Energy Flow in Semiconductor Devices and its
Applications for Semiconductor Laser Diodes
6.772/SMA5111 Term Paper
Ronggui Yang
Massachusetts Institute of Technology
Cambridge, MA 02139
Courtesy of Ronggui Yang. Used with permission.
Outline
™ Motivation
™
™
™
™
Energy Source in Semiconductor Devices
Internal Cooling in a p-n Diode
Applications to Laser Design (ICICLE)
Summary
Heat/Energy Flow in Semiconductor Devices
COLD SIDE
HOT SIDE
Mid-IR laser SOI MOSFET
Thermoelectric Cooler
Smaller, Faster, Denser & more powerful
More Heat
Understanding heat/energy flow in semiconductor devices, helps
understanding of:
¾ Thermal-induced failure in semiconductor devices
¾ Energy conversion in thermoelectric / thermionic devices
Approaches:
¾ Coupled Electron-phonon Boltzmann Transport Equation
¾ Electrohydrodynamics or Energy Transport Equations
¾ Drift-Diffusion Equations (Thermodynamic Approach)
Heating Effects in Semiconductor Lasers
Maximum optical output power limited
by active layer temperature rise
Threshold current density (left axis) and lasing
wavelength (right axis) versus operating temperature
for λ=1.2µm InGaAs laser.
T. K. Sharma, et al. IEEE Phot. Tech. Lett. 14, 887 (2002).
High temperature leads to:
• Increased threshold current
• Wavelength drift
• Decreased output power
• Decreased device lifetime
Temperature Control in Optoelectronic Devices
P
N
Traditional BiTe Thermoelectric Cooler
• Cooling power density ~10 W/cm2
• Difficult to integrate due to lack of processing
technology
• Device mounted on cooler
Integrated Superlattice Cooler
device
superlattice
substrate
• Cooling power density of several hundred W/cm2
• Integration possible
• Cooler can be grown near device
Temperature
A. Shakouri and J. E. Bowers, Appl. Phys. Lett. 71, 1234 (1997)
R. Venkatasubramanian, et. al, Nature 413, 597-602 (2001)
T.C. Harman, et al, Science 297, 2229-2232 (2002)
Internal Cooling Effects
p
n
• Device structure is such that the operating current
also produces cooling
K. P. Pipe, R. J. Ram, and A. Shakouri. Phys. Rev. B, Sept 15 2002.
Non-isothermal Carrier Flow
- Thermodynamics Approach
Transport under both Electrical and Temperature Field
r
r
J e = − µ e n(∇E fe + Pe∇T )
Particle Flux: J h = µ h p (∇E fh − Ph∇T )
Current Flux:
r
J h = eJ h
r
J e = −eJ e
Heat Flux:
rQ
r
J h = ePhTJ h − k h∇T
rQ
r
J e = ePeTJ e − ke∇T
Energy Flux:
ru rQ
r
J e = J e + eE fe J e
ru rQ
r
J h = J h − eE fh J h
ru
∂u
+ ∇J = 0
∂t
Energy Conservation Equation:
Energy Source
Heat Conduction Equation:
C
∂T
= ∇(k∇T ) + q&
∂t
Energy Source in Semiconductor Devices
r
r
∂E fe dn
∂E fh dp
] − e[ E fe − T
]
q& = −e∇[(π e + E fe ) J e + (π h + E fh ) J h ] + e[ E fh − T
∂T
Definition of Peltier Coefficient:
Maxwell-Boltzmann
where
π e = PeT =
π = PT =
Ec − E fe
k BT
π e0 = (r + 1)
2
v
∫ τ(E − E f )
e∫ v 2 τ
3
+ k BT + π e0
2
k BT
e
∂T
dt
dt
∂f o
D(E )dE
∂E
∂ fo
D(E ) dE
∂E
π h = PhT =
π h0 = (r + 1)
E fh − Ev
k BT
3
+ k BT + π h0
2
k BT
e
This r is related to the energy-dependent electron relaxation time
r=-1/2 for acoustic-phonon scattering and r =3/2 for impurity scattering
Steady State, Homojunction
r
r
r
∇Ev
0
0
q& = −( E g + 3k BT )∇J e − ∇(π h J h + π e J e ) +
J
e
Recombination Thompson Resistive heat
p-n Diode under Forward Bias
Energy Source
Distribution
Recombination Heat
Resistive Heat
Lp
Xp
Xn
Ln
Cooling at junction (SCR)
J
Jh
Increase Net Cooling
¾ Short diodes
¾ Radiative recombination
Je
Lp
Xp
Xn
x
Ln
x
Why & How Large is the Cooling
Cooling at the Junction
Eeq
E
Eap
electron
p
J
hole
In SCR:
n
r r
q& = E ⋅ J
Total Cooling in the junction:
Q=
xn
∫
q&dx =
−xp
1
Emax J max
2
= J (φbi − V )
• Every junction causes heating or cooling.
• Cooling at the p-n junction is bias-dependent
9 Cooling under forward bias
9 Heating under reverse bias
Optimizing Cooling Effect in Lasers
Injection Current Internally
Cooled Light Emitter
Conventional SCH
p+ Cap
p-Cladding
Core
n-Cladding
EC
EC
n+ Substrate
PE
Structure
Fp
EFn
N
P
N+
EFp
EV
EFn
N
N+
x
qTE (W/cm2)
qTE (W/cm2)
EV
x
Active region cooling
Conclusions
• Thermal effects is very important for active
devices, such as transistors and lasers
• Energy source term is derived based on the
thermodynamic approach
• Internal cooling effect is found in p-n diode
under forward bias
• The internal cooling effect has been utilized
for semiconductor laser design.
Thank you for your attention!