1. CHAPTER 8: MICROWAVE DIODES, QUANTUM EFFECT & HOT ELECTRON DEVICES Part 2

2. QUANTUM-EFFECT DEVICES (QED)
QED uses quantum mechanical tunneling to provide carrier transport – active layer thickness is very small (10nm).
Give rise to a quantum size effect that can alter the band structures & enhance device transport properties
Resonant Tunneling Diode (RTD) (Basic QED)
Semiconductor double-barrier structure contains 4 heterojunctions (GaAs/AlAs/GaAs/AlAs/GaAs), 1 quantum well in the conduction band
Important parameter: energy barrier height E0, energy barrier thickness LB, quantum well thickness LW
Figure Band diagram of a resonant-tunneling diode.

3. If LB small – resonant tunneling will occur
If LW small (10nm) – a set of energy levels will exist inside the well (E1, E2, E3, E4) –fig.13 (a)
If LB small – resonant tunneling will occur
incident electron (has energy E = one of the discrete energy levels in the well) – it will tunnel thru the double barrier with a unity (100%) transmission coefficient.
Transmission coefficient decreases rapidly as energy E deviates from the discrete energy levels
e.g.: electron with energy 10meV higher or lower than the level E1  105 times reduction in the transmission coefficient (Tt) – fig.8.13 (b)
Figure (a) Schematic illustration of AlAs/GaAs/AlAs double-barrier structure with a 2.5 nm barrier and a 7 nm well. (b) Transmission coefficient versus electron energy for the structure.

4. Figure 8.15. A mesa-type resonant tunneling diode (cross-section)
GaAs/AlAs layers are grown on an n+ GaAs substrate
LB = 1.7nm
LW = 4.5nm
active regions are defined with ohmic contacts
Figure A mesa-type resonant tunneling diode (cross-section)

5. Note: I-V curve is similar to that of a tunnel diode (fig.4)
At thermal equilibrium (V=0) energy diagram is similar to fig.13(a)
Increase the applied V – electrons in the occupied energy states near the Fermi level to the left side of the 1st barrier tunnel into the quantum well
the electrons tunnel thru the 2nd barrier into the unoccupied states in the right side.
Resonance occurs when the energy of the injected electrons = E1
V=V1=Vp – the conduction band edge on the left side is lined up with E1
When V=V2, the conduction band edge is above E1 – electrons that can tunnel decreases – small I
Iv due mainly to the excess I components: electrons that tunnel via an upper valley in the barrier
Figure Measured current-voltage characteristics of the diode in Fig

6. To minimize the Iv – must improve the quality of the heterojunction interfaces & eliminate impurities in the barrier & well regions
For higher applied V (V>Vv) – Ith due to electrons injected thru higher discrete energy levels in the well or thermionically injected over the barrier
Ith increases with increasing V (similar to tunnel diode)
To reduce Ith: increase the barrier height & design a diode that operates at relatively low bias voltages
Resonant Tunneling Diodes can be operated at very high freqency.

7. HOT ELECTRON DEVICES
Hot electrons: electrons with kinetic energies substantially above kT (k is Boltzman’s constant & T is lattice temp.)
As the dimensions of semicond. devices shrink & internal fields rise, a large fraction of carriers in the active regions of the device during its operation is in states of high kinetic energy
Fig.8.18: an AlInAs/GaInAs HBT
Electrons are injected by thermionic emission over the emitter-base barrier at an energy Ec=0.5eV above the conduction band-edge in the p-GaInAs base
Figure Energy band diagram of a hot electron heterojunction bipolar transistor.

8. Real-Space-Transfer Transistor
In thermal equilibrium: mobile electrons reside in the undoped GaAs quantum wells & spatially seperated from their parent donors in AlGaAs layers – fig.8.19(a)
Give power input to the structure – the carriers heat up and undergo partial transfer into the wide-gap layer – fig.8.19(b)
If the mobility in layer 2 is lower, negative differential resistance will occur in the 2-terminal circuit – fig.8.19(c)
Transferred-electron effect, based on the momentum-space intervalley transfer  named real-space transfer
Figure (a) A heterostructure with alternate GaAs and AlGaAs layers. (b) Electrons, heated by an applied electric field, transfer into the wide-gap layers. (c) If the mobility in layer 2 is lower, the transfer results in a negative differential conductivity.

9. Real-Space-Transfer Transistor
Source & drain contacts are to undoped GaInAs channel
Collector contact is to a doped GaInAs conducting layer – separated from the channel by a larger bandgap material (i.e. AlInAs; Eg=1.45eV)
At VD=0, electron density is induced in the source-drain channel by +ve Vc – but no Ic flows because of the AlInAs barrier
VD increases, ID begins to flow & the channel electrons heat up to some effective temp. Te
The injected electrons are swept into the collector by the Vc – induced electric field, giving rise to Ic
Transistor action results from control of the Te in the source-drain channel
Figure Cross section and band diagram of a real-space-transfer transistor in a GaInAs/AlInAs material system.

10. Exercise (Microwave)
Find the characteristic impedance of a nearly lossless transmission line (R is very small) that has a unit-length inductance of 10nH and a unit-length capacitance of 4pF
Solution
Impedance

11. Exercise (Transferred Electron Devices)
A GaAs TED is 10m long and is operated in the transit-time domain mode. Find the minimum electron density n0 required and the time between current pulses, where v=107.
Solution:
For transit-time domain mode, we require n0L1012 cm-2
n0 1012/L = 1012/10x10-4 = 1x1015cm-3
The time between current pulses is the time required for the domain to travel from the cathode to anode:
t = L/v = 10x10-4/107 = 10-10s = 0.1ns