How does a bias resistor built-in transistor (BRT) operate?

The following describes how a BRT operates when voltage (V_I) is applied to the B terminal in the “off” state to turn on the BRT in the saturation region.
The V_I voltage is gradually increased.

1. The internal transistor (Q) is off.
When V_I is applied to the B terminal when Q is off, current flows only through the built-in bias resistors, R₁ and R₂.
Therefore, a voltage divided by R₁ and R₂ is applied to the base (b) of Q (V_b = R₂ / ( R₁ + R₂ )).

2. Q turns on.
When V_b reaches roughly 0.5 V, base current (I_b) begins to flow, turning on Q, as indicated by the I_B - V_BE curve (Figure 2). This causes collector current, which is I_b times h_FE, to flow. At this point in time, Q is still in the active region, not in the saturation region. Therefore, its h_FE is 120 to 700, as is the case with the h_FE of general-purpose transistors (such as the 2SC2712).
As V_I further increases, V_be increases, causing I_C to increase exponentially as shown in Figure 2.
In practice, however, the base voltage (V_b) hardly increases with V_I. V_BE varies only between 0.6 V and 1.0 V at an ambient temperature of 25°C as shown in Figure 3. Therefore, the base voltage is often treated as being constant in a simplified calculation. Here, let’s assume that V_BE = 0.7 V.
I_b is expressed as:
    I_b = I_B – I_R2 = ( V_I – V_be ) / R₁ – V_be / R₂
As I_b increases, the collector current (I_C) increases proportionally.
Let the collector-emitter (C-E) voltage in the basic BRT circuit of Figure 1 be V_CE. Then:
    V_CE = V_CC – R_L * I_C
As I_C increases further , V_CE decreases, causing the BRT to enter the saturation region.

3. Q enters the saturation region.
As V_CE decreases, the transistor (Q) enters the saturation region.
(There is no clear definition of the saturation region. Toshiba regards the region in which h_FE ≤ 20 as the saturation region^*.)
An increase in I_b causes I_C to increase, causing a voltage drop across R_L to increase and therefore V_CE to approach the GND level.
That is, Q traces the I_C – V_CE curve (Figure 4) from #2 to #3. Eventually, V_CE becomes nearly zero.
Figure 5 shows the V_CE(sat) – I_C curves of an actual BRT.

Let the collector-emitter voltage in the saturation region be V_CE(sat). Then,
    I_C = ( V_CC – V_CE(sat) ) / R_L ＝ constant
As V_I increases, I_B increases, but I_C remains almost constant. Therefore, h_FE decreases as V_I increases.