Introduction

1. Background

In this applet, we study the dependence of the minority-carrier 'collection efficiency' of the device.

The minority carriers are injected at Emitter junction (e) and are collected at the Collector junction (c). In an ideal transistor, all the carriers injected by the Emitter-junction will be collected by the Collector-junction (B = base trasport factor =1.0). The Base transport factor is the measure of this collection efficiency.


Fig.1 The cross-section of an NPN transistor in an integrated circuit. The n^- Collector layer is the white region.	Fig.2 The region that dominates the transistor action is shaded. The gray layer on top is SiO₂.

This applet models only the region dominating the transistor action, as represented by the shaded region (including the n⁺ Emitter region) in Figure 2.

2. Current

The injected minority current density is given at the emitter junction as

_ep

_en

evaluated at the Emitter-junction (e)

The collected current density is given by

_cp

_cn

evaluated at the Collector-junction (c)

These diffusion current densities are proportional to the slope, dn/dx or dp/dx, of minority carrier contentration profile in the Base at the two respective junctions. The minority carrier density profile is dependent on the relative magnitude of the Base width, Wb, relative to the diffusion length (Ln or Lp) of the minority carrier in the Base.

3. Applet

In this applet, you can control the Base width, Wb, by the arrow buttons in the upper-left corner of the applet or by a mouse drag of the Collector junction region (indicated by |) . You can change the diffusion length of the minority carrier by the choices given for the minority carrier lifetime and the diffusion coefficient as L_p = sqrt( lifetime_p * D_p) and L_n = sqrt( lifetime_n * D_n).

In this applet, the BJT is in the normal active biasing condition (Emitter junction=forward= 0.7 Volts; Collector junction=reverse= -6 Volts). You can change the Base width, Wb, and observe the resulting changes in the minority carrier density profile (particularly its slope at the collector junction) and the corresponding changes in the collected current density.

Note that the minority carrier concentration profile in the base approximates a linear profile if W_b << L_p (or L_n). But otherwise it is an exponential profile. A strictly linear profile means that dp/dx (or dn/dx) is constant and the same both at E and at C, meaning that J_ep = J_cp (or J_en = J_cn) and thus B=Base transport factor=1.

For an exponential profile of the minority carrier density in the Base, when W_b > L_p (or L_n), the dp/dx (or dn/dx) value is much smaller at C than at E, making Jcp << Jep (or Jcn << Jen) and B << 1.

another Introduction

For a back-to-back PN junction structure to operate as a transistor, it is essential that a substantial fraction of the excess minority carriers, injected by forward bias at one junction, survive the recombination in the Base region and successfully arrive by diffusion at the other junction where they are collected.

1). Injection at the forward-biased Emitter-junction is proportional to the slope, dp/dx, of the minority concentration for a PNP device at the E-junction edge in the Base. This is based on the assumption that all the minority carriers move by diffusion. The diffusion flux is given by - D_p dp/dx.

2). Collection at the reverse-biased Collector-junction is proportional to the slope, dp/dx, at the C-junction edge in the Base.

Collected current by the Collector junction = - q Dp dp/dx for PNP The above two together mean that for transistor action, the dp/dx at the C-junction should be a good fraction of dp/dx at the E-junction (ideally, the same value).

At the given doping levels (N-value) and Diffusion coefficient of minority carrier (D) and minority carrier lifetime in the Base, observe the following:

PNP :

When Wb (base width) << Lp

linear

When Wb >> Lp, the excess minority hole profile in the Base is exponential. The absolute magnitude of dp/dx at E is large, and dp/dx at C is small. This means that many injected carriers are lost in the Base (by recombination) and only a small fraction is collected. In the limit that Wb -> infinity, the dp/dx at C becomes zero, and the two Junctions are completely 'decoupled' and the device is a triode.