External (differential) quantum efficiency Number of additional photons emitted / number of additional electrons injected

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Rolf McGee
6 years ago
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1 Semiconductor Lasers Comparison with LEDs The light emitted by a laser is generally more directional, more intense and has a narrower frequency distribution than light from an LED. The external efficiency of a laser is much greater than that of an LED. Light emitted from a laser is coherent. Light power output (P) LED-like Laser-like External (differential) quantum efficiency Number of additional photons emitted / number of additional electrons injected e hν ΔP ΔI Current applied to device (I) LASER Light Amplification by the Stimulated Emission of Radiation Need to understand the physics of stimulated emission

2 Consider a system with two electronic levels (1 and 2). There are 3 possible electron-photon processes photon E photon Absorption a photon of energy E excites an electron from level 1 to level 2. The photon is destroyed. Spontaneous emission An electron in level 2 relaxes to level 1. A photon of energy E is created. The relaxation is a random process the created photon has a random phase and is emitted in a random direction. 2 1 Stimulated emission An electron in level 2 is stimulated into relaxing to level 1 by a passing photon. The new photon has the same phase, energy and direction as the original photon. Absorption causes a beam of light (stream of photons) to be attenuated as it passes through a material. Stimulated emission causes a beam of light to be amplified as it passes through a material.

3 Intensity (I) Absorption Intensity (I) Stimulated emission Distance (x) Distance (x) In a real system a mixture of absorption and stimulated emission will occur (spontaneous emission can be ignored once stimulated emission becomes important as electrons will relax by stimulated emission before they have time to relax spontaneously). For laser action to occur, overall amplification is required i.e. STIMULATED EMISSION > ABSORPTION If there are n 1 electrons in level 1 and n 2 electrons in level 2: Strength of absorption = A abs n 1 Strength of stimulated emission = A stim n 2 (can be shown that A abs =A stim ) Therefore laser action requires n 2 > n 1

4 Population Inversion For thermal equilibrium n n 2 = E kt < 1 e 1 Hence n 2 > n 1 (a population inversion) is only possible under non-equilibrium conditions In a semiconductor a population inversion can be obtained if there are a large number of occupied states (electrons) in the conduction band and unoccupied states (holes) in the valence band. electrons holes Such a condition is not easily obtained in a bulk semiconductor but can be created and maintained in a forward biased p-n junction: p-type A large density of electrons (holes) are injected into the p-type (n-type) material to create the population inversion n-type

5 Laser construction Require a material in which a population inversion is maintained (this requires constant energy input). Generally require a very long optical path length through material for sufficient amplification. Hence place material between 2 mirrors so that the light can keep passing through the material: Lasing material High refl. mirror Energy in to maintain population inversion Partially reflecting mirror allows some light to escape from the cavity Semiconductor laser: Current flow Coherent radiation Optically flat parallel faces

6 Variation of gain with carrier density and current cb vb Low current and carrier density (n) Absorption > stimulated emission High current and carrier density (n) Absorption < stimulated emission g GAIN LOSS n th (I th ) n (or I) n trans (I trans ) Point at which line passes through zero (g=0) is known as TRANSPARENCY - Gain balances absorption - Light travelling along the cavity is neither absorbed or amplified Lasing does not occur at transparency. A positive non-zero gain is required to overcome losses in the system. Lasing occurs at g=g th where g th is the threshold gain (occurs when I=I th, n=n th )

7 As light travels along the cavity it is amplified by the active region at a rate g per unit length. However, there will be some losses due to imperfections in the material, which scatter the light, and also by absorption of the part of the light field which extends beyond the active region. We describe these losses by α. Hence the amplification per unit length is (g-α) When light hits an end mirror only a fraction R, where R is the mirror reflectivity, is reflected back into the cavity the remainder escapes After passing along a cavity of length L, the light is amplified by e ( g α )L But only a fraction R is returned to the cavity. Hence, if the initial light intensity is I 0 after traversing one cavity length and hitting one mirror, the new intensity is I 1 = 0 e ( g I α ) L R Three cases.

8 1. I 1 < I ( g α ) L 0 e R < 1 I 0 L L L TOTAL LOSSES EXCEED GAIN NO LASING 2. I 1 > I ( g α ) L 0 e R > 1 L L L I 0 GAIN EXCEEDS TOTAL LOSS LIGHT LEVEL INCREASES INDEFINITELY PHYSICALLY IMPOSSIBLE 3. I 1 = I ( g α ) L 0 e R = 1 L L L I 0 GAIN EQUALS TOTAL LOSS CONDITION FOR LASING TO OCCUR

9 Lasing condition: e ( g α ) L R = 1 ( g α) L 1 = ln R g th 1 1 = α + ln L R g th is the gain required to achieve lasing. Known as the threshold gain. Result shows that g th increases as cavity length decreases.

10 What happens to the carrier density at and above threshold? At threshold, carrier density is just sufficient so that the resultant gain equals all losses and lasing starts (g=g th ) If the carrier density increased as current increased further then gain would increase above g th (case 2 above) this is physically impossible The gain of a laser can never exceed g th. This implies that the carrier density can never exceed the threshold value n th. Above threshold, both g and n are clamped (or saturate) to their threshold values g th and n th : n th g th n g n or g I th I

11 Water analogy I/eV Current leakage ηi G I gen = ev Overflow R st R L n th R nr R sp Water level has reached the overflow and the depth of water (and hence escape processes) is clamped to a value n th. Overflow provides an infinitely large escape path. All additional water added to the tank leaves via the overflow. Real Device At threshold n and g clamp to their threshold values Because carrier loss processes (spontaneous emission, leakage, non-radiative recombination) have rates which are a function of n these processes must also clamp / saturate at threshold Therefore, above threshold carrier loss mechanisms no longer increase Stimulated emission is the only process which can continue to increase All additional carriers injected into the active region must produce a photon by stimulated emission.

12 External efficiency above threshold Above threshold loss mechanisms are clamped to their threshold values Above threshold additional carriers injected into the active region result in photons produced by stimulated emission

LASER. Light Amplification by Stimulated Emission of Radiation

LASER. Light Amplification by Stimulated Emission of Radiation LASER Light Amplification by Stimulated Emission of Radiation Laser Fundamentals The light emitted from a laser is monochromatic, that is, it is of one color/wavelength. In contrast, ordinary white light