PreLab:
 [If you are familiar with the topics below, then you may skip the applets in this PreLab.  However, you still need to answer the questions.]
1) Review:   Fermi Level (E_F) versus Doping Concentration

Question: For a bulk n-type Si doped with N_d=10¹⁶/cm³ donor impurities at room temperature, find the Fermi energy level with respect to the intrinsic Fermi energy level.  Sketch the energy band diagram showing the band edges (E_c and E_v), intrinsic Fermi level E_i,  and Fermi level E_F.  Indicate the approximate energy spacing between these levels.  Use a rectangle whose height is proportional to the logarithm of majority (or minority) carrier concentration to indicate the carrier density.  The rectangle should be drawn relative to the band edges of the conduction band (in blue color for electrons) or valence band (in red color for holes).

Useful formulas:
n₀=n_i exp[(E_f-E_i)/kT]; p₀ = n_i²/n₀; n_i = 10¹⁰/cm³ for Si at 300K; kT = 25.9meV at 300K; and E_g = 1.12eV for Si at 300K.

Grade your answer: Grade your sketch using the Carrier Concentration vs. Fermi Level applet at http://jas2.eng.buffalo.edu/applets/education/semicon/fermi/bandAndLevel/fermi.html

2) Review: PN Junction in an Open-Circuit condition (That is, under Equilibrium)

(2.1) The PN Junction is in thermal equilibrium when/if the Fermi Level E_F is constant throughout the PN junction diode.  Use the applet at http://jas2.eng.buffalo.edu/applets/education/pn/pnformation_B/index.html
to verify that the final equilibrium band diagram is achieved when the Fermi Level (Green horizontal line) is the same throughout the device structure.
(2.2) Question: Sketch the energy band diagram of a PN junction for N_A=10¹⁵/cm³and N_D=10¹⁵/cm³; and for N_A=10¹⁵/cm³ and N_D=10¹⁶/cm³.  Pay attention to the E_F level relative to the band edge of each side, band bending in the depletion region, and using an approximate depletion thickness at each side of the junction.
Grade your answer: Grade your sketch of the energy band diagram using the applet given above in (2.1) or using this applet:
http://jas2.eng.buffalo.edu/applets/education/pn/pnformation3/index.html

3) Carrier Energy and the Energy Band

Refer to the figure below (a pn junction energy band diagram) and answer the questions further below.

Electrons in the n-side (the large blue rectangle on the right hand side) will ‘see’ a potential barrier when looking toward the p-side of the left hand side of the junction.   This potential barrier must be overcome in order to cross the junction.  The energy of carrier electrons in the conduction band of n-side is distributed, increasing with the increasing distance from the band edge, within the blue rectangle.

(3.1) Question: Suppose that we divide the electrons of the n-side into two portions: (a) above the dashed line and (b) below the dashed line.  Which portion is responsible for the ‘injection’ current ?  Explain your answer.
(3.2) Note in the blue rectangle above, the vertical heights are given in mixed units.  The potential barrier, V0 - V, is in [Volts], while the logarithm of Numbers Nn and Nd are unitless.  The appropriate convertion of units will be: multiply q/kT to the potential.
Question: Verify the following relation from the figure: ln(Nn) + (q/kT)(V0-V) = ln(Nd).  Also verify the counterpart equation for the holes:  ln(Np) + (q/kT)(V0-V) = ln(Na). Explain what these relations mean.  If you can't explain, then this lab will definitely help you.

Procedure:  Junction Diode I-V Characteristics Virtual Lab

1) Visit the virtual lab entitled "Biased PN Diode" at http://jas2.eng.buffalo.edu/applets/education/pn/biasedPN/index.html.

This applet lets you visualize the current flow across a PN junction under 0 bias, forward bias, or reverse bias.  In this applet, the PN diode cross section is shown on top with the applied bias shown as a scroll-bar on its left; and the Energy Band diagram is shown at bottom.  Color conventions are as follows: PN Diode --- Red=P-side, White=Depletion-region, Blue=N-side; and Energy Band Diagram --- Red=Holes, and Blue=Electrons.

2) Current Components
    Use the default setting (Bias=0V, Na=1E16, Nd=1E16). On top of applet, select injection and electron only.  Observe the applet.  The injection electrons flow from N to P-side: P <- N; and its current flows from P to N-side: P -> N.  Complete the table below by examining each current component.  In the last column, show if the current component increases, decreases, or stays constant with increasing the Bias voltage.

	Flow Direction of Charge Carriers	Current Flow Direction	Increasing the Bias
electron-injection	P-side <- N-side	P  -> N	Increases
electron-leakage	P       N	P       N
hole-injection	P       N	P       N
hole-leakage	P       N	P       N

3) Carrier Processes
    Set the applet at: Bias=0.5V; and select injection, recombination and electron only.  Turn off all other options for simplification. The applet visualizes the injection of electrons at the junction and the recombination of the injected minority carrier electrons with the majority carrier holes within a diffusion length distance from the depletion edge of the P-side.

Now consider the 'physical' continuity of current flow within the PN diode: start at the metal (Ohmic) contact at the P-side and end at the Ohmic contact of the N-side of the PN diode.  These carrier processes are involved: electron injection (thermionic emission over the potential barrier); minority electron diffusion; majority electron drift; minority electron - majority hole recombination; majority hole drift.  Give the process next to the location number below:

 

(1):__________________________
(2):__________________________
(3):__________________________
(4):__________________________
(5):__________________________
 
 
 
 

What can you say about the physical process of current flow throughout the PN diode ?  Does the total current level change as you  travel though the device between the two electrodes ?
 
 
 

4) Width of Depletion Region vs. Applied Bias
Click the "showParameter" button.

Set Na=1E16 and Nd=1E16.  Record the depletion width of p-side, x_p, and n-side, x_n, at +0.35V, 0V, and -0.6V.  Is the depletion width symmetric in the n-side and p-side ?

Now set Na=1E17 and  Nd=1E16.  Record the widths at +0.35V, 0V, and -0.6V.  Is the depletion regions symmetric ?

Check if qN_ax_p = qN_dx_n holds true for all of the above cases.  What does this relation say about the net space charge in the device ?

Discuss your observation of the depletion widths as a function of the applied bias and doping levels.
Discussion
 
 
 

[PN junction diode under the applied bias: both the current-voltage (I-V) and capacitance-voltage (C-V) characteristics are important.  I-V characteristic is important for both DC and ac operation of device, and C-V is important for the ac operation, particularly at high frequency.  Below we shall consider only the I-V characteristic; the C-V characteristic will be discussed in another applet.]
5) Reverse-Bias
Click "showParameter" button.  Set Na=1E17, and Nd=1E15, check all boxes: leakage, injection, recombination, electron and hole.  Apply a bias of -0.3V.  Observe the flow across the junction.  Change the bias to -0.5V and observe.  Change the doping levels and do the same.
Discuss what you observe here: Specifically, does the current change as the reverse bias changes ?  Why or why not ?  What seems to limit the reverse current ?
 
 
 
 

6) Forward-Bias
[This exercise is to derive Diode current equation from a simple intuition. In the process, we hope to gain physical insights into the nature of forward current and reverse current. Attention should be paid to: in forward bias, which part of carriers are injected, in view of the potential barrier V0-V ?; and the  reverse saturation current, do the number of minority carriers that flow down the potential hill change with bias ?   In short, which carriers comprise the forward current in view of their energy in the band. ]
Click the "showParameter" and "helper" buttons. Set Na=1E16 and Nd=1E16.

(a) Turn off leakage and recombination.  Apply a forward bias of 0.5V or so.  The number of electrons that can overcome the potential barrier, V0-V, and thus can be injected from the N-side to the P-side is given by Nn.  Express Nn using V0-V and Nd using the applet.  [Use a conversion factor q/kT for the potential V0-V. Nn = electrons that are above the potential barrier V0-V.]
Nn as a function of  V0-V and Nd:
[Hint: ln(Nn) = ln(Nd) - q(V0-V)/kT]
 

(b) Turn on leakage.  Set the bias at 0V (or click "reset" button.).  From the applet, express n_p0, the minority electron density of the P-side, in terms of V0 and Nd. [Hint:At bias = 0V, the injected electron is equal to the electron leakage current.]
 

(c) Net Electron Current: AT a forward bias, V, the net electron current is porportional to (Nn-n_p0), and therefore, Jn = C(Nn-n_p0) = Jn0 [exp(qV/kT) - 1] where C is a proportional constant.  Express Jn0 in terms of C, Nd, V₀, ...  [ Note-1: n_i² = NaNd exp(-V₀/V_T)   Note-2:  From textbooks you can find that C = qDn / [Ln tanh(W/Ln)] ]
 
 

(d) Turn off leakage and recombination.  Apply a forward bias of 0.5V or so.  Here, Np is he number of  holes that can overcome the potential barrier V0-V.  Express Np as a function of the potential barrier V0-V and the acceptor doping level Na.  Do it in the same way as in (a).
Np as a function of  V0-V and Na:
 
 
 
 

(e) Turn on the leakage.  Set the bias at 0V. From the applet, express p_n0, the minority hole density of the N-side, in terms of V0 and Na.
 
 

(f)  Net Hole current: AT a forward bias, V, the net electron current is porportional to (Np - p_n0), and therefore, Jp = B(Np-p_n0) = Jp0 [exp(qV/kT) - 1]  where B is a proportional constant.  Express Jp0 in terms of B, Na, V0, ...  [Note: From textbooks you can find that B = q Dp / [Lp tanh (W/Lp)] ]
 
 

(g) Total current:  The total current is given by the net injected electron current plus net hole current which is proportional to (Nn-n_p0) + (Np-p_n0).  Derive the diode I-V equation by setting I = A(Jn + Jp) where A is the device cross sectional area.  Is the diode current equation consistent with the formulas learned in class or from textbook ?  Verify the constants B and C by comparing the current formulas above with the Diode current formulas from the textbook.