Diode Lasers Bradley Klee Department of Physics, University Arkansas, Fayetteville, AR 72701 (Dated: April 23, 2015) 1
I. INTRODUCTION The study of semiconductors led to the discovery of their useful properties and to a large number of practical applications. The field is changing so rapidly that what we tell you today may be incorrect next year. It will certainly be incomplete. - R.P. Feynman 2 This quotation from the Feynman Lectures on physics dates back to the early 1960 s. At that time semiconductor technology began to simplify and miniaturize electronics. The diode became an important element of many different electrical circuits. Around the same time, scientists began to realize that the quantum mechanical parameters of diodes could be tuned to create more useful technologies. In 1962, the first light emitting diode was designed and demonstrated. During the same year, a semiconductor laser was also designed and demonstrated. Diodes, light emitting diodes, and laser diodes operate according to very similar principles, but these technologies differ from one another according to differences in design specifications. Following the evolution of technology from diode to laser diode illustrates the importance of concepts that are common in the design and operation of all three technologies. The semiconductor band structure helps to determine a difference between thermal diodes and light emitting diodes. Geometric design parameters determine the difference between LEDs and diode lasers. Many years later, Feynman s prognostications seem well placed. Laser diodes of all colors are in the classroom, the car, the home theater, and the presentation room. Consumers continue to purchase CD, DVD, and Blu-Ray drives for their computers and home entertainment systems. Laser pointers have also become affordable to consumers, and the decreasing price point enables these devices to enter more readily into classrooms and introductory labs. While many people will be more excited by physical processes that occur when using laser diodes as light sources, interesting physics also happens within the diode itself. 2
II. DIODES AND LEDS A. Classical Picture Diodes and LED s operate according to the principles of quantum mechanics and classical electromagnetism. While quantum mechanics draws a distinction between Didoes and LEDs, classical electromagnetism treats the components similarly. In a classical picture, both diodes and LEDs contain currents of holes and electrons. Maxwell s equations govern these and other electromagnetic quantities. P-type and n-type materials are doped to have holes and electrons as the majority charge carrier. The doping atom has a similar electronic structure and geometric dimensions to the base material so that it fits neatly into the preexisting structure. But the electronic structure of the dopant differs slightly. After formation either an extra electron or an extra hole binds only loosely to the atomic site. With some amount of extra energy, those charge carriers begin to move around as a current. FIG. 1. Diode Symbol. Source: Wikipedia. Manufacturers and physicists form diodes by combing a p-type and an n-type material in series between a pair of terminals, as in Figure 1. Immediately the holes and electrons begin to move according to internal electric fields and a tendency to diffuse into relatively flat distributions. The steady state equation for currents and holes are, 0 = q µ e n 0 (x) x Φ 0 (x) + q D e x n 0 (x), (1) 0 = q µ h p 0 (x) x Φ o (x) q D h x p 0 (x), (2) 3
where the first term describes the electron drift and the second term describes the electron diffusion. In these equations, µ are effective masses, D are drift coefficients, and indices e and h denote electrons and holes respectively. The functions n 0 (x), p 0 (x) and Φ 0 (x) are the unbiased negative carrier density, unbiased positive carrier density and the electrostatic potential. As eigenvalue equations, The solutions are, x n 0 (x) = (µ e / D e ) x Φ 0 (x), n 0 (x) (3) x p 0 (x) = ( µ h / D h ) x Φ 0 (x). p 0 (x) (4) n 0 (x) = n i Exp((µ e / D e ) Φ 0 (x)), (5) p 0 (x) = p i Exp( (µ h / D h )Φ 0 (x)). (6) The Einstein relation reveals a hidden temperature dependence (µ e / D e ) = (µ h / D h ) = q / (k b T ). (7) The undetermined potential is constrained by Laplace s equation, 2 xφ 0 (x) = q/ɛ(n 0 (x) + p 0 (x) + N d (x) + N a (x)). (8) In this equation N is the density of d donating or a accepting dopant, while n(x) and p(x) are the densities of charge carriers, possibly under some biasing voltage. In many other references, Laplace s equation is solved exactly using numerical methods or approximately using the depletion analysis, first in the unbiased steady state, and later with the bias of an external voltage. In the steady state depletion approximation, a depletion region forms when the drift and diffusion currents reach equilibrium. The excess charge carriers migrate toward the boundary of positively and negatively doped materials and form a uniform density on either side. Then the charge distribution, electric potential, and electric field become simple piecewise functions, as in Figure 2. Exact solutions and solutions using the depletion approximation vary only slightly around the depletion region. 4
FIG. 2. Diode Electromagnetic Quantities. Source: Wikipedia. When an external bias voltage is applied to a well designed diode, the potential will approximately raise from the steady state value in order to meet the newly imposed boundary equations, Φ(x) = Φ 0 (x) + V. (9) Under reverse bias, the potential gradient is increased, causing the drift current to become larger. The depletion region is extended, and no current flows. Under a forward bias, the drift current becomes smaller, and current flow becomes proportional to the excess of charge carriers. Finally it becomes possible to derive the all-important I-V curve 4, I = I 0 (Exp[qV/(k b T )] 1), (10) where I 0 is the current under reverse bias. This function relates two physical quantities, current and voltage, which are easily measurable in the laboratory using a combination of two multimeters. It applies equally well to diodes and LEDs because it does not depend on 5
the recombination mechanism by which holes and electrons annihilate one another. Understanding the difference between diode devices requires a closer look at this quantum process. B. Quantum Picture The classical picture neglects the binding of electrons to the solid in discrete energy levels. In quantum mechanics of solid state physics, every solid has a band structure, which is a dispersion relation between energy and momentum of electrons. All semiconductors are characterized by a band gap, as depicted in figure 3. When an electron or hole moves across the band gap, it becomes possible for conduction to occur. The conduction and valence band are mostly unpopulated by holes and electrons respectively, so momentum change occurs without impedance from other charge carriers. The IV-curve for diodes depends loosely on the band gap energy E 0 I 0 Exp[qE 0 /(k b T )]. (11) Even this dependence does not completely account for quantum-mechanical behavior. A true quantum picture goes beyond the assumption that recombination of holes and electrons in the depletion region only affects the current slightly. While this assumption may hold well for diodes and LEDs, it becomes untenable when stimulated emission accelerates recombination. In order to explain the distinction between diodes and LEDs it is important to consider electronic and vibronic transitions. After excitation occurs, electrons and holes relax quickly to the minima of the conduction band and the maxima of the valence band, where they wait some amount of time before recombination occurs. The band gap energy E 0 and the momentum offset k 0 characterize the band gap. If the band gap is indirect with k 0 0, as depicted in the right panel of figure 3, then conservation of energy and crystal momentum requires the transition between bands must involve a photon and a phonon. In a direct transition with k 0 = 0, as depicted in the left panel of figure 3, the crystal momentum does not change. Direct transitions involve only an electron and a photon. Diodes with indirect and direct band gaps find different applications. 6
FIG. 3. Band Structure. Left Panel: Direct band gap of Gallium Nitride. Right panel: indirect band gap of Silicon. Source: Wikipedia. In thermoelectric devices such as Peltier coolers, the most important physical quantity is the temperature gradient. As transitions in indirect band gap semiconductors couple to phonons, and thus to temperature, they necessarily create a heat gradient when pair creation and destruction occur on different interfaces. Creation and destruction of phonons transports heat from one interface to the other. Direct band gaptransitions cannot redistribute heat because they do not couple to phonon modes. In simple optoelectronic devices the most important quantity is the rate of recombination γ rc, which might also be called the rate of photon emission. Materials with large recombination rates make for good optoelectronic devices because they generate more photons per second, and will thus have large intensity. The magnitude of γ rc depends on the physical processes involved. While the photon interaction involves only relatively light holes and electrons, the phonon interaction involves relatively heavy atomic nuclei. The slow moving nuclei limit the timescale of the transition process. Then the recombination rate will be much smaller, and the intensity of emitted light will also be lower. LEDs and laser diodes are usually made from materials with direct band gaps. For all direct band gap semiconductors k 0 = 0, but the value of E 0 remains unconstrained. By designing materials to have specific values of E 0, LEDs can be made to have different colors according to the famous and simple Planck s Law relating energy E and frequency ν E = hν. (12) 7
As the band gap energy is approximately measurable via the amplitude of the IV-curve, the Planck relation can be tested by a comparison with the nominal wavelength of emitted light. III. LASER DIODES A. Overview FIG. 4. Laser Diode. Source: Wikipedia. Most laser diodes measure not larger in volume than 1cm 3. Figure 4 depicts a typical laser diode. The small canister of the laser diode contains a physical system similar to a diode or light emitting diode. The combination of P-type and N-type material enables more complicated physical processes to occur. By clever geometric design, diode manufacturers are able to package a physical system that works similarly to any other Fabry-Perot laser. The optical system of a laser diode performs two main functions in order to reach sufficient efficiency. An optical wave guide determined by relative indices of refraction ensures transverse containment. Flat facet cleaving of the material ends creates a Fabry-Perot type resonator for longitudinal confinement. Together the confinement functions trap light in a segment of space where quantum mechanical processes necessary for lasing are most likely to occur. In three or four state lasers, rates of spontaneous emission determine the feasibility of population inversion. After population inversion occurs, absorption suddenly becomes stimulated emission, the fundamental quantum process that allows lasing to occur. Laser diodes 8
achieve population inversion by injecting a current directly into the excited state. Rates of spontaneous emission are not as important as the electronic quantities and the gain coefficient. A simplified perspective only needs two rate equations to characterize optical and electric behavior. B. Optics I. Waveguide A simple model for a laser diode is a rectangular prism with a rectangular transverse section. The transverse section divides into three regions: P-type, active region, N-type. Figure 5 depicts a simple laser diode structure. The active region has a higher index of refraction than either the P-type or N-type material. Outside of the material, the index of refraction equals approximately to 1. Then, the central active region acts like a waveguide, confining most of the traveling light. FIG. 5. Laser Diode Crossection. Left Panel: Regions for the Marcatili method applied to a surface mounted waveguide. Right Panel: Typical laser diode structure. Source: Wikipedia. Maxwell s equations must be satisfied in nine distinct regions, as in figure 5. In a perfect solution the boundary conditions must be satisfied along twelve interfaces between nine separate regions. When the wave propagates mainly in the active material, the Marcatili approximation applies. The Marcatili approximation ignores the eight second-order interfaces, and treats separately the x and y interfaces. Solutions in this approximation do not obey second order boundary conditions, but this error of approximation is often negligible. 9
The approximation assumes negligible field amplitude in the external regions. This method is sufficient for analytically computing a single mode that is sharply peaked in the center of the active region, but could fail for higher order harmonics. When the transverse intensity distribution is known throughout the nine distinct regions, the optical confinement factors Γ f are computed by the simple regional integrals Γ f = (1/P ) I(x, y)da, (13) f where index f denotes one of the nine spatial regions, I the transverse intensity distribution, and P the total power of the light passing through the transverse plane. The confinement factors are of fundamental importance to the operation of the laser. Light in different regions of space contributes differently to the lasing feedback. For example, light in the free space surrounding the diode is not contained by the Fabry-Perot in the longitudinal direction. Neither does this light contribute to stimulated emission. C. Optics II. Fabry-Perot In the longitudinal direction, the stack of materials is cleaved at the ends by two flat surfaces separated by a characteristic length L. At either flat surface, the difference in index of refraction again allows the surface to reflect a portion of the light while transmitting the remainder. Then the material acts like a Fabry-Perot resonator, especially because the waveguide limits the divergence of the beam. The characteristic length L factors into the main operational parameters of the Fabry- Perot including the resonance wavelengths, the free spectral range, the transmission FWHM. The resonance condition constrains the cavity length according to the desired wavelength of emitted light λ 0 L = Nλ 0 /(2 n), (14) where N is an arbitrary integer, and n is the index of refraction. In general, the values for N and L are small compared to values for other laser systems. Then the free spectral range and the transmission FWHM are also large compared to other laser systems. In units of wavelength the free spectral range is 1, λ F SR λ 2 0/(2 n L). (15) 10
The transmission FWHM is a function of the free spectral range and the cavity finesse F λ = λ F SR /F. (16) A large free spectral range is desirable because it prevents degradation of the output signal by a wide range of light waves with wavelength outside of the transmission FWHM. But a large free spectral range requires a large finesse in order to suppress degradation of output signal by modes near to the transmission maxima. Obviously the finesse is an important parameter for limiting the laser to single mode operation. In the complicated three dimensional system, gain and loss determine the finesse. The transmission / reflection coefficients for normal incidence are simple functions of internal and external index of refraction, R = (n 1) 2 /(n + 1) 2. (17) Recalling the confinement factors, the absorption loss α i is expressed as a summation over the three regions of the diode material 3 α i = Γ f α f. (18) f The finesse is then determined by α i and R according to 3, F = π R Exp[ α i L/2]/(1 R Exp[ α i L]) (19) Usually R is not large, so the cavities should have unimpressive finesse. Then the signal usually degrades from emission modes near to the transmission maxima. Applications that require single-mode operation use diodes with more complicated optical systems 1. The total loss L = 2α i L 2Ln[R], (20) also plays an important role in the operation of the laser diode. This quantity determines how quickly photons will escape from the resonant cavity. The photon lifetime is τ ph = 2 n L/(c L). (21) Again the cavity length is small ( 10 3 m ), and the loss for typical R.3 will be somewhere around 3, which makes the photon lifetime on the order of one picosecond, 10 12 s. 11
D. Rate Equations During operation the laser diode balances carrier and photon density. The rate equations relating these two quantities are constructed from phenomenological considerations. The carrier concentration depends on the injected current density J, the average lifetime of a carrier excitation τ n, and stimulated emission. Meanwhile the photon density depends on photon lifetime τ ph, spontaneous emission coupling β, and stimulated emission. Assuming the density of holes and electrons can be approximated by one carrier density, the rate equations are 1, t n = J/(ed) n/τ n Γ a g 0 (n n 0 ) S, (22) t S = S/τ ph + β n/τ n + Γ a g 0 (n n 0 ) S, (23) where g 0 is a first order expansion coefficient of the gain around n 0 the transparency carrier density. In the limit where photon density is small, photons produced by radiative decay are immediately absorbed or escape the cavity due to poor confinement. Setting S 0 and applying the steady state approximation, the injection current becomes solely a function of the carrier density J = (ev a /τ n ) n, (24) where V a = da, and A is the crossection area. This recapitulates earlier results for diode characteristic curves, and implies that the diode IV-curve should be equally applicable to laser diodes whenever generation of photons by carrier recombination is a negligible effect. This caveat begs a tricky question: When does the optical behavior begin to affect the electrical behavior? With regard to optical behavior, the rate equations have two unique turning points. When the carrier-density equals to the transparency density n = n 0, absorption changes into stimulated emission. When the carrier density equals to the threshold density, stimulated emission overpowers photon decay, and the photon density becomes the dominant term of both rate equations. In between the transparency and threshold density n th, the laser system undergoes a phase transition where behavior is comparatively difficult to predict. 12
The abruptness of the phase transition depends on the ratio n th /n 0. The onset of exponential growth in rate equation defines the threshold density 1/τ ph = Γ a g 0 (n th n 0 ) (25) n th = 1/(τ ph Γ a g 0 ) + n 0 (26) Then the ratio becomes n th /n 0 = 1 + (τ ph Γ a g 0 n 0 ) 1, (27) where Γ a is the confinement factor for the active region. Population density is not directly measurable, so it is better to recast this ratio in terms of electrical currents. In the steady state approximation, the current density is n = (τ n /ed)j τ n Γ a g 0 (n n 0 ) S. (28) Assuming that a small photon density is sustained at n = n th, the measurable ratio is (I th δi S )/I 0 = 1 + (τ ph Γ a g 0 n 0 ) 1. (29) Although n 0 is typically a large number τ ph is small, and Γ a g 0 is also typically a very small number. For reasonable parameter values, the second term can range between 0 2. During the onset of lasing, the stimulated emission becomes noticeable, especially in the electrical behavior. The steady state rate equations are After some substitution the IV curve takes a modified form I = e V a (G(n) S + n/τ n ), (30) S = β n/τ n (G(n) τ 1 ph ) 1, (31) G(n) = Γ a g 0 (n n 0 ). (32) I e V a (n/τ n )(1 + β n n 0 ). (33) n th n Taking n = n th δ and proceeding to the limit where δ 0 n th I e V a β n th n 0. (34) τ n δ 13
Clearly the current has a pole at the threshold density. Often this pole is explained in terms of resistance. The Inverse of resistance is n th V I e V a β n th n 0 ( τ n δ 2 V δ) = e2 k b T V n 2 th a β n th n 0. (35) τ n δ 2 Then as n n th the resistance tends to zero I V (n th n) 2 (I I th ) 2. (36) This equation can be misleading. The laser diode does not become a superconductor. The device has a minimum built in resistance, which it quickly reaches around threshold. However, if I th /I 0 is large, then it is possible that the diode will reach minimum resistance before it reaches threshold. Figure 6 shows typical IV and RI curves. FIG. 6. Laser IV and RI Curves. Right Panel: IV Curve can transition into linear resistance before or after reaching pole. Right panel: RI curve shows a sharp drop, if the minimum resistance is low enough. Typically laser diodes will operate away from threshold where the steady state behavior is independent of radiative decay (β n th τ ph /τ n << S ). In this regime the steady state equations become J/(ed) = n th /τ n + Γ a g 0 (n th n 0 ) S, (37) S/τ ph Γ a g 0 (n th n 0 ) S. (38) 14
In full operational condition, injection of extra carriers from some external source cannot actually raise the carrier density beyond the threshold current without invalidating the steadystate equation for photon density. Then extra carriers injected by increasing the current density J must increase the pressure towards stimulated emission, thus raising the photon density S. The linear relationship can be recast as S = τ ph /(ed)(j J th ). (39) This simple relationship predicts the most commonly observed behavior of the laser diode. E. Transients The communications industry uses diodes to send pulsing messages through cables. Laser projectors create real color, real time images by mixing intensity of RGB diodes. CD and DVD burners quickly switch the laser diode on and off to encode data on a disc. These operations require understanding of time dependent behavior of laser diodes, such as the switch on time, and the time for relaxation to steady state. It would be worthwhile to study rate equations, which are already well known 1. IV. MEASUREMENTS A. LEDs Light emitting diodes are now commonly available at low cost. Online electronics stores sell high quality CREE LEDs for as little as twenty cents a piece, and other LEDs are available in local electronics stores such as Radio Shack. An experiment to explore the dependence of turn on voltage with wavelength measures the IV curve for infrared (940 nm), red (624 nm), amber (591 nm), green (527 nm), blue (470 nm), and ultraviolet (395 nm) LEDs. The IV curve is measured by a combination of ammeter and voltmeter, using the circuit depicted in figure 7. Turning the potentiometer eventually shorts out the LED, allowing 15
FIG. 7. LED IV Measurement Circuit. A voltage divider shorts out the LED, which is protected by a shunt resistance. readings at current arbitrarily close to zero. Although linear response potentiometers are most commonly available, it would be better to use a logarithmic potentiometer because of the exponential form of the IV curve. There are many ways to analyze the ensemble of IV data, and some care must be taken to avoid incorrect conclusions. In a low reverse bias current approximation, three values determine the ideal IV curves I i I 0 Exp[k(V i V i0 )], (40) where V i0 is the starting voltage, and I 0 is the reverse bias current. Setting the i and j curves equal and rearranging terms (V i V j ) = (V i0 V j0 ) = h/e (ν i ν j ), (41) where ν are the nominal frequencies of light emitted by the various LEDs. Then a plot of V i vs ν i, for any current value, should reveal the constant h/e as the slope. Figure 8 depicts data for the six LEDs with nominal wavelengths 940, 624, 591, 527, 470, 395 (nm). The ultraviolet data looks clearly suspicious and does not seem to fit with other curves 16
FIG. 8. LED Experiment. IV-Curves for diodes of six distinct wavelengths. in the data set. Furthermore, inclusion of this LED in analysis results in conclusions inconsistent with the assumption of ideal diode behavior. It then makes sense to exclude this point from analysis. Figure 9 shows the linear analysis with values I = 10 x, x 0...5. FIG. 9. Linear Analysis. Inclusion of UV data point causes wide variation in slope. Without the UV data point, slope remains approximately constant. 17
As expected, inclusion of the ultraviolet curve leads to an inconsistent running of the extracted slope parameter. The values fall in a wide range.003.007 (V/THz). When the ultraviolet curve is excluded, as it should be, the extracted parameter is essentially constant at.005 (V/THz), it remains almost constant. The expected value is.00414 (V/THz), fifteen to twenty percent below the measured value, but still within one standard deviation. Figure 10 shows the likelihood function of h/e. FIG. 10. Parameter Extraction. Left Panel: Excluding UV data, extracted Josephson constant h/e remains approximately constant. Right Panel: Likelihood function for the extracted parameter. The experiment gives a first order value for the Josephson constant h/e, and thus demonstrates that the turn on voltage of a diode depends linearly on the band gap. The analysis used to reach this conclusion follows from the assumption that diodes operate with similar k and I 0 values, but this assumption obviously does not hold for all diodes. Similar techniques should be expected to show that the Planck relation also determines some of the behavior of laser diodes, especially in the limit of low photon intensity. B. Laser Diodes Laser diodes are also commonly available at low cost from online electronics stores or even through the online auction site EBAY. Diodes can also be salvaged from decommissioned 18
technology such as CD / DVD burners or laser projectors. Here, a laser diode is salvaged from an excess DVD burner, and experiments characterize the response of voltage and light intensity as a function of the injection current. A laser diode designed for writing on blank DVDs can cause lasting damage if it shines directly into a persons eyes, so care must be taken during all experiments to direct the diode away from any line of sight. Risk can be reduced by removing any collimating lenses, so that light is not emitted in a focused beam. In operating and testing a laser diode, the can should be embedded into a heat conducting material. During operation, power not dissipated as light energy will dissipate as Joule heating. As the IV-curve depends strongly on temperature, performance severely declines when the diode is not protected by a heat sink. FIG. 11. LD IVP Measurement Circuit. Similar to the LED measurement circuit, but lm317 provides current regulation, and a capacitor protects the laser diode from voltage spikes. An extra LED is connected to a voltmeter to measure light intensity. 19
Usually two or three leads protrude from the back side of the can. As with a diode or LED, two of the leads are anode and cathode. The optional third lead is sometimes connected to an internal sensor and used to permit a feedback signal into a control loop. It is relatively easy to determine the identity of the leads by connecting them in series with a current controlled power supply. If the current is not controlled there is a danger that the laser diode will draw too much current. Under extreme operating conditions a laser diode can easily become irreversibly damaged. Figure 11 shows a current controlled circuit used for measuring an I-V-P Curve. Current control by the LM317 ensures that the laser diode draws a low-fluctuation current. This experiment uses an extra red LED as the optical sensor. The LED has been tested to assure linear response to red light intensity. Unfortunately this setup cannot measure the power output of the laser diode in any familiar power units. FIG. 12. Laser Diode IV and RI Curves. Left Panel: The diode IV curve is exponential until I.02A, where it then becomes linear. Right Panel: The resistance reaches minimum value of 4.6Ω at I.02A without an abrupt drop. Figure 12 shows the IV and RI curves measured for the salvaged laser diode. The laser diode rate equations predict that resistance will drop sharply at the threshold. In this data, the transition from diode resistance to constant resistance occurs smoothly. Without a sharp drop in resistance it is not possible to identify the critical point at I?.02A as the threshold. This value coincides with the maximum operational current for many of the LEDs in the previous experiment. 20
FIG. 13. Laser Diode PI Curve. The laser diode has two range of linear operation, one at low power and one at high power. Figure 13 shows the PI curve measured for the salvaged laser diode. The laser diode rate equations predict that output power will become linear at the threshold. This graph identifies the threshold current to be I th.06a. In fact, the output power is linear above and below threshold. This could possibly be related to the Laser diode s original use: reading and writing DVD media. For such an application the diode would need to have two separate and stable operational ranges. When the beam is focused, and the diode is powered around.1a, it certainly can burn plastic material. Comparing the IV and PI curves, notice that the threshold occurs much after the IV curve reaches minimum resistance, rationalizing the absence of a steep drop in the resistance curve. This behavior implies a large ratio of I th /I 0. The ratio of the the threshold current to the IV critical current is I th /I? 3. This could be the correct order of magnitude to suggest that I? = I 0, the transparency current. Without a series of tests to extract the many laser diode parameters, it is impossible to say for sure if the IV critical point relates at all to transparency. 21
V. CONCLUSION Diodes, light emitting diodes, and laser diodes show common behavior, especially when operated at low voltages. Specifically, each of these three components operate according to an exponential relation between the current and voltage. Despite similarities, key differences become apparent with the consideration of other physical quantities. Diodes have interesting thermal behavior that LEDs and laser diodes do not share. Light emitting diodes and laser diodes emit light at appreciable power. IV curves for LEDs and LDs depend on the wavelength of emitted light. Finally, high current behavior distinguishes laser diodes from other diodes. The operational differences of a laser diode arise from its special design. Optical confinement traps light into a region where it stimulates recombination of charge carriers. At threshold, the laser diode begins to emit coherent light. After the threshold the output power of the diode depends linearly on the injection current. The linear relation of power to a simple electrical quantity makes diodes easy to utilize in experiments or consumer technology. The low price and easy availability of diode technologies make possible do-it-yourself experiments for testing theoretical predictions. For the most part these experiments show positive results, but some non-ideal behavior should be expected. Manufacturers design commercial technologies to have practical behavior rather than ideal behavior. Feynman s prognostication seems no more invalid today than it did fifty years ago. New frontiers in diode technology include nanoscale fabrication and a continued search for materials with desirable spectral characteristics. Despite progress at specific wavelengths, physics and industry have yet to produce a tunable diode laser. The search for this technology will likely continue. With such strong foundation, laser diodes will likely remain a key technology for physicists and consumers. bjklee@email.uark.edu 1 T. Numai, Fundamentals of semiconductor lasers, (Springer 2015). 2 R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics, (Basic Books 2013). 22
3 R. Vyas, Laser Physics Notes, (2015). 4 K. Hess, Advanced theory of semiconductor device, (IEEE press 2000). 23