Avalanche breakdown

The following section can only give a brief overview over the physics of avalanche break-down which are needed for the understanding of the studies performed in this thesis. For details of the avalanche breakdown, the reader may refer to the plentiful literature, see for example [140-147] and references therein.

The schematic in Figure 6.1 depicts the current understanding of the mechanism which leads to avalanche breakdown: In reverse-biased pn-junctions, large electric fields accel-erate free carriers in the space charge region. Usually, the movement of the carriers is hampered by collisions with other (quasi-) particles. However, when the electric field is adequately high (in the order of 10⁵ V/cm, see [140] for an overview over the results obtained by different groups), the kinetic energy gained by the carriers can suffice to knock valence electrons out of their state and lift them to the conduction band (impact ionization) which in turn may then be accelerated and participate in the multiplication process; this mechanism is called avalanche breakdown.

Figure 6.1: Schematic of the avalanche breakdown process. (a) Electrons in the conduc-tion band are accelerated by the large electric fields, depicted in image (b), in the pn-junction in reverse bias. If the kinetic energy is large enough, valence electrons can be knocked out and lifted to the conduction band, taking part in the electron multiplication process.

For the onset of the breakdown, i.e. the breakdown voltage VB, various definitions exist (in section 6.3, our uses of the term are illustrated). Whatever the definition, in the ideal case of one-sided abrupt junctions the breakdown voltage is proportional to the maxi-mum absolute value squared of the electric field in the space charge region Er_m

and in-versally proportional to the doping concentration of the lower doped side of the pn-junction Nmin in at/cm³ according to [30]:

min 2

2qN V_B E^rm ε

= (6-1),

with ε the silicon permittivity and q the elementary charge.

Since the carriers are accelerated by the electric field, its maximum value at avalanching conditions is of high interest. Avalanche breakdown does not start at a fixed value of the electric field, but varies depending on the properties of the pn-junction. Sze [30] esti-mates that Er_m

at breakdown depends on the doping concentration of the lower doped side as

(

)

3log 1 1

10 4

16 min

5

N E_m

−

= × r

(6-2), which is plotted in Figure 6.2 for the case that the base is the lower doped side.

Figure 6.2: Maximum electric field in the space charge region of a one-sided abrupt junc-tion at breakdown versus the background doping concentrajunc-tion in the base according to Sze [30].

Microscopically, the onset of AB, happening in small breakdown sites with a diameter in the order of a few 100 nm to a few µm [141, 148], is often marked by current instabili-ties which have been described in literature as “microplasma noise” [148]. As compre-hensively described by Marinov et al. [149], the current through the microplasma chan-nel is unstable when more carriers are lost due to recombination and / or out-diffusion from the channel than are generated in the multiplication process. In order to sustain avalanche breakdown, each free carrier in the space charge region needs to set at least 2-5 additional carriers free [149]. With increasing reverse bias, more and more carriers gain sufficient kinetic energy to multiply via impact ionization; the avalanche breakdown becomes stable.

As soon as this happens, the many charge carriers flowing through the microplasma channel cause an adjustment (a decrease) of the local electric field. A balance is estab-lished between the multiplication of free carriers due to the electric field, the reduction of the electric field due to the avalanche current and the carrier transport away from the microplasma channel limited by the spreading resistance, that is by the doping concen-tration in the lower doped side Nmin. In fact, the latter determines the current density J_µ in the microplasma channel [149]:

2qv Nmin

J_µ = _s (6-3),

with vs the saturation velocity of the free carriers in the semiconductor [30]. Note that Jµ

does not depend on the reverse bias or the electric field in the space charge region. A current increase with increasing reverse bias hence means that the cross-sectional area of the microplasma channel increases for which there are also indications in literature (see e.g. [141, 150]).

As the doping concentration in usual pn-junction does barely vary laterally, breakdown happens in many sites at once. Hence, the global current (not the current density) in-crease is usually large as soon as the breakdown voltage is passed. Therefore, AB is as-sociated with “hard” breakdown characteristics.

Microplasma channels emit bright light in the visible spectral range [148, 151-153]. By carefully comparing the number and size of light-emitting breakdown sites with the global current, it was shown that most if not all of the current is concentrated within the visible breakdown spots [150], each carrying about 100 µA.

The light emitted in the AB sites shows a broad spectral distribution, see Figure 6.3. A series of publications has dealt with the underlying physical mechanisms of avalanche breakdown light emission. Various causes for the spectral distribution have been pro-posed (compilation after Akil et al. [154]):

(i) Interband recombination between hot electrons and holes [152, 155, 156];

(ii) intraband electron transitions (bremsstrahlung radiation from hot electrons scattered by charged coulombic centers) [157-159];

(iii) ionization and indirect interband recombination of electrons and holes under high field conditions [160];

(iv) intraband transitions of hot holes between the light- and the heavy-mass valence bands [161].

In the most recent publication, Akil et al. [154] obtain reasonable fits for observed spec-tra of different silicon pn-junction devices with a combination of mechanisms (i) - (iii).

However, the contributions of the different mechanisms are still topic of ongoing discus-sions due to the difficulty of experimental verification of existing models.

Disregarding the different possibilities of radiative transition, the most important point consists in the statement that breakdown light emission always involves hot electrons and holes far away from the conduction and valence band edge, respectively. They can be generated either directly by acceleration in a large electric field or indirectly via en-ergy / momentum transfer processes as a secondary effect resulting from large field strengths.

Figure 6.3: Examples for the corrected spectral distribution of avalanche breakdown in different silicon pn-junctions measured by (a) Newman et al. [151] and (b) Chynoweth et al. [152] (open circles).

Highly localized AB, attributed to locally enhanced electric fields, has been ascribed to various inhomogeneities of the pn-junction:

• Chynoweth et al. for example observed that breakdown light emission was centered at dislocations [162, 163].

• Scratches on the surface of the pn-junction also resulted in highly localized AB [152].

• In structurally perfect pn-junctions, Goetzberger et al. noticed light emission along so-called striation rings. They explained this behavior by slight inhomogeneities of the base doping concentration due to the crystallization process [164].

• Kikuchi [165] and Shockley [166] suspected that oxygen precipitates could cause AB due to electric field enhancement which is a result of the different permittivities of Si and SiOx.

• After intentional contamination of silicon pn-junctions with Cu, junction breakdown was observed at singular, highly localized sites [167]. The authors attributed this be-havior to metal precipitates in the space charge region without further proof. In their opinion, the reverse I-V characteristics, however, did not fit to AB; therefore, they claimed that internal field emission processes (see next section) were involved.

A singular property of AB, which allows for a distinction between the different breakdown mechanisms, is the negative temperature coefficient (TC) [141], which means that with increasing sample temperature, the breakdown voltage increases. The reason is that at higher temperature, the mean free path of the charge carriers in the space charge region decreases because they encounter more scattering events with phonons.