 2)1(F 9)iexp(-i(κ)_c-κ)_v) (S 1).(F 4)r(F 1u*(F 4)_k(S -3)c((F 4)r(F 1(F 9)D (F 4)_Au (F 4)_k(S -3)v((F 4)r(F 1d(F 4)r.

The functions u*(F 4)_k(S -3)c((F 4)r(F 1 and u (F 4)_k(S -3)v((F 4)r(F 1 have the periodicity of the lattice. In general exp(-i(κ)_c-κ)_v) (S 1).(F 4)r(F 1 does not have the periodicity of the lattice. Therefore the integral will be zero unless exp(-i(κ)_c-κ)_v) (S 1).(F 4)r(F 1 has no periodicity. This will be the case if (κ)_c-κ)_v) = (F 4)0, but it will also be the case if (κ)_c-κ)_v) = (F 4)G, where (F 4)G is a vector in the reciprocal lattice and hence exp(-i(κ)_c-κ)_v) (S 1).(F 4)r(F 1 = exp(-i(F 4)G (S 1).(F 4)r(F 1 = 1. The possible transitions are thus those such that κ)_c=κ)_v (direct transition)

or κ)_c=κ)_v+(F 4)G (indirect transition).

Appendix 3:

The Einstein Relations for Broadband Emission and Absorption

Although Einstein formulated his famous relations for transitions between two sharply defined energy levels his method can also be applied to transitions between ranges of energy (energy bands).

Let E_{1 be an energy state within the valence band and E₂ an
energy state within the conduction band. A transition from E_{1 to
E₂ would involve the absorption of a photon of energy}}

hν=E₂_{1=E₂-E_{1. Let f_{1 and f₂ denote the probabilities that there
are electrons in states E_{1 and E₂. For a transition from E_{1 to
E₂, state E_{1 must be occupied and E₂ vacant. Let B_{1₂ be the
probability of a transition occuring given that the two preceding
conditions are fulfilled. Let P(E₂_{1) be the probability density
for a photon of energy E₂_{1. The rate of transition from E_{1 to
E₂, R_{1₂ is given by}}}}}}}}}}}

R_{1₂ = f_{1(1-f₂)B_{1₂P(E₂_1).}}}

The occupancy probabilities f_{1 and f₂ are given by Fermi-Dirac
distributions; i.e.,}

f_{1 = [exp((E_{1-F_{1)/kT)+1] (S 2)- (S 2)1}}}

f₂ = [exp((E₂-F₂)/kT)+1] (S 2)- (S 2)1,

where F_{1 and F₂ are the Fermi levels for the valence band and
conduction band, respectively. It is assumed that equilibrium
exists within the bands. Equilibrium exists between the bands
only if F_{1 = F₂.}}

There can also be stimulated emission in which a photon of energy E₂_{1 triggers the creation of another photon of the same energy
and an electron falls from state E₂ to state E_{1. The rate for
this transition R₂_{1 is given by:}}}

R₂_{1 = f₂(1-f_{1)B₂_{1P(E₂_1).}}}

There can also be the spontaeous transition of an electron from E₂ to E_{1 if E₂ is occupied and E_{1 is vacant. Let A₂_{1 be the
probability of this transition given that these two conditions
are met. The rate of spontaneous transition R₂(S 2)s_{1(S 2)p is then}}}}

R₂(S 2)s_{1(S 2)p = f₂(1-f_{1)A₂_1.}}

For thermal equilibrium the rate of transition from E₂ to E_{1 must
equal the rate of transition from E_{1 to E₂; i.e.,}}

R₂_{1 + R₂(S 2)s_{1(S 2)p = R_1₂.}}

This implies that the energy distribution function for the radiation is

P(E₂_{1) = (BOX (DIM 3 1)
(BINFO (NAME Fraction)(BPOINT X1)(BASE 0)(BLINE 5)
(RINFO 6 0 0 0 2 0 0 -1 6 0 0 0)
(CINFO 23 1 C)
(RB (NAME HNormalF)(POSITION H 1)(EXTENT 0 0)
A₂_{1f₂(1-f_{1
\c)
B_{1₂f_{1(1-f₂)+B₂_{1f₂(1-f_1).}}}}}}

If, in fact, the energy distribution of the radiation is that of black body radiation; i.e.,

P(E) = (BOX (DIM 3 1) (BINFO (NAME Fraction)(BPOINT X1)(BASE 0)(BLINE 5) (RINFO 6 0 0 2 2 0 0 -1 6 0 0 2) (CINFO 17 1 C) (RB (NAME HNormalF)(POSITION H 1)(EXTENT 0 0) 8_pE (S 2)2) \c) h (S 2)3v (S 2)3[exp(E/kT)-1],

(where v is the speed of light in the medium)

then it follows that

A₂_{1 = (BOX (DIM 3 1)
(BINFO (NAME Fraction)(BPOINT X1)(BASE 0)(BLINE 7)
(RINFO 8 0 0 2 2 0 0 -1 6 0 0 2)
(CINFO 5 1 C)
(RB (NAME HNormalF)(POSITION H 1)(EXTENT 0 0)
8_pE₂(S 2)2_{1)
\c)
h (S 2)3v (S 2)3B₂₁}}

and B₂_{1 = B_1₂.}

Given these results then the conditions for net stimulation in a nonequilibrium condition can be derived. The condition for net stimulation is that R₂_{1>R_{1₂. This condition will prevail if}}

F₂ - F_{1 > E₂ - E_1,}

the Bernard-Duraffourg condition.

References:

R.L. Aggarwal, P.A. Maki, R.J. Molnar, Z.-L. Liau and I. Melngailis, "Optically pumped GaN/Al_{0_{._{1Ga_{0_{._{9N double
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vol. 79 (February 15, 1996), pp. 2148-2150.}}}}}}

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G. Fasol, "Room-Temperature Blue Gallium Nitride Laser Diode,"

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S. Nakamura, T. Mukai, and M. Senoh, "High-Power GaN P-N Junction Blue-Light-Emitting Diodes," J(S -1)_a(S -1)_p(S -1)_a(S -1)_n(S -1)_e(S -1)_s(S -1)_e(S -1)_ (S -1)_J(S -1)_o(S -1)_u(S -1)_r(S -1)_n(S -1)_a(S -1)_l(S -1)_ (S -1)_o(S -1)_f(S -1)_ (S -1)_A(S -1)_p(S -1)_p(S -1)_l(S -1)_i(S -1)_e(S -1)_d(S -1)_ (S -1)_P(S -1)_h(S -1)_y(S -1)_s(S -1)_i(S -1)_c(S -1)_s(S -1)_ L(S -1)_e(S -1)_t(S -1)_t(S -1)_e(S -1)_r(S -1)_s(S -1)_, vol. 30 (December 1991), pp. 1998-2001.

S. Nakamura, N. Iwasa, M. Senoh, and T. Mukai, "Hole Compensation Mechanism of P-Type GaN Films," J(S -1)_a(S -1)_p(S -1)_a(S -1)_n(S -1)_e(S -1)_s(S -1)_e(S -1)_ (S -1)_J(S -1)_o(S -1)_u(S -1)_r(S -1)_n(S -1)_a(S -1)_l(S -1)_ (S -1)_o(S -1)_f(S -1)_ (S -1)_A(S -1)_p(S -1)_p(S -1)_l(S -1)_i(S -1)_e(S -1)_d(S -1)_ (S -1)_P(S -1)_h(S -1)_y(S -1)_s(S -1)_i(S -1)_c(S -1)_s(S -1)_ L(S -1)_e(S -1)_t(S -1)_t(S -1)_e(S -1)_r(S -1)_s(S -1)_, vol. 31 (May 1992), pp.1258-1266.

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General References:

Proposal for a paper on

A Blue Light Gallium Nitride Laser Diode

References:

G. Fasol, "Room-Temperature Blue Gallium Nitride Laser Diode,"

S(S -1)_c(S -1)_i(S -1)_e(S -1)_n(S -1)_c(S -1)_e(S -1)_, Vol. 272 (June 21, 1996) pp. 1751-1752.

S. Nakamura, M. Senoh, N. Iwasa, Japanese Journal of Applied Physics, vol. 34 (1995).

S. Nakamura, M. Senoh, N. Iwasa, Japanese Journal of Applied Physics, vol. 35 (1996).

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