1. Deep Level Transient Spectroscopy (DLTS)
FYS4310
Christoffer Matre
Master student

2. Introduction DLTS was developed by D.V. Lang in 1974
Investigates energetically «deep» charge trapping levels
Performance of semiconductors are influenced by impurities and trapping levels

3. Measuring Principle
The depletion capacitance of a Schottky diode or pn-junction changes with the emission of trapped charge carriers Capacitance transient measurement gives information on the defect levels in the band gap Electrical properties of defects are: - Position in the bandgap - Capture cross section - Concentration of defects

4. Basic semiconductor theory
Connection of p- and n-type material
Charge carriers diffuse into the opposite region.
Creates an electric field, depletion region (W) with capacitance C.
𝐶= 𝜀𝐴 𝑊
In the depletion region there are no free charge carriers as they are swept away by the electric field.

5. Size of the depletion region is dependent on doping concentration and applied voltage.
𝑊= 2𝜀 𝑉 0 −𝑉 𝑞 1 𝑁 𝑎 𝑁 𝑑

6. DLTS Principle Schottky diode
A: equilibrium, all trap states are empty
B: Filling pulse
C: Return to reverse bias, change in depletion zone width gives change in capacitance
D: Emission, depletion zone will go back to equilibrium over time. Capacitance transient.

7. DLTS Principle
For a schottky, p+n or pn+ contact the depletion width is:
𝑊= 2𝜀 𝑉 0 −𝑉 𝑞𝑁
C then becomes:
𝐶=𝐴 𝜀𝑞𝑁 2 𝑉 0 −𝑉 = 𝐶 0
If t=0 at the time the filling pulse is finished, then:
𝐶 𝑡=0 =𝐴 𝜀𝑞 𝑁− 𝑛 𝑇 2 𝑉 0 −𝑉
And:
𝐶 𝑡→∞ =𝐴 𝜀𝑞𝑁 2 𝑉 0 −𝑉
The change in capacitance is then:
∆𝐶=𝐶 𝑡=0 −𝐶 𝑡→∞
∆𝐶=𝐴 𝜀𝑞𝑁 2 𝑉 0 −𝑉 −𝐴 𝜀𝑞 𝑁− 𝑛 𝑇 2 𝑉 0 −𝑉
∆𝐶= 𝐶 0 − 𝐶 0 1− 𝑛 𝑇 𝑁
If nT<<N then:
∆𝐶≈ 𝐶 0 − 𝐶 0 1− 𝑛 𝑇 𝑁
∆𝐶≈ 𝑛 𝑇 𝑁 𝐶 0
𝑛 𝑇 = 2𝑁∆𝐶 𝐶 0

8. Recombination center:
Impurity levels acts as recombination centers or trap levels. Depends on energy level, location of Fermi level, temperature and capture cross section.
Recombination center:
Will interact with both conduction band and valance band. Generally positioned close to the middle of the bandgap. 𝐶 𝑛 = 𝐶 𝑝
Electron trap:
Captured electrons will return to the conduction band by emission. Generally positioned closer to the conduction band. 𝐶 𝑛 ≫ 𝐶 𝑝
Hole trap:
Captured holes will return to valance band by emission. Generally positioned closer to the valance band. 𝐶 𝑛 ≪ 𝐶 𝑝
Capture coefficient Cn,p:
𝐶 𝑛,𝑝 = 𝜎 𝑛,𝑝 𝑣 𝑡ℎ
σ is capture cross section and v is thermal velocity.
Capture cross section depends on charge, whether the charge is repulsive, attractive or neutral.

9. The density of nT and pT is equal the total density. 𝑁 𝑇 = 𝑛 𝑇 + 𝑝 𝑇
A impurity center can exist in two states, when occupied by an electron a nT state, and when occupied by a hole a pT state.
If the impurity center is a donor, nT is neutral and pT positive charged.
The density of nT and pT is equal the total density.
𝑁 𝑇 = 𝑛 𝑇 + 𝑝 𝑇
Electron density in the conduction band is reduced by electron capture and increased by electron emission.
Electron emission is the density of impurity centers occupied by electrons ( 𝑛 𝑇 ) times the emission rate (en).
Electron capture is unoccupied impurity centers ( 𝑝 𝑇 ) times the capture coefficient (cn) times the electron density in the conduction band (n).
𝑑𝑛 𝑑𝑡 = 𝑒 𝑛 𝑛 𝑇 − 𝑐 𝑛 𝑛 𝑝 𝑇
In equilibrium conditions each fundamental process and its inverse must balance independent of any other process.
𝑑𝑛 𝑑𝑡 =0
𝑒 𝑛0 𝑛 𝑇0 = 𝑐 𝑛0 𝑛 0 𝑝 𝑇0 = 𝑐 𝑛0 𝑛 0 𝑁 𝑇 − 𝑛 𝑇0
Where:
𝑛 0 = 𝑛 𝑖 𝑒 𝐸 𝐹 − 𝐸 𝑖 𝑘𝑇
𝑛 𝑇0 = 𝑁 𝑇 1+ 𝑒 𝐸 𝑇 − 𝐸 𝐹 𝑘𝑇
Combining gives:
𝑒 𝑛0 = 𝑐 𝑛0 𝑛 𝑖 𝑒 𝐸 𝑇 − 𝐸 𝑖 𝑘𝑇

10. 𝑒 𝑛 = 𝑐 𝑛 𝑛 𝑖 𝑒 𝐸 𝑇 − 𝐸 𝑖 𝑘𝑇 = 𝜎 𝑛 𝑣 𝑡ℎ 𝑛 𝑖 𝑒 𝐸 𝑇 − 𝐸 𝑖 𝑘𝑇
Crucial assumption!
The emission and capture coefficients remain equal to their equilibrium values under non-equilibrium conditions.
𝑒 𝑛 = 𝑐 𝑛 𝑛 𝑖 𝑒 𝐸 𝑇 − 𝐸 𝑖 𝑘𝑇 = 𝜎 𝑛 𝑣 𝑡ℎ 𝑛 𝑖 𝑒 𝐸 𝑇 − 𝐸 𝑖 𝑘𝑇
𝑒 𝑛 = 𝜎 𝑛 𝑣 𝑡ℎ 𝑁 𝑐 𝑒 − 𝐸 𝑐 − 𝐸 𝑇 𝑘𝑇
𝑒 𝑛 = 1 𝜏 𝑒
𝜏 𝑒 = 𝑒 𝐸 𝑐 − 𝐸 𝑇 𝑘𝑇 𝜎 𝑛 𝑣 𝑡ℎ 𝑁 𝑐
Heat capacity is:
𝛾 𝑛 = 𝑣 𝑡ℎ 𝑇 𝑁 𝑐 𝑇 3 2
That gives:
𝜏 𝑒 𝑇 2 = 𝑒 𝐸 𝑐 − 𝐸 𝑇 𝑘𝑇 𝜎 𝑛 𝛾 𝑛
Electron thermal velocity:
𝑣 𝑡ℎ = 3𝑘𝑇 𝑚 𝑛
Density of states in the conduction band:
𝑁 𝐶 =2 2𝜋 𝑚 𝑛 𝑘𝑇 ℎ
Both temperature dependent, makes the emission rate and the emission time coefficient also temperature dependent.
The capacitance change slope is temperature dependent.
D.K.Schroder "Semiconductor material and device characterization"

11. Plotting the slope
Assuming 𝑒 𝑛 ≫ 𝑒 𝑝 gives that the time dependence of nT can be written as:
𝑛 𝑇 𝑡 = 𝑛 𝑇 (0) 𝑒 − 𝑡 𝜏 𝑒
Plotting the capacitance change then is:
∆𝐶=𝐶 ∞ −𝐶(𝑡)= 𝑛 𝑇0 𝑁 𝑐 𝐶 0 ∗𝑒 − 𝑡 𝜏 𝑒
𝐶 𝑡 = 𝐶 0 − 𝑛 𝑇0 𝑁 𝑐 𝐶 0 ∗𝑒 − 𝑡 𝜏 𝑒
By repeating the measurements while changing the temperature, the measured capacitance difference changes, giving a peak.
D.K.Schroder "Semiconductor material and device characterization"

12. 𝛿𝐶=𝐶 𝑡 1 −𝐶 𝑡 2
𝛿𝐶= 𝑛 𝑇0 𝐶 0 2 𝑁 𝑐 𝑒 − 𝑡 2 𝜏 𝑒 − 𝑒 − 𝑡 1 𝜏 𝑒
Derivate with respect to 𝜏 𝑒 and finding a maximum gives max 𝜏 𝑒 at max 𝛿𝐶:
𝜏 𝑒−𝑚𝑎𝑥 = 𝑡 2 − 𝑡 1 𝑙𝑛 𝑡 2 𝑡 1
By doing multiple temperature cycling with different rate windows, the peak is shifted in temperature. Most common settings are 𝑡 2 𝑡 1 is fixed, 𝑡 2 and 𝑡 1 varying.
Each set of measurements gives a 𝜏 𝑒 at a temperature T. Plotting 𝑙𝑛 𝜏 𝑒 𝑇 2 versus 1/T gives an arrhenius plot with slope 𝐸 𝑐 − 𝐸 𝑇 𝑘 that intersects with the vertical axis at 𝑙𝑛 𝛾 𝑛 𝜎 𝑛 , and 𝜎 𝑛 can be calculated.
D.K.Schroder "Semiconductor material and device characterization"

13. O. Breitenstein “DLTS Manual"

14. [3] O. Breitenstein, DLTS Manual (2003)
References
[1] B.G. Streetman and S. K. Banerjee, Solid State Electronic Devices (Pearson, England, 2016)
[2] D. K. Schroder, Semiconductor Material and Device Characterization (John Wiley & Sons, USA, 2006)
[3] O. Breitenstein, DLTS Manual (2003)