1. CROSS FIELD TUBES AND MICROWAVE SEMICONDUCTOR DEVICES
BY: P. Vijaya & M. Niraja

2. Transferred Electron Devices (TED)
TED’s are semiconductor devices with no junctions and gates.
They are fabricated from compound semiconductors like GaAs, InP, CdTe etc.
TED’s operate with hot electrons whose energy is much greater than the thermal energy.

3. Gunn Diode
Invented by J.B Gunn

4. Gunn Effect:
Above some critical voltage (Corresponding to Electric field of 2k-4k V/cm) the current passing through n-type GaAs becomes a periodic fluctuating function of time.
Frequency of oscillation is determined mainly by the specimen, not by the external circuit.
Period of oscillation is inversely proportional to the specimen length and is equal to the transit time of electrons between the electrodes

8. The current waveform was produced by applying a voltage pulse of 16V and 10ns duration to an n-type GaAs of 2.5 x 10-3 cm length. The oscillation frequency was 4.5Ghz

9. RWH Theory Explanation for Gunn Effect:
Ridley – Watkins – Hilsum (RWH) Theory
Two concepts related with RWH Theory.
Differential negative resistance
Two valley model

10. Differential negative resistance
Fundamental concept of RWH Theory.
Developed in bulk solid state III-V compound when a voltage is applied

11. Differential negative resistance make the sample electrically unstable.

12. Two valley model theory

13. Data for two valleys in GaAs

14. Electron transfer mechanism

15. Conductivity of n-type GaAs:
e = Electron charge
μ = Electron mobility
= Electron density in the lower valley
= Electron density in the upper valley
is the electron density

17. Possessed by GaAs, InP, CdTe etc
According to RWH theory, in order to exhibit negative resistance the energy band structure of semiconductor should satisfy
The energy difference between two valleys must be several times larger than the thermal energy (KT ~ eV)
The energy difference between the valleys must be smaller than the bandgap energy (Eg)
Electron in lower valley must have a higher mobility and smaller effective mass than that of in upper valley
Possessed by GaAs, InP, CdTe etc

18. Formation of high field domain
In GaAs, at electric fields exceeding the critical value of Ec ≈ 3.2 kV/cm the differential mobility is –ve.
When the field exceeds Ec and further increases, the electron drift velocity decreases.

31. Modes of Operation LSA Oscillation Mode Bias-circuit
Gunn Oscillation Mode:
(f x L) = 107 cm/s and (n x L) > 1012 /cm2
Cyclic formation of High field domain
Stable Amplification Mode
(f x L) = 107 cm/s and 1011/cm2 < (n x L) >1012/cm2
LSA Oscillation Mode
(f x L) >107 cm/s and 2 x 104 < (n/f) > 2 X105/cm2
Bias-circuit
(f x L) is small. L is very small. When E=Eth current falls as Gunn oscillation begins, leads to oscillation in bias circuit (1KHz to 100MHz)

32. Gunn Oscillation Mode Condition for successful domain drift:
Transit time (L/vs) > Electric relaxation time
Frequency of oscillation = vdom/Leff.
Gunn diode with a resistive circuit -> Voltage change across diode is constant-> Period of oscillation is the time required for the domain to drift from the cathode to anode. Not suitable for microwave applications because of low efficiency.
Gunn diode with a resonant circuit has high efficiency.

33. There are three domain modes for Gunn oscillation modes.
1. Transit time domain mode, (Gunn mode)

34. 2. Delayed domain mode Here domain is collected while
New domain cannot form until E rises above threshold again. ,
Also called inhibited mode.
Efficiency: 20%

35. 3. Quenched domain mode:
If bias field drops below Es, domain collapses before it reaches anode.
When the bias field swings above Eth, a new domain starts and process repeats.
Frequency of oscillation is determined by resonant circuit.
Efficiency : 13%

36. Limited Space charge Accumulation Mode (LSA)
Most Important mode for Gunn oscillator.
Domain is not allowed to form.
Efficiency : 20%

37. Gunn Characteristics Power: 1W (Between 4HHz and 16GHz)
Gain Bandwidth product : >10dB
Average gain : 1 – 12 dB
Noise figure : 15 dB

38. Applications of Gunn Diode
In radar transmitters
Air traffic control (ATC) and Industrial Telemetry
Broadband linear amplifier
Fast combinational and sequential logic circuit
Low and medium power oscillators in microwave receivers
As pump sources

39. InP Diode

40. Peak to valley current ratio

41. Avalanche transit time devices

42. Principle of operation
Negative resistance is achieved by creating a delay (1800 Phase shift) between the voltage and current.
Delay is achieved by,
Delay in generating the avalanche current multiplication
Delay due to transit time through the material
So called Avalanche transit time (ATT) devices
Avalanche is generated by Carrier impact ionization
TT is due to the drift in the high field domain

43. Features Presence of P-N junctions Diode is reverse biased
High field (potential gradient) is applied of the order 400 KV/cm
Two modes of ATT
IMPATT- Impact ionization ATT (Efficiency 5-10%)
TRAPATT- Trapped plasma ATT (Efficiency 20-60%)

44. Read diode(IMPATT)

45. Read diode (IMPATT)

46. Read diode is n+ p i p+ diode
Avalanche multiplication at p region
Intrinsic region acts as the drift space where the generated holes must drift toward p+
Space between n+ p junction and i p+ junction is called the space charge region
The device operation delivers power from the dc bias to the oscillation

47. Operation:
Avalanche multiplication and drift of the high field zone

48. Carrier current I0(t) and External current Ie(t)

49. IMPATT DIode
The physical mechanism is the interaction of impact ionization avalanche and the transit time of charge carriers.
So Read-type diodes are also called IMPATT diode
Most simplest IMPATT diodes are the basic Read diodes
Three typical Si IMPATT diodes are shown below. Operations are similar to Read diode

52. TRAPATT DIOde Derived from IMPATT diode Presence of P-N junctions
Diode is reverse biased
High current densities than normal avalanche operation
It is diode.

53. Operation:

54. Parametric Devices

55. Uses non linear reactance or time varying reactance
Parametric term is derived from parametric excitation, since the capacitance or inductance, which is a reactive parameter, can be used to produce capacitive or inductive excitation.
Parametric excitation is subdivided into parametric amplification and oscillation.
Many of the essential properties of non linear energy storage systems were described by Faraday and Lord Rayleigh.

56. The first analysis of non linear capacitance was given by Van der Ziel in 1948 which suggested that such a device might be useful as a low noise amplifier, since it was essentially a reactive device in which no thermal noise is generated.
In 1949 Landon analyzed and presented experimental results of such circuits used as amplifiers, converters, and oscillators.
In the age of solid state electronics, microwave electronics engineers thought of a solid state microwave device to replace the noisy electron beam amplifier.

57. In 1957 Suhl proposed a microwave solid state amplifier that used ferrite.
The first realization of a microwave parametric amplifier was made by Weiss in 1957 after which the parametric amplifier was last discovered.
At present the soild state varactor diode is the most widely used parametric amplifier.
Unlike microwave tubes, transistors and lasers, the parametric diode is of reactive nature and thus generates a very small amount of Johnson (thermal) noise.

58. Parametric amplifier utilizes an ac rather than a dc power supply as microwave tubes do. In this respect, the parametric amplifier is analogous to the quantum amplifier laser or maser in which an ac power supply is used.

59. A reactance is defined as a circuit element that stores and releases electromagnetic energy as opposed to a resistance, which dissipates energy.
If the stored energy is predominantly in the electric field, the reactance is said to be capacitive; inductive if in the magnetic field.
C = Q/V
If the ratio is not linear, the capacitive reactance is said to be nonlinear. In this case it is convenient to define a non linear capacitance as the partial derivative of charge with respect to voltage.

60. i.e
C(v) = dQ/dt
The analogous definition of non linear inductance is
L(i) = dΦ/di.
In the operation of parametric devices, the mixing effects occur when voltages at two or more different frequencies are impressed on a nonlinear reactance.

61. Derived a set of general energy relations regarding power flowing into and out of an ideal nonlinear reactance.
These relations are useful in predicting whether power gain is possible in a parametric amplifier.

63. One signal generator and one pump generator at their respective frequencies , together with
associated series resistances and bandpass filters, are applied to a nonlinear capacitance C(t).
These resonating circuits of filters are designed to reject power at all frequencies other than their respective signal frequencies.
In the presence of two applied frequencies
an infinite number of resonant frequencies of are generated, where m and n are any integers.

64. Each of the resonating circuits is assumed to be ideal.
The power loss by the nonlinear susceptance is negligible. That is the power entering the nonlinear capacitor at the pump frequency is equal to the power leaving the capacitor at the other frequencies through the nonlinear interaction.
Manley and Rowe established the power relations between the input power at the frequencies
and the output power at the other frequencies

65. It is assumed that the signal voltage vs is much smaller than the pumping voltage vp, and the total voltage across the nonlinear capacitance C(t) is given by
The general expressionof the charge Q deposited on the capacitor is given by

66. For Q to be real,
The total voltage v can be expressed as a function of the charge Q.
A similar taylor series expression of v(Q) shows that
V to be real,

67. The current flowing through C(t) is the total derivative of Q w r t time. Hence,
Where

68. Since the capacitance C(t) is assumed to be pure reactance, the average power at the frequencies
Then conservation of power can be written

69. Multiply the above equation by a factor of
and rearrangement of the resultant into two parts yield
Since
Then,
Becomes,
And is independent of ωp or ωs.

70. For any choice of the frequencies fp and fs, the resonating circuit external to thatof the nonlinear capacitance C(t) can be so adjusted that the currents may keep all the voltage amplitudes
Unchanged.
The charges are also unchanged, sincethey are functions of the voltages

71. Consequently, the frequencies can be arbitrarily adjusted in order to require
Eqn I can be expressed as

72. Since , then Similarly, Where are replaced by respectively.

73. The above equations are standard forms for the Manley-Rowe power relations.
The term indicates the realpower flowing into or leaving the nonlinear capacitor at a frequency of
.The frequency represents the fundamental frequency of the pumping voltage oscillator and the frequency signifies the fundamental frequency of the signal voltage generator.

74. The sign convention for the power term will follow that power flowing into the nonlinear capacitance or the power coming from the two voltage generators is positive, whereas the power leaving from the nonlinear capacitance or the power flowing into the load resistance is negative.
Consider for instance, the case where the power output flow is allowed at a frequency of as shown in fig.