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**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
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**Paper No. : 09 Electronics **

**Module: 3.3 Avalanche Transit time devices (Reed, Impatt diodes, parametric **
devices)

Prof. Vinay Gupta ,Department of Physics and Astrophysics, University of Delhi, Delhi

**Development Team **

**Principal Investigator **

**Paper Coordinator **

**Content Writer **

**Content Reviewer **

Dr. Monika Tomar ,Physics Department ,Miranda House University of Delhi, Delhi

Prof. Vinay Gupta, Department of Physics and Astrophysics, University of Delhi, Delhi Dr. Ayushi Paliwal, Department of Physics, Deshbandhu College, University of Delhi, Delhi

Prof. R. P. Tondon,Department of Physics and Astrophysics, University of Delhi, Delhi

### Physics

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**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
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**Description of Module **
**Subject Name ** Physics

**Paper Name ** Electronics

**Module Name/Title ** Avalanche Transit time devices (Reed, Impatt diodes, parametric devices)

**Module Id ** 3.3

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**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
**Contents of the unit**

1. Introduction 2. IMPATT diode

3. BARITT DIODE (Barrier injection transmit time devices) 4. Read Diode (hi-lo type)

5. Modified read diode (Lo-Hi-Lo structure) 6. Summary

**Learning Objectives **

IMPATT diode along with its schematic and working

Benefits or advantages of IMPATT diode

Drawbacks or disadvantages of IMPATT diode

BARITT DIODE (Barrier injection transmit time devices)

Read Diode (hi-lo type)

Modified read diode (Lo-Hi-Lo structure) along with Dynamic characteristics:

(operational principles)

Temperature effect on its characteristics

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**1. ** **Introduction **

The IMPATT diode or IMPact ionisation Avalanche Transit Time diode is an RF semiconductor device that is used for generating microwave radio frequency signals.The IMPATT diode technology is able to generate signals typically from about 3 and 100 GHz or more. One of the main advantages of this microwave diode is the relatively high power capability (often ten watts and more) which is much higher than many other forms of microwave diode. Although the IMPATT diode is not as widely used these days as other technologies have been able to provide higher levels of performance, it nevertheless fits a niche in the microwave signal generation market, especially where relatively cost effective sources are needed.

The original idea for the diode was put forward by Shockley in 1954. He thought of the idea of creating negative resistance using a transit time delay mechanism. The method of injection for the carriers was a forward biased PN junction. He published this in the Bell Systems Technical Journal in 1954 in an item entitled: 'Negative resistance arising from transit time in semiconductor diodes’. However it was not until 1958 that W.T. Read of Bell Laboratories proposed the p+ n i n+ diode structure which was later called the Read diode. This diode used the avalanche multiplication as the injection mechanism. Again this was published in the Bell Systems Technical Journal in 1958 under the title: A proposed high- frequency, negative resistance diode.'

Although the injection mechanism and diode had been postulated, it was not until 1965 that the first practical operating diodes were made that enabled oscillations to be observed. The diode used for this demonstration was fabricated using silicon and had a p+ n structure. After this, operation of the Read diode was demonstrated and then in 1966 a p i n diode was also demonstrated to work.

**2. ** **IMPATT diode **

IMPATT (Impact Ionization Avalanche Transit Time) diode employ the avalanche (impact ionization)
and transit time (for carrier drift) properties of semiconductor devices to produce a dynamic negative
resistance at microwave frequencies. IMPATT diode is the most powerful solid-state source of
microwave power. IMPATT diode family includes several different function and metal-semiconductor
devices. First IMPATT diode was a simple p-n junction diode biased into avalanche breakdown (one-
sided abrupt n^{+}-p junction diode).

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Figure 1: IMPATT diode

Most e-h pairs are generated in high-field region (i.e. 0x0.5 m where > 3x10^{5 }V/cm) because
avalanche phenomenon (ionization coefficient) depend strongly on . (therefore avalanche region is
highly localized). The generated electrons move to n^{+ }region, while holes drift to p-region, time required
for holes to reach the p^{+} contact constitutes the transit time delay.

Subsequently, the another structure for a microwave device of IMPATT type diode was originally
proposed by Read et al. as n^{+}-p-i-p^{+} or n^{+}-p--p^{+} known as Read diode.

Central region is weakly doped p-type (called as ) or intrinsic (i). Also, weakly doped n-type (called

). Typical dopant concentration may be 10^{12}-10^{13} cm^{-3}., so that this region is fully depleted only at a
small reverse bias and even by virtue of built-in-voltage (in extreme case).

Figure 2: Energy band diagram

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**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
**Benefits or advantages of IMPATT diode **

Following are the benefits or advantages of IMPATT diode:

➨Operates from 3 to 100 GHz frequency range.

➨It has high power capabilities compare to other microwave diodes.

➨Its output is more reliable compare to other microwave diodes.

➨It acts as a narrow band device when used as amplifier.

➨It can be used as excellent microwave generators. It can produce carrier signal for microwave transmission system.

**Drawbacks or disadvantages of IMPATT diode **

Following are the disadvantages of IMPATT diode:

➨It has high noise figure due to avalanche process & higher operating current. The shot noise is generated in the device due to high operating current. Typically noise figure of IMPATT is about 30 dB.

➨It produces spurious noise (AM and FM) with higher levels compare to klystron and Gunn diodes.

➨The tuning range of IMPATT diode is not as good as Gunn diode.

➨It offers lower efficiency compare to TRAPATT diode.

**Applications of IMPATT Diodes: **

(i) Used in the final power stage of solid state microwave transmitters for communication purpose. (ii) Used in the transmitter of TV system. (iii) Used in FDM/TDM systems. (iv) Used as a microwave source in laboratory for measurement purposes.

**3. ** **BARITT DIODE (Barrier injection transmit time devices) **

BARITT devices are an improved version of IMPATT devices. IMPATT devices employ impact ionization techniques which is too noisy. Hence in order to achieve low noise figures, impact ionization is avoided in BARRITT devices. The minority injection is provided by punch-through of the intermediate region (depletion region). The process is basically of lower noise than impact ionization responsible for current injection in an IMPATT. The negative resistance is obtained on

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account of the drift of the injected holes to the collector end of the p material. The construction of a
BARITT device consisting of emitter, base, intermediate or drift or depleted region and collector.

An essential requirement for the BARITT device is therefore that the intermediate drift region be entirely depleted to cause punch through to the emitter-base junction without causing avalanche breakdown of the base-collector junction.

Figure 2: BARITT diode

The parasitic should be kept as low as possible. The equivalent circuit depends on the type of encapsulation and mounting make. For many applications, there should be a large capacitance

variation, small value of minimum capacitance and series resistance Rs' Operation is normally limited to f/l0 [25 GHz for Si and 90 GHz for GaAs]. Frequency of operation beyond (f /10) leads to increase in R, decrease in efficiency and increase in noise.

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Figure 3: MnM diode and its operation

**4. ** **Read Diode (hi-lo type) **
Read diode have two regions:

(i) Avalanche region (p1-region which relatively high doping and high field, 0xb), in which avalanche multiplication occurs under reverse bias

(ii) Drift region (p2-region with intrinsic doping and constant field, bxb+W), where
generated holes drift towards p^{+} contact.

Similarly, p^{+}-n-i-n^{+} can be made where generated electrons move from avalanche multiplication drift
through intrinsic region.

Voltage drop across avalanche region is VA (0<x<XA narrow region where is high). Both XA and VA

have effect on optimum current density and efficiency of IMPATT diode.

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Figure 4: Read diode (hi-lo type)

**5. ** **Modified read diode (Lo-Hi-Lo structure) **

Here a “clump” of charge Q (charge/area) is located at x=b and the doping p1 and p2 are nearly
intrinsic. (device can be made by epitaxial techniques such as MBE). The “clump” of charge in the
central p+ region keeps the electric field almost constant in the p^{-} (or p1) region. The field in (p2)
region is kept below that required for avalanching. Therefore, field in avalanche region (at x=b) is no
longer limited by space charge.

Lo-Hi-Lo

Figure 5: Lo-hi-lo type of modified Read diode

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The electric field across Lo-Hi-Lo device at breakdown is

𝜉 = 𝜉_{𝑐} − 1
𝜖_{𝑠} ∫ 𝜌_{𝑠}

𝑥 0

𝑑𝑥

Where 𝜉_{𝑐} is the critical field and 𝜌_{𝑠} is the space charge density, p1 is nearly intrinsic and field is
essentially constant from x=0 to b at 𝜉_{𝑐}.

**At x=b, “ clump of charges causes a field reduction by an amount of **^{𝒒𝑸}

𝝐_{𝒔}** ( because ∫**_{𝒃−𝜹}^{𝒃+𝜹}𝝆_{𝒔} 𝒅𝒙=
𝒒𝑸)

From x=b to p+ contact, field remain constant at value (𝜉_{𝑐}−^{𝒒𝑸}

𝝐𝒔**) **
The breakdown voltage is

𝑉_{𝐵}= 𝜉_{𝑐}𝑏 + (𝜉_{𝑐}−𝒒𝑸
𝝐_{𝒔}) 𝑊

Because of nearly uniform high-field region (0xb), the value of critical field and thus the junction temperature can be kept much lower than for Read diode.

The IMPATT diode generally mounted in a microwave package, with high field region close to the copper heat sink so that the generated heat at junction can be conducted away readily.

**6. ** **Dynamic characteristics: (operational principles) **

Consider a reverse dc bias VB is applied to diode so that critical field for avalanche (𝜉_{𝑐}) is just reached
(figure a) (i.e. the voltage just required to cause breakdown). Avalanche multiplication will begin. An
ac voltage of sufficient large magnitude is superimposed on this dc bias at t=0 (a in figure). During
positive cycle, diode is driven deep into avalanche breakdown. A t=0, pre-breakdown current flows
through diode. As t>0, voltage > VB, secondary electron-hole pairs produced by impact ionization. As
long as >𝜉_{𝑐} (field in avalanche region), e-h pairs grows exponentially with time. Generated electrons
in avalanche region moves to n^{+} region (figure b). The generated holes drift to p^{+} via p2 region.

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At t=T/4, field reaches its maximum value (𝜉_{𝑐} + |𝜉|), and concentration of e-h pairs starts building up.

Here, ionization coefficient (αn and αp) have maximum values. However, αn and αp follow the instantaneous the generated hole concentration does not, because it also depends on the number of e-h pairs already present in the avalanche region.

Therefore, hole concentration at t=T/4, does not have maximum value. Even after has passed its maximum value, e-h concentration continue to grow, because the secondary carrier generation rate still remains above its average value.

This implies that hole concentration (hole pulse) in avalanche region attain maximum value at t=T/2,
when drop to 𝜉_{𝑐} value.

Important consequences: Because avalanche region introduces a 90 phase shift (delay) between the
applied ac signal and hole concentration in this region, i.e. injected carrier density (hole pulse) lags the
ac voltage by 90. With t>T/2, ac voltage <0, field in avalanche region drops below 𝜉_{𝑐}. Bunch of holes
injected into drift region (d). The movement of hole through drift region induces the current in external
circuit (which has phase opposite to that of ac voltage). The hole drift towards p+ contact (figure d),
provided in drift region is sufficiently high. Therefore, introducing the transit time delay. Compare
figure (d) diode exhibits a negative differential resistance (NDR) characteristics.

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Ideal phase shift between diode current and ac signal is achieved if thickness of drift region is such that
hole pulse is collected at p^{+-} contact at t=T, where ac field is equal to zero. This condition is obtained
by making ‘hole transit time’ d =T/2 through drift zone. Induced current starts when hole pulse
injected into drift zone (t=T/2) and continues until bunch is collected at p+ contact (t=T).

𝜏_{𝑑} =𝑇
2 = 1

2𝑓= 𝑊
𝜈_{𝑠}

𝑓 = 𝜈_{𝑠}
2𝑊

The injected hole pulse will traverse the length W of the drift region during negative half cycle, if we
choose the transit time 𝜏_{𝑑} to be ½ (oscillation period)

**Temperature effect: **

Breakdown voltage increases with increase in T. As dc power (reverse voltage multiplied by reverse current) increases, both junction temperature increases and breakdown voltage increased. This implies that diode fails to operate, mainly because of permanent damage that results from excessive heating in localized spots.

Solution: Use a suitable heat sink

5. Summary

IMPATT diode along with its schematic and working

Benefits or advantages of IMPATT diode

Drawbacks or disadvantages of IMPATT diode

BARITT DIODE (Barrier injection transmit time devices)

Read Diode (hi-lo type)

Modified read diode (Lo-Hi-Lo structure) along with Dynamic characteristics:

(operational principles)

Temperature effect on its characteristics

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**1. ** **Introduction **

First observed in 1963. A microwave output was generated when a dc field (>critical threshold value) of several 1000 V/cm was applied across a short (very thin active region) n-type GaAs as InP, CdTe. It utilize a voltage-controlled differential negative resistance (DNR). The phenomenon that gives rise to DNR is the decrease in electron mobility with electric field. This decrease is caused by transfer of conduction of electrons electrons from a high mobility low-energy state to a low mobility, high-energy state under the action of high (> few kV/cm). This transfer is made possible by the peculiar band structures of semiconductors like GaAs and InP, CdTe used as local oscillator and power amplifier (1 to 100 GHz).

**2. ** **Negative differential Resistance **

At low , drift velocity of electrons (Vn) is linearly proportional to .

Force on each electron = -q and will accelerate opposite to during the time between collision (c).

therefore, additional v component will be superimposed upon the thermal (random) motion of electrons (drift velocity) and net displacement of electrons in direction opposite to .

Momentum applied to electron during free flight between collisions (force x time) = momentum gained by electron in same period.

−𝑞𝜉 𝜏_{𝑐} = 𝑚_{𝑛} 𝑣_{𝑛}
Where 𝜏_{𝑐} is mean free time.

This implies that 𝑣_{𝑛} = − [^{𝑞𝜏}^{𝑐}

𝑚_{𝑛}] 𝜉

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Where 𝜇_{𝑛} = ^{𝑞 𝜏}^{𝑐}

𝑚𝑛 is the carrier transport parameters implies that how strongly motion of an electron is influenced by applied .

𝑣_{𝑛} = −𝜇_{𝑛} 𝜉

Here we assume that c is independent of and is reasonable as long as vd is small compared to thermal velocity (vt) of carriers. As vd > vt, the field dependence on will begin to depart from linear relationship.

Figure 1: Variation of vd with for GaAs and Si

For n-type GaAs, vd reaches maximum and then shows a decrease with increase in . This phenomenon is due to energy band structure of GaAs. The band structure of GaAs allows the transfer of conduction electrons from a high mobility, energy minimum (called a valley; valley 1) to low mobility, higher energy satellite valleys.

**3. ** **Two valley model **

Consider a E-𝑝 diagram of GaAs conduction band: (Two valley model)

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Figure 2: E-𝑝 diagram of GaAs conduction band

Free electrons K.E., 𝐸 = ^{𝑝}^{2}

2𝑚0 where p is particle momentum and m0 is the free electron mass. Because
of periodic potential of nuclei, effective mass of a conduction electron (mn) is different from the mass
of free electron (me). Therefore, for conduction electron 𝐸 = ^{𝑝}

2

2𝑚_{𝑛} where 𝑝 is the crystal momentum.

Maximum in V.B. at 𝑝 =0, min. in C.B. at 𝑝 =0. Therefore, transmission V.B. approaches C.B. can
occur without change in 𝑝 value (only change in E required). Therefore, GaAs is direct band gap
semiconductor. The E-𝑝 relation near 𝐶. 𝐵. ⌋min or near 𝑉. 𝐵. ⌋max are parabolic [𝐸 = ^{𝑝}

2

2𝑚_{𝑛}]. From known
E-𝑝 relation, we can obtain the effective mass as

𝑚_{𝑛} = [𝑑^{2}𝐸
𝑑𝑝̅^{2}]

−1

This implied that narrower parabola, smaller the effective mass. Therefore, very narrow C.B. parabola for lower valley of GaAs, the electron effective mass is small (0.07 m0 ). However, satellite valley (upper valley) has higher effective mass (due to wider C.B. parabola).

The two valley model has following features:

1) Sharp Curvature of C.B. Lowest min.at 𝑝̅=0 [Lower Valley; Valley-1 ]

Electrons in Valley-1 have Low effective mass( m1)

High mobility (𝜇1). Another energy min. in C.B. along [111] occur [ satellite Valley;

valley-2] which is separated from Valley-1 by energy ΔE=0.31 eV. The curvature of valley –
2 is broader, the electron effective mass (me) is high Low mobility (𝜇_{2}).

2) Density of states in satellite valley is higher than that in Lowest Valley.

3) ΔE> KT (thermal energy) of electrons at RT.[Lattice temp. must be low].

Transfer of electrons from valley-1 to valley-2 by thermal agitation is not very likely.

Also,ΔE <Eg, electrons transfer can occur at ξ much lower than those required for avalanche breakdown.

Let n1 and n2 are electron density in valley-1 and valley-2 respectively. The steady state conductivity of n-GaAs is

σ= q(μ1n1+μ1n1)=qn𝜇̅ or qn^{v}^{n}^{(𝜉)}

𝜉

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where n=n1+n2 (total electronic conc.), 𝑛 ≈ND and 𝜇̅ =^{v}^{n}

𝜉 is average mobility, Vn= average drift velocity

where 𝜇̅=^{𝜇}^{1}^{𝑛}^{1}^{+𝜇}^{2}^{𝑛}^{2}

𝑛1+𝑛2 (from 1; n=n1+n2)……(2) and vn=𝜇̅𝜉…….(3)

If field is low,(𝜉<𝜉a), all conduction electrons are located in valley-1. As ξ increases, some electrons gain sufficient energies from 𝜉and makes a transition to satellite valley (valley-2). If 𝜉 is high enough, all the conduction electrons transfer to valley-2.

i.e. n1≈n and n2≈0 for 0<𝜉<ξa

n1+n2=n for 𝜉a<𝜉<𝜉b (4) n1≈0 and n2≈n for 𝜉b<𝜉

Effective drift velocity will be [using equation (3) and (4)]

Vn= μ1𝜉for 0<𝜉<𝜉a[ valley-1]

&Vn= μ2𝜉for 𝜉 b<𝜉[ valley-2] (5)

& Vn= ^{𝜇}^{1}^{𝑛}^{1}^{+𝜇}^{2}^{𝑛}^{2}

𝑛_{1}+𝑛_{2} *𝜉for 𝜉 a< 𝜉< 𝜉 b[ both valley 1and valley 2]

if μ1𝜉a>μ2𝜉b, there exist a region where drift velocity decreases with increasing field between
𝜉a &𝜉 b. thus differential mobility μ=^{𝜕Vn}

𝜕𝜉 < 0 𝑖𝑛 𝑁𝐷𝑅 if 𝜉 > 𝜉_{𝑇}
𝜉_{𝑇}=3.5 kv/cm for GaAs.

The current density (J=σE)(using eqn.1 and 4).

J=qnμ1𝜉for 0<𝜉<𝜉 a

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andJ=qnμ2𝜉for 𝜉 b>𝜉.

If μ1𝜉a>μ2𝜉bNDR exist.

𝜉_{𝑇}onset of NDR ( threshold field).

𝜉v valley field

𝑁𝐷𝑅between 𝜉_{𝑇} and 𝜉v.

Differential Conductivity,σd=^{𝑑𝐽}

𝑑𝜉<0 in NDR.

Figure 4: J versus curve

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A semiconductor exhibiting NDR is inherently unstable, because a random fluctuation of carrier
density at any point in semiconductor produces a momentary space charge that will grow exponentially
with time. The 1D continuity equation is

𝜕𝑛

𝜕𝑡 − 1 𝑞 𝜕𝐽

𝜕𝑥 = 0 − − − − − − − − − −(1)

If there is a small local fluctuation of majority carriers from the uniform equilibrium concentration, the locally created space charge density is n-n0.

Poisson’s equation and current density are

𝜕𝜉

𝜕𝑥= −𝑞(𝑛 − 𝑛_{0})

𝜖_{𝑠} − − − − − − − − − −(2)

𝐽 =𝜉

𝜌+𝑞𝐷𝜕𝑛

𝜕𝑥 − − − − − − − − − −(3) n(x,t) → electron concentration at any point x & time t

εs → dielectric permittivity ρ → Resistivity

D → Diffusion constant

Differentiating equation (3) w.r.t. x,

𝜕𝐽

𝜕𝑥= 1 𝜌

𝜕𝜉

𝜕𝑥+ 𝑞𝐷𝜕^{2}𝑛

𝜕𝑥^{2}

→ 1 𝑞

𝜕𝐽

𝜕𝑥= −𝑛 − 𝑛_{0}

𝜌 ∈_{𝑠} + 𝐷𝜕^{2}𝑛

𝜕𝑥^{2} (𝑓𝑟𝑜𝑚 2) − − − − − −(4)
J = q n ν(E); J is constant with x & ν = ν (E)

Substitute equation (4) into (1)

𝜕𝑛

𝜕𝑡 +𝑛 − 𝑛_{0}

𝜌 ∈_{𝑠} − 𝐷𝜕^{2}𝑛

𝜕𝑥^{2} = 0 − − − − − − − − − (5)

Equation (5) can be solved for both spatial response or temporal response by separation of variables i.e.

let n(x,t) = n1(x)n2(t). For special response, the solution of (5) is
𝑛 − 𝑛_{0} = [𝑛 − 𝑛_{0}]_{𝑥=0}𝑒^{−}

𝑥

𝐿𝐷 − − − − − − − (6)

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Where LD is Debye length given by

𝐿_{𝐷} = √𝐾𝑇 ∈_{𝑠}

𝑞^{2}𝑛_{0} − − − − − − − −(7)

LD → distance over which a small unbalanced charge decays.

For the temporal response, the solution of equation (5) is
𝑛 − 𝑛_{0} = (𝑛 − 𝑛_{0})_{𝑡=0}𝑒^{−}

𝑡

𝜏𝑅 − − − − − − − − − (8)

Where τR is dielectric relaxation time (Maxwell differential dielectric relaxation time) given by
𝜏_{𝑅} = 𝜌𝜖_{𝑠} = ^{𝜖}^{𝑠}

𝑞𝜇𝑛 ≈ ^{𝜖}^{𝑠}

𝑞𝜇𝑛0 − − − − − −(9); 𝜇 → 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦

τR → time constant for decay of space charge to neutrality if differential resistivity (or differential mobility μ) is +ve.

τR ≈ 10^{-10}to 10^{-11} s for GaAs [εs = 12.8 ε0, μ = 8500 cm^{2}/vs, no = 10^{15} cm^{-3}]

However, if semiconductor exhibits a NDM, any charge imbalance will grow with time constant (τR)

instead of decay.

The +ve differential resistivity ↑ with ξ ↑

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i.e. ^{𝜕𝜌}

𝜕𝜉 > 0

If a region has slightly higher field, the resistance there is larger.

→ Less current will flow through it.

→ Results in an elongation of the region, and a high-field domain is formed separating regions of low field.

The interfaced separating low & high – field domain lie along equipotentials, so that they are in planes perpendicular to current direction.

Equation (8) → For device with NDR, initial space charge ↑ with time given by equation (9) where μ is –ve differential mobility.

If equation (8) remains valid throughout entire transition time of space charge layer, the maximum growth factor would be

exp [ 𝐿

𝜈_{𝑠}|𝜏_{𝑅}|] , 𝐿 → 𝑑𝑒𝑣𝑖𝑐𝑒 𝑙𝑒𝑛𝑔𝑡ℎ; 𝜈_{𝑠} → 𝑎𝑣𝑔. 𝑑𝑟𝑖𝑓𝑡 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠𝑝𝑎𝑐𝑒 𝑐ℎ𝑎𝑟𝑔𝑒 𝑙𝑎𝑦𝑒𝑟
For large space charge growth, ^{𝐿}

𝜈|𝜏𝑅|> 1

→ 𝑛_{0}𝐿 >^{𝜖}^{𝑠}^{𝜈}^{𝑠}

𝑞𝜇 (𝑓𝑟𝑜𝑚 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 (9))

≈ 10^{12}𝑐𝑚^{−2} [𝑓𝑜𝑟 𝑛 − 𝑡𝑦𝑝𝑒 𝐺𝑎𝐴𝑠 𝑎𝑛𝑑 𝐼𝑃)

21

**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
The simplest form of space charge instability is an accumulation layer. Lightly doped or short samples
(n0L < 10^{12} cm^{-2}) exhibits a stable field distribution when a constant voltage is applied. In a device with
n0L > 10^{12} cm^{-2}, a travelling accumulation layer will be formed.

The NDR may lead to a growth of small fluctuations in the space charge in a sample.

An equivalent circuit,

Where differential resistance,

And differential capacitance,

RC time constant

(9) Also known as Maxwell differential dielectric relaxation time.

In a material with positive differential conductivity, a space charge fluctuation decays exponentially with time as eq(8), where (n-no)t=0 is fluctuation magnitude at t=0.

When differential conductivity is negative, the space charge fluctuation may actually grow with time.

Consider a device (TED) made of n-type GaAs with n^{+}-end contacts. Let at point A in the device there
exists an excess (or accumulation) of negative charge that could be due to a random noise fluctuation
or possibly a permanent non-uniformity in doping (Figure C).

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**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
Integration of Poisson’s equation gives ξ distribution (Figure D) where ξ (on left of A) < ξ (on right of
A). If device biased at ξA (Figure A), carriers flowing into point A are greater than carriers flowing out
of A. Electrons flowing in left A are in low ξ and hence higher velocity. On right in high ξ, the velocity
is low. Electrons accumulate at boundary i.e. notch causing large discontinuity in ξ and velocity

becomes more different in two regions. This increases the excess negative space charge at A.

Accumulation of electrons continues.

Since J is constant throughout device, an increase in ‘n’ at point A causes vn (drift velocity) to decrease.

Therefore, electrons in this region are slow down and cause increase in negative charge. Now the field to the left of point A is even less than it was originally, and the field to the right is space-charge accumulation. The process continues until the low fields and high fields both obtain values outside NDR and settled at ξ1 and ξ2 (Figure A), where current in two regions are equal. A travelling space-charge accumulation is formed.

This process depends on the condition that the number of electrons inside crystal be large enough to allow the necessary amount of space-charge to build up during the transit time of space-charge layer.

Here space charge increases exponentially with time and continues to until attains maturity. When collected at anode, field rises above ξT and new space-charge is nucleating at cathode. Cycle repeats itself and current oscillates in microwave. This is the simplest form of space charge instability.

23

**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
**4. ** **IV characteristics of Transferred Electron Devices **

Consider a practical TED device. When there are positive and negative charges separated by a small distance, a dipole (domain) is formed. ξ (inside dipole) ˃ ξ (on either side). Because of NDR, I (low field) ˃ I (high field). Two field values will tend towards equilibrium values outside NDR region, where I (low field) = I (high field).

The diode has now reached a stable state, and moves through the crystal and disappears at the anode.

Here ξ begins to rise uniformly across the sample through ξT (i.e. ξ˃ ξT), thus forming a new dipole, and the process repeats itself.

The applied potential V is

v = ξAL = ξ2d + ξ1(L − d) where L is sample length.

Dipole width is

d = L[ξA − ξ1]

[ ξ2 − ξ1]

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**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
The time required for domain to travel from cathode and anode = L/vs where L is the active device
length and vs is the average velocity. Frequency for the transit time domain mode is

f =vs L Many GUNN diode oscillate at a frequency

≈ 107 cm/s L

≈100 (GHz) L (um) Therefore, sample with L = 10 um will oscillate at ≈ 10GHz.

If L = 25 um, oscillate at ≈ 4 GHz

The increase in free electrons in one region cause decrease in its concentration in another

region.______higher field for electrons in this region. Higher field slow down these electrons relative to other part(due to NDR).

Excess electrons will grow because the electrons in trailing part arrive with higher velocity(for lower field than Ea) and depleted electrons area also grow(becoz electrons slightly ahead of this region with excess electrons can move faster).

Perturbation increases, the peaks will traverse across Gunn diode applied potential and growing as it transit the diode due to NDR.

25

**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
Consider the following

Let applied field in sample is greater than Et. Initially electric field and concentration distribution is uniform in the sample.

Let sample has a fluctuation of electron concentration

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**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
This fluctation leads to an electric field fluctation .^{𝑑𝐸}

𝑑𝑥= -q(n-ne)/Es eqn(2)

In the higher field region the electrons "slow down" .These slow electrons increses the original concentration fluctation .high field increases increases and lower field decreases with fluctation and hence velocity decrease continuously.

The fluctation develops in such a way that accumulation layer remains behind and front edge is depleted with electrons.

At the same time the entire flucation drifts towards the positive contact(the anode) with the velocity of slow electrons.

If sample is long enough fluctation develops into a high field domain.

when domain is moving between catode and anode the current at device electrodes Iv=qnvs

However, when domain dissipates in the anode and new domain did not form yet current at the device electrodes

Im=qnvs where vm>vs

where vm is the initial high current (before activation the fluctations) Characteristic time of high field domain formation is

tR=RdCd=Es/qnoµ (9) (effective RC time constant)

also known as maxwell relaxation time where µ is differential electron mobility.

27

**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **
**Gunn diode mode of operations: **

Characteristic domain transit time in the sample of length L is ttR=L/vs (10)

if domain formation time (tR)>domain transit time(ttR)

Then domain does not have enough time to develop and the diode is stable.GUNN diode works as a stable amplifier

However,if tR<ttR Then GUNN diode may oscillate due to instabilites.

Kroemer criterion for domain formation ttR>tR

L/vs>Es/qnoµ

therefore noL>Esvs/qµ (11)

in general the transit time for domain travels=3*tR

HENCE distance travel by domain in 3*tR time is LtR=vs*3tR

Therefore Length of GUNN diode for instability is kept as L>3vstR

>3Esvs/qµno (12)

When sample meet Kroemer Criterion, a high field domain periodically develops at Cathode side, drifts towards the anode and dissolves there.

Always one domain propagating in the sample if the applied voltage is above the threshold and constant.

Current decreases with domain formation and increases when the domain dissipates.

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**Physics **

**Electronics **

**Avalanche Transit time devices (Reed, Impatt diodes, parametric devices) **

The oscillation frequency (‘transit time frequency’),
𝑓_{𝑇} ≈ 1

𝜏_{𝑡𝑟} = 𝑣_{𝑠}
𝐿

• For sample with L=100µm, and for GaAs vs = 10^{7} cm/s.

𝜏_{𝑡𝑟} = 𝐿

𝑣_{𝑠} = 100 ∗ 10^{−4}

10^{7} = 10^{−9}𝑠

• Frequency of transit- time osciillations,

• However, for L= 10µm; ftr = 10 GHz

𝑓_{𝑡𝑟} = 1

𝜏_{𝑡𝑟} ≈ 10^{9}𝐻𝑧 = 1 𝐺𝐻𝑧

Therefore Operating frequency is controlled by the sample length.No tuning, varies from sample to sample, sensitive to sample non- uniformities.

Current waveform consists of short pulses with width << half- a – period.

**5. ** **Summary **

Negative differential Resistance

Two valley model

Detailed description about the semiconductor exhibiting negative differential resistance

Transferred electron devices along with its I-V characteristics and working